Sample records for mathematical word problem

  1. Using Technology to Meet the Developmental Needs of Deaf Students To Improve Their Mathematical Word Problem Solving Skills.

    ERIC Educational Resources Information Center

    Kelly, Ronald R.

    2003-01-01

    Presents "Project Solve," a web-based problem-solving instruction and guided practice for mathematical word problems. Discusses implications for college students for whom reading and comprehension of mathematical word problem solving are difficult, especially learning disabled students. (Author/KHR)

  2. Child-Level Predictors of Responsiveness to Evidence-Based Mathematics Intervention.

    PubMed

    Powell, Sarah R; Cirino, Paul T; Malone, Amelia S

    2017-07-01

    We identified child-level predictors of responsiveness to 2 types of mathematics (calculation and word-problem) intervention among 2nd-grade children with mathematics difficulty. Participants were 250 children in 107 classrooms in 23 schools pretested on mathematics and general cognitive measures and posttested on mathematics measures. We assigned classrooms randomly assigned to calculation intervention, word-problem intervention, or business-as-usual control. Intervention lasted 17 weeks. Path analyses indicated that scores on working memory and language comprehension assessments moderated responsiveness to calculation intervention. No moderators were identified for responsiveness to word-problem intervention. Across both intervention groups and the control group, attentive behavior predicted both outcomes. Initial calculation skill predicted the calculation outcome, and initial language comprehension predicted word-problem outcomes. These results indicate that screening for calculation intervention should include a focus on working memory, language comprehension, attentive behavior, and calculations. Screening for word-problem intervention should focus on attentive behavior and word problems.

  3. The relation between children’s constructive play activities, spatial ability, and mathematical word problem-solving performance: a mediation analysis in sixth-grade students

    PubMed Central

    Oostermeijer, Meike; Boonen, Anton J. H.; Jolles, Jelle

    2014-01-01

    The scientific literature shows that constructive play activities are positively related to children’s spatial ability. Likewise, a close positive relation is found between spatial ability and mathematical word problem-solving performances. The relation between children’s constructive play and their performance on mathematical word problems is, however, not reported yet. The aim of the present study was to investigate whether spatial ability acted as a mediator in the relation between constructive play and mathematical word problem-solving performance in 128 sixth-grade elementary school children. This mediating role of spatial ability was tested by utilizing the current mediation approaches suggested by Preacher and Hayes (2008). Results showed that 38.16% of the variance in mathematical word problem-solving performance is explained by children’s constructive play activities and spatial ability. More specifically, spatial ability acted as a partial mediator, explaining 31.58% of the relation between constructive play and mathematical word problem-solving performance. PMID:25101038

  4. The Association between Mathematical Word Problems and Reading Comprehension

    ERIC Educational Resources Information Center

    Vilenius-Tuohimaa, Piia Maria; Aunola, Kaisa; Nurmi, Jari-Erik

    2008-01-01

    This study aimed to investigate the interplay between mathematical word problem skills and reading comprehension. The participants were 225 children aged 9-10 (Grade 4). The children's text comprehension and mathematical word problem-solving performance was tested. Technical reading skills were investigated in order to categorise participants as…

  5. Examining How Students with Diverse Abilities Use Diagrams to Solve Mathematics Word Problems

    ERIC Educational Resources Information Center

    van Garderen, Delinda; Scheuermann, Amy; Jackson, Christa

    2013-01-01

    This study examined students' understanding of diagrams and their use of diagrams as tools to solve mathematical word problems. Students with learning disabilities (LD), typically achieving students, and gifted students in Grades 4 through 7 ("N" = 95) participated. Students were presented with novel mathematical word problem-solving…

  6. Culturally and Linguistically Responsive Schema Intervention: Improving Word Problem Solving for English Language Learners with Mathematics Difficulty

    ERIC Educational Resources Information Center

    Driver, Melissa K.; Powell, Sarah R.

    2017-01-01

    Word problems are prevalent on high-stakes assessments, and success on word problems has implications for grade promotion and graduation. Unfortunately, English Language Learners (ELLs) continue to perform significantly below their native English-speaking peers on mathematics assessments featuring word problems. Little is known about the…

  7. A Strategy for Improving US Middle School Student Mathematics Word Problem Solving Performance

    NASA Technical Reports Server (NTRS)

    Thomas, Valerie L.

    2004-01-01

    U.S. middle school students have difficulty understanding and solving mathematics word problems. Their mathematics performance on the Third International Mathematics and Science Study (TIMMS) is far below their international peers, and minority students are less likely than high socioeconomic status (SES) White/Asian students to be exposed to higher-level mathematics concepts. Research literature also indicates that when students use both In-School and Out-of-School knowledge and experiences to create authentic mathematics word problems, student achievement improves. This researcher developed a Strategy for improving mathematics problem solving performance and a Professional Development Model (PDM) to effectively implement the Strategy.

  8. Students’ Representation in Mathematical Word Problem-Solving: Exploring Students’ Self-efficacy

    NASA Astrophysics Data System (ADS)

    Sahendra, A.; Budiarto, M. T.; Fuad, Y.

    2018-01-01

    This descriptive qualitative research aims at investigating student represented in mathematical word problem solving based on self-efficacy. The research subjects are two eighth graders at a school in Surabaya with equal mathematical ability consisting of two female students with high and low self-efficacy. The subjects were chosen based on the results of test of mathematical ability, documentation of the result of middle test in even semester of 2016/2017 academic year, and results of questionnaire of mathematics word problem in terms of self-efficacy scale. The selected students were asked to do mathematical word problem solving and be interviewed. The result of this study shows that students with high self-efficacy tend to use multiple representations of sketches and mathematical models, whereas students with low self-efficacy tend to use single representation of sketches or mathematical models only in mathematical word problem-solving. This study emphasizes that teachers should pay attention of student’s representation as a consideration of designing innovative learning in order to increase the self-efficacy of each student to achieve maximum mathematical achievement although it still requires adjustment to the school situation and condition.

  9. The Motivation of Secondary School Students in Mathematical Word Problem Solving

    ERIC Educational Resources Information Center

    Gasco, Javier; Villarroel, Jose-Domingo

    2014-01-01

    Introduction: Motivation is an important factor in the learning of mathematics. Within this area of education, word problem solving is central in most mathematics curricula of Secondary School. The objective of this research is to detect the differences in motivation in terms of the strategies used to solve word problems. Method: It analyzed the…

  10. How Can One Learn Mathematical Word Problems in a Second Language? A Cognitive Load Perspective

    ERIC Educational Resources Information Center

    Moussa-Inaty, Jase; Causapin, Mark; Groombridge, Timothy

    2015-01-01

    Language may ordinarily account for difficulties in solving word problems and this is particularly true if mathematical word problems are taught in a language other than one's native language. Research into cognitive load may offer a clear theoretical framework when investigating word problems because memory, specifically working memory, plays a…

  11. Mathematical Word Problem Solving Ability of Children with Autism Spectrum Disorder and their Typically Developing Peers.

    PubMed

    Bae, Young Seh; Chiang, Hsu-Min; Hickson, Linda

    2015-07-01

    This study examined the difference between children with autism spectrum disorders (ASD) and children with typical development (TD) in mathematical word problem solving ability and the factors associated with these children's word problem-solving ability. A total of 20 children with ASD and 20 children with TD participated in this study. Independent sample t tests and Spearman's rho correlations were used for data analysis. This study found: (a) Children with TD had higher word problem solving ability than did children with ASD; (b) Sentence comprehension, math vocabulary, computation, and everyday mathematical knowledge were associated with word problem solving ability of children with ASD and children with TD; and (c) Children with TD had higher everyday mathematical knowledge than did children with ASD.

  12. Do word-problem features differentially affect problem difficulty as a function of students' mathematics difficulty with and without reading difficulty?

    PubMed

    Powell, Sarah R; Fuchs, Lynn S; Fuchs, Douglas; Cirino, Paul T; Fletcher, Jack M

    2009-01-01

    This study examined whether and, if so, how word-problem features differentially affect problem difficulty as a function of mathematics difficulty (MD) status: no MD (n = 109), MD only (n = 109), or MD in combination with reading difficulties (MDRD; n = 109). The problem features were problem type (total, difference, or change) and position of missing information in the number sentence representing the word problem (first, second, or third position). Students were assessed on 14 word problems near the beginning of third grade. Consistent with the hypothesis that mathematical cognition differs as a function of MD subtype, problem type affected problem difficulty differentially for MDRD versus MD-only students; however, the position of missing information in word problems did not. Implications for MD subtyping and for instruction are discussed.

  13. The Effects of Using Drawings in Developing Young Children's Mathematical Word Problem Solving: A Design Experiment with Third-Grade Hungarian Students

    ERIC Educational Resources Information Center

    Csikos, Csaba; Szitanyi, Judit; Kelemen, Rita

    2012-01-01

    The present study aims to investigate the effects of a design experiment developed for third-grade students in the field of mathematics word problems. The main focus of the program was developing students' knowledge about word problem solving strategies with an emphasis on the role of visual representations in mathematical modeling. The experiment…

  14. Procedural versus Content-Related Hints for Word Problem Solving: An Exploratory Study

    ERIC Educational Resources Information Center

    Kock, W. D.; Harskamp, E. G.

    2016-01-01

    For primary school students, mathematical word problems are often more difficult to solve than straightforward number problems. Word problems require reading and analysis skills, and in order to explain their situational contexts, the proper mathematical knowledge and number operations have to be selected. To improve students' ability in solving…

  15. Different Procedures for Solving Mathematical Word Problems in High School

    ERIC Educational Resources Information Center

    Gasco, Javier; Villarroel, Jose Domingo; Zuazagoitia, Dani

    2014-01-01

    The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…

  16. Contribution of Equal-Sign Instruction beyond Word-Problem Tutoring for Third-Grade Students with Mathematics Difficulty.

    PubMed

    Powell, Sarah R; Fuchs, Lynn S

    2010-05-01

    Elementary school students often misinterpret the equal sign (=) as an operational rather than a relational symbol. Such misunderstanding is problematic because solving equations with missing numbers may be important for higher-order mathematics skills including word problems. Research indicates equal-sign instruction can alter how typically-developing students use the equal sign, but no study has examined effects for students with mathematics difficulty (MD) or how equal-sign instruction contributes to word-problem skill for students with or without MD. The present study assessed the efficacy of equal-sign instruction within word-problem tutoring. Third-grade students with MD (n = 80) were assigned to word-problem tutoring, word-problem tutoring plus equal-sign instruction (combined) tutoring, or no-tutoring control. Combined tutoring produced better improvement on equal sign tasks and open equations compared to the other 2 conditions. On certain forms of word problems, combined tutoring but not word-problem tutoring alone produced better improvement than control. When compared at posttest to 3(rd)-grade students without MD on equal sign tasks and open equations, only combined tutoring students with MD performed comparably.

  17. Embedding Number-Combinations Practice Within Word-Problem Tutoring

    PubMed Central

    Powell, Sarah R.; Fuchs, Lynn S.; Fuchs, Douglas

    2012-01-01

    Two aspects of mathematics with which students with mathematics learning difficulty (MLD) often struggle are word problems and number-combination skills. This article describes a math program in which students receive instruction on using algebraic equations to represent the underlying problem structure for three word-problem types. Students also learn counting strategies for answering number combinations that they cannot retrieve from memory. Results from randomized-control trials indicated that embedding the counting strategies for number combinations produces superior word-problem and number-combination outcomes for students with MLD beyond tutoring programs that focus exclusively on number combinations or word problems. PMID:22661880

  18. Embedding Number-Combinations Practice Within Word-Problem Tutoring.

    PubMed

    Powell, Sarah R; Fuchs, Lynn S; Fuchs, Douglas

    2010-09-01

    Two aspects of mathematics with which students with mathematics learning difficulty (MLD) often struggle are word problems and number-combination skills. This article describes a math program in which students receive instruction on using algebraic equations to represent the underlying problem structure for three word-problem types. Students also learn counting strategies for answering number combinations that they cannot retrieve from memory. Results from randomized-control trials indicated that embedding the counting strategies for number combinations produces superior word-problem and number-combination outcomes for students with MLD beyond tutoring programs that focus exclusively on number combinations or word problems.

  19. Helping Students with Emotional and Behavioral Disorders Solve Mathematics Word Problems

    ERIC Educational Resources Information Center

    Alter, Peter

    2012-01-01

    The author presents a strategy for helping students with emotional and behavioral disorders become more proficient at solving math word problems. Math word problems require students to go beyond simple computation in mathematics (e.g., adding, subtracting, multiplying, and dividing) and use higher level reasoning that includes recognizing relevant…

  20. Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development

    ERIC Educational Resources Information Center

    Bae, Young Seh

    2013-01-01

    Mathematical Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development Young Seh Bae This study investigated mathematical word problem solving and the factors associated with the solution paths adopted by two groups of participants (N=40), students with autism spectrum disorders (ASDs) and typically…

  1. The Use of a Bar Model Drawing to Teach Word Problem Solving to Students with Mathematics Difficulties

    ERIC Educational Resources Information Center

    Morin, Lisa L.; Watson, Silvana M. R.; Hester, Peggy; Raver, Sharon

    2017-01-01

    For students with mathematics difficulties (MD), math word problem solving is especially challenging. The purpose of this study was to examine the effects of a problem-solving strategy, bar model drawing, on the mathematical problem-solving skills of students with MD. The study extended previous research that suggested that schematic-based…

  2. Teaching Problem Solving to Students Receiving Tiered Interventions Using the Concrete-Representational-Abstract Sequence and Schema-Based Instruction

    ERIC Educational Resources Information Center

    Flores, Margaret M.; Hinton, Vanessa M.; Burton, Megan E.

    2016-01-01

    Mathematical word problems are the most common form of mathematics problem solving implemented in K-12 schools. Identifying key words is a frequent strategy taught in classrooms in which students struggle with problem solving and show low success rates in mathematics. Researchers show that using the concrete-representational-abstract (CRA)…

  3. Cognitive Benefits and Costs of Bilingualism in Elementary School Students: The Case of Mathematical Word Problems

    ERIC Educational Resources Information Center

    Kempert, Sebastian; Saalbach, Henrik; Hardy, Ilonca

    2011-01-01

    Previous research has emphasized the importance of language for learning mathematics. This is especially true when mathematical problems have to be extracted from a meaningful context, as in arithmetic word problems. Bilingual learners with a low command of the instructional language thus may face challenges when dealing with mathematical…

  4. Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training

    PubMed Central

    Boonen, Anton J. H.; de Koning, Björn B.; Jolles, Jelle; van der Schoot, Menno

    2016-01-01

    Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more) prominent role during word problem solving instruction in RME. PMID:26925012

  5. Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training.

    PubMed

    Boonen, Anton J H; de Koning, Björn B; Jolles, Jelle; van der Schoot, Menno

    2016-01-01

    Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more) prominent role during word problem solving instruction in RME.

  6. Contribution of Equal-Sign Instruction beyond Word-Problem Tutoring for Third-Grade Students with Mathematics Difficulty

    PubMed Central

    Powell, Sarah R.; Fuchs, Lynn S.

    2010-01-01

    Elementary school students often misinterpret the equal sign (=) as an operational rather than a relational symbol. Such misunderstanding is problematic because solving equations with missing numbers may be important for higher-order mathematics skills including word problems. Research indicates equal-sign instruction can alter how typically-developing students use the equal sign, but no study has examined effects for students with mathematics difficulty (MD) or how equal-sign instruction contributes to word-problem skill for students with or without MD. The present study assessed the efficacy of equal-sign instruction within word-problem tutoring. Third-grade students with MD (n = 80) were assigned to word-problem tutoring, word-problem tutoring plus equal-sign instruction (combined) tutoring, or no-tutoring control. Combined tutoring produced better improvement on equal sign tasks and open equations compared to the other 2 conditions. On certain forms of word problems, combined tutoring but not word-problem tutoring alone produced better improvement than control. When compared at posttest to 3rd-grade students without MD on equal sign tasks and open equations, only combined tutoring students with MD performed comparably. PMID:20640240

  7. Tutoring Mathematical Word Problems Using Solution Trees: Text Comprehension, Situation Comprehension, and Mathematization in Solving Story Problems. Research Report No. 8.

    ERIC Educational Resources Information Center

    Reusser, Kurt; And Others

    The main concern of this paper is on the psychological processes of how students understand and solve mathematical word problems, and on how this knowledge can be applied to computer-based tutoring. It is argued that only a better understanding of the psychological requirements for understanding and solving those problems will lead to…

  8. Mathematical Word Problem Solving Ability of Children with Autism Spectrum Disorder and Their Typically Developing Peers

    ERIC Educational Resources Information Center

    Bae, Young Seh; Chiang, Hsu-Min; Hickson, Linda

    2015-01-01

    This study examined the difference between children with autism spectrum disorders (ASD) and children with typical development (TD) in mathematical word problem solving ability and the factors associated with these children's word problem-solving ability. A total of 20 children with ASD and 20 children with TD participated in this study.…

  9. Use of a Mathematics Word Problem Strategy to Improve Achievement for Students with Mild Disabilities

    ERIC Educational Resources Information Center

    Taber, Mary R.

    2013-01-01

    Mathematics can be a difficult topic both to teach and to learn. Word problems specifically can be difficult for students with disabilities because they have to conceptualize what the problem is asking for, and they must perform the correct operation accurately. Current trends in mathematics instruction stem from the National Council of Teachers…

  10. Semantic Similarity Graphs of Mathematics Word Problems: Can Terminology Detection Help?

    ERIC Educational Resources Information Center

    John, Rogers Jeffrey Leo; Passonneau, Rebecca J.; McTavish, Thomas S.

    2015-01-01

    Curricula often lack metadata to characterize the relatedness of concepts. To investigate automatic methods for generating relatedness metadata for a mathematics curriculum, we first address the task of identifying which terms in the vocabulary from mathematics word problems are associated with the curriculum. High chance-adjusted interannotator…

  11. Can Group Discussions and Individualized Assignments Help More Students Succeed in Developmental Mathematics?

    ERIC Educational Resources Information Center

    Jaafar, Reem

    2015-01-01

    Students taking developmental mathematics courses resist attempting word problems when they are presented to them. Although word problems can help students contextualize learning, develop better understanding of the concepts and apply world knowledge, they constitute an impediment to students' progress in developmental mathematics courses. A…

  12. Mathematics Word Problem Solving: An Investigation into Schema-Based Instruction in a Computer-Mediated Setting and a Teacher-Mediated Setting with Mathematically Low-Performing Students

    ERIC Educational Resources Information Center

    Leh, Jayne

    2011-01-01

    Substantial evidence indicates that teacher-delivered schema-based instruction (SBI) facilitates significant increases in mathematics word problem solving (WPS) skills for diverse students; however research is unclear whether technology affordances facilitate superior gains in computer-mediated (CM) instruction in mathematics WPS when compared to…

  13. The Effects of Differing Presentations of Mathematical Word Problems Upon the Achievement of Tenth Grade Students.

    ERIC Educational Resources Information Center

    Sherrill, James M.

    Described is a study concerned with the mode of presentation of printed mathematical word problems. Tenth grade students were given twenty word problems to solve, presented in one of three ways: (1) prose only, (2) prose with an accurate picture included, or (3) prose with a distorted picture. Experimental results showed that the group with an…

  14. Working Memory Components as Predictors of Children's Mathematical Word Problem Solving

    ERIC Educational Resources Information Center

    Zheng, Xinhua; Swanson, H. Lee; Marcoulides, George A.

    2011-01-01

    This study determined the working memory (WM) components (executive, phonological loop, and visual-spatial sketchpad) that best predicted mathematical word problem-solving accuracy of elementary school children in Grades 2, 3, and 4 (N = 310). A battery of tests was administered to assess problem-solving accuracy, problem-solving processes, WM,…

  15. Effect of Causal Stories in Solving Mathematical Story Problems

    ERIC Educational Resources Information Center

    Smith, Glenn Gordon; Gerretson, Helen; Olkun, Sinan; Joutsenlahti, Jorma

    2010-01-01

    This study investigated whether infusing "causal" story elements into mathematical word problems improves student performance. In one experiment in the USA and a second in USA, Finland and Turkey, undergraduate elementary education majors worked word problems in three formats: 1) standard (minimal verbiage), 2) potential causation…

  16. Linguistic Challenges in the Mathematical Register for EFL Learners: Linguistic and Multimodal Strategies to Help Learners Tackle Mathematics Word Problems

    ERIC Educational Resources Information Center

    Chan, Simon

    2015-01-01

    In learning mathematics through English, one of the major challenges facing English as a Foreign Language (EFL) learners is understanding the language used to present word problems in mathematics texts. Without comprehending such language, learners are not able to carry out the targeted calculations no matter how familiar they are with the…

  17. Characteristics of Students at Risk for Mathematics Difficulties Predicting Arithmetic Word Problem Solving Performance: The Role of Attention, Behavior, and Reading

    ERIC Educational Resources Information Center

    Jitendra, Asha K.; Corroy, Kelly Cozine; Dupuis, Danielle N.

    2013-01-01

    The purposes of this study were (a) to evaluate differences in arithmetic word problem solving between high and low at-risk students for mathematics difficulties (MD) and (b) to assess the influence of attention, behavior, reading, and socio-economic status (SES) in predicting the word problem solving performance of third-grade students with MD.…

  18. The Influence of English-Korean Bilingualism in Solving Mathematics Word Problems.

    ERIC Educational Resources Information Center

    Whang, Woo-Hyung

    1996-01-01

    Purposeful sampling was used to select six English-Korean bilingual students to investigate language difficulties and cognitive processes in solving mathematics word problems. These six case studies revealed distinct patterns of difficulties in solving problems written in English and Korean, especially for students in transition stage. (Author/KMC)

  19. Cognitive Skills Used to Solve Mathematical Word Problems and Numerical Operations: A Study of 6- to 7-Year-Old Children

    ERIC Educational Resources Information Center

    Bjork, Isabel Maria; Bowyer-Crane, Claudine

    2013-01-01

    This study investigates the relationship between skills that underpin mathematical word problems and those that underpin numerical operations, such as addition, subtraction, division and multiplication. Sixty children aged 6-7 years were tested on measures of mathematical ability, reading accuracy, reading comprehension, verbal intelligence and…

  20. Secondary School Students' Construction and Use of Mathematical Models in Solving Word Problems

    ERIC Educational Resources Information Center

    Llinares, Salvador; Roig, Ana Isabel

    2008-01-01

    This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15-16 years old). Four levels of the development of constructing and using mathematical models were…

  1. Problem Solving Frameworks for Mathematics and Software Development

    ERIC Educational Resources Information Center

    McMaster, Kirby; Sambasivam, Samuel; Blake, Ashley

    2012-01-01

    In this research, we examine how problem solving frameworks differ between Mathematics and Software Development. Our methodology is based on the assumption that the words used frequently in a book indicate the mental framework of the author. We compared word frequencies in a sample of 139 books that discuss problem solving. The books were grouped…

  2. Following the Template: Transferring Modeling Skills to Nonstandard Problems

    ERIC Educational Resources Information Center

    Tyumeneva, Yu. A.; Goncharova, M. V.

    2017-01-01

    This study seeks to analyze how students apply a mathematical modeling skill that was previously learned by solving standard word problems to the solution of word problems with nonstandard contexts. During the course of an experiment involving 106 freshmen, we assessed how well they were able to transfer the mathematical modeling skill that is…

  3. VStops: A Thinking Strategy and Visual Representation Approach in Mathematical Word Problem Solving toward Enhancing STEM Literacy

    ERIC Educational Resources Information Center

    Abdullah, Nasarudin; Halim, Lilia; Zakaria, Effandi

    2014-01-01

    This study aimed to determine the impact of strategic thinking and visual representation approaches (VStops) on the achievement, conceptual knowledge, metacognitive awareness, awareness of problem-solving strategies, and student attitudes toward mathematical word problem solving among primary school students. The experimental group (N = 96)…

  4. The Role of Cognitive Processes, Foundational Math Skill, and Calculation Accuracy and Fluency in Word-Problem Solving versus Pre-Algebraic Knowledge

    PubMed Central

    Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.

    2016-01-01

    The purpose of this study was to examine child-level pathways in development of pre-algebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of grade 2; calculation accuracy and calculation fluency at end of grade 2; and pre-algebraic knowledge and word-problem solving at end of grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than pre-algebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students’ foundational mathematics skills or cognitive processes. PMID:27786534

  5. Effectiveness of Mathematical Word Problem Solving Interventions for Students with Learning Disabilities and Mathematics Difficulties: A Meta-Analysis

    ERIC Educational Resources Information Center

    Lein, Amy E.

    2016-01-01

    This meta-analysis synthesized the findings from 23 published and five unpublished experimental or quasi-experimental group design studies on word problem-solving instruction for K-12 students with learning disabilities (LD) and mathematics difficulties (MD). A secondary purpose of this meta-analysis was to analyze the relation between treatment…

  6. Remediating Number Combination and Word Problem Deficits Among Students With Mathematics Difficulties: A Randomized Control Trial

    PubMed Central

    Fuchs, Lynn S.; Powell, Sarah R.; Seethaler, Pamela M.; Cirino, Paul T.; Fletcher, Jack M.; Fuchs, Douglas; Hamlett, Carol L.; Zumeta, Rebecca O.

    2009-01-01

    The purposes of this study were to assess the efficacy of remedial tutoring for 3rd graders with mathematics difficulty, to investigate whether tutoring is differentially efficacious depending on students’ math difficulty status (mathematics difficulty alone vs. mathematics plus reading difficulty), to explore transfer from number combination (NC) remediation, and to examine the transportability of the tutoring protocols. At 2 sites, 133 students were stratified on mathematics difficulty status and site and then randomly assigned to 3 conditions: control (no tutoring), tutoring on automatic retrieval of NCs (i.e., Math Flash), or tutoring on word problems with attention to the foundational skills of NCs, procedural calculations, and algebra (i.e., Pirate Math). Tutoring occurred for 16 weeks, 3 sessions per week and 20–30 min per session. Math Flash enhanced fluency with NCs with transfer to procedural computation but without transfer to algebra or word problems. Pirate Math enhanced word problem skill as well as fluency with NCs, procedural computation, and algebra. Tutoring was not differentially efficacious as a function of students’ mathematics difficulty status. The tutoring protocols proved transportable across sites. PMID:19865600

  7. Students' Mathematics Word Problem-Solving Achievement in a Computer-Based Story

    ERIC Educational Resources Information Center

    Gunbas, N.

    2015-01-01

    The purpose of this study was to investigate the effect of a computer-based story, which was designed in anchored instruction framework, on sixth-grade students' mathematics word problem-solving achievement. Problems were embedded in a story presented on a computer as computer story, and then compared with the paper-based version of the same story…

  8. An Evaluation of Curriculum-Based Measurement of Mathematics Word Problem--Solving Measures for Monitoring Third-Grade Students' Mathematics Competence

    ERIC Educational Resources Information Center

    Leh, Jayne M.; Jitendra, Asha K.; Caskie, Grace I. L.; Griffin, Cynthia C.

    2007-01-01

    The purpose of this study was to examine the tenability of a curriculum-based mathematical word problem-solving (WPS) measure as a progress-monitoring tool to index students' rate of growth or slope of achievement over time. Participants consisted of 58 third-grade students, who were assessed repeatedly over 16 school weeks. Students were measured…

  9. Student’s thinking process in solving word problems in geometry

    NASA Astrophysics Data System (ADS)

    Khasanah, V. N.; Usodo, B.; Subanti, S.

    2018-05-01

    This research aims to find out the thinking process of seventh grade of Junior High School in solve word problem solving of geometry. This research was descriptive qualitative research. The subject of the research was selected based on sex and differences in mathematical ability. Data collection was done based on student’s work test, interview, and observation. The result of the research showed that there was no difference of thinking process between male and female with high mathematical ability, and there were differences of thinking process between male and female with moderate and low mathematical ability. Also, it was found that male with moderate mathematical ability took a long time in the step of making problem solving plans. While female with moderate mathematical ability took a long time in the step of understanding the problems. The importance of knowing the thinking process of students in solving word problem solving were that the teacher knows the difficulties faced by students and to minimize the occurrence of the same error in problem solving. Teacher could prepare the right learning strategies which more appropriate with student’s thinking process.

  10. A Design To Improve Children's Competencies in Solving Mathematical Word Problems.

    ERIC Educational Resources Information Center

    Zimmerman, Helene

    A discrepancy exists between children's ability to compute and their ability to solve mathematical word problems. The literature suggests a variety of methods that have been attempted to improve this skill with varying success. The utilization of manipulatives, visualization, illustration, and emphasis on improving listening skills all were…

  11. Guiding Preservice Teachers to Adapt Mathematics Word Problems through Interactions with ELLs

    ERIC Educational Resources Information Center

    Kurz, Terri L.; Gómez, Conrado; Jimenez-Silva, Margarita

    2017-01-01

    In this article, the authors present a framework for guiding elementary preservice teachers in adapting mathematics word problems to better meet English language learners' (ELLs) needs. They analyze preservice teachers' ELL adaptations implemented in a one-on-one setting. Through qualitative methods, four themes regarding implemented adaptations…

  12. A Review of the Effects of Visual-Spatial Representations and Heuristics on Word Problem Solving in Middle School Mathematics

    ERIC Educational Resources Information Center

    Kribbs, Elizabeth E.; Rogowsky, Beth A.

    2016-01-01

    Mathematics word-problems continue to be an insurmountable challenge for many middle school students. Educators have used pictorial and schematic illustrations within the classroom to help students visualize these problems. However, the data shows that pictorial representations can be more harmful than helpful in that they only display objects or…

  13. The role of cognitive processes, foundational math skill, and calculation accuracy and fluency in word-problem solving versus prealgebraic knowledge.

    PubMed

    Fuchs, Lynn S; Gilbert, Jennifer K; Powell, Sarah R; Cirino, Paul T; Fuchs, Douglas; Hamlett, Carol L; Seethaler, Pamela M; Tolar, Tammy D

    2016-12-01

    The purpose of this study was to examine child-level pathways in development of prealgebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of Grade 2; calculation accuracy and calculation fluency at end of Grade 2; and prealgebraic knowledge and word-problem solving at end of Grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than prealgebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students' foundational mathematics skills or cognitive processes. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

  14. Challenges in Math.

    ERIC Educational Resources Information Center

    Feng, Chengde

    1992-01-01

    Fourteen mathematics problems from the 1987 Chinese Primary School Mathematics Examination for fifth and sixth grade students are presented. The word problems, accompanied by answers, involve algebra, division, ratios, areas, and other mathematical processes. (JDD)

  15. Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

    ERIC Educational Resources Information Center

    Inoue, Noriyuki

    2008-01-01

    Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…

  16. Primary School Text Comprehension Predicts Mathematical Word Problem-Solving Skills in Secondary School

    ERIC Educational Resources Information Center

    Björn, Piia Maria; Aunola, Kaisa; Nurmi, Jari-Erik

    2016-01-01

    This longitudinal study aimed to investigate the extent to which primary school text comprehension predicts mathematical word problem-solving skills in secondary school among Finnish students. The participants were 224 fourth graders (9-10 years old at the baseline). The children's text-reading fluency, text comprehension and basic calculation…

  17. Contribution of Equal-Sign Instruction beyond Word-Problem Tutoring for Third-Grade Students with Mathematics Difficulty

    ERIC Educational Resources Information Center

    Powell, Sarah R.; Fuchs, Lynn S.

    2010-01-01

    Elementary school students often misinterpret the equal sign (=) as an operational rather than a relational symbol. Such misunderstanding is problematic because solving equations with missing numbers may be important for the development of higher order mathematics skills, including solving word problems. Research indicates equal-sign instruction…

  18. Effects of Three Modes of Personalisation on Students' Achievement in Mathematical Word Problems in Nigeria

    ERIC Educational Resources Information Center

    Awofala, A. O. A.; Balogun, T. A.; Olagunju, M. A.

    2011-01-01

    This study investigated the effects of modes of personalisation of instruction crossed with two levels each of verbal ability and cognitive style as moderator variables on the mathematical word problems achievement of 450 junior secondary Nigerian students. Personalisation was accomplished by incorporating selected information with students'…

  19. Cognitive and Linguistic Predictors of Mathematical Word Problems with and without Irrelevant Information

    ERIC Educational Resources Information Center

    Wang, Amber Y.; Fuchs, Lynn S.; Fuchs, Douglas

    2016-01-01

    The purpose of this study was to identify cognitive and linguistic predictors of word problems with versus without irrelevant information. The sample was 701 2nd-grade students who received no specialized intervention on word problems. In the fall, they were assessed on initial arithmetic and word-problem skill as well as language ability, working…

  20. Problem Solving Concretely with the Word "Like"

    ERIC Educational Resources Information Center

    Yee, Sean

    2013-01-01

    While the average teenager's conversation may seem inundated with the word "like", in the mathematics classroom, teenagers use it with purpose. Linguists study the word "like" to understand and categorize comparative statements. By overlapping linguistics and mathematics education within the frame of cognitive science, this study found that high…

  1. Dynamic Assessment of Algebraic Learning in Predicting Third Graders’ Development of Mathematical Problem Solving

    PubMed Central

    Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Hollenbeck, Kurstin N.; Craddock, Caitlin F.; Hamlett, Carol L.

    2008-01-01

    Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting 3rd graders’ development of mathematics problem solving. In the fall, 122 3rd-grade students were assessed on language, nonverbal reasoning, attentive behavior, calculations, word-problem skill, and DA. On the basis of random assignment, students received 16 weeks of validated instruction on word problems or received 16 weeks of conventional instruction on word problems. Then, students were assessed on word-problem measures proximal and distal to instruction. Structural equation measurement models showed that DA measured a distinct dimension of pretreatment ability and that proximal and distal word-problem measures were needed to account for outcome. Structural equation modeling showed that instruction (conventional vs. validated) was sufficient to account for math word-problem outcome proximal to instruction; by contrast, language, pretreatment math skill, and DA were needed to forecast learning on word-problem outcomes more distal to instruction. Findings are discussed in terms of responsiveness-to-intervention models for preventing and identifying learning disabilities. PMID:19884957

  2. Examining Personalisation of Instruction, Attitudes toward and Achievement in Mathematics Word Problems among Nigerian Senior Secondary School Students

    ERIC Educational Resources Information Center

    Awofala, Adeneye O. A.

    2014-01-01

    This study investigated the effect of a personalised print-based instruction versus a non-personalised print-based instruction on the attitudes toward mathematics word problems of 350 senior secondary school year one Nigerian students within the blueprint of a quantitative research of pre-treatment-intervention-post-treatment non-equivalent…

  3. Exploring the Learning of Mathematics Word Problems by African Immigrant Early Learners

    ERIC Educational Resources Information Center

    Mahofa, Ernest; Adendorff, Stanley; Kwenda, Chiwimbiso

    2018-01-01

    The aim of this study was to explore the learning of mathematics word problems by African immigrant early learners in the Western Cape Province of South Africa (SA). Phenomenology was used as the philosophical underpinning for this study and also informed the research method. Purposive sampling methods were used to select 10 African immigrant…

  4. Bilingual College Writers' Collaborative Writing of Word Problems

    ERIC Educational Resources Information Center

    Esquinca, Alberto

    2011-01-01

    Numerous researchers have studied bilingual students' performance on word problems given that reading and writing these requires that they draw on linguistic and mathematical knowledge (Barwell, 2009a, 2009b). Some researchers have studied how bilinguals write word problems in the second language, but few have considered how bilinguals use their…

  5. Cognitive Strategy Instruction for Teaching Word Problems to Primary-Level Struggling Students

    ERIC Educational Resources Information Center

    Pfannenstiel, Kathleen Hughes; Bryant, Diane Pedrotty; Bryant, Brian R.; Porterfield, Jennifer A.

    2015-01-01

    Students with mathematics difficulties and learning disabilities (LD) typically struggle with solving word problems. These students often lack knowledge about efficient, cognitive strategies to utilize when solving word problems. Cognitive strategy instruction has been shown to be effective in teaching struggling students how to solve word…

  6. The Impossibility of "Real-Life" Word Problems (According to Bakhtin, Lacan, Zizek and Baudrillard)

    ERIC Educational Resources Information Center

    Gerofsky, Susan

    2010-01-01

    In recent years a great deal of work on mathematical word problems has focused on efforts to bring more of "real life" into the problems themselves and students' uptake of these problems. Following on from earlier studies of the word problem as a pedagogical and literary genre, the author argues that we cannot unproblematically assume an ability…

  7. Teaching Fifth Grade Mathematical Concepts: Effects of Word Problems Used with Traditional Methods.

    ERIC Educational Resources Information Center

    Coy, Jessica

    The view of the researcher is that students in the upper elementary to middle school range need to increase their problem-solving skills by making logical deductions and organizing and structuring their thoughts through the use of word problems. Giving children a daily word problem challenged and introduced them to the lesson. This activity…

  8. A Joint Probabilistic Classification Model of Relevant and Irrelevant Sentences in Mathematical Word Problems

    ERIC Educational Resources Information Center

    Cetintas, Suleyman; Si, Luo; Xin, Yan Ping; Zhang, Dake; Park, Joo Young; Tzur, Ron

    2010-01-01

    Estimating the difficulty level of math word problems is an important task for many educational applications. Identification of relevant and irrelevant sentences in math word problems is an important step for calculating the difficulty levels of such problems. This paper addresses a novel application of text categorization to identify two types of…

  9. Process Inquiry: Analysis of Oral Problem-Solving Skills in Mathematics of Engineering Students

    ERIC Educational Resources Information Center

    Trance, Naci John C.

    2013-01-01

    This paper presents another effort in determining the difficulty of engineering students in terms of solving word problems. Students were presented with word problems in algebra. Then, they were asked to solve the word problems orally; that is, before they presented their written solutions, they were required to explain how they understood the…

  10. Math in Plain English: Literacy Strategies for the Mathematics Classroom

    ERIC Educational Resources Information Center

    Benjamin, Amy

    2011-01-01

    Do word problems and math vocabulary confuse students in your mathematics classes? Do simple keywords like "value" and "portion" seem to mislead them? Many words that students already know can have a different meaning in mathematics. To grasp that difference, students need to connect English literacy skills to math. Successful students speak,…

  11. Working Memory and Literacy as Predictors of Performance on Algebraic Word Problems

    ERIC Educational Resources Information Center

    Lee, Kerry; Ng, Swee-Fong; Ng, Ee-Lynn; Lim, Zee-Ying

    2004-01-01

    Previous studies on individual differences in mathematical abilities have shown that working memory contributes to early arithmetic performance. In this study, we extended the investigation to algebraic word problem solving. A total of 151 10-year-olds were administered algebraic word problems and measures of working memory, intelligence quotient…

  12. Does Calculation or Word-Problem Instruction Provide a Stronger Route to Prealgebraic Knowledge?

    ERIC Educational Resources Information Center

    Fuchs, Lynn S.; Powell, Sarah R.; Cirino, Paul T.; Schumacher, Robin F.; Marrin, Sarah; Hamlett, Carol L.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.

    2014-01-01

    The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and prealgebraic knowledge. We extended the literature, which is dominated by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other…

  13. Why Do Disadvantaged Filipino Children Find Word Problems in English Difficult?

    ERIC Educational Resources Information Center

    Bautista, Debbie; Mulligan, Joanne

    2010-01-01

    Young Filipino students are expected to solve mathematical word problems in English, a language that many encounter only in schools. Using individual interviews of 17 Filipino children, we investigated why word problems in English are difficult and the extent to which the language interferes with performance. Results indicate that children could…

  14. Duality of Mathematical Thinking When Making Sense of Simple Word Problems: Theoretical Essay

    ERIC Educational Resources Information Center

    Polotskaia, Elena; Savard, Annie; Freiman, Viktor

    2015-01-01

    This essay proposes a reflection on the learning difficulties and teaching approaches associated with arithmetic word problem solving. We question the development of word problem solving skills in the early grades of elementary school. We are trying to revive the discussion because first, the knowledge in question--reversibility of arithmetic…

  15. Cognitive and Linguistic Predictors of Mathematical Word Problems With and Without Irrelevant Information.

    PubMed

    Wang, Amber Y; Fuchs, Lynn S; Fuchs, Douglas

    2016-12-01

    The purpose of this study was to identify cognitive and linguistic predictors of word problems with versus without irrelevant information. The sample was 701 2nd-grade students who received no specialized intervention on word problems. In the fall, they were assessed on initial arithmetic and word-problem skill as well as language ability, working memory capacity, and processing speed; in the spring, they were tested on a word-problem measure that included items with versus without irrelevant information. Significant predictors common to both forms of word problems were initial arithmetic and word problem-solving skill as well as language and working memory. Nonverbal reasoning predicted word problems with irrelevant information, but not word problems without irrelevant information. Findings are discussed in terms of implications for intervention and future research.

  16. The effects of using diagramming as a representational technique on high school students' achievement in solving math word problems

    NASA Astrophysics Data System (ADS)

    Banerjee, Banmali

    Methods and procedures for successfully solving math word problems have been, and continue to be a mystery to many U.S. high school students. Previous studies suggest that the contextual and mathematical understanding of a word problem, along with the development of schemas and their related external representations, positively contribute to students' accomplishments when solving word problems. Some studies have examined the effects of diagramming on students' abilities to solve word problems that only involved basic arithmetic operations. Other studies have investigated how instructional models that used technology influenced students' problem solving achievements. Still other studies have used schema-based instruction involving students with learning disabilities. No study has evaluated regular high school students' achievements in solving standard math word problems using a diagramming technique without technological aid. This study evaluated students' achievement in solving math word problems using a diagramming technique. Using a quasi-experimental experimental pretest-posttest research design, quantitative data were collected from 172 grade 11 Hispanic English language learners (ELLS) and African American learners whose first language is English (EFLLs) in 18 classes at an inner city high school in Northern New Jersey. There were 88 control and 84 experimental students. The pretest and posttest of each participating student and samples of the experimental students' class assignments provided the qualitative data for the study. The data from this study exhibited that the diagramming method of solving math word problems significantly improved student achievement in the experimental group (p<.01) compared to the control group. The study demonstrated that urban, high school, ELLs benefited from instruction that placed emphasis on the mathematical vocabulary and symbols used in word problems and that both ELLs and EFLLs improved their problem solving success through careful attention to the creation and labeling of diagrams to represent the mathematics involved in standard word problems. Although Learnertype (ELL, EFLL), Classtype (Bilingual and Mixed), and Gender (Female, Male) were not significant indicators of student achievement, there was significant interaction between Treatment and Classtype at the level of the Bilingual students ( p<.01) and between Treatment and Learnertype at the level of the ELLs (p<.01).

  17. Math and Humane Education.

    ERIC Educational Resources Information Center

    DeRosa, Bill

    1986-01-01

    Describes an activity designed to improve students' skills at solving mathematical word problems through an awareness of the pet overpopulation problem. Uses the concept of cumulative female offspring as a focal point in assisting students to analyze and work through word problems. (ML)

  18. An Exploratory Study Contrasting High- and Low-Achieving Students' Percent Word Problem Solving

    ERIC Educational Resources Information Center

    Jitendra, Asha K.; Star, Jon R.

    2012-01-01

    This study evaluated whether schema-based instruction (SBI), a promising method for teaching students to represent and solve mathematical word problems, impacted the learning of percent word problems. Of particular interest was the extent that SBI improved high- and low-achieving students' learning and to a lesser degree on the indirect effect of…

  19. Young Filipino Students Making Sense of Arithmetic Word Problems in English

    ERIC Educational Resources Information Center

    Bautista, Debbie; Mulligan, Joanne; Mitchelmore, Michael

    2009-01-01

    Young Filipino children are expected to solve mathematical word problems in English, a task which they typically encounter only in schools. In this exploratory study, task-based interviews were conducted with seven Filipino children from a public school. The children were asked to read and solve addition and subtraction word problems in English or…

  20. Cognitive and Linguistic Predictors of Mathematical Word Problems With and Without Irrelevant Information

    PubMed Central

    Fuchs, Lynn S.; Fuchs, Douglas

    2016-01-01

    The purpose of this study was to identify cognitive and linguistic predictors of word problems with versus without irrelevant information. The sample was 701 2nd-grade students who received no specialized intervention on word problems. In the fall, they were assessed on initial arithmetic and word-problem skill as well as language ability, working memory capacity, and processing speed; in the spring, they were tested on a word-problem measure that included items with versus without irrelevant information. Significant predictors common to both forms of word problems were initial arithmetic and word problem-solving skill as well as language and working memory. Nonverbal reasoning predicted word problems with irrelevant information, but not word problems without irrelevant information. Findings are discussed in terms of implications for intervention and future research. PMID:28190942

  1. Are middle school mathematics teachers able to solve word problems without using variable?

    NASA Astrophysics Data System (ADS)

    Gökkurt Özdemir, Burçin; Erdem, Emrullah; Örnek, Tuğba; Soylu, Yasin

    2018-01-01

    Many people consider problem solving as a complex process in which variables such as x, y are used. Problems may not be solved by only using 'variable.' Problem solving can be rationalized and made easier using practical strategies. When especially the development of children at younger ages is considered, it is obvious that mathematics teachers should solve problems through concrete processes. In this context, middle school mathematics teachers' skills to solve word problems without using variables were examined in the current study. Through the case study method, this study was conducted with 60 middle school mathematics teachers who have different professional experiences in five provinces in Turkey. A test consisting of five open-ended word problems was used as the data collection tool. The content analysis technique was used to analyze the data. As a result of the analysis, it was seen that the most of the teachers used trial-and-error strategy or area model as the solution strategy. On the other hand, the teachers who solved the problems using variables such as x, a, n or symbols such as Δ, □, ○, * and who also felt into error by considering these solutions as without variable were also seen in the study.

  2. Visual Representations in Mathematics Teaching: An Experiment with Students

    ERIC Educational Resources Information Center

    Debrenti, Edith

    2015-01-01

    General problem-solving skills are of central importance in school mathematics achievement. Word problems play an important role not just in mathematical education, but in general education as well. Meaningful learning and understanding are basic aspects of all kinds of learning and it is even more important in the case of learning mathematics. In…

  3. Improvement of Word Problem Solving and Basic Mathematics Competencies in Students with Attention Deficit/Hyperactivity Disorder and Mathematical Learning Difficulties

    ERIC Educational Resources Information Center

    González-Castro, Paloma; Cueli, Marisol; Areces, Débora; Rodríguez, Celestino; Sideridis, Georgios

    2016-01-01

    Problem solving represents a salient deficit in students with mathematical learning difficulties (MLD) primarily caused by difficulties with informal and formal mathematical competencies. This study proposes a computerized intervention tool, the integrated dynamic representation (IDR), for enhancing the early learning of basic mathematical…

  4. Elementary Students' Spontaneous Metacognitive Functions in Different Types of Mathematical Problems

    ERIC Educational Resources Information Center

    Mokos, Evagelos; Kafoussi, Sonia

    2013-01-01

    Metacognition is the mind's ability to monitor and control itself or, in other words, the ability to know about our knowing (Dunlosky & Bjork, 2008). In mathematics education, the importance of the investigation of students' metacognition during their mathematical activity has been focused on the area of mathematics problem solving. This study…

  5. The Acquisition of Problem-Solving Skills in Mathematics: How Animations Can Aid Understanding of Structural Problem Features and Solution Procedures

    ERIC Educational Resources Information Center

    Scheiter, Katharina; Gerjets, Peter; Schuh, Julia

    2010-01-01

    In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…

  6. Automatic Item Generation of Probability Word Problems

    ERIC Educational Resources Information Center

    Holling, Heinz; Bertling, Jonas P.; Zeuch, Nina

    2009-01-01

    Mathematical word problems represent a common item format for assessing student competencies. Automatic item generation (AIG) is an effective way of constructing many items with predictable difficulties, based on a set of predefined task parameters. The current study presents a framework for the automatic generation of probability word problems…

  7. Middle School Children's Problem-Solving Behavior: A Cognitive Analysis from a Reading Comprehension Perspective

    ERIC Educational Resources Information Center

    Pape, Stephen J.

    2004-01-01

    Many children read mathematics word problems and directly translate them to arithmetic operations. More sophisticated problem solvers transform word problems into object-based or mental models. Subsequent solutions are often qualitatively different because these models differentially support cognitive processing. Based on a conception of problem…

  8. Teaching Mathematical Word Problem Solving: The Quality of Evidence for Strategy Instruction Priming the Problem Structure

    ERIC Educational Resources Information Center

    Jitendra, Asha K.; Petersen-Brown, Shawna; Lein, Amy E.; Zaslofsky, Anne F.; Kunkel, Amy K.; Jung, Pyung-Gang; Egan, Andrea M.

    2015-01-01

    This study examined the quality of the research base related to strategy instruction priming the underlying mathematical problem structure for students with learning disabilities and those at risk for mathematics difficulties. We evaluated the quality of methodological rigor of 18 group research studies using the criteria proposed by Gersten et…

  9. A Comparative Analysis of Word Problems in Selected United States and Russian First Grade Textbooks

    ERIC Educational Resources Information Center

    Grishchenko, Svetlana

    2009-01-01

    The purpose of this study was to explore word problems as a subject matter in mathematics textbook curricula. The motivation for the study derived from the following evidence: (a) American students find some word problems are more difficult than others (Garcia, Jimenez, & Hess, 2006; Riley & Green, 1988; Stern, 2001), and (b) one of the…

  10. The Effects of Using Diagramming as a Representational Technique on High School Students' Achievement in Solving Math Word Problems

    ERIC Educational Resources Information Center

    Banerjee, Banmali

    2010-01-01

    Methods and procedures for successfully solving math word problems have been, and continue to be a mystery to many U.S. high school students. Previous studies suggest that the contextual and mathematical understanding of a word problem, along with the development of schemas and their related external representations, positively contribute to…

  11. Anticipation Guides: Reading for Mathematics Understanding

    ERIC Educational Resources Information Center

    Adams, Anne E.; Pegg, Jerine; Case, Melissa

    2015-01-01

    With the acceptance by many states of the Common Core State Standards for Mathematics, new emphasis is being placed on students' ability to engage in mathematical practices such as understanding problems (including word problems), reading and critiquing arguments, and making explicit use of definitions (CCSSI 2010). Engaging students in…

  12. Kindergarten Students Solving Mathematical Word Problems

    ERIC Educational Resources Information Center

    Johnson, Nickey Owen

    2013-01-01

    The purpose of this study was to explore problem solving with kindergarten students. This line of inquiry is highly significant given that Common Core State Standards emphasize deep, conceptual understanding in mathematics as well as problem solving in kindergarten. However, there is little research on problem solving with kindergarten students.…

  13. MONTO: A Machine-Readable Ontology for Teaching Word Problems in Mathematics

    ERIC Educational Resources Information Center

    Lalingkar, Aparna; Ramnathan, Chandrashekar; Ramani, Srinivasan

    2015-01-01

    The Indian National Curriculum Framework has as one of its objectives the development of mathematical thinking and problem solving ability. However, recent studies conducted in Indian metros have expressed concern about students' mathematics learning. Except in some private coaching academies, regular classroom teaching does not include problem…

  14. Transition Mathematics. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2007

    2007-01-01

    "Transition Mathematics" aims to increase 7th- through 12th-grade students' skills in applied arithmetic, pre-algebra, and pre-geometry. This one-year curriculum also addresses general application to different wordings of problems, types of numbers, and contexts for problems and aims to promote mathematical reading skills. The curriculum…

  15. Effects of the SOLVE Strategy on the Mathematical Problem Solving Skills of Secondary Students with Learning Disabilities

    ERIC Educational Resources Information Center

    Freeman-Green, Shaqwana M.; O'Brien, Chris; Wood, Charles L.; Hitt, Sara Beth

    2015-01-01

    This study examined the effects of explicit instruction in the SOLVE Strategy on the mathematical problem solving skills of six Grade 8 students with specific learning disabilities. The SOLVE Strategy is an explicit instruction, mnemonic-based learning strategy designed to help students in solving mathematical word problems. Using a multiple probe…

  16. The Effect of Dynamic and Interactive Mathematics Learning Environments (DIMLE), Supporting Multiple Representations, on Perceptions of Elementary Mathematics Pre-Service Teachers in Problem Solving Process

    ERIC Educational Resources Information Center

    Ozdemir, S.; Reis, Z. Ayvaz

    2013-01-01

    Mathematics is an important discipline, providing crucial tools, such as problem solving, to improve our cognitive abilities. In order to solve a problem, it is better to envision and represent through multiple means. Multiple representations can help a person to redefine a problem with his/her own words in that envisioning process. Dynamic and…

  17. How Readability Factors Are Differentially Associated with Performance for Students of Different Backgrounds When Solving Mathematics Word Problems

    ERIC Educational Resources Information Center

    Walkington, Candace; Clinton, Virginia; Shivraj, Pooja

    2018-01-01

    The link between reading and mathematics achievement is well known, and an important question is whether readability factors in mathematics problems are differentially impacting student groups. Using 20 years of data from the National Assessment of Educational Progress and the Trends in International Mathematics and Science Study, we examine how…

  18. Reading-Enhanced Word Problem Solving: A Theoretical Model

    ERIC Educational Resources Information Center

    Capraro, Robert M.; Capraro, Mary Margaret; Rupley, William H.

    2012-01-01

    There is a reciprocal relationship between mathematics and reading cognition. Metacognitive training within reading-enhanced problem solving should facilitate students developing an awareness of what good readers do when reading for meaning in solving mathematical problems enabling them to apply these strategies. The constructs for each cognitive…

  19. Socially Shared Metacognition of Dyads of Pupils in Collaborative Mathematical Problem-Solving Processes

    ERIC Educational Resources Information Center

    Iiskala, Tuike; Vauras, Marja; Lehtinen, Erno; Salonen, Pekka

    2011-01-01

    This study investigated how metacognition appears as a socially shared phenomenon within collaborative mathematical word-problem solving processes of dyads of high-achieving pupils. Four dyads solved problems of different difficulty levels. The pupils were 10 years old. The problem-solving activities were videotaped and transcribed in terms of…

  20. Teaching Methods for Modelling Problems and Students' Task-Specific Enjoyment, Value, Interest and Self-Efficacy Expectations

    ERIC Educational Resources Information Center

    Schukajlow, Stanislaw; Leiss, Dominik; Pekrun, Reinhard; Blum, Werner; Muller, Marcel; Messner, Rudolf

    2012-01-01

    In this study which was part of the DISUM-project, 224 ninth graders from 14 German classes from middle track schools (Realschule) were asked about their enjoyment, interest, value and self-efficacy expectations concerning three types of mathematical problems: intra-mathematical problems, word problems and modelling problems. Enjoyment, interest,…

  1. Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities?

    PubMed

    Fuchs, Lynn S; Geary, David C; Compton, Donald L; Fuchs, Douglas; Hamlett, Carol L; Seethaler, Pamela M; Bryant, Joan D; Schatschneider, Christopher

    2010-11-01

    The purpose of this study was to examine the interplay between basic numerical cognition and domain-general abilities (such as working memory) in explaining school mathematics learning. First graders (N = 280; mean age = 5.77 years) were assessed on 2 types of basic numerical cognition, 8 domain-general abilities, procedural calculations, and word problems in fall and then reassessed on procedural calculations and word problems in spring. Development was indexed by latent change scores, and the interplay between numerical and domain-general abilities was analyzed by multiple regression. Results suggest that the development of different types of formal school mathematics depends on different constellations of numerical versus general cognitive abilities. When controlling for 8 domain-general abilities, both aspects of basic numerical cognition were uniquely predictive of procedural calculations and word problems development. Yet, for procedural calculations development, the additional amount of variance explained by the set of domain-general abilities was not significant, and only counting span was uniquely predictive. By contrast, for word problems development, the set of domain-general abilities did provide additional explanatory value, accounting for about the same amount of variance as the basic numerical cognition variables. Language, attentive behavior, nonverbal problem solving, and listening span were uniquely predictive.

  2. Effectiveness of Small-Group Tutoring Interventions for Improving the Mathematical Problem-Solving Performance of Third-Grade Students with Mathematics Difficulties: A Randomized Experiment

    ERIC Educational Resources Information Center

    Jitendra, Asha K.; Dupuis, Danielle N.; Rodriguez, Michael C.

    2012-01-01

    The present research assessed the efficacy of two tutoring protocols for improving the mathematics outcomes of at-risk third-grade students. Results indicated that students in the schema-based instruction (SBI) group outperformed students in the control group on word problem solving performance after 30 hours of problem-solving experience, but the…

  3. Does Calculation or Word-Problem Instruction Provide A Stronger Route to Pre-Algebraic Knowledge?

    PubMed Central

    Fuchs, Lynn S.; Powell, Sarah R.; Cirino, Paul T.; Schumacher, Robin F.; Marrin, Sarah; Hamlett, Carol L.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.

    2014-01-01

    The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and pre-algebraic knowledge. We extended the literature, which is dominated by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other domain and whether intervention in either or both domains contributes to pre-algebraic knowledge. Participants were 1102 children in 127 2nd-grade classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation intervention, word-problem intervention, and business-as-usual control. Intervention, which lasted 17 weeks, was designed to provide research-based linkages between arithmetic calculations or arithmetic word problems (depending on condition) to pre-algebraic knowledge. Multilevel modeling suggested calculation intervention improved calculation but not word-problem outcomes; word-problem intervention enhanced word-problem but not calculation outcomes; and word-problem intervention provided a stronger route than calculation intervention to pre-algebraic knowledge. PMID:25541565

  4. Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

    PubMed

    Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

    2015-01-01

    Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

  5. Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

    PubMed Central

    Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

    2015-01-01

    Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806

  6. Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study

    PubMed Central

    Geary, David C.

    2011-01-01

    The study's goal was to identify the beginning of first grade quantitative competencies that predict mathematics achievement start point and growth through fifth grade. Measures of number, counting, and arithmetic competencies were administered in early first grade and used to predict mathematics achievement through fifth (n = 177), while controlling for intelligence, working memory, and processing speed. Multilevel models revealed intelligence, processing speed, and the central executive component of working memory predicted achievement or achievement growth in mathematics and, as a contrast domain, word reading. The phonological loop was uniquely predictive of word reading and the visuospatial sketch pad of mathematics. Early fluency in processing and manipulating numerical set size and Arabic numerals, accurate use of sophisticated counting procedures for solving addition problems, and accuracy in making placements on a mathematical number line were uniquely predictive of mathematics achievement. Use of memory-based processes to solve addition problems predicted mathematics and reading achievement but in different ways. The results identify the early quantitative competencies that uniquely contribute to mathematics learning. PMID:21942667

  7. Effects of Cognitive Strategy Interventions on Word Problem Solving and Working Memory in Children with Math Disabilities

    ERIC Educational Resources Information Center

    Swanson, H. Lee; Lussier, Catherine; Orosco, Michael

    2011-01-01

    Although current categories of learning disabilities include as specific disabilities calculation and mathematical problem solving [see IDEA reauthorization, 2004, Sec. 300.8(c)(10)], the majority of research focuses on calculation disabilities. Previous studies have shown, however, that deficits in word problem solving difficulties are persistent…

  8. Scaffold Seeking: A Reverse Design of Scaffolding in Computer-Supported Word Problem Solving

    ERIC Educational Resources Information Center

    Cheng, Hercy N. H.; Yang, Euphony F. Y.; Liao, Calvin C. Y.; Chang, Ben; Huang, Yana C. Y.; Chan, Tak-Wai

    2015-01-01

    Although well-designed scaffolding may assist students to accomplish learning tasks, its insufficient capability to dynamically assess students' abilities and to adaptively support them may result in the problem of overscaffolding. Our previous project has also shown that students using scaffolds to solve mathematical word problems for a long time…

  9. Evaluation of the Effectiveness of a Tablet Computer Application (App) in Helping Students with Visual Impairments Solve Mathematics Problems

    ERIC Educational Resources Information Center

    Beal, Carole R.; Rosenblum, L. Penny

    2018-01-01

    Introduction: The authors examined a tablet computer application (iPad app) for its effectiveness in helping students studying prealgebra to solve mathematical word problems. Methods: Forty-three visually impaired students (that is, those who are blind or have low vision) completed eight alternating mathematics units presented using their…

  10. Child-Level Predictors of Responsiveness to Evidence-Based Mathematics Intervention

    ERIC Educational Resources Information Center

    Powell, Sarah R.; Cirino, Paul T.; Malone, Amelia S.

    2017-01-01

    We identified child-level predictors of responsiveness to 2 types of mathematics intervention (calculation and word problem) among second-grade children with mathematics difficulty. Participants were 250 children in 107 classrooms in 23 schools pretested on mathematics and general cognitive measures and posttested on mathematics measures. We…

  11. Effects of a Multitier Support System on Calculation, Word Problem, and Prealgebraic Performance Among At-Risk Learners.

    PubMed

    Powell, Sarah R; Fuchs, Lynn S; Cirino, Paul T; Fuchs, Douglas; Compton, Donald L; Changas, Paul C

    2015-07-01

    The focus of the present study was enhancing word-problem and calculation achievement in ways that support pre-algebraic thinking among 2 nd -grade students at risk for mathematics difficulty. Intervention relied on a multi-tier support system (i.e., responsiveness-to-intervention or RTI) in which at-risk students participate in general classroom instruction and receive supplementary small-group tutoring. Participants were 265 students in 110 classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation RTI, word-problem RTI, and business-as-usual control. Intervention lasted 17 weeks. Multilevel modeling indicated that calculation RTI improved calculation but not word-problem outcomes; word-problem RTI enhanced proximal word-problem outcomes as well as performance on some calculation outcomes; and word-problem RTI provided a stronger route than calculation RTI to pre-algebraic knowledge.

  12. Effects of a Multitier Support System on Calculation, Word Problem, and Prealgebraic Performance Among At-Risk Learners

    PubMed Central

    Powell, Sarah R.; Fuchs, Lynn S.; Cirino, Paul T.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.

    2014-01-01

    The focus of the present study was enhancing word-problem and calculation achievement in ways that support pre-algebraic thinking among 2nd-grade students at risk for mathematics difficulty. Intervention relied on a multi-tier support system (i.e., responsiveness-to-intervention or RTI) in which at-risk students participate in general classroom instruction and receive supplementary small-group tutoring. Participants were 265 students in 110 classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation RTI, word-problem RTI, and business-as-usual control. Intervention lasted 17 weeks. Multilevel modeling indicated that calculation RTI improved calculation but not word-problem outcomes; word-problem RTI enhanced proximal word-problem outcomes as well as performance on some calculation outcomes; and word-problem RTI provided a stronger route than calculation RTI to pre-algebraic knowledge. PMID:26097244

  13. Tuning Out the World with Noise-Canceling Headphones

    ERIC Educational Resources Information Center

    McCulloch, Allison W.; Whitehead, Ashley; Lovett, Jennifer N.; Whitley, Blake

    2017-01-01

    Context is what makes mathematical modeling tasks different from more traditional textbook word problems. Math problems are sometimes stripped of context as they are worked on. For modeling problems, however, context is important for making sense of the mathematics. The task should be brought back to its real-world context as often as possible. In…

  14. The Effect of Contextual and Conceptual Rewording on Mathematical Problem-Solving Performance

    ERIC Educational Resources Information Center

    Haghverdi, Majid; Wiest, Lynda R.

    2016-01-01

    This study shows how separate and combined contextual and conceptual problem rewording can positively influence student performance in solving mathematical word problems. Participants included 80 seventh-grade Iranian students randomly assigned in groups of 20 to three experimental groups involving three types of rewording and a control group. All…

  15. Preservice Middle and High School Mathematics Teachers' Strategies When Solving Proportion Problems

    ERIC Educational Resources Information Center

    Arican, Muhammet

    2018-01-01

    The purpose of this study was to investigate eight preservice middle and high school mathematics teachers' solution strategies when solving single and multiple proportion problems. Real-world missing-value word problems were used in an interview setting to collect information about preservice teachers' (PSTs) reasoning about proportional…

  16. The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems

    ERIC Educational Resources Information Center

    Ng, Swee Fong; Lee, Kerry

    2009-01-01

    Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

  17. Factors Influencing Filipino Children's Solutions to Addition and Subtraction Word Problems

    ERIC Educational Resources Information Center

    Bautista, Debbie; Mitchelmore, Michael; Mulligan, Joanne

    2009-01-01

    Young Filipino children are expected to solve mathematical word problems in English, which is not their mother tongue. Because of this, it is often assumed that Filipino children have difficulties in solving problems because they cannot read or comprehend what they have read. This study tested this assumption by determining whether presenting word…

  18. Word Problems versus Image-Rich Problems: An Analysis of Effects of Task Characteristics on Students' Performance on Contextual Mathematics Problems

    ERIC Educational Resources Information Center

    Hoogland, Kees; Pepin, Birgit; de Koning, Jaap; Bakker, Arthur; Gravemeijer, Koeno

    2018-01-01

    This article reports on a "post hoc" study using a randomised controlled trial with 31,842 students in the Netherlands and an instrument consisting of 21 paired problems. The trial showed a variability in the differences of students' results in solving contextual mathematical problems with either a descriptive or a depictive…

  19. Early Mathematics Fluency with CCSSM

    ERIC Educational Resources Information Center

    Matney, Gabriel T.

    2014-01-01

    To develop second-grade students' confidence and ease, this author presents examples of learning tasks (Number of the Day, Word Problem Solving, and Modeling New Mathematical Ideas) that align with Common Core State Standards for Mathematics and that build mathematical fluency to promote students' creative expression of mathematical…

  20. Effects of Preventative Tutoring on the Mathematical Problem Solving of Third-Grade Students With Math and Reading Difficulties.

    PubMed

    Fuchs, Lynn S; Seethaler, Pamela M; Powell, Sarah R; Fuchs, Douglas; Hamlett, Carol L; Fletcher, Jack M

    2008-01-01

    This study assessed the effects of preventative tutoring on the math problem solving of third-grade students with math and reading difficulties. Students (n = 35) were assigned randomly to continue in their general education math program or to receive secondary preventative tutoring 3 times per week, 30 min per session, for 12 weeks. Schema-broadening tutoring taught students to (a) focus on the mathematical structure of 3 problem types; (b) recognize problems as belonging to those 3 problem-type schemas; (c) solve the 3 word-problem types; and (d) transfer solution methods to problems that include irrelevant information, 2-digit operands, missing information in the first or second positions in the algebraic equation, or relevant information in charts, graphs, and pictures. Also, students were taught to perform the calculation and algebraic skills foundational for problem solving. Analyses of variance revealed statistically significant effects on a wide range of word problems, with large effect sizes. Findings support the efficacy of the tutoring protocol for preventing word-problem deficits among third-grade students with math and reading deficits.

  1. Effects of Preventative Tutoring on the Mathematical Problem Solving of Third-Grade Students With Math and Reading Difficulties

    PubMed Central

    Fuchs, Lynn S.; Seethaler, Pamela M.; Powell, Sarah R.; Fuchs, Douglas; Hamlett, Carol L.; Fletcher, Jack M.

    2009-01-01

    This study assessed the effects of preventative tutoring on the math problem solving of third-grade students with math and reading difficulties. Students (n = 35) were assigned randomly to continue in their general education math program or to receive secondary preventative tutoring 3 times per week, 30 min per session, for 12 weeks. Schema-broadening tutoring taught students to (a) focus on the mathematical structure of 3 problem types; (b) recognize problems as belonging to those 3 problem-type schemas; (c) solve the 3 word-problem types; and (d) transfer solution methods to problems that include irrelevant information, 2-digit operands, missing information in the first or second positions in the algebraic equation, or relevant information in charts, graphs, and pictures. Also, students were taught to perform the calculation and algebraic skills foundational for problem solving. Analyses of variance revealed statistically significant effects on a wide range of word problems, with large effect sizes. Findings support the efficacy of the tutoring protocol for preventing word-problem deficits among third-grade students with math and reading deficits. PMID:20209074

  2. Raise the Bar on Problem Solving

    ERIC Educational Resources Information Center

    Englard, Lisa

    2010-01-01

    In a 1981 diagnostic test, the Ministry of Education in Singapore found its country facing a challenge: Only 46 percent of students in grades 2-4 could solve word problems that were presented without such key words as "altogether" or "left." Yet today, according to results from the Trends in International Mathematics and…

  3. It's Not a Math Lesson--We're Learning to Draw! Teachers' Use of Visual Representations in Instructing Word Problem Solving in Sixth Grade of Elementary School

    ERIC Educational Resources Information Center

    Boonen, Anton J. H.; Reed, Helen C.; Schoonenboom, Judith; Jolles, Jelle

    2016-01-01

    Non-routine word problem solving is an essential feature of the mathematical development of elementary school students worldwide. Many students experience difficulties in solving these problems due to erroneous problem comprehension. These difficulties could be alleviated by instructing students how to use visual representations that clarify the…

  4. Math in a Can

    ERIC Educational Resources Information Center

    Cupillari, Antonella

    2015-01-01

    Practical problems that use mathematical concepts are among the highlights of any mathematics class, for better and for worse. Teachers are thrilled to show applications of new theoretical ideas, whereas most students dread "word problems." This article presents a sequence of three activities designed to get students to think about…

  5. Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students' Proportional Reasoning: A Randomized Experiment

    ERIC Educational Resources Information Center

    Jitendra, Asha K.; Star, Jon R.; Dupuis, Danielle N.; Rodriguez, Michael C.

    2013-01-01

    This study examined the effect of schema-based instruction (SBI) on 7th-grade students' mathematical problem-solving performance. SBI is an instructional intervention that emphasizes the role of mathematical structure in word problems and also provides students with a heuristic to self-monitor and aid problem solving. Using a…

  6. An Efficacy Study of Interleaved Mathematics Practice. Revised

    ERIC Educational Resources Information Center

    Rohrer, Doug; Dedrick, Robert F.; Burgess, Kaleena

    2013-01-01

    In a typical mathematics course, the material is divided into many lessons, and each lesson is followed by an assignment consisting of practice problems. Most commonly, each assignment consists solely of problems on the preceding lesson. For example, a lesson on ratios might be followed by an assignment with 12 problems on ratios. In other words,…

  7. Understanding Problem-Solving Errors by Students with Learning Disabilities in Standards-Based and Traditional Curricula

    ERIC Educational Resources Information Center

    Bouck, Emily C.; Bouck, Mary K.; Joshi, Gauri S.; Johnson, Linley

    2016-01-01

    Students with learning disabilities struggle with word problems in mathematics classes. Understanding the type of errors students make when working through such mathematical problems can further describe student performance and highlight student difficulties. Through the use of error codes, researchers analyzed the type of errors made by 14 sixth…

  8. Application of Graph Theory in an Intelligent Tutoring System for Solving Mathematical Word Problems

    ERIC Educational Resources Information Center

    Nabiyev, Vasif V.; Çakiroglu, Ünal; Karal, Hasan; Erümit, Ali K.; Çebi, Ayça

    2016-01-01

    This study is aimed to construct a model to transform word "motion problems" in to an algorithmic form in order to be processed by an intelligent tutoring system (ITS). First; categorizing the characteristics of motion problems, second; suggesting a model for the categories were carried out. In order to solve all categories of the…

  9. The semantic system is involved in mathematical problem solving.

    PubMed

    Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

    2018-02-01

    Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

  10. Effects of a Mathematics Fluency Program on Mathematics Performance of Students with Challenging Behaviors

    ERIC Educational Resources Information Center

    Whitney, Todd; Hirn, Regina G.; Lingo, Amy S.

    2016-01-01

    In the present study, we examined the effects of a fluency-building mathematics program called Great Leaps Math on fluency of basic addition mathematics facts zero to nine and word problem solving using a multiple probe design across participants. Three elementary students with challenging behaviors and mathematics difficulty participated in the…

  11. Automatic Item Generation via Frame Semantics: Natural Language Generation of Math Word Problems.

    ERIC Educational Resources Information Center

    Deane, Paul; Sheehan, Kathleen

    This paper is an exploration of the conceptual issues that have arisen in the course of building a natural language generation (NLG) system for automatic test item generation. While natural language processing techniques are applicable to general verbal items, mathematics word problems are particularly tractable targets for natural language…

  12. Reflective thinking in solving an algebra problem: a case study of field independent-prospective teacher

    NASA Astrophysics Data System (ADS)

    Agustan, S.; Juniati, Dwi; Yuli Eko Siswono, Tatag

    2017-10-01

    Nowadays, reflective thinking is one of the important things which become a concern in learning mathematics, especially in solving a mathematical problem. The purpose of this paper is to describe how the student used reflective thinking when solved an algebra problem. The subject of this research is one female student who has field independent cognitive style. This research is a descriptive exploratory study with data analysis using qualitative approach to describe in depth reflective thinking of prospective teacher in solving an algebra problem. Four main categories are used to analyse the reflective thinking in solving an algebra problem: (1) formulation and synthesis of experience, (2) orderliness of experience, (3) evaluating the experience and (4) testing the selected solution based on the experience. The results showed that the subject described the problem by using another word and the subject also found the difficulties in making mathematical modelling. The subject analysed two concepts used in solving problem. For instance, geometry related to point and line while algebra is related to algebra arithmetic operation. The subject stated that solution must have four aspect to get effective solution, specifically the ability to (a) understand the meaning of every words; (b) make mathematical modelling; (c) calculate mathematically; (d) interpret solution obtained logically. To test the internal consistency or error in solution, the subject checked and looked back related procedures and operations used. Moreover, the subject tried to resolve the problem in a different way to compare the answers which had been obtained before. The findings supported the assertion that reflective thinking provides an opportunity for the students in improving their weakness in mathematical problem solving. It can make a grow accuracy and concentration in solving a mathematical problem. Consequently, the students will get the right and logic answer by reflective thinking.

  13. The Relation between Students' Math and Reading Ability and Their Mathematics, Physics, and Chemistry Examination Grades in Secondary Education

    ERIC Educational Resources Information Center

    Korpershoek, Hanke; Kuyper, Hans; van der Werf, Greetje

    2015-01-01

    Word problems are math- or science-related problems presented in the context of a story or real-life scenario. Literature suggests that, to solve these problems, advanced reading skills are required, in addition to content-related skills in, for example, mathematics. In the present study, we investigated the relation between students' reading…

  14. "Explicame tu Respuesta": Supporting the Development of Mathematical Discourse in Emergent Bilingual Kindergarten Students

    ERIC Educational Resources Information Center

    Celedon-Pattichis, Sylvia; Turner, Erin E.

    2012-01-01

    This study investigated Spanish-speaking kindergarten students' participation in mathematical discourse as they solved and discussed a range of word problems. Specifically, we draw upon sociocultural perspectives on mathematics learning to frame mathematical discourse and to examine specific teacher and student actions that seemed to support the…

  15. A Conceptual Metaphor Framework for the Teaching of Mathematics

    ERIC Educational Resources Information Center

    Danesi, Marcel

    2007-01-01

    Word problems in mathematics seem to constantly pose learning difficulties for all kinds of students. Recent work in math education (for example, [Lakoff, G. & Nunez, R. E. (2000). "Where mathematics comes from: How the embodied mind brings mathematics into being." New York: Basic Books]) suggests that the difficulties stem from an…

  16. Use of Common-Sense Knowledge, Language and Reality in Mathematical Word Problem Solving

    ERIC Educational Resources Information Center

    Sepeng, Percy

    2014-01-01

    The study reported in this article sought to explore and observe how grade 9 learners solve real-wor(l)d problems (a) without real context and (b) without real meaning. Learners' abilities to make sense of the decontextualised word problems set in the real world were investigated with regard to learners' use of common sense in relation to problem…

  17. The Functional Use of a Mathematical Sign

    ERIC Educational Resources Information Center

    Berger, Margot

    2004-01-01

    The question of how a mathematics student at university-level makes sense of a new mathematical sign, presented to her or him in the form of a definition, is a fundamental problem in mathematics education. Using an analogy with Vygotsky's theory (1986, 1994) of how a child learns a new word, I argue that a learner uses a new mathematical sign both…

  18. Improving Pupils' Mathematical Communication Abilities through Computer-Supported Reciprocal Peer Tutoring

    ERIC Educational Resources Information Center

    Yang, Euphony F. Y.; Chang, Ben; Cheng, Hercy N. H.; Chan, Tak-Wai

    2016-01-01

    This study examined how to foster pupils' mathematical communication abilities by using tablet PCs. Students were encouraged to generate math creations (including mathematical representation, solution, and solution explanation of word problems) as their teaching materials and reciprocally tutor classmates to increase opportunities for mathematical…

  19. Analysis of space telescope data collection system

    NASA Technical Reports Server (NTRS)

    Ingels, F. M.; Schoggen, W. O.

    1982-01-01

    An analysis of the expected performance for the Multiple Access (MA) system is provided. The analysis covers the expected bit error rate performance, the effects of synchronization loss, the problem of self-interference, and the problem of phase ambiguity. The problem of false acceptance of a command word due to data inversion is discussed. A mathematical determination of the probability of accepting an erroneous command word due to a data inversion is presented. The problem is examined for three cases: (1) a data inversion only, (2) a data inversion and a random error within the same command word, and a block (up to 256 48-bit words) containing both a data inversion and a random error.

  20. Is the Role of Equations in the Doing of Word Problems in School Algebra Changing? Initial Indications from Teacher Study Groups

    ERIC Educational Resources Information Center

    Chazan, Daniel; Sela, Hagit; Herbst, Patricio

    2012-01-01

    We illustrate a method, which is modeled on "breaching experiments," for studying tacit norms that govern classroom interaction around particular mathematical content. Specifically, this study explores norms that govern teachers' expectations for the doing of word problems in school algebra. Teacher study groups discussed representations of…

  1. Cognitive Correlates of Mathematical Achievement in Children with Cerebral Palsy and Typically Developing Children

    ERIC Educational Resources Information Center

    Jenks, Kathleen M.; van Lieshout, Ernest C. D. M.; de Moor, Jan M. H.

    2012-01-01

    Background: Remarkably few studies have investigated the nature and origin of learning difficulties in children with cerebral palsy (CP). Aims: To investigate math achievement in terms of word-problem solving ability in children with CP and controls. Because of the potential importance of reading for word-problem solving, we investigated reading…

  2. Preservice Teachers' Algebraic Reasoning and Symbol Use on a Multistep Fraction Word Problem

    ERIC Educational Resources Information Center

    Cullen, Amanda L.; Tobias, Jennifer M.; Safak, Elif; Kirwan, J. Vince; Wessman-Enzinger, Nicole M.; Wickstrom, Megan H.; Baek, Jae M.

    2017-01-01

    Previous research on preservice teachers' understanding of fractions and algebra has focused on one or the other. To extend this research, we examined 85 undergraduate elementary education majors and middle school mathematics education majors' solutions and solution paths (i.e., the ways or methods in which preservice teachers solve word problems)…

  3. Syntactic Awareness and Arithmetic Word Problem Solving in Children with and without Learning Disabilities

    ERIC Educational Resources Information Center

    Peake, Christian; Jiménez, Juan E.; Rodríguez, Cristina; Bisschop, Elaine; Villarroel, Rebeca

    2015-01-01

    Arithmetic word problem (AWP) solving is a highly demanding task for children with learning disabilities (LD) since verbal and mathematical information have to be integrated. This study examines specifically how syntactic awareness (SA), the ability to manage the grammatical structures of language, affects AWP solving. Three groups of children in…

  4. Predicting First Graders' Development of Calculation versus Word-Problem Performance: The Role of Dynamic Assessment

    ERIC Educational Resources Information Center

    Seethaler, Pamela M.; Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.

    2012-01-01

    The purpose of this study was to assess the value of dynamic assessment (DA; degree of scaffolding required to learn unfamiliar mathematics content) for predicting 1st-grade calculations (CAs) and word problems (WPs) development, while controlling for the role of traditional assessments. Among 184 1st graders, predictors (DA, Quantity…

  5. Where Are the Quadratic's Complex Roots?

    ERIC Educational Resources Information Center

    Páll-Szabó, Ágnes Orsolya

    2015-01-01

    A picture is worth more than a thousand words--in mathematics too. Many students fail in learning mathematics because, in some cases, teachers do not offer the necessary visualization. Nowadays technology overcomes this problem: computer aided instruction is one of the most efficients methods in teaching mathematics. In this article we try to…

  6. On the Role of Engineering in Mathematical Development

    ERIC Educational Resources Information Center

    Fernandez, Isabel; Pacheco, Jose

    2005-01-01

    It is customary for engineering syllabuses to include a substantial amount of mathematics, a fact traditionally justified through their usefulness in the analysis and resolution of many technological problems. In other words, usually the role of mathematics in engineering is emphasized. Nevertheless, the opposite viewpoint could be considered as…

  7. Conceptual Complexity and Apparent Contradictions in Mathematics Language

    ERIC Educational Resources Information Center

    Gough, John

    2007-01-01

    Mathematics is like a language, although technically it is not a natural or informal human language, but a formal, that is, artificially constructed language. Importantly, educators use their natural everyday language to teach the formal language of mathematics. At times, however, instructors encounter problems when the technical words they use,…

  8. Does Early Algebraic Reasoning Differ as a Function of Students’ Difficulty with Calculations versus Word Problems?

    PubMed Central

    Powell, Sarah R.; Fuchs, Lynn S.

    2014-01-01

    According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2nd- grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty. PMID:25309044

  9. Puzzles, Pastimes, Problems.

    ERIC Educational Resources Information Center

    Eperson, D. B.

    1985-01-01

    Presents six mathematical problems (with answers) which focus on: (1) chess moves; (2) patterned numbers; (3) quadratics with rational roots; (4) number puzzles; (5) Euclidean geometry; and (6) Carrollian word puzzles. (JN)

  10. Enhancing Arithmetic and Word-Problem Solving Skills Efficiently by Individualized Computer-Assisted Practice

    ERIC Educational Resources Information Center

    Schoppek, Wolfgang; Tulis, Maria

    2010-01-01

    The fluency of basic arithmetical operations is a precondition for mathematical problem solving. However, the training of skills plays a minor role in contemporary mathematics instruction. The authors proposed individualization of practice as a means to improve its efficiency, so that the time spent with the training of skills is minimized. As a…

  11. Ways of Thinking Associated with Mathematics Teachers' Problem Posing in the Context of Division of Fractions

    ERIC Educational Resources Information Center

    Koichu, Boris; Harel, Guershon; Manaster, Alfred

    2013-01-01

    Twenty-four mathematics teachers were asked to think aloud when posing a word problem whose solution could be found by computing 4/5 divided by 2/3. The data consisted of verbal protocols along with the written notes made by the subjects. The qualitative analysis of the data was focused on identifying the structures of the problems produced and…

  12. Effects of a Multitier Support System on Calculation, Word Problem, and Prealgebraic Performance among At-Risk Learners

    ERIC Educational Resources Information Center

    Powell, Sarah R.; Fuchs, Lynn S.; Cirino, Paul T.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.

    2015-01-01

    The focus of the present study was enhancing word problem and calculation achievement in ways that support prealgebraic thinking among second-grade students at risk for mathematics difficulty. Intervention relied on a multitier support system (i.e., responsiveness to intervention, or RTI) in which at-risk students participate in general classroom…

  13. Word Problems and Make-Believe: Using Frame Analysis and Ethnomethodology to Explore Aspects of the Culture of Schooling

    ERIC Educational Resources Information Center

    Benincasa, Luciana

    2017-01-01

    The paper applies Goffman's frame analysis and ethnomethodology to student performance on mathematical word problems. In educational research, frame analysis has usually been limited to primary frames. Instead, in this paper I focus on the kind of secondary frame that Goffman calls 'utilitarian make-believe'. The data consist of a fragment of…

  14. Let's Talk Math: Encouraging Children To Explore Ideas.

    ERIC Educational Resources Information Center

    Lilburn, Pat; Rawson, Pam

    This book presents mathematics activities to help children talk and write mathematically. Children are encouraged to talk about and share their ideas, to use everyday language to describe mathematical situations, and to restate problems in their own words. There are two sections in this book. Part 1 discusses the following issues and implications…

  15. Building Conceptual Understanding in a Remedial College Mathematics Classroom: A Study of Effectiveness

    ERIC Educational Resources Information Center

    Bachman, Rachel Marie

    2013-01-01

    This study investigated the effectiveness of two remedial mathematics courses that aimed to (a) present topics conceptually, (b) construct adequate schemata, and (c) introduce students to the culture of mathematics. The topics covered during the two courses were word problems, equivalence, variables and expressions, equations and inequalities, and…

  16. Video-Based Intervention in Teaching Fraction Problem-Solving to Students with Autism Spectrum Disorder.

    PubMed

    Yakubova, Gulnoza; Hughes, Elizabeth M; Hornberger, Erin

    2015-09-01

    The purpose of this study was to determine the effectiveness of a point-of-view video modeling intervention to teach mathematics problem-solving when working on word problems involving subtracting mixed fractions with uncommon denominators. Using a multiple-probe across students design of single-case methodology, three high school students with ASD completed the study. All three students demonstrated greater accuracy in solving fraction word problems and maintained accuracy levels at a 1-week follow-up.

  17. Perceptual and academic patterns of learning-disabled/gifted students.

    PubMed

    Waldron, K A; Saphire, D G

    1992-04-01

    This research explored ways gifted children with learning disabilities perceive and recall auditory and visual input and apply this information to reading, mathematics, and spelling. 24 learning-disabled/gifted children and a matched control group of normally achieving gifted students were tested for oral reading, word recognition and analysis, listening comprehension, and spelling. In mathematics, they were tested for numeration, mental and written computation, word problems, and numerical reasoning. To explore perception and memory skills, students were administered formal tests of visual and auditory memory as well as auditory discrimination of sounds. Their responses to reading and to mathematical computations were further considered for evidence of problems in visual discrimination, visual sequencing, and visual spatial areas. Analyses indicated that these learning-disabled/gifted students were significantly weaker than controls in their decoding skills, in spelling, and in most areas of mathematics. They were also significantly weaker in auditory discrimination and memory, and in visual discrimination, sequencing, and spatial abilities. Conclusions are that these underlying perceptual and memory deficits may be related to students' academic problems.

  18. Microcomputers and Preschoolers.

    ERIC Educational Resources Information Center

    Evans, Dina

    Preschool children can benefit by working with microcomputers. Thinking skills are enhanced by software games that focus on logic, memory, problem solving, and pattern recognition. Counting, sequencing, and matching games develop mathematics skills, and word games focusing on basic letter symbol and word recognition develop language skills.…

  19. "I like It Instead of Maths": How Pupils with Moderate Learning Difficulties in Scottish Primary Special Schools Intuitively Solved Mathematical Word Problems

    ERIC Educational Resources Information Center

    Moscardini, Lio

    2010-01-01

    This study by Lio Moscardini of the University of Strathclyde shows how a group of 24 children in three Scottish primary schools for pupils with moderate learning difficulties responded to word problems following their teachers' introduction to the principles of Cognitively Guided Instruction (CGI). CGI is a professional development programme in…

  20. Achievement of First-, Second-, and Third-Grade Students on Multiplication and Division Word Problems in Two Different Solution Environments.

    ERIC Educational Resources Information Center

    O'Brien, Aileen; Cabral, Sheryl Ann

    This is a project in an emerging line of research investigating children's informed knowledge of mathematics questions. The purpose of this study was to analyze the ability of students who had not received multiplication or division instruction to solve multiplication and division word problems. The study consisted of videotaped interviews with 89…

  1. Problem-Solving Support for English Language Learners

    ERIC Educational Resources Information Center

    Wiest, Lynda R.

    2008-01-01

    Although word problems pose greater language demands, they also encourage more meaningful problem solving and mathematics understanding. With proper instructional support, a student-centered, investigative approach to contextualized problem solving benefits all students. This article presents a lesson built on an author-adapted version of the…

  2. Strategy Instruction in Mathematics.

    ERIC Educational Resources Information Center

    Goldman, Susan R.

    1989-01-01

    Experiments in strategy instruction for mathematics have been conducted using three models (direct instruction, self-instruction, and guided learning) applied to the tasks of computation and word problem solving. Results have implications for effective strategy instruction for learning disabled students. It is recommended that strategy instruction…

  3. Rethinking Mathematics Teaching in Liberia: Realistic Mathematics Education

    ERIC Educational Resources Information Center

    Stemn, Blidi S.

    2017-01-01

    In some African cultures, the concept of division does not necessarily mean sharing money or an item equally. How an item is shared might depend on the ages of the individuals involved. This article describes the use of the Realistic Mathematics Education (RME) approach to teach division word problems involving money in a 3rd-grade class in…

  4. Who's Wrong? Tasks Fostering Understanding of Mathematical Relationships in Word Problems in Elementary Students

    ERIC Educational Resources Information Center

    Savard, Annie; Polotskaia, Elena

    2017-01-01

    Mathematical relationships are crucial elements to consider for learning mathematics. However, too often students pay more attention to the calculations to be done rather than the reasons for doing them. Relying on the relational paradigm to support elementary school students, we proposed two specially designed tasks to help students recognize and…

  5. Preschool predictors of mathematics in first grade children with autism spectrum disorder.

    PubMed

    Titeca, Daisy; Roeyers, Herbert; Josephy, Haeike; Ceulemans, Annelies; Desoete, Annemie

    2014-11-01

    Up till now, research evidence on the mathematical abilities of children with autism spectrum disorder (ASD) has been scarce and provided mixed results. The current study examined the predictive value of five early numerical competencies for four domains of mathematics in first grade. Thirty-three high-functioning children with ASD were followed up from preschool to first grade and compared with 54 typically developing children, as well as with normed samples in first grade. Five early numerical competencies were tested in preschool (5-6 years): verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Four domains of mathematics were used as outcome variables in first grade (6-7 years): procedural calculation, number fact retrieval, word/language problems, and time-related competences. Children with ASD showed similar early numerical competencies at preschool age as typically developing children. Moreover, they scored average on number fact retrieval and time-related competences and higher on procedural calculation and word/language problems compared to the normed population in first grade. When predicting first grade mathematics performance in children with ASD, both verbal subitizing and counting seemed to be important to evaluate at preschool age. Verbal subitizing had a higher predictive value in children with ASD than in typically developing children. Whereas verbal subitizing was predictive for procedural calculation, number fact retrieval, and word/language problems, counting was predictive for procedural calculation and, to a lesser extent, number fact retrieval. Implications and directions for future research are discussed. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

  6. Effects of computer-based graphic organizers to solve one-step word problems for middle school students with mild intellectual disability: A preliminary study.

    PubMed

    Sheriff, Kelli A; Boon, Richard T

    2014-08-01

    The purpose of this study was to examine the effects of computer-based graphic organizers, using Kidspiration 3© software, to solve one-step word problems. Participants included three students with mild intellectual disability enrolled in a functional academic skills curriculum in a self-contained classroom. A multiple probe single-subject research design (Horner & Baer, 1978) was used to evaluate the effectiveness of computer-based graphic organizers to solving mathematical one-step word problems. During the baseline phase, the students completed a teacher-generated worksheet that consisted of nine functional word problems in a traditional format using a pencil, paper, and a calculator. In the intervention and maintenance phases, the students were instructed to complete the word problems using a computer-based graphic organizer. Results indicated that all three of the students improved in their ability to solve the one-step word problems using computer-based graphic organizers compared to traditional instructional practices. Limitations of the study and recommendations for future research directions are discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.

  7. Artifacts as Sources for Problem-Posing Activities

    ERIC Educational Resources Information Center

    Bonotto, Cinzia

    2013-01-01

    The problem-posing process represents one of the forms of authentic mathematical inquiry which, if suitably implemented in classroom activities, could move well beyond the limitations of word problems, at least as they are typically utilized. The two exploratory studies presented sought to investigate the impact of "problem-posing" activities when…

  8. The Interference of Stereotype Threat with Women's Generation of Mathematical Problem-Solving Strategies.

    ERIC Educational Resources Information Center

    Quinn, Diane M.; Spencer, Steven J.

    2001-01-01

    Investigated whether stereotype threat would depress college women's math performance. In one test, men outperformed women when solving word problems, though women performed equally when problems were converted into numerical equivalents. In another test, participants solved difficult problems in high or reduced stereotype threat conditions. Women…

  9. A Comparison of Two Mathematics Problem-Solving Strategies: Facilitate Algebra-Readiness

    ERIC Educational Resources Information Center

    Xin, Yan Ping; Zhang, Dake; Park, Joo Young; Tom, Kinsey; Whipple, Amanda; Si, Luo

    2011-01-01

    The authors compared a conceptual model-based problem-solving (COMPS) approach with a general heuristic instructional approach for teaching multiplication-division word-problem solving to elementary students with learning problems (LP). The results indicate that only the COMPS group significantly improved, from pretests to posttests, their…

  10. How the Relational Paradigm Can Transform the Teaching and Learning of Mathematics: Experiment in Quebec

    ERIC Educational Resources Information Center

    Polotskaia, Elena

    2017-01-01

    The main goal of this paper is to show how Vasily Davydov's powerful ideas about the nature of mathematical thinking and learning can transform the teaching and learning of additive word problem solving. The name Vasily Davydov is well known in the field of mathematics education in Russia. However, the transformative value of Davydov's theoretical…

  11. Pork Puzzlers.

    ERIC Educational Resources Information Center

    National Pork Producers Council, Des Moines, IA.

    Pork Puzzlers is a nutrition education activity booklet for elementary-level students. It includes word scrambles; quizzes with pictures that describe the Food Guide Pyramid; a nutrition word search; a mathematics problem that includes questions on pork; a maze that uses food clues; a letter decoding activity that focuses on a pork dinner; a meal…

  12. Don't Just Do the Math--Type It!

    ERIC Educational Resources Information Center

    Stephens, Greg

    2016-01-01

    Most word processors, including Google Docs™ and Microsoft® Word, include an equation editor. These are great tools for the occasional homework problem or project assignment. Getting the mathematics to display correctly means making decisions about exactly which elements of an expression go where. The feedback is immediate: Students can see…

  13. Reading Coaching for Math Word Problems

    ERIC Educational Resources Information Center

    Edwards, Sharon A.; Maloy, Robert W.; Anderson, Gordon

    2009-01-01

    "Math is language, too," Phyllis and David Whitin (2000) remind everyone in their informative book about reading and writing in the mathematics classroom. This means that students in elementary school math classes are learning two distinct, yet related languages--one of numbers, the other of words. These languages of numbers and words…

  14. The Effects of a Modified Learning Strategy on the Multiple Step Mathematical Word Problem Solving Ability of Middle School Students with High-Functioning Autism or Asperger's Syndrome

    ERIC Educational Resources Information Center

    Schaefer Whitby, Peggy J.

    2009-01-01

    Children with HFA/AS are outperformed by their neuro-typical peers on mathematical problem solving skills even though they have average-to-above-average intelligence (Dickerson Mayes & Calhoun, 2003b); have average-to-above-average computation skills (Chiang & Lin, 2007); and, are educated in the general education setting (Twenty Eighth…

  15. The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children.

    PubMed

    Träff, Ulf

    2013-10-01

    This study examined the relative contributions of general cognitive abilities and number abilities to word problem solving, calculation, and arithmetic fact retrieval in a sample of 134 children aged 10 to 13 years. The following tasks were administered: listening span, visual matrix span, verbal fluency, color naming, Raven's Progressive Matrices, enumeration, number line estimation, and digit comparison. Hierarchical multiple regressions demonstrated that number abilities provided an independent contribution to fact retrieval and word problem solving. General cognitive abilities contributed to problem solving and calculation. All three number tasks accounted for a similar amount of variance in fact retrieval, whereas only the number line estimation task contributed unique variance in word problem solving. Verbal fluency and Raven's matrices accounted for an equal amount of variance in problem solving and calculation. The current findings demonstrate, in accordance with Fuchs and colleagues' developmental model of mathematical learning (Developmental Psychology, 2010, Vol. 46, pp. 1731-1746), that both number abilities and general cognitive abilities underlie 10- to 13-year-olds' proficiency in problem solving, whereas only number abilities underlie arithmetic fact retrieval. Thus, the amount and type of cognitive contribution to arithmetic proficiency varies between the different aspects of arithmetic. Furthermore, how closely linked a specific aspect of arithmetic is to the whole number representation systems is not the only factor determining the amount and type of cognitive contribution in 10- to 13-year-olds. In addition, the mathematical complexity of the task appears to influence the amount and type of cognitive support. Copyright © 2013 Elsevier Inc. All rights reserved.

  16. Matematica 1. Livro do Aluno (Mathematics 1. Student Workbook).

    ERIC Educational Resources Information Center

    D'Alu, Maria Jose

    Matematica 1 is the first book of a mathematics program in Portuguese "designed for first graders." The book contains 15 chapters dealing with: sets, numeration, place value, numbers from 0 through 99, addition and subtraction, geometric shapes, measurements (money, time, length), fractions, word problems, and commutative and associative…

  17. The Contribution of Domain-Specific Knowledge in Predicting Students' Proportional Word Problem Solving Performance

    ERIC Educational Resources Information Center

    Jitendra, Asha K.; Lein, Amy E.; Star, Jon R.; Dupuis, Danielle N.

    2013-01-01

    Proportional thinking, which requires understanding fractions, ratios, and proportions, is an area of mathematics that is cognitively challenging for many children and adolescents (Fujimura, 2001; Lamon, 2007; Lobato, Ellis, Charles, & Zbiek, 2010; National Mathematics Advisory Panel [NMAP], 2008) and "transcends topical barriers in adult…

  18. Mathematics Interventions for Students with High Functioning Autism/Asperger's Syndrome

    ERIC Educational Resources Information Center

    Donaldson, Jeffrey B.; Zager, Dianne

    2010-01-01

    Teachers are often at a loss when considering how to address mathematics difficulties for students with high functioning autism/Asperger's syndrome (HFA/AS). Students may show difficulty remembering operations throughout an equation, organizing information on the page, and comprehending the language in instructions of word problems. These…

  19. Intellectual Abilities That Discriminate Good and Poor Problem Solvers.

    ERIC Educational Resources Information Center

    Meyer, Ruth Ann

    1981-01-01

    This study compared good and poor fourth-grade problem solvers on a battery of 19 "reference" tests for verbal, induction, numerical, word fluency, memory, perceptual speed, and simple visualization abilities. Results suggest verbal, numerical, and especially induction abilities are important to successful mathematical problem solving.…

  20. Hating School, Loving Mathematics: On the Ideological Function of Critique and Reform in Mathematics Education

    ERIC Educational Resources Information Center

    Lundin, Sverker

    2012-01-01

    Students' engagement with fictions in the form of "word problems" plays an important role in classroom practice as well as in theories of mathematical learning. Drawing on the Dutch historian Johan Huizinga and the Austrian philosopher Robert Pfaller, I show that this activity can be seen as a form of "play" or "game," where it is pretended that…

  1. Problem-Solving: Scaling the "Brick Wall"

    ERIC Educational Resources Information Center

    Benson, Dave

    2011-01-01

    Across the primary and secondary phases, pupils are encouraged to use and apply their knowledge, skills, and understanding of mathematics to solve problems in a variety of forms, ranging from single-stage word problems to the challenge of extended rich tasks. Amongst many others, Cockcroft (1982) emphasised the importance and relevance of…

  2. Working Memory Components and Problem-Solving Accuracy: Are There Multiple Pathways?

    ERIC Educational Resources Information Center

    Swanson, H. Lee; Fung, Wenson

    2016-01-01

    This study determined the working memory (WM) components (executive, phonological short-term memory [STM], and visual-spatial sketchpad) that best predicted mathematical word problem-solving accuracy in elementary schoolchildren (N = 392). The battery of tests administered to assess mediators between WM and problem-solving included measures of…

  3. Predicting First Graders' Development of Calculation versus Word-Problem Performance: The Role of Dynamic Assessment.

    PubMed

    Seethaler, Pamela M; Fuchs, Lynn S; Fuchs, Douglas; Compton, Donald L

    2012-02-01

    The purpose of this study was to assess the value of dynamic assessment (DA; degree of scaffolding required to learn unfamiliar mathematics content) for predicting 1(st)-grade calculations (CA) and word problems (WP) development, while controlling for the role of traditional assessments. Among 184 1(st) graders, predictors (DA, Quantity Discrimination, Test of Mathematics Ability, language, and reasoning) were assessed near the start of 1(st) grade. CA and WP were assessed near the end of 1(st) grade. Planned regression and commonality analyses indicated that for forecasting CA development, Quantity Discrimination, which accounted for 8.84% of explained variance, was the single most powerful predictor, followed by Test of Mathematics Ability and DA; language and reasoning were not uniquely predictive. By contrast, for predicting WP development, DA was the single most powerful predictor, which accounted for 12.01% of explained variance, with Test of Mathematics Ability, Quantity Discrimination, and language also uniquely predictive. Results suggest that different constellations of cognitive resources are required for CA versus WP development and that DA may be useful in predicting 1(st)-grade mathematics development, especially WP.

  4. Predicting First Graders’ Development of Calculation versus Word-Problem Performance: The Role of Dynamic Assessment

    PubMed Central

    Seethaler, Pamela M.; Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.

    2012-01-01

    The purpose of this study was to assess the value of dynamic assessment (DA; degree of scaffolding required to learn unfamiliar mathematics content) for predicting 1st-grade calculations (CA) and word problems (WP) development, while controlling for the role of traditional assessments. Among 184 1st graders, predictors (DA, Quantity Discrimination, Test of Mathematics Ability, language, and reasoning) were assessed near the start of 1st grade. CA and WP were assessed near the end of 1st grade. Planned regression and commonality analyses indicated that for forecasting CA development, Quantity Discrimination, which accounted for 8.84% of explained variance, was the single most powerful predictor, followed by Test of Mathematics Ability and DA; language and reasoning were not uniquely predictive. By contrast, for predicting WP development, DA was the single most powerful predictor, which accounted for 12.01% of explained variance, with Test of Mathematics Ability, Quantity Discrimination, and language also uniquely predictive. Results suggest that different constellations of cognitive resources are required for CA versus WP development and that DA may be useful in predicting 1st-grade mathematics development, especially WP. PMID:22347725

  5. Mathematical Modeling with MyMaps and Spreadsheets

    ERIC Educational Resources Information Center

    Weber, Victoria; Fortune, Nicholas; Williams, Derek; Whitehead, Ashley

    2016-01-01

    Software programs such as Tinkerplots ® or Geometer's Sketchpad ® can help students solve problems in mathematics classes, but may not be available to them after high school. In contrast, many students who become familiar with Internet tools and programs in office packages (word processing, spreadsheets, etc.) may use them daily to enhance their…

  6. Teaching between Desks

    ERIC Educational Resources Information Center

    Ermeling, Bradley A.; Graff-Ermeling, Genevieve

    2014-01-01

    Watch one of the Japan videos from the Trends in International Mathematics and Science Study (TIMSS)--more specifically, mathematics video 3 on solving inequalities1--and you'll see that after giving his students a word problem to solve, the 8th grade math teacher strolls among the students' desks for almost 15 minutes, leaning over to see what…

  7. Improving the Fraction Word Problem Solving of Students with Mathematics Learning Disabilities: Interactive Computer Application

    ERIC Educational Resources Information Center

    Shin, Mikyung; Bryant, Diane P.

    2017-01-01

    Students with mathematics learning disabilities (MLD) have a weak understanding of fraction concepts and skills, which are foundations of algebra. Such students might benefit from computer-assisted instruction that utilizes evidence-based instructional components (cognitive strategies, feedback, virtual manipulatives). As a pilot study using a…

  8. Types of Mathematics-Language Reading Interactions that Unnecessarily Hinder Algebra Learning and Assessment

    ERIC Educational Resources Information Center

    Lager, Carl A.

    2006-01-01

    English language learners (ELLs)--one of the lowest-achieving and fastest growing middle-school subpopulations--are challenged in the classroom by language components which could potentially jumpstart real mathematical growth for these and, eventually, all other students as well. Going beyond traditional word problems, this study documented and…

  9. Not All Created Equally: Exploring Calculator Use by Students with Mild Intellectual Disability

    ERIC Educational Resources Information Center

    Yakubova, Gulnoza; Bouck, Emily C.

    2014-01-01

    Calculators are widely used in mathematics education, yet limited research examines the effects of calculators for students with mild intellectual disability. An alternating treatments design was used to study the effects of calculator types (i.e., scientific and graphing) on the mathematical performance (i.e., computation and word problems) of…

  10. Multimedia Cai Program for Students with Mathematics Difficulties

    ERIC Educational Resources Information Center

    Seo, You-Jin; Bryant, Diane

    2012-01-01

    This study investigated the effectiveness of "Math Explorer" at enhancing the word problem-solving skills of students with mathematics difficulties (MD). The study, which had a multiple-probe-across-subjects design, was conducted over 18 weeks. Four students with MD in Grades 2 and 3 participated. All students were able to use the four-step…

  11. Mathematics Education for Hispanic Students in the Border College Consortium.

    ERIC Educational Resources Information Center

    Rendon, Laura I.

    The Border College Consortium (BCC), formed by six Texas, California, and Arizona community colleges along the United States and Mexico border, used a survey to derive a profile of its mathematics and science students. The profile revealed that both Hispanic and White students had difficulties with word problems and study habits, wanted…

  12. Words to Argue By

    ERIC Educational Resources Information Center

    Pourciau, Bruce

    2018-01-01

    In a first proof-oriented mathematics course, students will often ask questions--for example, "What is this problem asking me to do?" or "What would a proof of this even look like"--that have more to do with logic than mathematics. The logical structure of a proof is a dance involving those basic logical forms--such as "p…

  13. Are Middle School Mathematics Teachers Able to Solve Word Problems without Using Variable?

    ERIC Educational Resources Information Center

    Gökkurt Özdemir, Burçin; Erdem, Emrullah; Örnek, Tugba; Soylu, Yasin

    2018-01-01

    Many people consider problem solving as a complex process in which variables such as "x," "y" are used. Problems may not be solved by only using "variable." Problem solving can be rationalized and made easier using practical strategies. When especially the development of children at younger ages is considered, it is…

  14. Longitudinal Mediators of Achievement in Mathematics and Reading in Typical and Atypical Development

    PubMed Central

    Barnes, Marcia A.; Raghubar, Kimberly P.; English, Lianne; Williams, Jeffrey M.; Taylor, Heather; Landry, Susan

    2014-01-01

    Longitudinal studies of neurodevelopmental disorders that are diagnosed at or before birth and which are associated with specific learning difficulties at school-age provide one method for investigating developmental precursors of later-emerging academic disabilities. Spina bifida myelomeningocele (SBM) is a neurodevelopmental disorder associated with particular problems in mathematics, in contrast to well-developed word reading. Children with SBM (n = 30) and typically developing children (n = 35) were used to determine whether cognitive abilities measured at 36 and 60 months of age mediated the effect of group on mathematical and reading achievement outcomes at 8.5 and 9.5 years of age. A series of multiple mediator models showed that: visual-spatial working memory at 36 months and phonological awareness at 60 months partially mediated the effect of group on math calculations; phonological awareness partially mediated the effect of group on small addition and subtraction problems on a test of math fluency; and visual-spatial working memory mediated the effect of group on a test of math problem solving. Groups did not differ on word reading, and phonological awareness was the only mediator for reading fluency and reading comprehension. The findings are discussed with reference to theories of mathematical development and disability and with respect to both common and differing cognitive correlates of math and reading. PMID:24269579

  15. Teaching mathematical word problem solving: the quality of evidence for strategy instruction priming the problem structure.

    PubMed

    Jitendra, Asha K; Petersen-Brown, Shawna; Lein, Amy E; Zaslofsky, Anne F; Kunkel, Amy K; Jung, Pyung-Gang; Egan, Andrea M

    2015-01-01

    This study examined the quality of the research base related to strategy instruction priming the underlying mathematical problem structure for students with learning disabilities and those at risk for mathematics difficulties. We evaluated the quality of methodological rigor of 18 group research studies using the criteria proposed by Gersten et al. and 10 single case design (SCD) research studies using criteria suggested by Horner et al. and the What Works Clearinghouse. Results indicated that 14 group design studies met the criteria for high-quality or acceptable research, whereas SCD studies did not meet the standards for an evidence-based practice. Based on these findings, strategy instruction priming the mathematics problem structure is considered an evidence-based practice using only group design methodological criteria. Implications for future research and for practice are discussed. © Hammill Institute on Disabilities 2013.

  16. Investigation of learning environment for arithmetic word problems by problem posing as sentence integration in Indonesian language

    NASA Astrophysics Data System (ADS)

    Hasanah, N.; Hayashi, Y.; Hirashima, T.

    2017-02-01

    Arithmetic word problems remain one of the most difficult area of teaching mathematics. Learning by problem posing has been suggested as an effective way to improve students’ understanding. However, the practice in usual classroom is difficult due to extra time needed for assessment and giving feedback to students’ posed problems. To address this issue, we have developed a tablet PC software named Monsakun for learning by posing arithmetic word problems based on Triplet Structure Model. It uses the mechanism of sentence-integration, an efficient implementation of problem-posing that enables agent-assessment of posed problems. The learning environment has been used in actual Japanese elementary school classrooms and the effectiveness has been confirmed in previous researches. In this study, ten Indonesian elementary school students living in Japan participated in a learning session of problem posing using Monsakun in Indonesian language. We analyzed their learning activities and show that students were able to interact with the structure of simple word problem using this learning environment. The results of data analysis and questionnaire suggested that the use of Monsakun provides a way of creating an interactive and fun environment for learning by problem posing for Indonesian elementary school students.

  17. Learning Results from the Viewpoint of Equity: Boys, Girls and Mathematics.

    ERIC Educational Resources Information Center

    Pehkonen, Erkki

    1997-01-01

    Explores why girls successful in mathematics choose advanced courses in upper secondary school less than did boys. Analyzes the results of tests and a student questionnaire (N=739) in Finland. Findings indicate that in the case of word problems and calculation without calculators, boys are significantly better than girls. Reports that the boys…

  18. Assessing Translation Misconceptions inside the Classroom: A Presentation of an Instrument and Its Results

    ERIC Educational Resources Information Center

    Mangulabnan, Pauline Anne Therese M.

    2013-01-01

    This is a descriptive research on the difficulties of Filipino high school students in translating algebraic word problems into mathematical equations. This research is composed of three parts: (1) development of an 11-page "Filipinized" questionnaire; (2) analysis of the mathematical thinking processes of the respondents based on the answers to…

  19. Comparison of the Effects of Computer-Based Practice and Conceptual Understanding Interventions on Mathematics Fact Retention and Generalization

    ERIC Educational Resources Information Center

    Kanive, Rebecca; Nelson, Peter M.; Burns, Matthew K.; Ysseldyke, James

    2014-01-01

    The authors' purpose was to determine the effects of computer-based practice and conceptual interventions on computational fluency and word-problem solving of fourth- and fifth-grade students with mathematics difficulties. A randomized pretest-posttest control group design found that students assigned to the computer-based practice intervention…

  20. Investigating a Link between Pre-Calculus Students' Uses of Graphing Calculators and Their Understanding of Mathematical Symbols

    ERIC Educational Resources Information Center

    Kenney, Rachael H.

    2014-01-01

    This study examined ways in which students make use of a graphing calculator and how use relates to comfort and understanding with mathematical symbols. Analysis involved examining students' words and actions in problem solving to identify evidence of algebraic insight. Findings suggest that some symbols and symbolic structures had strong…

  1. Relationship between the Learning Hierarchy and Academic Achievement on Strategies Used by Third-Grade Students When Solving Multiplication Word Problems

    ERIC Educational Resources Information Center

    Kanive, Rebecca A.

    2016-01-01

    Distinguishing between sources of variability in mathematics performance may contribute to a more comprehensive theory of mathematics skills. Research has examined student differences based upon scores on achievement tests, which provide overall proficiency, but may not provide the detailed information for identifying and remediating difficulties.…

  2. Performance in Mathematical Problem Solving as a Function of Comprehension and Arithmetic Skills

    ERIC Educational Resources Information Center

    Voyer, Dominic

    2011-01-01

    Many factors influence a student's performance in word (or textbook) problem solving in class. Among them is the comprehension process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal representations, based on pupils' real-world knowledge, which support the construction of a…

  3. Schema-Based Instruction with Concrete and Virtual Manipulatives to Teach Problem Solving to Students with Autism

    ERIC Educational Resources Information Center

    Root, Jenny R.; Browder, Diane M.; Saunders, Alicia F.; Lo, Ya-yu

    2017-01-01

    The current study evaluated the effects of modified schema-based instruction on the mathematical word problem solving skills of three elementary students with autism spectrum disorders and moderate intellectual disability. Participants learned to solve compare problem type with themes that related to their interests and daily experiences. In…

  4. Video-Based Intervention in Teaching Fraction Problem-Solving to Students with Autism Spectrum Disorder

    ERIC Educational Resources Information Center

    Yakubova, Gulnoza; Hughes, Elizabeth M.; Hornberger, Erin

    2015-01-01

    The purpose of this study was to determine the effectiveness of a point-of-view video modeling intervention to teach mathematics problem-solving when working on word problems involving subtracting mixed fractions with uncommon denominators. Using a multiple-probe across students design of single-case methodology, three high school students with…

  5. Percentage Problems in Bridging Courses

    ERIC Educational Resources Information Center

    Kachapova, Farida; Kachapov, Ilias

    2012-01-01

    Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives…

  6. Iranian bilingual students reported use of language switching when doing mathematics

    NASA Astrophysics Data System (ADS)

    Parvanehnezhad, Zahra; Clarkson, Philip

    2008-04-01

    Teachers are often unaware that bilingual students often switch between their languages when doing mathematics. Little research has been undertaken into this phenomenon. Results are reported here from a study of language switching by sixteen Year 4/5 Iranian bilingual students as they solved mathematical problems in an interview situation. Reasons given for switching between English and their L1 language (Persian or Farsi) were the difficulty of the problem, familiarity with particular numbers or words they used habitually in Persian, and being in the Persian school or interview environment. It seems likely that these Iranian bilingual students will continue to use some form of language switching to help them understand and complete mathematical tasks in mainstream classrooms.

  7. The Relationship between Performance on Mathematical Word Problems and Language Proficiency for Students Learning through the Medium of Irish

    ERIC Educational Resources Information Center

    Riordain, Maire Ni; O'Donoghue, John

    2009-01-01

    Ireland has two official languages--Gaeilge (Irish) and English. Similarly, primary- and second-level education can be mediated through the medium of Gaeilge or through the medium of English. This research is primarily focused on students (Gaeilgeoiri) in the transition from Gaeilge-medium mathematics education to English-medium mathematics…

  8. Are Patterns Important? An Investigation of the Relationships between Proficiencies in Patterns, Computation, Executive Functioning, and Algebraic Word Problems

    ERIC Educational Resources Information Center

    Lee, Kerry; Ng, Swee Fong; Bull, Rebecca; Pe, Madeline Lee; Ho, Ringo Ho Moon

    2011-01-01

    Although mathematical pattern tasks are often found in elementary school curricula and are deemed a building block for algebra, a recent report (National Mathematics Advisory Panel, 2008) suggests the resources devoted to its teaching and assessment need to be rebalanced. We examined whether children's developing proficiency in solving algebraic…

  9. DOE Fundamentals Handbook: Mathematics, Volume 1

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Not Available

    1992-06-01

    The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclearmore » facility operations.« less

  10. DOE Fundamentals Handbook: Mathematics, Volume 2

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Not Available

    1992-06-01

    The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclearmore » facility operations.« less

  11. Longitudinal mediators of achievement in mathematics and reading in typical and atypical development.

    PubMed

    Barnes, Marcia A; Raghubar, Kimberly P; English, Lianne; Williams, Jeffrey M; Taylor, Heather; Landry, Susan

    2014-03-01

    Longitudinal studies of neurodevelopmental disorders that are diagnosed at or before birth and are associated with specific learning difficulties at school-age provide one method for investigating developmental precursors of later-emerging academic disabilities. Spina bifida myelomeningocele (SBM) is a neurodevelopmental disorder associated with particular problems in mathematics, in contrast to well-developed word reading. Children with SBM (n=30) and typically developing children (n=35) were used to determine whether cognitive abilities measured at 36 and 60 months of age mediated the effect of group on mathematical and reading achievement outcomes at 8.5 and 9.5 years of age. A series of multiple mediator models showed that: visual-spatial working memory at 36 months and phonological awareness at 60 months partially mediated the effect of group on math calculations, phonological awareness partially mediated the effect of group on small addition and subtraction problems on a test of math fluency, and visual-spatial working memory mediated the effect of group on a test of math problem solving. Groups did not differ on word reading, and phonological awareness was the only mediator for reading fluency and reading comprehension. The findings are discussed with reference to theories of mathematical development and disability and with respect to both common and differing cognitive correlates of math and reading. Copyright © 2013 Elsevier Inc. All rights reserved.

  12. Fraction Multiplication and Division Word Problems Posed by Different Years of Pre-Service Elementary Mathematics Teachers

    ERIC Educational Resources Information Center

    Aydogdu Iskenderoglu, Tuba

    2018-01-01

    It is important for pre-service teachers to know the conceptual difficulties they have experienced regarding the concepts of multiplication and division in fractions and problem posing is a way to learn these conceptual difficulties. Problem posing is a synthetic activity that fundamentally has multiple answers. The purpose of this study is to…

  13. Quantitative Literacy across the Curriculum: Integrating Skills from English Composition, Mathematics, and the Substantive Disciplines

    ERIC Educational Resources Information Center

    Miller, Jane E.

    2010-01-01

    Quantitative literacy is an important proficiency that pertains to "word problems" from science, history, and other fields. Unfortunately, teaching how to solve such problems often is relegated to math courses alone. This article examines how quantitative literacy also involves concepts and skills from English composition and the substantive…

  14. Predicting Development of Mathematical Word Problem Solving Across the Intermediate Grades

    PubMed Central

    Tolar, Tammy D.; Fuchs, Lynn; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Fletcher, Jack M.

    2012-01-01

    This study addressed predictors of the development of word problem solving (WPS) across the intermediate grades. At beginning of 3rd grade, 4 cohorts of students (N = 261) were measured on computation, language, nonverbal reasoning skills, and attentive behavior and were assessed 4 times from beginning of 3rd through end of 5th grade on 2 measures of WPS at low and high levels of complexity. Language skills were related to initial performance at both levels of complexity and did not predict growth at either level. Computational skills had an effect on initial performance in low- but not high-complexity problems and did not predict growth at either level of complexity. Attentive behavior did not predict initial performance but did predict growth in low-complexity, whereas it predicted initial performance but not growth for high-complexity problems. Nonverbal reasoning predicted initial performance and growth for low-complexity WPS, but only growth for high-complexity WPS. This evidence suggests that although mathematical structure is fixed, different cognitive resources may act as limiting factors in WPS development when the WPS context is varied. PMID:23325985

  15. Mathematics is differentially related to reading comprehension and word decoding: Evidence from a genetically-sensitive design

    PubMed Central

    Harlaar, Nicole; Kovas, Yulia; Dale, Philip S.; Petrill, Stephen A.; Plomin, Robert

    2013-01-01

    Although evidence suggests that individual differences in reading and mathematics skills are correlated, this relationship has typically only been studied in relation to word decoding or global measures of reading. It is unclear whether mathematics is differentially related to word decoding and reading comprehension. The current study examined these relationships at both a phenotypic and etiological level in a population-based cohort of 5162 twin pairs at age 12. Multivariate genetic analyses of latent phenotypic factors of mathematics, word decoding and reading comprehension revealed substantial genetic and shared environmental correlations among all three domains. However, the phenotypic and genetic correlations between mathematics and reading comprehension were significantly greater than between mathematics and word decoding. Independent of mathematics, there was also evidence for genetic and nonshared environmental links between word decoding and reading comprehension. These findings indicate that word decoding and reading comprehension have partly distinct relationships with mathematics in the middle school years. PMID:24319294

  16. Mathematics is differentially related to reading comprehension and word decoding: Evidence from a genetically-sensitive design.

    PubMed

    Harlaar, Nicole; Kovas, Yulia; Dale, Philip S; Petrill, Stephen A; Plomin, Robert

    2012-08-01

    Although evidence suggests that individual differences in reading and mathematics skills are correlated, this relationship has typically only been studied in relation to word decoding or global measures of reading. It is unclear whether mathematics is differentially related to word decoding and reading comprehension. The current study examined these relationships at both a phenotypic and etiological level in a population-based cohort of 5162 twin pairs at age 12. Multivariate genetic analyses of latent phenotypic factors of mathematics, word decoding and reading comprehension revealed substantial genetic and shared environmental correlations among all three domains. However, the phenotypic and genetic correlations between mathematics and reading comprehension were significantly greater than between mathematics and word decoding. Independent of mathematics, there was also evidence for genetic and nonshared environmental links between word decoding and reading comprehension. These findings indicate that word decoding and reading comprehension have partly distinct relationships with mathematics in the middle school years.

  17. Bilingual Test as a Test Accommodation to Determine the Mathematics Achievement of Mainstream Students with Limited English Proficiency

    ERIC Educational Resources Information Center

    Shanmugam, S. Kanageswari Suppiah; Lan, Ong Saw

    2013-01-01

    Purpose: This study aims to investigate the validity of using bilingual test to measure the mathematics achievement of students who have limited English proficiency (LEP). The bilingual test and the English-only test consist of 20 computation and 20 word problem multiple-choice questions (from TIMSS 2003 and 2007 released items. The bilingual test…

  18. Do Authors of Online Electronic Materials for Teaching Mathematics Use Their Potential to Use Non-Stereotypical Cultural Settings?

    ERIC Educational Resources Information Center

    Moraová, Hana

    2017-01-01

    The paper focuses on the cultural content of online electronic materials developed primarily by Czech in-service teachers of mathematics for smartboards. The author presents an analysis of these materials with a focus on the cultural settings of word problems they contain. The paper builds on a poster presented on ECEL 2015 conference and a paper…

  19. Cognitive mechanisms underlying third graders' arithmetic skills: Expanding the pathways to mathematics model.

    PubMed

    Träff, Ulf; Olsson, Linda; Skagerlund, Kenny; Östergren, Rickard

    2018-03-01

    A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills. Copyright © 2017 Elsevier Inc. All rights reserved.

  20. Mathematical intelligence developed in math learning with classical backsound music of the classical era

    NASA Astrophysics Data System (ADS)

    Karlimah

    2018-05-01

    This study examines the application of classical music backsound in mathematics learning. The method used is quasi experimental design nonequivalent pretest-posttest control group in elementary school students in Tasikmalaya city, Indonesia. The results showed that classical music contributed significantly to the mathematical intelligence of elementary school students. The mathematical intelligence shown is in the cognitive ability ranging from the level of knowledge to evaluation. High level mathematical intelligence is shown by students in reading and writing integers with words and numbers. The low level of mathematical intelligence exists in projecting the story into a mathematical problem. The implication of this research is the use of classical music backsound on learning mathematics should pay attention to the level of difficulty of mathematics material being studied.

  1. Reflections on Language and Mathematics Problem Solving: A Case Study of a Bilingual First-Grade Teacher

    ERIC Educational Resources Information Center

    Musanti, Sandra I.; Celedon-Pattichis, Sylvia; Marshall, Mary E.

    2009-01-01

    This case study investigates a professional development initiative in which a first-grade bilingual teacher engages in learning and teaching Cognitively Guided Instruction, a framework for understanding student thinking through context-rich word-problem lessons. The study explores (a) the impact of classroom-based professional development on a…

  2. Middle School Deaf Students' Problem-Solving Behaviors and Strategy Use

    ERIC Educational Resources Information Center

    Lee, ChongMin

    2010-01-01

    The purpose of this research is to describe and understand the ways in which deaf middle school students understood and solved compare word problems, and to examine their overall strategy use in learning mathematics. The participants in the study were deaf middle school students, attending a residential state school for the deaf. Most of them used…

  3. Word problems: a review of linguistic and numerical factors contributing to their difficulty

    PubMed Central

    Daroczy, Gabriella; Wolska, Magdalena; Meurers, Walt Detmar; Nuerk, Hans-Christoph

    2015-01-01

    Word problems (WPs) belong to the most difficult and complex problem types that pupils encounter during their elementary-level mathematical development. In the classroom setting, they are often viewed as merely arithmetic tasks; however, recent research shows that a number of linguistic verbal components not directly related to arithmetic contribute greatly to their difficulty. In this review, we will distinguish three components of WP difficulty: (i) the linguistic complexity of the problem text itself, (ii) the numerical complexity of the arithmetic problem, and (iii) the relation between the linguistic and numerical complexity of a problem. We will discuss the impact of each of these factors on WP difficulty and motivate the need for a high degree of control in stimuli design for experiments that manipulate WP difficulty for a given age group. PMID:25883575

  4. A synthesis of mathematical and cognitive performances of students with mathematics learning disabilities.

    PubMed

    Shin, Mikyung; Bryant, Diane Pedrotty

    2015-01-01

    The purpose of this study was to synthesize the findings from 23 articles that compared the mathematical and cognitive performances of students with mathematics learning disabilities (LD) to (a) students with LD in mathematics and reading, (b) age- or grade-matched students with no LD, and (c) mathematical-ability-matched younger students with no LD. Overall results revealed that students with mathematics LD exhibited higher word problem-solving abilities and no significant group differences on working memory, long-term memory, and metacognition measures compared to students with LD in mathematics and reading. Findings also revealed students with mathematics LD demonstrated significantly lower performance compared to age- or grade-matched students with no LD on both mathematical and cognitive measures. Comparison between students with mathematics LD and younger students with no LD revealed mixed outcomes on mathematical measures and generally no significant group differences on cognitive measures. © Hammill Institute on Disabilities 2013.

  5. Arithmetic learning with the use of graphic organiser

    NASA Astrophysics Data System (ADS)

    Sai, F. L.; Shahrill, M.; Tan, A.; Han, S. H.

    2018-01-01

    For this study, Zollman’s four corners-and-a-diamond mathematics graphic organiser embedded with Polya’s Problem Solving Model was used to investigate secondary school students’ performance in arithmetic word problems. This instructional learning tool was used to help students break down the given information into smaller units for better strategic planning. The participants were Year 7 students, comprised of 21 male and 20 female students, aged between 11-13 years old, from a co-ed secondary school in Brunei Darussalam. This study mainly adopted a quantitative approach to investigate the types of differences found in the arithmetic word problem pre- and post-tests results from the use of the learning tool. Although the findings revealed slight improvements in the overall comparisons of the students’ test results, the in-depth analysis of the students’ responses in their activity worksheets shows a different outcome. Some students were able to make good attempts in breaking down the key points into smaller information in order to solve the word problems.

  6. Numeracy, Literacy and Newman's Error Analysis

    ERIC Educational Resources Information Center

    White, Allan Leslie

    2010-01-01

    Newman (1977, 1983) defined five specific literacy and numeracy skills as crucial to performance on mathematical word problems: reading, comprehension, transformation, process skills, and encoding. Newman's Error Analysis (NEA) provided a framework for considering the reasons that underlay the difficulties students experienced with mathematical…

  7. Mathematics Education and the Objectivist Programme in HPS

    NASA Astrophysics Data System (ADS)

    Glas, Eduard

    2013-06-01

    Using history of mathematics for studying concepts, methods, problems and other internal features of the discipline may give rise to a certain tension between descriptive adequacy and educational demands. Other than historians, educators are concerned with mathematics as a normatively defined discipline. Teaching cannot but be based on a pre-understanding of what mathematics `is' or, in other words, on a normative (methodological, philosophical) view of the identity or nature of the discipline. Educators are primarily concerned with developments at the level of objective mathematical knowledge, that is: with the relations between successive theories, problems and proposed solutions—relations which are independent of whatever has been the role of personal or collective beliefs, convictions, traditions and other historical circumstances. Though not exactly `historical' in the usual sense, I contend that this `objectivist' approach does represent one among other entirely legitimate and valuable approaches to the historical development of mathematics. Its retrospective importance to current practitioners and students is illustrated by a reconstruction of the development of Eudoxus's theory of proportionality in response to the problem of irrationality, and the way in which Dedekind some two millennia later almost literally used this ancient theory for the rigorous introduction of irrational numbers and hence of the real number continuum.

  8. Long-Range Memory in Literary Texts: On the Universal Clustering of the Rare Words.

    PubMed

    Tanaka-Ishii, Kumiko; Bunde, Armin

    2016-01-01

    A fundamental problem in linguistics is how literary texts can be quantified mathematically. It is well known that the frequency of a (rare) word in a text is roughly inverse proportional to its rank (Zipf's law). Here we address the complementary question, if also the rhythm of the text, characterized by the arrangement of the rare words in the text, can be quantified mathematically in a similar basic way. To this end, we consider representative classic single-authored texts from England/Ireland, France, Germany, China, and Japan. In each text, we classify each word by its rank. We focus on the rare words with ranks above some threshold Q and study the lengths of the (return) intervals between them. We find that for all texts considered, the probability SQ(r) that the length of an interval exceeds r, follows a perfect Weibull-function, SQ(r) = exp(-b(β)rβ), with β around 0.7. The return intervals themselves are arranged in a long-range correlated self-similar fashion, where the autocorrelation function CQ(s) of the intervals follows a power law, CQ(s) ∼ s-γ, with an exponent γ between 0.14 and 0.48. We show that these features lead to a pronounced clustering of the rare words in the text.

  9. Brain Stretchers Book 4--Advanced.

    ERIC Educational Resources Information Center

    Anderson, Carolyn

    This book provides puzzles, games, and mathematical activities for students in elementary grades. Number concepts and arithmetic are common topics. These classic math, logic, and word-problem activities encourage students to become flexible, creative thinkers while teaching them to draw valid conclusions based on logic and evidence. Each activity…

  10. Computer-Based Instruction Research: Implications for Design.

    ERIC Educational Resources Information Center

    Ross, Steven M.; And Others

    The development and evaluation of several microcomputer-based strategies designed to facilitate learning how to solve mathematics word problems by personalizing examples in accord with individuals' background and interests are described in this paper. The first of two studies conducted with fifth and sixth grade students to evaluate these…

  11. One-Step "Change" and "Compare" Word Problems: Focusing on Eye-Movements

    ERIC Educational Resources Information Center

    Moutsios-Rentzos, Andreas; Stamatis, Panagiotis J.

    2015-01-01

    Introduction. In this study, we focus on the relationship between the students' mathematical thinking and their non-mechanically identified eye-movements with the purpose to gain deeper understanding about the students' reasoning processes and to investigate the feasibility of incorporating eye-movement information in everyday pedagogy. Method.…

  12. The Great Debate in Reading Instruction

    ERIC Educational Resources Information Center

    Ediger, Marlow

    2012-01-01

    The reading curriculum receives more attention than any other academic discipline. It is true that individuals engage in much reading in school subjects such as word problems in mathematics as well as reading numerals and symbols, science content in doing experiments and demonstrations, social studies with its emphasis upon diverse social science…

  13. The solution of the sixth Hilbert problem: the ultimate Galilean revolution

    NASA Astrophysics Data System (ADS)

    D'Ariano, Giacomo Mauro

    2018-04-01

    I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: `physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as `clock', `rigid rod', `force', `inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory. This article is part of the theme issue `Hilbert's sixth problem'.

  14. The solution of the sixth Hilbert problem: the ultimate Galilean revolution.

    PubMed

    D'Ariano, Giacomo Mauro

    2018-04-28

    I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: 'physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as 'clock', 'rigid rod', 'force', 'inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

  15. Long-Range Memory in Literary Texts: On the Universal Clustering of the Rare Words

    PubMed Central

    2016-01-01

    A fundamental problem in linguistics is how literary texts can be quantified mathematically. It is well known that the frequency of a (rare) word in a text is roughly inverse proportional to its rank (Zipf’s law). Here we address the complementary question, if also the rhythm of the text, characterized by the arrangement of the rare words in the text, can be quantified mathematically in a similar basic way. To this end, we consider representative classic single-authored texts from England/Ireland, France, Germany, China, and Japan. In each text, we classify each word by its rank. We focus on the rare words with ranks above some threshold Q and study the lengths of the (return) intervals between them. We find that for all texts considered, the probability SQ(r) that the length of an interval exceeds r, follows a perfect Weibull-function, SQ(r) = exp(−b(β)rβ), with β around 0.7. The return intervals themselves are arranged in a long-range correlated self-similar fashion, where the autocorrelation function CQ(s) of the intervals follows a power law, CQ(s) ∼ s−γ, with an exponent γ between 0.14 and 0.48. We show that these features lead to a pronounced clustering of the rare words in the text. PMID:27893737

  16. Proofs without Words in Geometry

    ERIC Educational Resources Information Center

    Nirode, Wayne

    2017-01-01

    Since the 1970s, the Mathematical Association of America's (MAA) journals "Mathematics Magazine" and "College Mathematics Journal" have published "Proofs without Words" (PWWs) (Nelsen 1993). "PWWs are pictures or diagrams that help the reader see why a particular mathematical statement may be true and how one…

  17. Social class and mathematics school knowledge of two private schools in Banten Province

    NASA Astrophysics Data System (ADS)

    Siahaan, M. F.

    2018-05-01

    The purpose of this study was to identify school mathematics topics and mathematics learning experiences of two elementary schools in contrasting social class settings under an umbrella of one institution. A case study research methodology was used to examine data collected from those two Elementary schools. The data revealed that there were similarities in curriculum framework, curriculum materials but there were also significant differences in what was taught and what was experienced in those two schools. The data suggested that word problem and a pedagogy of critical thinking were implemented in one of the schools. The differences were assessed in terms of theoretical and social implications. It was concluded that social stratification of mathematical knowledge occurred

  18. Teaching Quantitative Management to Evening MBA Students.

    ERIC Educational Resources Information Center

    Libby, Barbara

    1984-01-01

    The author discusses the mathematics background of Masters of Business Administration (MBA) students and asks what math tools are necessary for an MBA. While she finds useful the ability to deal with linear and quadratic equations; interest, depreciation, and growth rates; and word problems, she concludes that calculus is of little use apart from…

  19. Successfully Transitioning to Linear Equations

    ERIC Educational Resources Information Center

    Colton, Connie; Smith, Wendy M.

    2014-01-01

    The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…

  20. GAMES AND PUZZLES FOR THE MORE ABLE STUDENT.

    ERIC Educational Resources Information Center

    GOLDSMITH, JOHN

    SUCH MATHEMATICAL GAMES AS DOMINOES FOR PRIMARY NUMBER RECOGNITION AND AS MILK BOTTLE TOPS FOR ADDITION AND SUBTRACTION ARE LISTED. A LIST OF SEVERAL MATH PROBLEMS, PUZZLES AND BRAIN TEASERS FOLLOW. QUIET GAMES OF PAPER CUTTING AND CROSS WORD PUZZLES FOR MATH VOCABULARY ARE INCLUDED. THE NEXT SECTION OF GAMES CONCERNS LANGUAGE. THESE INCLUDE…

  1. Myth #8: Reading Is More Important than Math.

    ERIC Educational Resources Information Center

    Literacy Beat, 1988

    1988-01-01

    Adeptness in abstractions and analysis--the language of math--is at least as important as adeptness at reading words for individuals in business and industry. Mathematics literacy stimulates the problem-solving and critical thinking skills that the workplace now demands. A National Assessment of Educational Progress study found that about half of…

  2. Modeling discrete and continuous entities with fractions and decimals.

    PubMed

    Rapp, Monica; Bassok, Miriam; DeWolf, Melissa; Holyoak, Keith J

    2015-03-01

    When people use mathematics to model real-life situations, their use of mathematical expressions is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric "contain" relation), which people align with analogous mathematical relations (e.g., the noncommutative division operation, tulips/vases). Here we investigate the possibility that semantic alignment is also involved in the comprehension and use of rational numbers (fractions and decimals). A textbook analysis and results from two experiments revealed that both mathematic educators and college students tend to align the discreteness versus continuity of the entities in word problems (e.g., marbles vs. distance) with distinct symbolic representations of rational numbers--fractions versus decimals, respectively. In addition, fractions and decimals tend to be used with nonmetric units and metric units, respectively. We discuss the importance of the ontological distinction between continuous and discrete entities to mathematical cognition, the role of symbolic notations, and possible implications of our findings for the teaching of rational numbers. PsycINFO Database Record (c) 2015 APA, all rights reserved.

  3. Strengthening Connections between Elementary Classroom Mathematics and Literacy

    ERIC Educational Resources Information Center

    Altieri, Jennifer L.

    2009-01-01

    Enjoyable literacy strategies help elementary teachers reinforce students' mathematics knowledge. This article shares a number of literacy strategies that can easily connect with mathematics. These strategies include word associations, multimeaning word cards, and games. (Contains 7 figures.)

  4. Dissociations in mathematical knowledge: case studies in Down's syndrome and Williams syndrome.

    PubMed

    Robinson, Sally J; Temple, Christine M

    2013-02-01

    A study is reported of mathematical vocabulary and factual mathematical knowledge in PQ, a 22 year old with Down's syndrome (DS) who has a verbal mental age (MA) of 9 years 2 months and ST, a 15 year old with Williams syndrome (WS) who has a verbal MA of 9 years 6 months, matched to typically developing controls. The number of mathematical words contained within PQ's lexical stores was significantly reduced as reflected by performance on lexical decision. PQ was also impaired at both naming from descriptions and describing mathematical words. These results contrast with normal lexical decision and item descriptions for concrete words reported recently for PQ (Robinson and Temple, 2010). PQ's recall of mathematical facts was also impaired, whilst his recall of general knowledge facts was normal. This performance in DS indicates a deficit in both lexical representation and semantic knowledge for mathematical words and mathematical facts. In contrast, ST, the teenager with WS had good accuracy on lexical decision, naming and generating definitions for mathematical words. This contrasted with the atypical performance with concrete words recently reported for ST (Robinson and Temple, 2009). Knowledge of addition facts and general knowledge facts was also unimpaired for ST, though knowledge of multiplication facts was weak. Together the cases form a double dissociation and provide support for the distinct representation of mathematical and concrete items within the lexical-semantic system during development. The dissociations between mathematical and general factual knowledge also indicate that different types of factual knowledge may be selectively impaired during development. There is further support for a modular structure within which mathematical vocabulary and mathematical knowledge have distinct representations. This supports the case for the independent representation of factual and language-based knowledge within the semantic system during development. Copyright © 2011 Elsevier Ltd. All rights reserved.

  5. Remembering Larkin

    NASA Astrophysics Data System (ADS)

    Varlamov, Andrei

    2013-06-01

    Knowing Anatoly Ivanovich - Tolya for his friends and colleagues - for years I can't recall him ever writing mathematical expressions on a sheet of paper as he was usually solving problems in his head. Tolya was Homo Sapiens in its true, literal sense of this word. A side observer would hardly notice his mastery and deep understanding of modern methods of theoretical physics and mathematics as there were no piles of paper speckled with math symbols on his desk. But there was a blackboard in his office, all covered with fragments of problems he was discussing with various coauthors. He was famous among his students and coauthors for "falling asleep" in the chair in his office and then writing the solution on the board immediately after awakening...

  6. Interactive Whiteboards in Early Childhood Mathematics: Strategies for Effective Implementation in Pre-K-Grade 3

    ERIC Educational Resources Information Center

    Linder, Sandra M.

    2012-01-01

    Teachers are using technological innovations--including interactive whiteboards--in pre-K-grade 3 classrooms across the country. An IWB is a wall-mounted, touch-sensitive flat screen. When connected to a computer (or another electronic device) and a projector, it displays enlarged instructional content (such as a math word problem, pictures or…

  7. Preservice Teachers' Reasoning about Relationships That Are and Are Not Proportional: A Knowledge-in-Pieces Account

    ERIC Educational Resources Information Center

    Izsák, Andrew; Jacobson, Erik

    2017-01-01

    Past studies have documented students' and teachers' persistent difficulties in determining whether 2 quantities covary in a direct proportion, especially when presented missing-value word problems. In the current study, we combine a mathematical analysis with a psychological perspective to offer a new explanation for such difficulties. The…

  8. Development of color-grapheme synesthesia and its effect on mathematical operations.

    PubMed

    Mills, Carol Bergfeld; Metzger, Shari R; Foster, Catherine A; Valentine-Gresko, Melaina N; Ricketts, Stephanie

    2009-01-01

    SE, a 19-year-old female college student and a color-grapheme synesthete, reported consistent synesthetic experiences (photisms) for digits, and most letters in the Roman and Hebrew alphabets over a 6-month period. Photisms for later-learned Hebrew letters were influenced by those of the Roman alphabet and photisms for auditorily presented words were influenced by the spelling of the words. As hypothesized, in two studies, SE's solution times for addition problems were significantly slower when the colors of the digits in the problems mismatched her synesthetic photisms than when they matched or were in black (p < 0.001), whereas color had no effect on solution times for six female non-synesthetes (aged 19 to 22 years). Implications for learning and cognitive processing are discussed.

  9. Language matters in demonstrations of understanding in early years mathematics assessment

    NASA Astrophysics Data System (ADS)

    Mushin, Ilana; Gardner, Rod; Munro, Jennifer M.

    2013-09-01

    In classrooms tests, students are regularly required to demonstrate their understanding of mathematical concepts. When children encounter problems in demonstrating such understanding, it is often not clear whether this is because of the language of the teachers' questions and instructions or a genuine non-understanding of the concept itself. This paper uses Conversation Analysis to investigate the role that language plays in Year 1 oral maths assessment in an Australian Indigenous community school. This approach allows us to monitor the very subtle communicative gestures, verbal and non-verbal, that contribute to the trajectory of a particular test task. Here we are able to bring to light a range of ways in which language may interfere with demonstrations of understanding of mathematical concepts. These include particular mathematical words (e.g., size, shape, same), as well as problems with what is being asked in an instruction. We argue that while all children must learn new mathematical language in their early years of schooling, the challenge for the students we have recorded may be compounded by the language differences between the Indigenous variety of language they speak in the community, and the Standard Australian English of the classroom and teachers.

  10. Word Search Packet: Climbing the Hills of Math Skills. California Demonstration Mathematics Program.

    ERIC Educational Resources Information Center

    Ontario-Montclair School District, Ontario, CA.

    Thirty word-search puzzles on mathematics and mathematicians are presented. The puzzles are used periodically as homework assignments in a self-paced, individualized mathematics program which is designed to improve the achievement of junior high school students. Answers to the puzzles are not included. (DC)

  11. Chinese Number Words, Culture, and Mathematics Learning

    ERIC Educational Resources Information Center

    Ng, Sharon Sui Ngan; Rao, Nirmala

    2010-01-01

    This review evaluates the role of language--specifically, the Chinese-based system of number words and the simplicity of Chinese mathematical terms--in explaining the relatively superior performance of Chinese and other East Asian students in cross-national studies of mathematics achievement. Relevant research is critically reviewed focusing on…

  12. Attending to Precision with Secret Messages

    ERIC Educational Resources Information Center

    Starling, Courtney; Whitacre, Ian

    2016-01-01

    Mathematics is a language that is characterized by words and symbols that have precise definitions. Many opportunities exist for miscommunication in mathematics if the words and symbols are interpreted incorrectly or used in imprecise ways. In fact, it is found that imprecision is a common source of mathematical disagreements and misunderstandings…

  13. Effects of Training on Pre-Service Special Educators' Abilities to Co-Teach Math Vocabulary in Preparation for Inclusion Settings

    ERIC Educational Resources Information Center

    Harris, Paulette Proctor; Pollingue, Alice B.; Hearrington, Doug; Holmes, Arthur

    2014-01-01

    New special education teachers often struggle to teach children the mathematics vocabulary necessary to understand and effectively solve math word problems. The authors designed and implemented a pilot program to prepare pre-service teachers majoring in special education to implement the Camelot Learning Math Intervention Program (CLMIP). We met…

  14. Connecting Lines of Research on Task Model Variables, Automatic Item Generation, and Learning Progressions in Game-Based Assessment

    ERIC Educational Resources Information Center

    Graf, Edith Aurora

    2014-01-01

    In "How Task Features Impact Evidence from Assessments Embedded in Simulations and Games," Almond, Kim, Velasquez, and Shute have prepared a thought-provoking piece contrasting the roles of task model variables in a traditional assessment of mathematics word problems to their roles in "Newton's Playground," a game designed…

  15. A Preliminary Analysis of the Linguistic Complexity of Numeracy Skills Test Items for Pre Service Teachers

    ERIC Educational Resources Information Center

    O'Keeffe, Lisa

    2016-01-01

    Language is frequently discussed as barrier to mathematics word problems. Hence this paper presents the initial findings of a linguistic analysis of numeracy skills test sample items. The theoretical perspective of multi-modal text analysis underpinned this study, in which data was extracted from the ten sample numeracy test items released by the…

  16. A Task Type for Measuring the Representational Component of Quantitative Proficiency. GRE Board Professional Report No. 92-05P.

    ERIC Educational Resources Information Center

    Bennett, Randy Elliot; And Others

    Two computer-based categorization tasks were developed and pilot tested. In study 1, the task asked examinees to sort mathematical word problem stems according to prototypes. Results with 9 faculty members and 107 undergraduates showed that those who sorted well tended to have higher Graduate Record Examination General Test scores and college…

  17. Semantic Contamination and Mathematical Proof: Can a Non-Proof Prove?

    ERIC Educational Resources Information Center

    Mejia-Ramos, Juan Pablo; Inglis, Matthew

    2011-01-01

    The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to…

  18. Creating Printed Materials for Mathematics with a Macintosh Computer.

    ERIC Educational Resources Information Center

    Mahler, Philip

    This document gives instructions on how to use a Macintosh computer to create printed materials for mathematics. A Macintosh computer, Microsoft Word, and objected-oriented (Draw-type) art program, and a function-graphing program are capable of producing high quality printed instructional materials for mathematics. Word 5.1 has an equation editor…

  19. What's the Word for... ? Is There a Word for... ? How Understanding Mi'kmaw Language Can Help Support Mi'kmaw Learners in Mathematics

    ERIC Educational Resources Information Center

    Borden, Lisa Lunney

    2013-01-01

    As part of a larger project focused on decolonising mathematics education for Aboriginal students in Atlantic Canada, this article reports on the role of the Mi'kmaw language in mathematics teaching. By exploring how mathematical concepts are talked about (or not talked about) in the Mi'kmaw language, teachers and researchers can gain insight into…

  20. Exploration of the Factors That Support Learning: Web-Based Activity and Testing Systems in Community College Algebra [Conference Long Paper

    ERIC Educational Resources Information Center

    Hauk, Shandy; Matlen, Bryan J.

    2017-01-01

    This is an extended conference proceedings report [Long Paper] based on a shorter contributed report at the same conference. A variety of computerized learning platforms exist. In mathematics, most include sets of problems to complete. Feedback to users ranges from a single word like "Correct!" to offers of hints and partially- to…

  1. Preparation in and Use of the Nemeth Braille Code for Mathematics by Teachers of Students with Visual Impairments

    ERIC Educational Resources Information Center

    Rosenblum, L. Penny; Amato, Sheila

    2004-01-01

    This study examined the preparation in and use of the Nemeth braille code by 135 teachers of students with visual impairments. Almost all the teachers had taken at least one course in the Nemeth code as part of their university preparation. In their current jobs, they prepared a variety of materials, primarily basic operations, word problems,…

  2. The role of mathematical models in understanding pattern formation in developmental biology.

    PubMed

    Umulis, David M; Othmer, Hans G

    2015-05-01

    In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

  3. Proof and Rhetoric: The Structure and Origin of Proof--From Ancient Greece to Abraham Lincoln's Speech in Defence of the Union and Paul Keating's Mabo Speech

    ERIC Educational Resources Information Center

    Padula, Janice

    2016-01-01

    According to the latest news about declining standards in mathematics learning in Australia, boys, and girls, in particular, need to be more engaged in mathematics learning. Only 30% of mathematics students at university level in Australia are female. Proofs are made up of words and mathematical symbols. One can assume the words would assist…

  4. Syntactic Awareness and Arithmetic Word Problem Solving in Children With and Without Learning Disabilities.

    PubMed

    Peake, Christian; Jiménez, Juan E; Rodríguez, Cristina; Bisschop, Elaine; Villarroel, Rebeca

    2015-01-01

    Arithmetic word problem (AWP) solving is a highly demanding task for children with learning disabilities (LD) since verbal and mathematical information have to be integrated. This study examines specifically how syntactic awareness (SA), the ability to manage the grammatical structures of language, affects AWP solving. Three groups of children in elementary education were formed: children with arithmetic learning disabilities (ALD), children with reading learning disabilities (RLD), and children with comorbid arithmetic and reading learning disabilities (ARLD). Mediation analysis confirmed that SA was a mediator variable for both groups of children with reading disabilities when solving AWPs, but not for children in the ALD group. All groups performed below the control group in the problem solving task. When SA was controlled for, semantic structure and position of the unknown set were variables that affected both groups with ALD. Specifically, children with ALD only were more affected by the place of the unknown set. © Hammill Institute on Disabilities 2014.

  5. Does the Value of Dynamic Assessment in Predicting End-of-First-Grade Mathematics Performance Differ as a Function of English Language Proficiency?

    ERIC Educational Resources Information Center

    Seethaler, Pamela M.; Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.

    2016-01-01

    The purpose of this study was to assess the added value of dynamic assessment (DA) for predicting individual differences in year-end first-grade calculation (CA) and word-problem (WP) performance as a function of limited English proficiency (LEP) status. Beginning first graders (129 LEP; 163 non-LEP) were assessed on brief and static mathematics…

  6. [The application of new technologies to solving maths problems for students with learning disabilities: the 'underwater school'].

    PubMed

    Miranda-Casas, A; Marco-Taverner, R; Soriano-Ferrer, M; Melià de Alba, A; Simó-Casañ, P

    2008-01-01

    Different procedures have demonstrated efficacy to teach cognitive and metacognitive strategies to problem solving in mathematics. Some studies have used computer-based problem solving instructional programs. To analyze in students with learning disabilities the efficacy of a cognitive strategies training for problem solving, with three instructional delivery formats: a teacher-directed program (T-D), a computer-assisted instructional (CAI) program, and a combined program (T-D + CAI). Forty-four children with mathematics learning disabilities, between 8 and 10 years old participated in this study. The children were randomly assigned to one of the three instructional formats and a control group without cognitive strategies training. In the three instructional conditions which were compared all the students learnt problems solving linguistic and visual cognitive strategies trough the self-instructional procedure. Several types of measurements were used for analysing the possible differential efficacy of the three instructional methods implemented: solving problems tests, marks in mathematics, internal achievement responsibility scale, and school behaviours teacher ratings. Our findings show that the T-D training group and the T-D + CAI group improved significantly on math word problem solving and on marks in Maths from pre- to post-testing. In addition, the results indicated that the students of the T-D + CAI group solved more real-life problems and developed more internal attributions compared to both control and CAI groups. Finally, with regard to school behaviours, improvements in school adjustment and learning problems were observed in the students of the group with a combined instructional format (T-D + CAI).

  7. Disentangling the effects of working memory, language, parental education, and non-verbal intelligence on children’s mathematical abilities

    PubMed Central

    Pina, Violeta; Fuentes, Luis J.; Castillo, Alejandro; Diamantopoulou, Sofia

    2014-01-01

    It is assumed that children’s performance in mathematical abilities is influenced by several factors such as working memory (WM), verbal ability, intelligence, and socioeconomic status. The present study explored the contribution of those factors to mathematical performance taking a componential view of both WM and mathematics. We explored the existing relationship between different WM components (verbal and spatial) with tasks that make differential recruitment of the central executive, and simple and complex mathematical skills in a sample of 102 children in grades 4–6. The main findings point to a relationship between the verbal WM component and complex word arithmetic problems, whereas language and non-verbal intelligence were associated with knowledge of quantitative concepts and arithmetic ability. The spatial WM component was associated with the subtest Series, whereas the verbal component was with the subtest Concepts. The results also suggest a positive relationship between parental educational level and children’s performance on Quantitative Concepts. These findings suggest that specific cognitive skills might be trained in order to improve different aspects of mathematical ability. PMID:24847306

  8. Measuring the Performance and Intelligence of Systems: Proceedings of the 2001 PerMIS Workshop

    DTIC Science & Technology

    2001-09-04

    35 1.1 Interval Mathematics for Analysis of Multiresolutional Systems V. Kreinovich, Univ. of Texas, R. Alo, Univ. of Houston-Downtown...the possible combinations. In non-deterministic real- time systems , the problem is compounded by the uncertainty in the execution times of various...multiresolutional, multiscale ) in their essence because of multiresolutional character of the meaning of words [Rieger, 01]. In integrating systems , the presence of a

  9. Does the Value of Dynamic Assessment in Predicting End-of-First-Grade Mathematics Performance Differ as a Function of English Language Proficiency?

    ERIC Educational Resources Information Center

    Seethaler, Pamela M.; Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.

    2016-01-01

    The purpose of this study was to assess the added value of dynamic assessment (DA) beyond more conventional static measures for predicting individual differences in year-end 1st-grade calculation (CA) and word-problem (WP) performance, as a function of limited English proficiency (LEP) status. At the start of 1st grade, students (129 LEP; 163…

  10. Spotlight on Spelling.

    ERIC Educational Resources Information Center

    Hardin County Board of Education, Elizabethtown, KY.

    Word lists and class activities are suggested for improving the spelling of elementary school students. The word lists contain rhyming words, antonyms, synonyms, homonyms, 100 spelling demons, look-alike words that are easily confused, and content area words (for geography, mathematics, science, sports, music, social studies). The suggested…

  11. "Weigh" to Go! Exploring Mathematical Language

    ERIC Educational Resources Information Center

    Adams, Thomasenia Lott; Thangata, Fiona; King, Cindy

    2005-01-01

    This article focuses on the dynamics of language in the context of mathematics. The interaction of everyday words and specialized mathematics vocabulary impacts students' development of mathematical understanding. (Contains 4 tables and 1 figure.)

  12. Thermodynamics and Spontaneity

    NASA Astrophysics Data System (ADS)

    Ochs, Raymond S.

    1996-10-01

    Despite the importance of thermodynamics as the foundation of chemistry, most students emerge from introductory courses with only a dim understanding of this subject. Generally students recognize that the information is significant, yet do not assimilate it into later studies, especially in applied fields such as biology and biochemistry. A clear sense of the problem is reflected in a number of other contributions to this Journal (e.g., 1 - 6). Most (1 - 4, 6) recommend increased rigor in derivation of equations. This may appeal to students in advanced courses in chemical thermodynamics, but not to most. A few other suggestions are to introduce the subject earlier in general chemistry courses (2) or to provide innovative ways to visualize reaction changes (3). I suggest that the problem lies at another level entirely: the meanings of the terms are not clear. Recently, MacNeal (7) introduced the concept of mathsemantics, the joining of mathematics with a deep understanding of the sense (semantics) in which it operates. For example, the author argues that not only can we add apples and oranges (yielding total fruit), but that anything less than such a synthesis is trivial. Mathematics is hard, not because of the actual mathematical part of the problem but because of the semantics. As discussed thoroughly by Weinburg (8), the very names we affix to ideas dominate how we think about them. A similar reorientation would benefit chemical education. By way of example, the word "spontaneous" is widely used in thermodynamics, presumably because the word is familiar and assists understanding of this subject. In the following, I will provide evidence that this word has contributed more to the obfuscation of chemical ideas than it has helped elucidate them. Literature Cited 1. Redlich, O. J. Chem. Educ. 1975, 52, 374 - 376. 2. Bergquist, W.; Heikkinen, H. J. Chem. Educ. 1990, 67, 1000 - 1003. 3. Macomber, R. S. J. Chem. Educ. 1994, 71, 311 - 312. 4. Sanchez, K. S.; Vergenz, R. A. J. Chem. Educ. 1994, 71, 562 - 566. 5. Feiner, A. S.; McEvoy, A. J. J. Chem. Educ. 1994, 71, 493 - 494. 6. Gerhartl, F. J. J. Chem. Educ. 1994, 71, 539 - 548. 7. MacNeal, E. Mathsemantics. Making Numbers Make Sense; Viking: New York, 1994. 8. Weinberg, G. M. An Introduction to General Systems Thinking; Wiley-Interscience: 1985.

  13. Deaf college students' mathematical skills relative to morphological knowledge, reading level, and language proficiency.

    PubMed

    Kelly, Ronald R; Gaustad, Martha G

    2007-01-01

    This study of deaf college students examined specific relationships between their mathematics performance and their assessed skills in reading, language, and English morphology. Simple regression analyses showed that deaf college students' language proficiency scores, reading grade level, and morphological knowledge regarding word segmentation and meaning were all significantly correlated with both the ACT Mathematics Subtest and National Technical Institute for the Deaf (NTID) Mathematics Placement Test scores. Multiple regression analyses identified the best combination from among these potential independent predictors of students' performance on both the ACT and NTID mathematics tests. Additionally, the participating deaf students' grades in their college mathematics courses were significantly and positively associated with their reading grade level and their knowledge of morphological components of words.

  14. Elementary Mathematics Student Assessment: Measuring the Performance of Grade 1 and 2 Students in Counting, Word Problems, and Computation in Fall 2014. Research Report No. 2016-04

    ERIC Educational Resources Information Center

    Schoen, Robert C.; LaVenia, Mark; Bauduin, Charity; Farina, Kristy

    2016-01-01

    The subject of this report is a pair of written, group-administered tests designed to measure the performance of grade 1 and grade 2 students at the beginning of the school year in the domain of number and operations. These tests build on previous versions field-tested in fall 2013 (Schoen, LaVenia, Bauduin, & Farina, 2016). Because the tests…

  15. Numbers and functional lateralization: A visual half-field and dichotic listening study in proficient bilinguals.

    PubMed

    Klichowski, Michal; Króliczak, Gregory

    2017-06-01

    Potential links between language and numbers and the laterality of symbolic number representations in the brain are still debated. Furthermore, reports on bilingual individuals indicate that the language-number interrelationships might be quite complex. Therefore, we carried out a visual half-field (VHF) and dichotic listening (DL) study with action words and different forms of symbolic numbers used as stimuli to test the laterality of word and number processing in single-, dual-language and mixed -task and language- contexts. Experiment 1 (VHF) showed a significant right visual field/left hemispheric advantage in response accuracy for action word, as compared to any form of symbolic number processing. Experiment 2 (DL) revealed a substantially reversed effect - a significant right ear/left hemisphere advantage for arithmetic operations as compared to action word processing, and in response times in single- and dual-language contexts for number vs. action words. All these effects were language independent. Notably, for within-task response accuracy compared across modalities significant differences were found in all studied contexts. Thus, our results go counter to findings showing that action-relevant concepts and words, as well as number words are represented/processed primarily in the left hemisphere. Instead, we found that in the auditory context, following substantial engagement of working memory (here: by arithmetic operations), there is a subsequent functional reorganization of processing single stimuli, whether verbs or numbers. This reorganization - their weakened laterality - at least for response accuracy is not exclusive to processing of numbers, but the number of items to be processed. For response times, except for unpredictable tasks in mixed contexts, the "number problem" is more apparent. These outcomes are highly relevant to difficulties that simultaneous translators encounter when dealing with lengthy auditory material in which single items such as number words (and possibly other types of key words) need to be emphasized. Our results may also shed a new light on the "mathematical savant problem". Copyright © 2017 Elsevier Ltd. All rights reserved.

  16. Predicting Children's Reading and Mathematics Achievement from Early Quantitative Knowledge and Domain-General Cognitive Abilities

    PubMed Central

    Chu, Felicia W.; vanMarle, Kristy; Geary, David C.

    2016-01-01

    One hundred children (44 boys) participated in a 3-year longitudinal study of the development of basic quantitative competencies and the relation between these competencies and later mathematics and reading achievement. The children's preliteracy knowledge, intelligence, executive functions, and parental educational background were also assessed. The quantitative tasks assessed a broad range of symbolic and nonsymbolic knowledge and were administered four times across 2 years of preschool. Mathematics achievement was assessed at the end of each of 2 years of preschool, and mathematics and word reading achievement were assessed at the end of kindergarten. Our goals were to determine how domain-general abilities contribute to growth in children's quantitative knowledge and to determine how domain-general and domain-specific abilities contribute to children's preschool mathematics achievement and kindergarten mathematics and reading achievement. We first identified four core quantitative competencies (e.g., knowledge of the cardinal value of number words) that predict later mathematics achievement. The domain-general abilities were then used to predict growth in these competencies across 2 years of preschool, and the combination of domain-general abilities, preliteracy skills, and core quantitative competencies were used to predict mathematics achievement across preschool and mathematics and word reading achievement at the end of kindergarten. Both intelligence and executive functions predicted growth in the four quantitative competencies, especially across the first year of preschool. A combination of domain-general and domain-specific competencies predicted preschoolers' mathematics achievement, with a trend for domain-specific skills to be more strongly related to achievement at the beginning of preschool than at the end of preschool. Preschool preliteracy skills, sensitivity to the relative quantities of collections of objects, and cardinal knowledge predicted reading and mathematics achievement at the end of kindergarten. Preliteracy skills were more strongly related to word reading, whereas sensitivity to relative quantity was more strongly related to mathematics achievement. The overall results indicate that a combination of domain-general and domain-specific abilities contribute to development of children's early mathematics and reading achievement. PMID:27252675

  17. Predicting Children's Reading and Mathematics Achievement from Early Quantitative Knowledge and Domain-General Cognitive Abilities.

    PubMed

    Chu, Felicia W; vanMarle, Kristy; Geary, David C

    2016-01-01

    One hundred children (44 boys) participated in a 3-year longitudinal study of the development of basic quantitative competencies and the relation between these competencies and later mathematics and reading achievement. The children's preliteracy knowledge, intelligence, executive functions, and parental educational background were also assessed. The quantitative tasks assessed a broad range of symbolic and nonsymbolic knowledge and were administered four times across 2 years of preschool. Mathematics achievement was assessed at the end of each of 2 years of preschool, and mathematics and word reading achievement were assessed at the end of kindergarten. Our goals were to determine how domain-general abilities contribute to growth in children's quantitative knowledge and to determine how domain-general and domain-specific abilities contribute to children's preschool mathematics achievement and kindergarten mathematics and reading achievement. We first identified four core quantitative competencies (e.g., knowledge of the cardinal value of number words) that predict later mathematics achievement. The domain-general abilities were then used to predict growth in these competencies across 2 years of preschool, and the combination of domain-general abilities, preliteracy skills, and core quantitative competencies were used to predict mathematics achievement across preschool and mathematics and word reading achievement at the end of kindergarten. Both intelligence and executive functions predicted growth in the four quantitative competencies, especially across the first year of preschool. A combination of domain-general and domain-specific competencies predicted preschoolers' mathematics achievement, with a trend for domain-specific skills to be more strongly related to achievement at the beginning of preschool than at the end of preschool. Preschool preliteracy skills, sensitivity to the relative quantities of collections of objects, and cardinal knowledge predicted reading and mathematics achievement at the end of kindergarten. Preliteracy skills were more strongly related to word reading, whereas sensitivity to relative quantity was more strongly related to mathematics achievement. The overall results indicate that a combination of domain-general and domain-specific abilities contribute to development of children's early mathematics and reading achievement.

  18. Semantic Processing of Mathematical Gestures

    ERIC Educational Resources Information Center

    Lim, Vanessa K.; Wilson, Anna J.; Hamm, Jeff P.; Phillips, Nicola; Iwabuchi, Sarina J.; Corballis, Michael C.; Arzarello, Ferdinando; Thomas, Michael O. J.

    2009-01-01

    Objective: To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect. Results: The N400 effect elicited by words primed with mathematical gestures…

  19. Comprehension and computation in Bayesian problem solving

    PubMed Central

    Johnson, Eric D.; Tubau, Elisabet

    2015-01-01

    Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian inferences relative to normalized formats (e.g., probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on “transparent” Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e., transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct vs. incorrect reasoners depart, and how individual differences might influence this time point. PMID:26283976

  20. Lincos: An interplanetary language. [mathematical method for cosmic radio contact with extraterrestrial life

    NASA Technical Reports Server (NTRS)

    Freudenthal, H.

    1974-01-01

    A language for cosmic contacts is envisioned that utilizes radio signals of different wavelengths as sounds to form words. These words are in most cases abbreviations of Latin words understood from their English and French cognates. The logistic syntax uses pauses for punctuation in a binary system; pairs of algebraic formulas are transmitted where in a such pair the second element is always derived from the first; between them is transmitted a word that is understood as -follows- by the listener. The concepts of difference in position, of motion, of space, and of mass can be mathematically described by this language.

  1. Use of Words and Visuals in Modelling Context of Annual Plant

    ERIC Educational Resources Information Center

    Park, Jungeun; DiNapoli, Joseph; Mixell, Robert A.; Flores, Alfinio

    2017-01-01

    This study looks at the various verbal and non-verbal representations used in a process of modelling the number of annual plants over time. Analysis focuses on how various representations such as words, diagrams, letters and mathematical equations evolve in the mathematization process of the modelling context. Our results show that (1) visual…

  2. On the Equidecomposability of a Regular Triangle and A Square of Equal Areas.

    DTIC Science & Technology

    1984-01-01

    Hogo Steinhaus OMathematical Snapshots , is not correct. ANS (MOS) Subject Classifications: 51-01, 51N20 Key Words: Equidecomposability of plane...It is shown that the solution of the problem of the title, as given in the first snapshot of H. Steinhaus ’ "Mathematical Snapshots" is not correct...490985 This accuracy should be sufficient for the realization of the ingenious linkage of four polygons (1) as described by Steinhaus (See (2, Figure 1.3

  3. A Likelihood Ratio Test Regarding Two Nested But Oblique Order Restricted Hypotheses.

    DTIC Science & Technology

    1982-11-01

    Report #90 DIC JAN 2 411 ISMO. H American Mathematical Society 1979 subject classification Primary 62F03 Secondary 62E15 Key words and phrases: Order...model. A likelihood ratio test for these two restrictions is studied . Asa *a .on . r 373 RA&J *iii - ,sa~m muwod [] v~ -F: :.v"’. os "- 1...investigation was stimulated partly by a problem encountered in psychiatric research. [Winokur et al., 1971] studied data on psychiatric illnesses afflicting

  4. Teachers' Perceptions of Teaching Mathematics at the Senior Secondary Level in Fiji

    ERIC Educational Resources Information Center

    Dayal, Hem Chand

    2013-01-01

    In recent times, there has been considerable interest shown in the affective domain of mathematics education with research findings pointing out that affective variables have profound impact on classroom practices of mathematics teachers. In other words, teachers' conceptions of mathematics and mathematics teaching are greatly influenced by…

  5. Communication and Representation as Elements in Mathematical Literacy

    ERIC Educational Resources Information Center

    Thompson, Denisse R.; Chappell, Michaele F.

    2007-01-01

    The process standards of communication and representation in the "Principles and Standards for School Mathematics" are critical tools to help students develop mathematical literacy. In the mathematics classroom, students need to be encouraged to use speaking, listening, reading, and writing to communicate their understanding of mathematics words,…

  6. The Role of Mathematical Models in Understanding Pattern Formation in Developmental Biology

    PubMed Central

    Umulis, David M.

    2016-01-01

    In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics—whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: “It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.” This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, “The laws of Nature are written in the language of mathematics…the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.” Mathematics has moved beyond the geometry-based model of Galileo’s time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837–838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades—that of how organisms can scale in size. Mathematical analysis alone cannot “solve” these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology. PMID:25280665

  7. The Cognitive and Academic Profiles of Reading and Mathematics Learning Disabilities

    PubMed Central

    Compton, Donald L.; Fuchs, Lynn S.; Fuchs, Douglas; Lambert, Warren; Hamlett, Carol

    2012-01-01

    The purpose of this study was to examine the cognitive and academic profiles associated with learning disability (LD) in reading comprehension, word reading, applied problems, and calculations. The goal was to assess the specificity hypothesis, in which unexpected underachievement associated with LD is represented in terms of distinctive patterns of cognitive and academic strengths and weaknesses. At the start of 3rd grade, the authors assessed 684 students on five cognitive dimensions (nonverbal problem solving, processing speed, concept formation, language, and working memory), and across Grades 3 through 5, the authors assessed performance in each academic area three to four times. Based on final intercept, the authors classified students as LD or not LD in each of the four academic areas. For each of these four LD variables, they conducted multivariate cognitive profile analysis and academic profile analysis. Results, which generally supported the specificity hypothesis, are discussed in terms of the potential connections between reading and mathematics LD. PMID:21444929

  8. The cognitive and academic profiles of reading and mathematics learning disabilities.

    PubMed

    Compton, Donald L; Fuchs, Lynn S; Fuchs, Douglas; Lambert, Warren; Hamlett, Carol

    2012-01-01

    The purpose of this study was to examine the cognitive and academic profiles associated with learning disability (LD) in reading comprehension, word reading, applied problems, and calculations. The goal was to assess the specificity hypothesis, in which unexpected underachievement associated with LD is represented in terms of distinctive patterns of cognitive and academic strengths and weaknesses. At the start of 3rd grade, the authors assessed 684 students on five cognitive dimensions (nonverbal problem solving, processing speed, concept formation, language, and working memory), and across Grades 3 through 5, the authors assessed performance in each academic area three to four times. Based on final intercept, the authors classified students as LD or not LD in each of the four academic areas. For each of these four LD variables, they conducted multivariate cognitive profile analysis and academic profile analysis. Results, which generally supported the specificity hypothesis, are discussed in terms of the potential connections between reading and mathematics LD.

  9. Finding exact constants in a Markov model of Zipfs law generation

    NASA Astrophysics Data System (ADS)

    Bochkarev, V. V.; Lerner, E. Yu.; Nikiforov, A. A.; Pismenskiy, A. A.

    2017-12-01

    According to the classical Zipfs law, the word frequency is a power function of the word rank with an exponent -1. The objective of this work is to find multiplicative constant in a Markov model of word generation. Previously, the case of independent letters was mathematically strictly investigated in [Bochkarev V V and Lerner E Yu 2017 International Journal of Mathematics and Mathematical Sciences Article ID 914374]. Unfortunately, the methods used in this paper cannot be generalized in case of Markov chains. The search of the correct formulation of the Markov generalization of this results was performed using experiments with different ergodic matrices of transition probability P. Combinatory technique allowed taking into account all the words with probability of more than e -300 in case of 2 by 2 matrices. It was experimentally proved that the required constant in the limit is equal to the value reciprocal to conditional entropy of matrix row P with weights presenting the elements of the vector π of the stationary distribution of the Markov chain.

  10. Master's Students' Perceptions of Microsoft Word for Mathematical Typesetting

    ERIC Educational Resources Information Center

    Loch, Birgit; Lowe, Tim W.; Mestel, Ben D.

    2015-01-01

    It is widely recognized that mathematical typesetting is more difficult than typesetting in most other disciplines due to the need for specialized mathematical notation and symbols. While most mathematicians type mathematical documents using LaTeX, with varying levels of proficiency, students often use other options or handwrite mathematics. Here,…

  11. Perceptual learning modules in mathematics: enhancing students' pattern recognition, structure extraction, and fluency.

    PubMed

    Kellman, Philip J; Massey, Christine M; Son, Ji Y

    2010-04-01

    Learning in educational settings emphasizes declarative and procedural knowledge. Studies of expertise, however, point to other crucial components of learning, especially improvements produced by experience in the extraction of information: perceptual learning (PL). We suggest that such improvements characterize both simple sensory and complex cognitive, even symbolic, tasks through common processes of discovery and selection. We apply these ideas in the form of perceptual learning modules (PLMs) to mathematics learning. We tested three PLMs, each emphasizing different aspects of complex task performance, in middle and high school mathematics. In the MultiRep PLM, practice in matching function information across multiple representations improved students' abilities to generate correct graphs and equations from word problems. In the Algebraic Transformations PLM, practice in seeing equation structure across transformations (but not solving equations) led to dramatic improvements in the speed of equation solving. In the Linear Measurement PLM, interactive trials involving extraction of information about units and lengths produced successful transfer to novel measurement problems and fraction problem solving. Taken together, these results suggest (a) that PL techniques have the potential to address crucial, neglected dimensions of learning, including discovery and fluent processing of relations; (b) PL effects apply even to complex tasks that involve symbolic processing; and (c) appropriately designed PL technology can produce rapid and enduring advances in learning. Copyright © 2009 Cognitive Science Society, Inc.

  12. Using LEGO for learning fractions, supporting or distracting?

    NASA Astrophysics Data System (ADS)

    Rejeki, Sri; Setyaningsih, Nining; Toyib, Muhamad

    2017-05-01

    The role of games used for learning mathematics is still in debate. However, many research revealed that it gave positive effects on both students' motivation and performance in mathematics. Therefore, this study aims at investigating the effects of using LEGO-as one of games which students are familiar with, for learning mathematics, on both students' conceptual knowledge of fractions and students' attitude in learning mathematics. A set of learning activities consisting three meetings of fractions learning was designed for this study. The activities were mainly about solving word-context problems using LEGO as the model. Thirty students of seven grade with high-ability in mathematics and thirty two students with low-ability in mathematics were involved in this study. The data were collected through students' written works, video registration and field notes during the teaching and learning activities. The results indicate that in general the use of LEGO in learning activities support the conceptual understanding on fractions for both students with high-ability and low-ability in mathematics. Moreover, for students with low-ability in mathematics, it promotes the computational skill of fractions operation. The evidences also suggest that bringing LEGO into classroom activities improve students' motivation and engagement. However, in some cases, students were more focus on playing than learning. Therefore, teachers play important roles on providing clear pedagogical instructions about the way to use LEGO properly.

  13. The Effects of Schema-Broadening Instruction on Second Graders’ Word-Problem Performance and Their Ability to Represent Word Problems with Algebraic Equations: A Randomized Control Study

    PubMed Central

    Fuchs, Lynn S.; Zumeta, Rebecca O.; Schumacher, Robin Finelli; Powell, Sarah R.; Seethaler, Pamela M.; Hamlett, Carol L.; Fuchs, Douglas

    2010-01-01

    The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders’ word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which taught students to represent the structural, defining features of word problems with overarching equations. Intervention lasted 16 weeks. We pretested and posttested 270 students on measures of word-problem skill; analyses that accounted for the nested structure of the data indicated superior word-problem learning for SBI students. Descriptive analyses of students’ word-problem work indicated that SBI helped students represent the structure of word problems with algebraic equations, suggesting that SBI promoted this aspect of students’ emerging algebraic reasoning. PMID:20539822

  14. Multiple Paths to Mathematics Practice in Al-Kashi's Key to Arithmetic

    NASA Astrophysics Data System (ADS)

    Taani, Osama

    2014-01-01

    In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his Key to Arithmetic, a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life and his contributions to mathematics and astronomy. Section 2 starts with a brief discussion of the contents and pedagogy of the Key to Arithmetic. Al-Kashi's multiple approaches are discussed through four different examples of his versatility in presenting a topic from multiple perspectives. These examples are multiple definitions, multiple algorithms, multiple formulas, and multiple methods for solving word problems. Section 3 is devoted to some benefits that can be gained by implementing al-Kashi's multiple paths approach in modern curricula. For this discussion, examples from two teaching modules taken from the Key to Arithmetic and implemented in Pre-Calculus and mathematics courses for preservice teachers are discussed. Also, the conclusions are supported by some aspects of these modules. This paper is an attempt to help mathematics educators explore more benefits from reading from original sources.

  15. Cognitive Profiles of Mathematical Problem Solving Learning Disability for Different Definitions of Disability

    PubMed Central

    Tolar, Tammy D.; Fuchs, Lynn; Fletcher, Jack M.; Fuchs, Douglas; Hamlett, Carol L.

    2014-01-01

    Three cohorts of third-grade students (N = 813) were evaluated on achievement, cognitive abilities, and behavioral attention according to contrasting research traditions in defining math learning disability (LD) status: low achievement versus extremely low achievement and IQ-achievement discrepant versus strictly low-achieving LD. We use methods from these two traditions to form math problem solving LD groups. To evaluate group differences, we used MANOVA-based profile and canonical analyses to control for relations among the outcomes and regression to control for group definition variables. Results suggest that basic arithmetic is the key distinguishing characteristic that separates low-achieving problem solvers (including LD, regardless of definition) from typically achieving students. Word problem solving is the key distinguishing characteristic that separates IQ-achievement-discrepant from strictly low-achieving LD students, favoring the IQ-achievement-discrepant students. PMID:24939971

  16. Masculinities in Mathematics. Educating Boys, Learning Gender

    ERIC Educational Resources Information Center

    Mendick, Heather

    2006-01-01

    This book illuminates what studying mathematics means for both students and teachers and offers a broad range of insights into students' views and practices. In addition to the words of young people learning mathematics, the masculinity of mathematics is explored through historical material and cinematic representations. The author discusses the…

  17. Does the Value of Dynamic Assessment in Predicting End-of-First-Grade Mathematics Performance Differ as a Function of English Language Proficiency?

    PubMed Central

    Seethaler, Pamela M.; Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.

    2015-01-01

    The purpose of this study was to assess the added value of dynamic assessment (DA) beyond more conventional static measures for predicting individual differences in year-end 1st-grade calculation (CA) and word-problem (WP) performance, as a function of limited English proficiency (LEP) status. At the start of 1st grade, students (129 LEP; 163 non-LEP) were assessed on a brief static mathematics test, an extended static mathematics test, static tests of domain-general abilities associated with CAs and WPs (vocabulary; reasoning), and DA. Near end of 1st grade, they were assessed on CA and WP. Regression analyses indicated that the value of the predictor depends on the predicted outcome and LEP status. In predicting CAs, the extended mathematics test and DA uniquely explained variance for LEP children, with stronger predictive value for the extended mathematics test; for non-LEP children, the extended mathematics test was the only significant predictor. However, in predicting WPs, only DA and vocabulary were uniquely predictive for LEP children, with stronger value for DA; for non-LEP children, the extended mathematics test and DA were comparably uniquely predictive. Neither the brief static mathematics test nor reasoning was significant in predicting either outcome. The potential value of a gated screening process, using an extended mathematics assessment to predict CAs and using DA to predict WPs, is discussed. PMID:26523068

  18. Uncertainty reasoning in expert systems

    NASA Technical Reports Server (NTRS)

    Kreinovich, Vladik

    1993-01-01

    Intelligent control is a very successful way to transform the expert's knowledge of the type 'if the velocity is big and the distance from the object is small, hit the brakes and decelerate as fast as possible' into an actual control. To apply this transformation, one must choose appropriate methods for reasoning with uncertainty, i.e., one must: (1) choose the representation for words like 'small', 'big'; (2) choose operations corresponding to 'and' and 'or'; (3) choose a method that transforms the resulting uncertain control recommendations into a precise control strategy. The wrong choice can drastically affect the quality of the resulting control, so the problem of choosing the right procedure is very important. From a mathematical viewpoint these choice problems correspond to non-linear optimization and are therefore extremely difficult. In this project, a new mathematical formalism (based on group theory) is developed that allows us to solve the problem of optimal choice and thus: (1) explain why the existing choices are really the best (in some situations); (2) explain a rather mysterious fact that fuzzy control (i.e., control based on the experts' knowledge) is often better than the control by these same experts; and (3) give choice recommendations for the cases when traditional choices do not work.

  19. Multiple Aspects of Self-Regulation Uniquely Predict Mathematics but Not Letter–Word Knowledge in the Early Elementary Grades

    PubMed Central

    Blair, Clancy; Ursache, Alexandra; Greenberg, Mark; Vernon-Feagans, Lynne

    2017-01-01

    The relation of self-regulation measured prior to school entry to developing math and reading ability in prekindergarten through the second grade was examined in a prospective longitudinal sample of 1,292 children and families in predominantly rural and low-income communities in 2 regions of high poverty in the United States. Direct assessments of executive function, effortful control, and stress response physiology (indexed by resting levels of cortisol and alpha amylase obtained from saliva) were measured at child age 48 months and parents and teachers reported on children’s effortful control using temperament rating scales at child age approximately 60 months. Math and reading ability, as measured by the Woodcock-Johnson III applied problems and letter–word subtests, respectively, were measured at prekindergarten through the second grade. Effects for self-regulation measures were seen primarily for initial level and to some extent growth in both mathematics and reading, even when controlling for family demographic characteristics that represent relevant selection factors into higher levels of both self-regulation and academic achievement. These effects persisted for mathematics but not for reading with the inclusion of child cognitive abilities, vocabulary, and speed of processing measured in prekindergarten, concurrent with the first time point for the academic measures. Results are interpreted as indicating a role for self-regulation in learning ability generally, likely through support for attention and reasoning abilities that are most specific to the assessment of mathematics in this analysis. Implications for instruction and for assessment and the best ways to support the development of early math and reading ability for children at risk for school failure are discussed. PMID:25688999

  20. Multiple aspects of self-regulation uniquely predict mathematics but not letter-word knowledge in the early elementary grades.

    PubMed

    Blair, Clancy; Ursache, Alexandra; Greenberg, Mark; Vernon-Feagans, Lynne

    2015-04-01

    The relation of self-regulation measured prior to school entry to developing math and reading ability in prekindergarten through the second grade was examined in a prospective longitudinal sample of 1,292 children and families in predominantly rural and low-income communities in 2 regions of high poverty in the United States. Direct assessments of executive function, effortful control, and stress response physiology (indexed by resting levels of cortisol and alpha amylase obtained from saliva) were measured at child age 48 months and parents and teachers reported on children's effortful control using temperament rating scales at child age approximately 60 months. Math and reading ability, as measured by the Woodcock-Johnson III applied problems and letter-word subtests, respectively, were measured at prekindergarten through the second grade. Effects for self-regulation measures were seen primarily for initial level and to some extent growth in both mathematics and reading, even when controlling for family demographic characteristics that represent relevant selection factors into higher levels of both self-regulation and academic achievement. These effects persisted for mathematics but not for reading with the inclusion of child cognitive abilities, vocabulary, and speed of processing measured in prekindergarten, concurrent with the first time point for the academic measures. Results are interpreted as indicating a role for self-regulation in learning ability generally, likely through support for attention and reasoning abilities that are most specific to the assessment of mathematics in this analysis. Implications for instruction and for assessment and the best ways to support the development of early math and reading ability for children at risk for school failure are discussed. (c) 2015 APA, all rights reserved).

  1. Automated speech understanding: the next generation

    NASA Astrophysics Data System (ADS)

    Picone, J.; Ebel, W. J.; Deshmukh, N.

    1995-04-01

    Modern speech understanding systems merge interdisciplinary technologies from Signal Processing, Pattern Recognition, Natural Language, and Linguistics into a unified statistical framework. These systems, which have applications in a wide range of signal processing problems, represent a revolution in Digital Signal Processing (DSP). Once a field dominated by vector-oriented processors and linear algebra-based mathematics, the current generation of DSP-based systems rely on sophisticated statistical models implemented using a complex software paradigm. Such systems are now capable of understanding continuous speech input for vocabularies of several thousand words in operational environments. The current generation of deployed systems, based on small vocabularies of isolated words, will soon be replaced by a new technology offering natural language access to vast information resources such as the Internet, and provide completely automated voice interfaces for mundane tasks such as travel planning and directory assistance.

  2. Exploring the impact of phonological awareness, visual-spatial working memory, and preschool quantity-number competencies on mathematics achievement in elementary school: findings from a 3-year longitudinal study.

    PubMed

    Krajewski, Kristin; Schneider, Wolfgang

    2009-08-01

    This longitudinal study explored the importance of kindergarten measures of phonological awareness, working memory, and quantity-number competencies (QNC) for predicting mathematical school achievement in third graders (mean age 8 years 8 months). It was found that the impact of phonological awareness and visual-spatial working memory, assessed at 5 years of age, was mediated by early QNC, which predicted math achievement in third grade. Importantly, and confirming our isolated number words hypothesis, phonological awareness had no impact on higher numerical competencies (i.e., when number words needed to be linked with quantities [QNC Level II and above]) but predicted basic numerical competencies (i.e., when number words were isolated from quantities [QNC Level I]), explaining the moderate relationship between early literacy development and the development of mathematical competencies.

  3. Do Different Types of School Mathematics Development Depend on Different Constellations of Numerical versus General Cognitive Abilities?

    PubMed Central

    Fuchs, Lynn S.; Geary, David C.; Compton, Donald L.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Bryant, Joan D.; Schatschneider, Christopher

    2010-01-01

    The purpose of this study was to examine the interplay between basic numerical cognition and domain-general abilities (such as working memory) in explaining school mathematics learning. First graders (n=280; 5.77 years) were assessed on 2 types of basic numerical cognition, 8 domain-general abilities, procedural calculations (PCs), and word problems (WPs) in fall and then reassessed on PCs and WPs in spring. Development was indexed via latent change scores, and the interplay between numerical and domain-general abilities was analyzed via multiple regression. Results suggest that the development of different types of formal school mathematics depends on different constellations of numerical versus general cognitive abilities. When controlling for 8 domain-general abilities, both aspects of basic numerical cognition were uniquely predictive of PC and WP development. Yet, for PC development, the additional amount of variance explained by the set of domain-general abilities was not significant, and only counting span was uniquely predictive. By contrast, for WP development, the set of domain- general abilities did provide additional explanatory value, accounting for about the same amount of variance as the basic numerical cognition variables. Language, attentive behavior, nonverbal problem solving, and listening span were uniquely predictive. PMID:20822213

  4. Spoken Language and Mathematics.

    ERIC Educational Resources Information Center

    Raiker, Andrea

    2002-01-01

    States teachers/learners use spoken language in a three part mathematics lesson advocated by the British National Numeracy Strategy. Recognizes language's importance by emphasizing correct use of mathematical vocabulary in raising standards. Finds pupils and teachers appear to ascribe different meanings to scientific words because of their…

  5. Promoting Decimal Number Sense and Representational Fluency

    ERIC Educational Resources Information Center

    Suh, Jennifer M.; Johnston, Chris; Jamieson, Spencer; Mills, Michelle

    2008-01-01

    The abstract nature of mathematics requires the communication of mathematical ideas through multiple representations, such as words, symbols, pictures, objects, or actions. Building representational fluency involves using mathematical representations flexibly and being able to interpret and translate among these different models and mathematical…

  6. Assimilating data into open ocean tidal models

    NASA Astrophysics Data System (ADS)

    Kivman, Gennady A.

    The problem of deriving tidal fields from observations by reason of incompleteness and imperfectness of every data set practically available has an infinitely large number of allowable solutions fitting the data within measurement errors and hence can be treated as ill-posed. Therefore, interpolating the data always relies on some a priori assumptions concerning the tides, which provide a rule of sampling or, in other words, a regularization of the ill-posed problem. Data assimilation procedures used in large scale tide modeling are viewed in a common mathematical framework as such regularizations. It is shown that they all (basis functions expansion, parameter estimation, nudging, objective analysis, general inversion, and extended general inversion), including those (objective analysis and general inversion) originally formulated in stochastic terms, may be considered as utilizations of one of the three general methods suggested by the theory of ill-posed problems. The problem of grid refinement critical for inverse methods and nudging is discussed.

  7. Separate but correlated: The latent structure of space and mathematics across development.

    PubMed

    Mix, Kelly S; Levine, Susan C; Cheng, Yi-Ling; Young, Chris; Hambrick, D Zachary; Ping, Raedy; Konstantopoulos, Spyros

    2016-09-01

    The relations among various spatial and mathematics skills were assessed in a cross-sectional study of 854 children from kindergarten, third, and sixth grades (i.e., 5 to 13 years of age). Children completed a battery of spatial mathematics tests and their scores were submitted to exploratory factor analyses both within and across domains. In the within domain analyses, all of the measures formed single factors at each age, suggesting consistent, unitary structures across this age range. Yet, as in previous work, the 2 domains were highly correlated, both in terms of overall composite score and pairwise comparisons of individual tasks. When both spatial and mathematics scores were submitted to the same factor analysis, the 2 domain specific factors again emerged, but there also were significant cross-domain factor loadings that varied with age. Multivariate regressions replicated the factor analysis and further revealed that mental rotation was the best predictor of mathematical performance in kindergarten, and visual-spatial working memory was the best predictor of mathematical performance in sixth grade. The mathematical tasks that predicted the most variance in spatial skill were place value (K, 3rd, 6th), word problems (3rd, 6th), calculation (K), fraction concepts (3rd), and algebra (6th). Thus, although spatial skill and mathematics each have strong internal structures, they also share significant overlap, and have particularly strong cross-domain relations for certain tasks. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

  8. Contributions from specific and general factors to unique deficits: two cases of mathematics learning difficulties

    PubMed Central

    Haase, Vitor G.; Júlio-Costa, Annelise; Lopes-Silva, Júlia B.; Starling-Alves, Isabella; Antunes, Andressa M.; Pinheiro-Chagas, Pedro; Wood, Guilherme

    2014-01-01

    Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties. PMID:24592243

  9. Observables and density matrices embedded in dual Hilbert spaces

    NASA Astrophysics Data System (ADS)

    Prosen, T.; Martignon, L.; Seligman, T. H.

    2015-06-01

    The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured that we deal with Hilbert spaces although the mathematical background was not entirely clear, particularly, when dealing with bosonic operators. This in turn caused some doubts about the correct way to combine bosonic and fermionic operators or, in other words, regular and Grassmann variables. In this paper we present a formal answer to the problems on a simple and very general basis. We illustrate the resulting construction by revisiting the Bargmann transform and finding the known connection between {{L}}2({{R}}) and the Bargmann-Hilbert space. We pursue this line of thinking one step further and discuss the representations of complex extensions of linear canonical transformations as isometries between dual Hilbert spaces. We then use the formalism to give an explicit formulation for Fock spaces involving both fermions and bosons thus solving the problem at the origin of our considerations.

  10. Number Words in "Her" Language, Dialogism and Identity-Work: The Case of Little Mariah

    ERIC Educational Resources Information Center

    Chronaki, Anna; Mountzouri, Georgia; Zaharaki, Maria; Planas, Núria

    2016-01-01

    Based on an ethnographic study, we explore the potential of experimenting with multiple languages for number words as part of young children's mathematical activity. Data from a preschool classroom activity on "number words in 'other' languages" exemplify a complex process of discursive identity-work and dialogism amongst children,…

  11. Spoken Word Recognition and Serial Recall of Words from Components in the Phonological Network

    ERIC Educational Resources Information Center

    Siew, Cynthia S. Q.; Vitevitch, Michael S.

    2016-01-01

    Network science uses mathematical techniques to study complex systems such as the phonological lexicon (Vitevitch, 2008). The phonological network consists of a "giant component" (the largest connected component of the network) and "lexical islands" (smaller groups of words that are connected to each other, but not to the giant…

  12. Formal Models of Word Recognition. Final Report.

    ERIC Educational Resources Information Center

    Travers, Jeffrey R.

    Existing mathematical models of word recognition are reviewed and a new theory is proposed in this research. The new theory integrates earlier proposals within a single framework, sacrificing none of the predictive power of the earlier proposals, but offering a gain in theoretical economy. The theory holds that word recognition is accomplished by…

  13. Specifying Theories of Developmental Dyslexia: A Diffusion Model Analysis of Word Recognition

    ERIC Educational Resources Information Center

    Zeguers, Maaike H. T.; Snellings, Patrick; Tijms, Jurgen; Weeda, Wouter D.; Tamboer, Peter; Bexkens, Anika; Huizenga, Hilde M.

    2011-01-01

    The nature of word recognition difficulties in developmental dyslexia is still a topic of controversy. We investigated the contribution of phonological processing deficits and uncertainty to the word recognition difficulties of dyslexic children by mathematical diffusion modeling of visual and auditory lexical decision data. The first study showed…

  14. Investigation of Mathematics Teacher Candidates' Conceptual Structures about "Measurement" through Word Association Test: The Example of Turkey

    ERIC Educational Resources Information Center

    Erdogan, Ahmet

    2017-01-01

    The purpose of this research is to determine mathematics teacher candidates' conceptual structures about the concept of "measurement" that is the one of the important learning fields of mathematics. Qualitative research method was used in this study. Participants of this study were 58 mathematics teacher candidates studying in one of the…

  15. Teachers and Textbooks: On Statistical Definitions in Senior Secondary Mathematics

    ERIC Educational Resources Information Center

    Dunn, Peter K.; Marshman, Margaret; McDougall, Robert; Wiegand, Aaron

    2015-01-01

    The new "Australian Senior Secondary Curriculum: Mathematics" contains more statistics than the existing Australian Curricula. This case study examines how a group of Queensland mathematics teachers define the word "statistics" and five statistical terms from the new curricula. These definitions are compared to those used in…

  16. Strength in Numbers? Women and Mathematics

    ERIC Educational Resources Information Center

    Beaton, Ann; Tougas, Francine; Rinfret, Natalie; Huard, Nathalie; Delisle, Marie-Noelle

    2007-01-01

    Two studies were conducted to test the link between numerical distinctiveness, stereotype threat and mathematical performance among women. In the first study, stereotype threat was measured with a stereotype activation task. Women in a solo, non-solo or control condition completed word fragments and a mathematical activity. Solo women, rather than…

  17. The Measurand: The Problem of Frequency

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kirkham, Harold

    The conceptual entity that metrologists term the measurand is a model selected to represent the physical entity being measured. In a world of digital measurements, it should be defined first mathematically, and only then put into words. Human linguistic processes lack the precision required when all we do is use labels. In this paper, reactive power and frequency are used as examples. The act of measurement finds the values of the coef-ficients of the model. In other words, it solves an equation. In a digital instrument, information about the quality of the fit between the physical entity being measured andmore » the conceptual model is often available. In essence the instrument can comment on the selection of the model. This comment should be reported as part of the statement of the result of the measurement, along with the declared value and the uncertainty.« less

  18. The impact of instructor pedagogy on college calculus students' attitude toward mathematics

    NASA Astrophysics Data System (ADS)

    Sonnert, Gerhard; Sadler, Philip M.; Sadler, Samuel M.; Bressoud, David M.

    2015-04-01

    College calculus teaches students important mathematical concepts and skills. The course also has a substantial impact on students' attitude toward mathematics, affecting their career aspirations and desires to take more mathematics. This national US study of 3103 students at 123 colleges and universities tracks changes in students' attitudes toward mathematics during a 'mainstream' calculus course while controlling for student backgrounds. The attitude measure combines students' self-ratings of their mathematics confidence, interest in, and enjoyment of mathematics. Three major kinds of instructor pedagogy, identified through the factor analysis of 61 student-reported variables, are investigated for impact on student attitude as follows: (1) instructors who employ generally accepted 'good teaching' practices (e.g. clarity in presentation and answering questions, useful homework, fair exams, help outside of class) are found to have the most positive impact, particularly with students who began with a weaker initial attitude. (2) Use of educational 'technology' (e.g. graphing calculators, for demonstrations, in homework), on average, is found to have no impact on attitudes, except when used by graduate student instructors, which negatively affects students' attitudes towards mathematics. (3) 'Ambitious teaching' (e.g. group work, word problems, 'flipped' reading, student explanations of thinking) has a small negative impact on student attitudes, while being a relatively more constructive influence only on students who already enjoyed a positive attitude toward mathematics and in classrooms with a large number of students. This study provides support for efforts to improve calculus teaching through the training of faculty and graduate students to use traditional 'good teaching' practices through professional development workshops and courses. As currently implemented, technology and ambitious pedagogical practices, while no doubt effective in certain classrooms, do not appear to have a reliable, positive impact on student attitudes toward mathematics.

  19. Memorizing Is Not a Dirty Word: What Should a Mathematics Teacher Know to Use It Effectively in Teaching and Learning Mathematics?

    ERIC Educational Resources Information Center

    Sharma, Mahesh C.

    1985-01-01

    This bulletin concerns the role of memorization in mathematics instruction. Sections of the bulletin are devoted to discussions of: old math vs. new math; the importance of memorization ability on mathematics learning; misconceptions about memory; how to enhance the memory, including short-term vs. long-term memory systems, attention, interest,…

  20. A Basic Vocabulary and a Bibliography for Scientific and Technical English.

    ERIC Educational Resources Information Center

    Brunt, Richard J.

    The selection of 594 words in this basic vocabulary list was compiled from various dictionaries and frequency lists for physics, mathematics and civil engineering. The list attempts to include those words which have been found to be unknown by German students learning English for science and technology. In addition to the word list, a bibliography…

  1. Learning How to Represent Mathematics on Paper

    ERIC Educational Resources Information Center

    Meaney, Tamsin; Trinick, Tony; Fairhall, Uenuku

    2009-01-01

    These authors have been working with a school in New Zealand that teaches mathematics, in the Maori language. In the last two years, the focus has been on improving the quantity and the quality of writing in mathematics. For the authors, "writing" meant using words, diagrams, symbols and graphs, either individually or in combination.…

  2. Early Childhood Mathematics Education: The Critical Issue Is Change

    ERIC Educational Resources Information Center

    Hachey, Alyse C.

    2013-01-01

    In this response to commentaries, the author states that she chose the term "revolution" because it comes from the Latin word "revolutio," which means "a turn around." Leading researchers in the early 20th century were advocating that young children were mathematically inept and that mathematics education was useless before elementary school…

  3. A Cognitive Analysis of Students’ Mathematical Problem Solving Ability on Geometry

    NASA Astrophysics Data System (ADS)

    Rusyda, N. A.; Kusnandi, K.; Suhendra, S.

    2017-09-01

    The purpose of this research is to analyze of mathematical problem solving ability of students in one of secondary school on geometry. This research was conducted by using quantitative approach with descriptive method. Population in this research was all students of that school and the sample was twenty five students that was chosen by purposive sampling technique. Data of mathematical problem solving were collected through essay test. The results showed the percentage of achievement of mathematical problem solving indicators of students were: 1) solve closed mathematical problems with context in math was 50%; 2) solve the closed mathematical problems with the context beyond mathematics was 24%; 3) solving open mathematical problems with contexts in mathematics was 35%; And 4) solving open mathematical problems with contexts outside mathematics was 44%. Based on the percentage, it can be concluded that the level of achievement of mathematical problem solving ability in geometry still low. This is because students are not used to solving problems that measure mathematical problem solving ability, weaknesses remember previous knowledge, and lack of problem solving framework. So the students’ ability of mathematical problems solving need to be improved with implement appropriate learning strategy.

  4. Visual Theorems.

    ERIC Educational Resources Information Center

    Davis, Philip J.

    1993-01-01

    Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)

  5. Nuevo enfoque de la ensenanza de las matematicas en el nivel de primaria (A New Approach to the Teaching of Mathematics at the Primary School Level).

    ERIC Educational Resources Information Center

    Jimenez Lozano, Blanca; And Others

    This document is an English-language abstract (approximately 1500 words) of a new approach to the teaching of mathematics in Mexican elementary schools. Three aspects of mathematical reform are discussed: (1) syllabus content; (2) teaching methods; and (3) the question of introducing the pupil to modern mathematics at the earliest possible stage…

  6. SCOPE (Standardized Curriculum-Oriented Pupil Evaluation) Mathematics. Test Book Grade Five.

    ERIC Educational Resources Information Center

    Northwest Territories Dept. of Education, Yellowknife. Programs and Evaluation Branch.

    The SCOPE Mathematics Achievement Test booklet for grade 5 presents 11 mathematical concepts with instructions for students to take the test with little or no teacher direction. Testing items include: writing number words; reading and writing numerals in sequence from 0.001 to 100,000; adding and subtracting whole numbers; multiplying up to four…

  7. Language and Mathematical Performance: A Comparison of Lower Secondary School Students with Different Level of Mathematical Skills

    ERIC Educational Resources Information Center

    Korhonen, Johan; Linnanmaki, Karin; Aunio, Pirjo

    2012-01-01

    This study investigated the connection between language (i.e., word comprehension, reading comprehension and spelling skills) and mathematical performance. The sample consisted of grade nine students (N = 810) in 14 lower secondary schools in the Swedish speaking areas of Finland. Standardized tests for reading and writing skills, and mathematical…

  8. Objects, Signs, and Representations in the Semio-Cognitive Analysis of the Processes Involved in Teaching and Learning Mathematics: A Duvalian Perspective

    ERIC Educational Resources Information Center

    Iori, Maura

    2017-01-01

    In mathematical activities and in the analysis of mathematics teaching-learning processes, "objects," "signs", and "representations" are often mentioned, where the meaning assigned to those words is sometimes very broad, sometimes limited, other times intuitive, allusive, or not completely clear. On the other hand, as…

  9. Pre-Service Science Teachers' Cognitive Structures Regarding Science, Technology, Engineering, Mathematics (STEM) and Science Education

    ERIC Educational Resources Information Center

    Hacioglu, Yasemin; Yamak, Havva; Kavak, Nusret

    2016-01-01

    The aim of this study is to reveal pre-service science teachers' cognitive structures regarding Science, Technology, Engineering, Mathematics (STEM) and science education. The study group of the study consisted of 192 pre-service science teachers. A Free Word Association Test (WAT) consisting of science, technology, engineering, mathematics and…

  10. A Model for Minimizing Numeric Function Generator Complexity and Delay

    DTIC Science & Technology

    2007-12-01

    allow computation of difficult mathematical functions in less time and with less hardware than commonly employed methods. They compute piecewise...Programmable Gate Arrays (FPGAs). The algorithms and estimation techniques apply to various NFG architectures and mathematical functions. This...thesis compares hardware utilization and propagation delay for various NFG architectures, mathematical functions, word widths, and segmentation methods

  11. Efficacy of the Cooperative Learning Method on Mathematics Achievement and Attitude: A Meta-Analysis Research

    ERIC Educational Resources Information Center

    Capar, Gulfer; Tarim, Kamuran

    2015-01-01

    This research compiles experimental studies from 1988 to 2010 that examined the influence of the cooperative learning method, as compared with that of traditional methods, on mathematics achievement and on attitudes towards mathematics. The related field was searched using the following key words in Turkish "matematik ve isbirlikli ögrenme,…

  12. Solving Word Problems using Schemas: A Review of the Literature

    PubMed Central

    Powell, Sarah R.

    2011-01-01

    Solving word problems is a difficult task for students at-risk for or with learning disabilities (LD). One instructional approach that has emerged as a valid method for helping students at-risk for or with LD to become more proficient at word-problem solving is using schemas. A schema is a framework for solving a problem. With a schema, students are taught to recognize problems as falling within word-problem types and to apply a problem solution method that matches that problem type. This review highlights two schema approaches for 2nd- and 3rd-grade students at-risk for or with LD: schema-based instruction and schema-broadening instruction. A total of 12 schema studies were reviewed and synthesized. Both types of schema approaches enhanced the word-problem skill of students at-risk for or with LD. Based on the review, suggestions are provided for incorporating word-problem instruction using schemas. PMID:21643477

  13. The Construction of Mathematical Literacy Problems for Geometry

    NASA Astrophysics Data System (ADS)

    Malasari, P. N.; Herman, T.; Jupri, A.

    2017-09-01

    The students of junior high school should have mathematical literacy ability to formulate, apply, and interpret mathematics in problem solving of daily life. Teaching these students are not enough by giving them ordinary mathematics problems. Teaching activities for these students brings consequence for teacher to construct mathematical literacy problems. Therefore, the aim of this study is to construct mathematical literacy problems to assess mathematical literacy ability. The steps of this study that consists of analysing, designing, theoretical validation, revising, limited testing to students, and evaluating. The data was collected with written test to 38 students of grade IX at one of state junior high school. Mathematical literacy problems consist of three essays with three indicators and three levels at polyhedron subject. The Indicators are formulating and employing mathematics. The results show that: (1) mathematical literacy problems which are constructed have been valid and practical, (2) mathematical literacy problems have good distinguishing characteristics and adequate distinguishing characteristics, (3) difficulty levels of problems are easy and moderate. The final conclusion is mathematical literacy problems which are constructed can be used to assess mathematical literacy ability.

  14. Neurally and mathematically motivated architecture for language and thought.

    PubMed

    Perlovsky, L I; Ilin, R

    2010-01-01

    Neural structures of interaction between thinking and language are unknown. This paper suggests a possible architecture motivated by neural and mathematical considerations. A mathematical requirement of computability imposes significant constraints on possible architectures consistent with brain neural structure and with a wealth of psychological knowledge. How language interacts with cognition. Do we think with words, or is thinking independent from language with words being just labels for decisions? Why is language learned by the age of 5 or 7, but acquisition of knowledge represented by learning to use this language knowledge takes a lifetime? This paper discusses hierarchical aspects of language and thought and argues that high level abstract thinking is impossible without language. We discuss a mathematical technique that can model the joint language-thought architecture, while overcoming previously encountered difficulties of computability. This architecture explains a contradiction between human ability for rational thoughtful decisions and irrationality of human thinking revealed by Tversky and Kahneman; a crucial role in this contradiction might be played by language. The proposed model resolves long-standing issues: how the brain learns correct words-object associations; why animals do not talk and think like people. We propose the role played by language emotionality in its interaction with thought. We relate the mathematical model to Humboldt's "firmness" of languages; and discuss possible influence of language grammar on its emotionality. Psychological and brain imaging experiments related to the proposed model are discussed. Future theoretical and experimental research is outlined.

  15. Neurally and Mathematically Motivated Architecture for Language and Thought

    PubMed Central

    Perlovsky, L.I; Ilin, R

    2010-01-01

    Neural structures of interaction between thinking and language are unknown. This paper suggests a possible architecture motivated by neural and mathematical considerations. A mathematical requirement of computability imposes significant constraints on possible architectures consistent with brain neural structure and with a wealth of psychological knowledge. How language interacts with cognition. Do we think with words, or is thinking independent from language with words being just labels for decisions? Why is language learned by the age of 5 or 7, but acquisition of knowledge represented by learning to use this language knowledge takes a lifetime? This paper discusses hierarchical aspects of language and thought and argues that high level abstract thinking is impossible without language. We discuss a mathematical technique that can model the joint language-thought architecture, while overcoming previously encountered difficulties of computability. This architecture explains a contradiction between human ability for rational thoughtful decisions and irrationality of human thinking revealed by Tversky and Kahneman; a crucial role in this contradiction might be played by language. The proposed model resolves long-standing issues: how the brain learns correct words-object associations; why animals do not talk and think like people. We propose the role played by language emotionality in its interaction with thought. We relate the mathematical model to Humboldt’s “firmness” of languages; and discuss possible influence of language grammar on its emotionality. Psychological and brain imaging experiments related to the proposed model are discussed. Future theoretical and experimental research is outlined. PMID:21673788

  16. Curriculum-Based Language Assessment With Culturally and Linguistically Diverse Students in the Context of Mathematics.

    PubMed

    Newkirk-Turner, Brandi L; Johnson, Valerie E

    2018-04-05

    The purpose of this tutorial is to discuss the use of curriculum-based language assessment (CBLA) with students who are English language learners and students who speak nonmainstream varieties of English, such as African American English. The article begins with a discussion of the discourse of mathematics and the role of the speech-language pathologist (SLP), followed by a review of studies that includes those that examined the performance of English language learner and nonmainstream dialect-speaking students on word-based math items. The literature review highlights the linguistic and content biases associated with word-based math problems. Useful strategies that SLPs and educators can incorporate in culturally and linguistically appropriate assessments are discussed. The tutorial ends with a discussion of CBLA as a viable assessment approach to use with culturally and linguistically diverse students. Tests used at national, state, and school levels to assess students' math abilities have associated linguistic bias and content bias often leading to an inaccurate depiction of culturally and linguistically diverse students' math skills. CBLA as an assessment method can be used by school-based SLPs to gather valid and useful information about culturally and linguistically diverse students' language for learning math. By using CBLA, SLPs can help modify curricular tasks in broader contexts in an effort to make math, including high-level math, "accessible and achievable for all" students (American Speech-Language-Hearing Association, 2017).

  17. Understanding words, understanding numbers: an exploration of the mathematical profiles of poor comprehenders.

    PubMed

    Pimperton, Hannah; Nation, Kate

    2010-06-01

    Poor comprehenders are children who show significant deficits in their reading comprehension performance, despite average, or above-average word reading ability. To date, there have been no in-depth studies of the mathematical performance profiles of such children. This study aimed to explore the mathematical profiles of poor comprehenders. Given that language impairment is associated with difficulties with mathematics, and that poor comprehenders tend to have oral language weaknesses, we hypothesized that poor comprehenders would show relative weaknesses in aspects of mathematical performance. From a sample of 109 children aged 7-8 years, we selected 14 poor comprehenders and 14 controls with age-appropriate reading comprehension ability. The groups were matched on non-verbal ability, multiple measures of reading accuracy, and chronological age. We compared the performance of the group of poor comprehenders with that of the matched controls on two standardized measures of mathematical ability, one measuring procedural arithmetic prowess and the other tapping higher-level mathematical reasoning. Although there were no group differences in performance on the arithmetic measure, the poor comprehenders showed significantly lower scores than the controls on the mathematical reasoning task. The poor comprehenders exhibited impaired verbal ability relative to controls, with these differences in verbal ability associated with the group differences found on the test of mathematical reasoning. Poor comprehenders' deficits are not limited to the domain of literacy; their underlying profile of impairments also seems to selectively impact on certain components of mathematical ability.

  18. "Just Don't": The Suppression and Invitation of Dialogue in the Mathematics Classroom

    ERIC Educational Resources Information Center

    Wagner, David; Herbel-Eisenmann, Beth

    2008-01-01

    Responding to concerns raised by grade 11 mathematics students, we examined a broad set of mathematics classroom transcripts from multiple teachers to examine how the word "just" was and could be used to suppress and invite dialogue. We used corpus linguistics tools to process and quantify the large body of text, not to describe the nature of the…

  19. A new cognitive rehabilitation programme for patients with multiple sclerosis: the 'MS-line! Project'.

    PubMed

    Gich, Jordi; Freixenet, Jordi; Garcia, Rafael; Vilanova, Joan Carles; Genís, David; Silva, Yolanda; Montalban, Xavier; Ramió-Torrentà, Lluís

    2015-09-01

    Cognitive rehabilitation is often delayed in multiple sclerosis (MS). To develop a free and specific cognitive rehabilitation programme for MS patients to be used from early stages that does not interfere with daily living activities. MS-line!, cognitive rehabilitation materials consisting of written, manipulative and computer-based materials with difficulty levels developed by a multidisciplinary team. Mathematical, problem-solving and word-based exercises were designed. Physical materials included spatial, coordination and reasoning games. Computer-based material included logic and reasoning, working memory and processing speed games. Cognitive rehabilitation exercises that are specific for MS patients have been successfully developed. © The Author(s), 2014.

  20. Children and adolescents' performance on a medium-length/nonsemantic word-list test.

    PubMed

    Flores-Lázaro, Julio César; Salgado Soruco, María Alejandra; Stepanov, Igor I

    2017-01-01

    Word-list learning tasks are among the most important and frequently used tests for declarative memory evaluation. For example, the California Verbal Learning Test-Children's Version (CVLT-C) and Rey Auditory Verbal Learning Test provide important information about different cognitive-neuropsychological processes. However, the impact of test length (i.e., number of words) and semantic organization (i.e., type of words) on children's and adolescents' memory performance remains to be clarified, especially during this developmental stage. To explore whether a medium-length non-semantically organized test can produce the typical curvilinear performance that semantically organized tests produce, reflecting executive control, we studied and compared the cognitive performance of normal children and adolescents by utilizing mathematical modeling. The model is based on the first-order system transfer function and has been successfully applied to learning curves for the CVLT-C (15 words, semantically organized paradigm). Results indicate that learning nine semantically unrelated words produces typical curvilinear (executive function) performance in children and younger adolescents and that performance could be effectively analyzed with the mathematical model. This indicates that the exponential increase (curvilinear performance) of correctly learned words does not solely depend on semantic and/or length features. This type of test controls semantic and length effects and may represent complementary tools for executive function evaluation in clinical populations in which semantic and/or length processing are affected.

  1. Using Self-Generated Drawings to Solve Arithmetic Word Problems.

    ERIC Educational Resources Information Center

    Van Essen, Gerard; Hamaker, Christiaan

    1990-01-01

    Results are presented from two intervention studies which investigate whether encouraging elementary students to generate drawings of arithmetic word problems facilitates problem-solving performance. Findings indicate that fifth graders (N=50) generated many drawings of word problems and improved problem solutions after the intervention, whereas…

  2. Case Study: Students’ Symbolic Manipulation in Calculus Among UTHM Students

    NASA Astrophysics Data System (ADS)

    Ali, Maselan; Sufahani, Suliadi; Ahmad, Wan N. A. W.; Ghazali Kamardan, M.; Saifullah Rusiman, Mohd; Che-Him, Norziha

    2018-04-01

    Words are symbols representing certain aspects of mathematics. The main purpose of this study is to gain insight into students’ symbolic manipulation in calculus among UTHM students. This study make use the various methods in collecting data which are documentation, pilot study, written test and follow up individual interviews. Hence, the results analyzed and interpreted based on action-process-object-schema framework which is based on Piaget’s ideas of reflective abstraction, the concept of relational and instrumental understanding and the zone of proximal development idea. The students’ reply in the interview session is analyzed and then the overall performance is discussed briefly to relate with the students flexibility in symbolic manipulation in linking to the graphical idea, the students interpretation towards different symbolic structure in calculus and the problem that related to overgeneralization in their calculus problems solving.

  3. Signs for Instructional Purposes.

    ERIC Educational Resources Information Center

    Kannapell, Barbara M.; And Others

    Illustrations depict 465 new manual signs for use in high school and college instruction of deaf students. The signs represent words or phrases, usually made up of many letters, which are important to the following subject matters; sciences and mathematics (general terms), biology, chemistry, mathematics, physics, psychology, humanities (general…

  4. Translating concepts of complexity to the field of ergonomics.

    PubMed

    Walker, Guy H; Stanton, Neville A; Salmon, Paul M; Jenkins, Daniel P; Rafferty, Laura

    2010-10-01

    Since 1958 more than 80 journal papers from the mainstream ergonomics literature have used either the words 'complex' or 'complexity' in their titles. Of those, more than 90% have been published in only the past 20 years. This observation communicates something interesting about the way in which contemporary ergonomics problems are being understood. The study of complexity itself derives from non-linear mathematics but many of its core concepts have found analogies in numerous non-mathematical domains. Set against this cross-disciplinary background, the current paper aims to provide a similar initial mapping to the field of ergonomics. In it, the ergonomics problem space, complexity metrics and powerful concepts such as emergence raise complexity to the status of an important contingency factor in achieving a match between ergonomics problems and ergonomics methods. The concept of relative predictive efficiency is used to illustrate how this match could be achieved in practice. What is clear overall is that a major source of, and solution to, complexity are the humans in systems. Understanding complexity on its own terms offers the potential to leverage disproportionate effects from ergonomics interventions and to tighten up the often loose usage of the term in the titles of ergonomics papers. STATEMENT OF RELEVANCE: This paper reviews and discusses concepts from the study of complexity and maps them to ergonomics problems and methods. It concludes that humans are a major source of and solution to complexity in systems and that complexity is a powerful contingency factor, which should be considered to ensure that ergonomics approaches match the true nature of ergonomics problems.

  5. Mathematical values in the processing of Chinese numeral classifiers and measure words.

    PubMed

    Her, One-Soon; Chen, Ying-Chun; Yen, Nai-Shing

    2017-01-01

    A numeral classifier is required between a numeral and a noun in Chinese, which comes in two varieties, sortal classifer (C) and measural classifier (M), also known as 'classifier' and 'measure word', respectively. Cs categorize objects based on semantic attributes and Cs and Ms both denote quantity in terms of mathematical values. The aim of this study was to conduct a psycholinguistic experiment to examine whether participants process C/Ms based on their mathematical values with a semantic distance comparison task, where participants judged which of the two C/M phrases was semantically closer to the target C/M. Results showed that participants performed more accurately and faster for C/Ms with fixed values than the ones with variable values. These results demonstrated that mathematical values do play an important role in the processing of C/Ms. This study may thus shed light on the influence of the linguistic system of C/Ms on magnitude cognition.

  6. Does understanding relational terminology mediate effects of intervention on compare word problems?

    PubMed

    Schumacher, Robin F; Fuchs, Lynn S

    2012-04-01

    The purpose of this study was to assess whether understanding relational terminology (i.e., more, less, and fewer) mediates the effects of intervention on compare word problems. Second-grade classrooms (N=31) were randomly assigned to one of three conditions: researcher-designed word-problem intervention, researcher-designed calculation intervention, or business-as-usual (teacher-designed) control. Students in word-problem intervention classrooms received instruction on the compare problem type, which included a focus on understanding relational terminology within compare word problems. Analyses, which accounted for variance associated with classroom clustering, indicated that (a) compared with the calculation intervention and business-as-usual conditions, word-problem intervention significantly increased performance on all three subtypes of compare problems and on understanding relational terminology, and (b) the intervention effect was fully mediated by students' understanding of relational terminology for one subtype of compare problems and partially mediated by students' understanding of relational terminology for the other two subtypes. Copyright © 2011 Elsevier Inc. All rights reserved.

  7. SCOPE (Standardized Curriculum-Oriented Pupil Evaluation) Mathematics. Test Book Grade Three.

    ERIC Educational Resources Information Center

    Northwest Territories Dept. of Education, Yellowknife. Programs and Evaluation Branch.

    Following instructions provided in the teacher's manual, the SCOPE Mathematics Achievement Test booklet for grade 3 presents 11 mathematical concepts. Testing items include: skip counting by 2's, 5's, and 10's to 100, 3's to 30, and 4's to 40; writing number words to 20; identifying and naming 100's, 10's, and 1's in three-digit numerals; reading…

  8. Find the Dimensions: Students Solving a Tiling Problem

    ERIC Educational Resources Information Center

    Obara, Samuel

    2018-01-01

    Students learn mathematics by solving problems. Mathematics textbooks are full of problems, and mathematics teachers use these problems to test students' understanding of mathematical concepts. This paper discusses how problem-solving skills can be fostered with a geometric tiling problem.

  9. What Makes a Problem Mathematically Interesting? Inviting Prospective Teachers to Pose Better Problems

    ERIC Educational Resources Information Center

    Crespo, Sandra; Sinclair, Nathalie

    2008-01-01

    School students of all ages, including those who subsequently become teachers, have limited experience posing their own mathematical problems. Yet problem posing, both as an act of mathematical inquiry and of mathematics teaching, is part of the mathematics education reform vision that seeks to promote mathematics as an worthy intellectual…

  10. Three-M in Word Problem Solving

    ERIC Educational Resources Information Center

    Hajra, Sayonita Ghosh; Kofman, Victoria

    2018-01-01

    We describe three activities that help undergraduates (pre-service teachers) to develop scientific vocabulary on measurable attributes and units of measurement. Measurable attributes are important features in understanding a word problem and solving the problem. These activities help students comprehend word problems better by identifying…

  11. Patterns of similarity and difference between the vocabularies of psychology and other subjects.

    PubMed

    Benjafield, John G

    2014-02-01

    The vocabulary of Anglophone psychology is shared with many other subjects. Previous research using the Oxford English Dictionary has shown that the subjects having the most words in common with psychology are biology, chemistry, computing, electricity, law, linguistics, mathematics, medicine, music, pathology, philosophy, and physics. The present study presents a database of the vocabularies of these 12 subjects that is similar to one previously constructed for psychology, enabling the histories of the vocabularies of these subjects to be compared with each other as well as with psychology. All subjects have a majority of word senses that are metaphorical. However, psychology is not among the most metaphorical of subjects, a distinction belonging to computing, linguistics, and mathematics. Indeed, the history of other subjects shows an increasing tendency to recycle old words and give them new, metaphorical meanings. The history of psychology shows an increasing tendency to invent new words rather than metaphorical senses of existing words. These results were discussed in terms of the degree to which psychology's vocabulary remains unsettled in comparison with other subjects. The possibility was raised that the vocabulary of psychology is in a state similar to that of chemistry prior to Lavoisier.

  12. Writing in Maths

    ERIC Educational Resources Information Center

    Australian Primary Mathematics Classroom, 2009

    2009-01-01

    Students write definitions or explanations of mathematical words or symbols in their own words. These can be collated and added to as the year progresses to form a class dictionary that all students can access as required, or students could create their own personal dictionaries. This article presents a collection of ideas for incorporating…

  13. Learning the Language of Statistics: Challenges and Teaching Approaches

    ERIC Educational Resources Information Center

    Dunn, Peter K.; Carey, Michael D.; Richardson, Alice M.; McDonald, Christine

    2016-01-01

    Learning statistics requires learning the language of statistics. Statistics draws upon words from general English, mathematical English, discipline-specific English and words used primarily in statistics. This leads to many linguistic challenges in teaching statistics and the way in which the language is used in statistics creates an extra layer…

  14. Barely started and already left behind: a descriptive analysis of the mathematics ability demonstrated by young deaf children.

    PubMed

    Kritzer, Karen L

    2009-01-01

    This study examined young deaf children's early informal/formal mathematical knowledge as measured by the Test of Early Mathematics Ability (TEMA-3). Findings from this study suggest that prior to the onset of formal schooling, young deaf children might already demonstrate evidence of academic delays. Of these 28 participants (4-6 years of age), for whom data were analyzed, none received a score on the TEMA-3, indicating above-"average" ability according to normative ranking. More than half of participants received scores substantially below average with 11 participants receiving scores a year or more behind normative age-equivalent scores. Upon more focused analysis, specific areas of difficulty were found to include word/story problems, skip counting (i.e., counting by twos, threes, etc.), number comparisons, the reading/writing of two to three digit numbers, and addition/subtraction number facts. A qualitative analysis of the answers participants gave and the behaviors they demonstrated while answering the test items was conducted and revealed possible explanations for why specific test items may have been challenging. Implications of findings for parents, early interventionists, and teachers of young deaf children are discussed.

  15. Show Me a Sign

    ERIC Educational Resources Information Center

    Wilson, Johnnie

    2012-01-01

    According to the author, much of their math teaching is through pictures and words. They write number sentences, they draw geometric figures, and they talk about math. The representations they use--numbers, shapes, operators, and mathematics vocabulary--make it possible for them to learn and communicate mathematical ideas. These representations…

  16. Pupils' over-reliance on linearity: a scholastic effect?

    PubMed

    Van Dooren, Wim; De Bock, Dirk; Janssens, Dirk; Verschaffel, Lieven

    2007-06-01

    From upper elementary education on, children develop a tendency to over-use linearity. Particularly, it is found that many pupils assume that if a figure enlarges k times, the area enlarges k times too. However, most research was conducted with traditional, school-like word problems. This study examines whether pupils also over-use linearity if non-linear problems are embedded in meaningful, authentic performance tasks instead of traditional, school-like word problems, and whether this experience influences later behaviour. Ninety-three sixth graders from two primary schools in Flanders, Belgium. Pupils received a pre-test with traditional word problems. Those who made a linear error on the non-linear area problem were subjected to individual interviews. They received one new non-linear problem, in the S-condition (again a traditional, scholastic word problem), D-condition (the same word problem with a drawing) or P-condition (a meaningful performance-based task). Shortly afterwards, pupils received a post-test, containing again a non-linear word problem. Most pupils from the S-condition displayed linear reasoning during the interview. Offering drawings (D-condition) had a positive effect, but presenting the problem as a performance task (P-condition) was more beneficial. Linear reasoning was nearly absent in the P-condition. Remarkably, at the post-test, most pupils from all three groups again applied linear strategies. Pupils' over-reliance on linearity seems partly elicited by the school-like word problem format of test items. Pupils perform much better if non-linear problems are offered as performance tasks. However, a single experience does not change performances on a comparable word problem test afterwards.

  17. Error Analysis for Arithmetic Word Problems--A Case Study of Primary Three Students in One Singapore School

    ERIC Educational Resources Information Center

    Cheng, Lu Pien

    2015-01-01

    In this study, ways in which 9-year old students from one Singapore school solved 1-step and 2-step word problems based on the three semantic structures were examined. The students' work and diagrams provided insights into the range of errors in word problem solving for 1- step and 2-step word problems. In particular, the errors provided some…

  18. Some unsolved problems in discrete mathematics and mathematical cybernetics

    NASA Astrophysics Data System (ADS)

    Korshunov, Aleksei D.

    2009-10-01

    There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

  19. Adult Gesture in Collaborative Mathematics Reasoning in Different Ages

    NASA Astrophysics Data System (ADS)

    Noto, M. S.; Harisman, Y.; Harun, L.; Amam, A.; Maarif, S.

    2017-09-01

    This article describes the case study on postgraduate students by using descriptive method. A problem is designed to facilitate the reasoning in the topic of Chi-Square test. The problem was given to two male students with different ages to investigate the gesture pattern and it will be related to their reasoning process. The indicators in reasoning problem can obtain the conclusion of analogy and generalization, and arrange the conjectures. This study refers to some questions—whether unique gesture is for every individual or to identify the pattern of the gesture used by the students with different ages. Reasoning problem was employed to collect the data. Two students were asked to collaborate to reason the problem. The discussion process recorded in using video tape to observe the gestures. The video recorded are explained clearly in this writing. Prosodic cues such as time, conversation text, gesture that appears, might help in understanding the gesture. The purpose of this study is to investigate whether different ages influences the maturity in collaboration observed from gesture perspective. The finding of this study shows that age is not a primary factor that influences the gesture in that reasoning process. In this case, adult gesture or gesture performed by order student does not show that he achieves, maintains, and focuses on the problem earlier on. Adult gesture also does not strengthen and expand the meaning if the student’s words or the language used in reasoning is not familiar for younger student. Adult gesture also does not affect cognitive uncertainty in mathematics reasoning. The future research is suggested to take more samples to find the consistency from that statement.

  20. Neuro-Cognitive Intervention for Working Memory: Preliminary Results and Future Directions.

    PubMed

    Bree, Kathleen D; Beljan, Paul

    2016-01-01

    Definitions of working memory identify it as a function of the executive function system in which an individual maintains two or more pieces of information in mind and uses that information simultaneously for some purpose. In academics, working memory is necessary for a variety of functions, including attending to the information one's teacher presents and then using that information simultaneously for problem solving. Research indicates difficulties with working memory are observed in children with mathematics learning disorder (MLD) and reading disorders (RD). To improve working memory and other executive function difficulties, and as an alternative to medication treatments for attention and executive function disorders, the Motor Cognition(2)® (MC(2)®)program was developed. Preliminary research on this program indicates statistically significant improvements in working memory, mathematics, and nonsense word decoding for reading. Further research on the MC(2)® program and its impact on working memory, as well as other areas of executive functioning, is warranted.

  1. The problem-solving approach in the teaching of number theory

    NASA Astrophysics Data System (ADS)

    Toh, Pee Choon; Hoong Leong, Yew; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Guan Tay, Eng; Him Ho, Foo

    2014-02-01

    Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to adopt a Pólya-style approach in learning mathematics. The Practical Worksheet is an instructional scaffold we adopted to help our pre-service mathematics teachers develop problem-solving dispositions alongside the learning of the subject matter. The Worksheet was initially used in a design experiment aimed at teaching problem solving in a secondary school. In this paper, we describe an application and adaptation of the MProSE (Mathematical Problem Solving for Everyone) design experiment to a university level number theory course for pre-service mathematics teachers. The goal of the enterprise was to help the pre-service mathematics teachers develop problem-solving dispositions alongside the learning of the subject matter. Our analysis of the pre-service mathematics teachers' work shows that the MProSE design holds promise for mathematics courses at the tertiary level.

  2. Word Problems: A "Meme" for Our Times.

    ERIC Educational Resources Information Center

    Leamnson, Robert N.

    1996-01-01

    Discusses a novel approach to word problems that involves linear relationships between variables. Argues that working stepwise through intermediates is the way our minds actually work and therefore this should be used in solving word problems. (JRH)

  3. Graphing and Percentage Applications Using the Personal Computer.

    ERIC Educational Resources Information Center

    Innes, Jay

    1985-01-01

    The paper describes how "IBM Graphing Assistant" and "Apple Softgraph" can foster a multifaceted approach to application of mathematical concepts and how a survey can be undertaken using the computer as word processor, data bank, and source of visual displays. Mathematical skills reinforced include estimating, rounding, graphing, and solving…

  4. Specific Early Number Skills Mediate the Association between Executive Functioning Skills and Mathematics Achievement

    ERIC Educational Resources Information Center

    Fuhs, Mary Wagner; Hornburg, Caroline Byrd; McNeil, Nicole M.

    2016-01-01

    A growing literature reports significant associations between children's executive functioning skills and their mathematics achievement. The purpose of this study was to examine if specific early number skills, such as quantity discrimination, number line estimation, number sets identification, fast counting, and number word comprehension, mediate…

  5. Pre-Algebra Lexicon.

    ERIC Educational Resources Information Center

    Hayden, Dunstan; Cuevas, Gilberto

    The pre-algebra lexicon is a set of classroom exercises designed to teach the technical words and phrases of pre-algebra mathematics, and includes the terms most commonly found in related mathematics courses. The lexicon has three parts, each with its own introduction. The first introduces vocabulary items in three groups forming a learning…

  6. Cactus: Writing an Article

    ERIC Educational Resources Information Center

    Hyde, Hartley; Spencer, Toby

    2010-01-01

    Some people became mathematics or science teachers by default. There was once such a limited range of subjects that students who could not write essays did mathematics and science. Computers changed that. Word processor software helped some people overcome huge spelling and grammar hurdles and made it easy to edit and manipulate text. Would-be…

  7. Deaf College Students' Mathematical Skills Relative to Morphological Knowledge, Reading Level, and Language Proficiency

    ERIC Educational Resources Information Center

    Kelly, Ronald R.; Gaustad, Martha G.

    2007-01-01

    This study of deaf college students examined specific relationships between their mathematics performance and their assessed skills in reading, language, and English morphology. Simple regression analyses showed that deaf college students' language proficiency scores, reading grade level, and morphological knowledge regarding word segmentation and…

  8. Ethical Concerns: Negotiating Truth and Trust

    ERIC Educational Resources Information Center

    McGarvey, Lynn M.; Sterenberg, Gladys

    2009-01-01

    Few studies in mathematics education explicitly address ethical issues arising from student interactions. The ethical concerns held by students are expressed in their words, actions, and interactions. The purpose of this article is to explore the ethical nature of copying as it arises in a mathematics classroom. We investigate the basis for…

  9. The Ideology of Certainty in Mathematics Education.

    ERIC Educational Resources Information Center

    Borba, Marcelo C.; Skovsmose, Ole

    1997-01-01

    Presents one aspect that makes mathematics the final word in many discussions, the ideology of certainty. Argues that one way of challenging the ideology of certainty is to change classroom practice by introducing a landscape of discussion on chaotic nature where relativity, provisional starting points, different points of view, and uncertainty…

  10. Mathematical versus English Meaning in Implication and Disjunction

    ERIC Educational Resources Information Center

    Shipman, Barbara A.

    2013-01-01

    As mathematicians, we assign rigid meanings to words that may have a variety of interpretations in common language. This article considers meanings of "if" and "or" from everyday English that have caused students to misinterpret mathematical statements, and that are consistently overlooked by instructional materials in addressing students'…

  11. Radical Thoughts on Simplifying Square Roots

    ERIC Educational Resources Information Center

    Schultz, Kyle T.; Bismarck, Stephen F.

    2013-01-01

    A picture is worth a thousand words. This statement is especially true in mathematics teaching and learning. Visual representations such as pictures, diagrams, charts, and tables can illuminate ideas that can be elusive when displayed in symbolic form only. The prevalence of representation as a mathematical process in such documents as…

  12. Problem Solving: How Do In-Service Secondary School Teachers of Mathematics Make Sense of a Non-Routine Problem Context?

    ERIC Educational Resources Information Center

    Mwei, Philip K.

    2017-01-01

    The concept of mathematical problem solving is an important mathematical process in mathematics curricula of education systems worldwide. These math curricula demand that learners are exposed to authentic problems that foster successful problem solving. To attain this very important goal, there must be mathematics teachers well versed in content…

  13. Evaluating the Suitability of Mathematical Thinking Problems for Senior High-School Students by Including Mathematical Sense Making and Global Planning

    ERIC Educational Resources Information Center

    van Velzen, Joke H.

    2016-01-01

    The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…

  14. Students’ Mathematical Problem-Solving Abilities Through The Application of Learning Models Problem Based Learning

    NASA Astrophysics Data System (ADS)

    Nasution, M. L.; Yerizon, Y.; Gusmiyanti, R.

    2018-04-01

    One of the purpose mathematic learning is to develop problem solving abilities. Problem solving is obtained through experience in questioning non-routine. Improving students’ mathematical problem-solving abilities required an appropriate strategy in learning activities one of them is models problem based learning (PBL). Thus, the purpose of this research is to determine whether the problem solving abilities of mathematical students’ who learn to use PBL better than on the ability of students’ mathematical problem solving by applying conventional learning. This research included quasi experiment with static group design and population is students class XI MIA SMAN 1 Lubuk Alung. Class experiment in the class XI MIA 5 and class control in the class XI MIA 6. The instrument of final test students’ mathematical problem solving used essay form. The result of data final test in analyzed with t-test. The result is students’ mathematical problem solving abilities with PBL better then on the ability of students’ mathematical problem solving by applying conventional learning. It’s seen from the high percentage achieved by the group of students who learn to use PBL for each indicator of students’ mathematical problem solving.

  15. The Performance of Chinese Primary School Students on Realistic Arithmetic Word Problems

    ERIC Educational Resources Information Center

    Xin, Ziqiang; Lin, Chongde; Zhang, Li; Yan, Rong

    2007-01-01

    Compared with standard arithmetic word problems demanding only the direct use of number operations and computations, realistic problems are harder to solve because children need to incorporate "real-world" knowledge into their solutions. Using the realistic word problem testing materials developed by Verschaffel, De Corte, and Lasure…

  16. Mapping among Number Words, Numerals, and Nonsymbolic Quantities in Preschoolers

    ERIC Educational Resources Information Center

    Hurst, Michelle; Anderson, Ursula; Cordes, Sara

    2017-01-01

    In mathematically literate societies, numerical information is represented in 3 distinct codes: a verbal code (i.e., number words); a digital, symbolic code (e.g., Arabic numerals); and an analogical code (i.e., quantities; Dehaene, 1992). To communicate effectively using these numerical codes, our understanding of number must involve an…

  17. Using Cognitive Tutor Software in Learning Linear Algebra Word Concept

    ERIC Educational Resources Information Center

    Yang, Kai-Ju

    2015-01-01

    This paper reports on a study of twelve 10th grade students using Cognitive Tutor, a math software program, to learn linear algebra word concept. The study's purpose was to examine whether students' mathematics performance as it is related to using Cognitive Tutor provided evidence to support Koedlinger's (2002) four instructional principles used…

  18. The Music of Mathematics: Toward a New Problem Typology

    NASA Astrophysics Data System (ADS)

    Quarfoot, David

    Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?". In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the journey by cataloging the features of problems delineated by the mathematics and mathematics education communities. These dimensions are explored in a large data set of students working thousands of problems at the Art of Problem Solving, an online company that provides adaptive mathematical training for students around the world. This analysis is able to concretely show how the fabric of mathematical problems changes across different subjects, difficulty levels, and students. Furthermore, it locates problems that stand out in the crowd -- those that synergize cognitive engagement, learning, and difficulty. This quantitatively-heavy side of the dissertation is partnered with a qualitatively-inspired portion that involves human scoring of 105 problems and their solutions. In this setting, I am able to capture elusive features of mathematical problems and derive a fuller picture of the space of mathematical problems. Using correlation matrices, principal components analysis, and clustering techniques, I explore the relationships among those features frequently discussed in mathematics problems (e.g., difficulty, creativity, novelty, affective engagement, authenticity). Along the way, I define a new set of uncorrelated features in problems and use these as the basis for a New Mathematical Problem Typology (NMPT). Grounded in the terminology of classical music, the NMPT works to quickly convey the essence and value of a problem, just as terms like "etude" and "mazurka" do for musicians. Taken together, these quantitative and qualitative analyses seek to terraform the landscape of mathematical problems and, concomitantly, the current thinking about that world. Most importantly, this work highlights and names the panoply of problems that exist, expanding the myopic vision of contemporary mathematical problem solving.

  19. Problem Posing with the Multiplication Table

    ERIC Educational Resources Information Center

    Dickman, Benjamin

    2014-01-01

    Mathematical problem posing is an important skill for teachers of mathematics, and relates readily to mathematical creativity. This article gives a bit of background information on mathematical problem posing, lists further references to connect problem posing and creativity, and then provides 20 problems based on the multiplication table to be…

  20. Unraveling the Mystery of the Origin of Mathematical Problems: Using a Problem-Posing Framework with Prospective Mathematics Teachers

    ERIC Educational Resources Information Center

    Contreras, Jose

    2007-01-01

    In this article, I model how a problem-posing framework can be used to enhance our abilities to systematically generate mathematical problems by modifying the attributes of a given problem. The problem-posing model calls for the application of the following fundamental mathematical processes: proving, reversing, specializing, generalizing, and…

  1. Problem solving in the borderland between mathematics and physics

    NASA Astrophysics Data System (ADS)

    Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas

    2017-01-01

    The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems, where a major challenge is to formalize the problems in mathematics and physics terms. We analyse four concrete examples of unformalized problems for which the formalization involves different order of mathematization and applying physics to the problem, but all require mathematization. The analysis leads to the formulation of a model by which we attempt to capture the important steps of the process of solving unformalized problems by means of mathematization and physicalization.

  2. The Definition of Mathematics: Philosophical and Pedagogical Aspects

    NASA Astrophysics Data System (ADS)

    Khait, Alexander

    There is a strange fact that many works written with the purpose to explain what is mathematics, somehow avoid the issue. This paper is aimed at filling this gap. After discussing various descriptions of mathematics as they appear in literature, it is suggested that mathematics is an essentially linguistic activity characterized by association of words with precise meanings. Educational implications of this idea are considered in the light of(1) a strong tendency of most humans to the fuzzy way of thought as described by the dual-process theory developed by researchers of human reasoning;

  3. Attentional Cuing in Math Word Problems for Girls At-Risk for ADHD and Their Peers in General Education Settings

    ERIC Educational Resources Information Center

    Kercood, Suneeta; Zentall, Sydney S.; Vinh, Megan; Tom-Wright, Kinsey

    2012-01-01

    The purpose of this theoretically-based study was to examine the effects of yellow-highlighting "relevant" words and units within math word problems. Initial differences were documented between 10 girls at-risk for ADHD and 10 comparisons on the performance of group and individual assessments of math computations and word problems, as had…

  4. Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

    NASA Astrophysics Data System (ADS)

    Fasni, N.; Turmudi, T.; Kusnandi, K.

    2017-09-01

    This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

  5. Computer Courseware Evaluations. A Series of Reports Compiled by the Clearinghouse Computer Technology Project.

    ERIC Educational Resources Information Center

    Alberta Dept. of Education, Edmonton.

    This report reviews Apple computer courseware in business education, library skills, mathematics, science, special education, and word processing based on the curricular requirements of Alberta, Canada. It provides detailed evaluations of 23 authorized titles in business education (2), mathematics (20), and science (1); 3 of the math titles are…

  6. Increasing Communication in Geometry by Using a Personal Math Concept Chart

    ERIC Educational Resources Information Center

    Friedman, Rhonda; Kazerouni, Gety; Lax, Stacey; Weisdorf, Elli

    2011-01-01

    The action research team developed a "Personal Math Concept Chart". This chart required students to describe the mathematical concepts that they were studying in the Geometry strand of Mathematics using their own images and words. In this study, students were encouraged to express their own understanding of geometric concepts in order to…

  7. "Universal Responsiveness" or "Splendid Isolation?" Episodes from the History of Mathematics Education in Russia

    ERIC Educational Resources Information Center

    Karp, Alexander

    2006-01-01

    This article investigates the prevalent attitudes toward foreign influences and methodologies in Russian mathematics education at different periods in Russian history. The words "universal responsiveness" belong to Dostoevsky, who, in his famous speech on Pushkin, used them to characterize Pushkin's openness to the genius of all other…

  8. In Their Own Words: Getting Pumped for Calculus

    ERIC Educational Resources Information Center

    Cardetti, Fabiana; McKenna, P. J.

    2011-01-01

    By understanding what motivates students to learn mathematics, instructors can adapt their teaching strategies to help students achieve a level of engagement conducive to learning mathematics. There is a substantial body of research on motivations and academic achievement at the elementary and high school levels, but less is known at the college…

  9. Environmental Print Activities for Teaching Mathematics and Content Areas.

    ERIC Educational Resources Information Center

    Rule, Audrey C., Ed.; McIntyre, Sandra, Ed.; Ranous, Meg, Ed.

    Twenty-three mathematics activities that use environmental print materials are presented, along with two activities that focus on music education, one that highlights history concepts, and five science activities. The environmental print materials are words and images cut from food or other product packaging and mounted on mat board cards.…

  10. Writing in Groups as a Tool for Non-Routine Problem Solving in First Year University Mathematics

    ERIC Educational Resources Information Center

    Taylor, J. A.; McDonald, C.

    2007-01-01

    Development of mathematical problem solving skills is an age old problem in mathematics. This paper details the design of a component of a first year university mathematics course in which group work and mathematical communication skills, especially writing skills, are used as a tool to develop non-routine problem solving skills. In this design…

  11. Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

    NASA Astrophysics Data System (ADS)

    E Siswono, T. Y.; Kohar, A. W.; Hartono, S.

    2017-02-01

    This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.

  12. Pathways to Third-Grade Calculation versus Word-Reading Competence: Are They More Alike or Different?

    ERIC Educational Resources Information Center

    Fuchs, Lynn S.; Geary, David C.; Fuchs, Douglas; Compton, Donald L.; Hamlett, Carol L.

    2016-01-01

    Children (n = 747; 6.5 years) were assessed on domain-general processes and mathematics and reading-related competencies (start of first grade), addition retrieval (end of second grade), and calculations and word reading (end of third grade). Attentive behavior, reasoning, visuospatial memory, and rapid automatized naming (RAN) indirectly…

  13. What Can Graph Theory Tell Us about Word Learning and Lexical Retrieval?

    ERIC Educational Resources Information Center

    Vitevitch, Michael S.

    2008-01-01

    Purpose: Graph theory and the new science of networks provide a mathematically rigorous approach to examine the development and organization of complex systems. These tools were applied to the mental lexicon to examine the organization of words in the lexicon and to explore how that structure might influence the acquisition and retrieval of…

  14. Studies of Braille Reading Rates and Implications for the Unified English Braille Code

    ERIC Educational Resources Information Center

    Wetzel, Robin; Knowlton, Marie

    2006-01-01

    Reading rate data was collected from both print and braille readers in the areas of mathematics and literary braille. Literary braille data was collected for contracted and uncontracted braille text with dropped whole-word contractions and part-word contractions as they would appear in the Unified English Braille Code. No significant differences…

  15. Pre-service mathematics teachers’ ability in solving well-structured problem

    NASA Astrophysics Data System (ADS)

    Paradesa, R.

    2018-01-01

    This study aimed to describe the mathematical problem-solving ability of undergraduate students of mathematics education in solving the well-structured problem. The type of this study was qualitative descriptive. The subjects in this study were 100 undergraduate students of Mathematics Education at one of the private universities in Palembang city. The data in this study was collected through two test items with essay form. The results of this study showed that, from the first problem, only 8% students can solve it, but do not check back again to validate the process. Based on a scoring rubric that follows Polya strategy, their answer satisfied 2 4 2 0 patterns. But, from the second problem, 45% students satisfied it. This is because the second problem imitated from the example that was given in learning process. The average score of undergraduate students mathematical problem-solving ability in solving well-structured problems showed 56.00 with standard deviation was 13.22. It means that, from 0 - 100 scale, undergraduate students mathematical problem-solving ability can be categorized low. From this result, the conclusion was undergraduate students of mathematics education in Palembang still have a problem in solving mathematics well-structured problem.

  16. Research Mathematicians' Practices in Selecting Mathematical Problems

    ERIC Educational Resources Information Center

    Misfeldt, Morten; Johansen, Mikkel Willum

    2015-01-01

    Developing abilities to create, inquire into, qualify, and choose among mathematical problems is an important educational goal. In this paper, we elucidate how mathematicians work with mathematical problems in order to understand this mathematical process. More specifically, we investigate how mathematicians select and pose problems and discuss to…

  17. Analysis of junior high school students' attempt to solve a linear inequality problem

    NASA Astrophysics Data System (ADS)

    Taqiyuddin, Muhammad; Sumiaty, Encum; Jupri, Al

    2017-08-01

    Linear inequality is one of fundamental subjects within junior high school mathematics curricula. Several studies have been conducted to asses students' perform on linear inequality. However, it can hardly be found that linear inequality problems are in the form of "ax + b < dx + e" with "a, d ≠ 0", and "a ≠ d" as it can be seen on the textbook used by Indonesian students and several studies. This condition leads to the research questions concerning students' attempt on solving a simple linear inequality problem in this form. In order to do so, the written test was administered to 58 students from two schools in Bandung followed by interviews. The other sources of the data are from teachers' interview and mathematics books used by students. After that, the constant comparative method was used to analyse the data. The result shows that the majority approached the question by doing algebraic operations. Interestingly, most of them did it incorrectly. In contrast, algebraic operations were correctly used by some of them. Moreover, the others performed expected-numbers solution, rewriting the question, translating the inequality into words, and blank answer. Furthermore, we found that there is no one who was conscious of the existence of all-numbers solution. It was found that this condition is reasonably due to how little the learning components concern about why a procedure of solving a linear inequality works and possibilities of linear inequality solution.

  18. Probing when Japanese junior high school students begin to feel difficulty in learning mathematics

    NASA Astrophysics Data System (ADS)

    Nishikawa, Tomoko; Izuta, Giido

    2017-05-01

    It is thought that the increasing number of Japanese students avoiding mathematics has become a serious problem in the last decades. Japanese junior high school students are learning the basic understanding and skills of mathematics during the years of mandatory education. To our knowledge, there are few reports about the time when Japanese junior high school students begin to feel difficulty in mathematics learning. The aim of this work is to examine this case. To accomplish this purpose, a typical public junior high school in a country city with 616 students (182 first-year, 212 second-year, 222 third-year) in all was chosen to be the field of investigation. Likert scale type questionnaires to assess their feelings were conducted, and the respondents who answered `difficulty' and `a little difficulty' were extracted. The number of respondents were 89 first-year (26 males, 63 females), 76 second-year (27 males, 49 females), and 112 third-year (45 males, 67 females) students. The beginning time was divided into school years when it was in elementary school, and semesters when it was in junior high school. Ordinary statistical processings for each grade and gender were performed to analyze them. It was found that the time when they began to have difficulty learning mathematics was different in gender. Male students tended to start from higher-grade of elementary school whereas female students from middle-grade of elementary school. In other words, these results showed differences in gender and time. Finally, these examinations suggest that teachers need to provide appropriate support for students at a suitable time in the elementary school. Also these results are useful in mathematics education of elementary school.

  19. A Comparative Analysis of a Generalized Lanchester Equation Model and a Stochastic Computer Simulation Model.

    DTIC Science & Technology

    1987-03-01

    model is one in which words or numerical descriptions are used to represent an entity or process. An example of a symbolic model is a mathematical ...are the third type of model used in modeling combat attrition. Analytical models are symbolic models which use mathematical symbols and equations to...simplicity and the ease of tracing through the mathematical computations. In this section I will discuss some of the shortcoming which have been

  20. Pre-Service Teachers' Free and Structured Mathematical Problem Posing

    ERIC Educational Resources Information Center

    Silber, Steven; Cai, Jinfa

    2017-01-01

    This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing…

  1. The Role of Expository Writing in Mathematical Problem Solving

    ERIC Educational Resources Information Center

    Craig, Tracy S.

    2016-01-01

    Mathematical problem-solving is notoriously difficult to teach in a standard university mathematics classroom. The project on which this article reports aimed to investigate the effect of the writing of explanatory strategies in the context of mathematical problem solving on problem-solving behaviour. This article serves to describe the…

  2. Using Diagrams as Tools for the Solution of Non-Routine Mathematical Problems

    ERIC Educational Resources Information Center

    Pantziara, Marilena; Gagatsis, Athanasios; Elia, Iliada

    2009-01-01

    The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems' structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first…

  3. The Problem-Solving Approach in the Teaching of Number Theory

    ERIC Educational Resources Information Center

    Toh, Pee Choon; Leong, Yew Hoong; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Tay, Eng Guan; Ho, Foo Him

    2014-01-01

    Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to…

  4. How Students Process Equations in Solving Quantitative Synthesis Problems? Role of Mathematical Complexity in Students' Mathematical Performance

    ERIC Educational Resources Information Center

    Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

    2017-01-01

    We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking,…

  5. Don't words come easy? A psychophysical exploration of word superiority

    PubMed Central

    Starrfelt, Randi; Petersen, Anders; Vangkilde, Signe

    2013-01-01

    Words are made of letters, and yet sometimes it is easier to identify a word than a single letter. This word superiority effect (WSE) has been observed when written stimuli are presented very briefly or degraded by visual noise. We compare performance with letters and words in three experiments, to explore the extents and limits of the WSE. Using a carefully controlled list of three letter words, we show that a WSE can be revealed in vocal reaction times even to undegraded stimuli. With a novel combination of psychophysics and mathematical modeling, we further show that the typical WSE is specifically reflected in perceptual processing speed: single words are simply processed faster than single letters. Intriguingly, when multiple stimuli are presented simultaneously, letters are perceived more easily than words, and this is reflected both in perceptual processing speed and visual short term memory (VSTM) capacity. So, even if single words come easy, there is a limit to the WSE. PMID:24027510

  6. Using the Relational Paradigm: Effects on Pupils' Reasoning in Solving Additive Word Problems

    ERIC Educational Resources Information Center

    Polotskaia, Elena; Savard, Annie

    2018-01-01

    Pupils' difficulties in solving word problems continue to attract attention: while researchers highlight the importance of relational reasoning and modelling, school curricula typically use short word problems to develop pupils' knowledge of arithmetic operations and calculation strategies. The Relational Paradigm attributes the leading role in…

  7. The effect of problem structure on problem-solving: an fMRI study of word versus number problems.

    PubMed

    Newman, Sharlene D; Willoughby, Gregory; Pruce, Benjamin

    2011-09-02

    It has long been thought that word problems are more difficult to solve than number/equation problems. However, recent findings have begun to bring this broadly believed idea into question. The current study examined the processing differences between these two types of problems. The behavioral results presented here failed to show an overwhelming advantage for number problems. In fact, there were more errors for the number problems than the word problems. The neuroimaging results reported demonstrate that there is significant overlap in the processing of what, on the surface, appears to be completely different problems that elicit different problem-solving strategies. Word and number problems rely on a general network responsible for problem-solving that includes the superior posterior parietal cortex, the horizontal segment of the intraparietal sulcus which is hypothesized to be involved in problem representation and calculation as well as the regions that have been linked to executive aspects of working memory such as the pre-SMA and basal ganglia. While overlap was observed, significant differences were also found primarily in language processing regions such as Broca's and Wernicke's areas for the word problems and the horizontal segment of the intraparietal sulcus for the number problems. Copyright © 2011 Elsevier B.V. All rights reserved.

  8. How do open-ended problems promote mathematical creativity? A reflection of bare mathematics problem and contextual problem

    NASA Astrophysics Data System (ADS)

    Wijaya, A.

    2018-03-01

    Creativity is often seen as one of the fundamental aspects of character education. As one of the 21st century skills, creativity has also been considered as an important goal of education across the world. This paper reports a study on promoting mathematical creativity through the use of open-ended mathematics problems. A total of 53 undergraduate students participated in the study. These students worked on open-ended problems in two types, i.e. bare mathematics problem and contextual problem. The contextual problem was presented in the form of paper-based and Geogebra-based. The students’ works were analysed qualitatively in order to describe how students’ mathematical creativity developed. It was found that the open-ended problems successfully promote students’ creativity as indicated by various solutions or strategies that were used by students to solve the problems. The analysis of students’ works show that students’ creativity developed through three kinds of exploration, i. e. (1) exploration of contexts, (2) exploration of software features, and (3) exploration of mathematics concepts. The use of metacognitive questioning was found to be helpful to develop the first two explorations into mathematical exploration.

  9. Proofs without Words: A Visual Application of Reasoning and Proof

    ERIC Educational Resources Information Center

    Bell, Carol J.

    2011-01-01

    Reasoning and Proof is one of the Process Standards set forth in National Council of Teachers of Mathematics' (NCTM) "Principles and Standards for School Mathematics." Thus, it is important to give students opportunities to build their reasoning skills and aid their understanding of the proof process. Teaching students how to do proofs is a…

  10. Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

    NASA Astrophysics Data System (ADS)

    Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

    2011-04-01

    'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

  11. What Is the Problem in Problem-Based Learning in Higher Education Mathematics

    ERIC Educational Resources Information Center

    Dahl, Bettina

    2018-01-01

    Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge…

  12. Learning to Solve Story Problems--Supporting Transitions between Reality and Mathematics

    ERIC Educational Resources Information Center

    Große, Cornelia S.

    2014-01-01

    Applying mathematics to real problems is increasingly emphasized in school education; however, it is often complained that many students are not able to solve mathematical problems embedded in contexts. In order to solve story problems, a transition from a textual description to a mathematical notation has to be found, intra-mathematical…

  13. Students’ Spatial Ability through Open-Ended Approach Aided by Cabri 3D

    NASA Astrophysics Data System (ADS)

    Priatna, N.

    2017-09-01

    The use of computer software such as Cabri 3D for learning activities is very unlimited. Students can adjust their learning speed according to their level of ability. Open-ended approach strongly supports the use of computer software in learning, because the goal of open-ended learning is to help developing creative activities and mathematical mindset of students through problem solving simultaneously. In other words, creative activities and mathematical mindset of students should be developed as much as possible in accordance with the ability of spatial ability of each student. Spatial ability is the ability of students in constructing and representing geometry models. This study aims to determine the improvement of spatial ability of junior high school students who obtained learning with open-ended approach aided by Cabri 3D. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2×3 factorial model. The instrument of the study is spatial ability test. Based on analysis of the data, it is found that the improvement of spatial ability of students who received open-ended learning aided by Cabri 3D was greater than students who received expository learning, both as a whole and based on the categories of students’ initial mathematical ability.

  14. Word Problem Strategy for Latino English Language Learners at Risk for Math Disabilities

    ERIC Educational Resources Information Center

    Orosco, Michael J.

    2014-01-01

    "English Language Learners" (ELLs) at risk for "math disabilities" (MD) are challenged in solving word problems for numerous reasons such as (a) learning English as a second language, (b) limited experience using math vocabulary, and (c) lack of strategies to improve word-problem-solving skills. As a result of these…

  15. Language, Arithmetic Word Problems, and Deaf Students: Linguistic Strategies Used To Solve Tasks.

    ERIC Educational Resources Information Center

    Zevenbergen, Robyn; Hyde, Merv; Power, Des

    2001-01-01

    Examines the performance of deaf and hearing-impaired students in Queensland, Australia when solving arithmetic word problems. Subjects' solutions of word problems confirmed trends for learning students but their performance was delayed in comparison. Confirms other studies in which deaf and hearing-impaired students are delayed in their language…

  16. Word Problem Solving: A Schema Approach in Year 3

    ERIC Educational Resources Information Center

    van Klinken, Eduarda

    2012-01-01

    This article outlines how a Brisbane independent school, Clayfield College, improved the ability of its Year 3 students to solve addition and subtraction word problems by utilising a schematic approach. It was observed that while students could read the words in the text of a written problem, many had difficulty identifying the core information…

  17. Individualized Math Problems in Percent. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume includes problems concerned with computing percents.…

  18. Individualized Math Problems in Algebra. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic, and contains problems related to diverse vocations. Solutions are provided for all problems. Problems presented in this package concern ratios used in food…

  19. Individualized Math Problems in Fractions. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This package contains problems involving computation with common…

  20. Individualized Math Problems in Geometry. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. The volume contains problems in applied geometry. Measurement of…

  1. Individualized Math Problems in Measurement and Conversion. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume includes problems involving measurement, computation of…

  2. Individualized Math Problems in Integers. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume presents problems involving operations with positive and…

  3. Improving mathematical problem solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic

    NASA Astrophysics Data System (ADS)

    Darma, I. K.

    2018-01-01

    This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.

  4. What is the problem in problem-based learning in higher education mathematics

    NASA Astrophysics Data System (ADS)

    Dahl, Bettina

    2018-01-01

    Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.

  5. Protocol Analysis of Group Problem Solving in Mathematics: A Cognitive-Metacognitive Framework for Assessment.

    ERIC Educational Resources Information Center

    Artzt, Alice F.; Armour-Thomas, Eleanor

    The roles of cognition and metacognition were examined in the mathematical problem-solving behaviors of students as they worked in small groups. As an outcome, a framework that links the literature of cognitive science and mathematical problem solving was developed for protocol analysis of mathematical problem solving. Within this framework, each…

  6. Mathematical Profiles and Problem Solving Abilities of Mathematically Promising Students

    ERIC Educational Resources Information Center

    Budak, Ibrahim

    2012-01-01

    Mathematically promising students are defined as those who have the potential to become the leaders and problem solvers of the future. The purpose of this research is to reveal what problem solving abilities mathematically promising students show in solving non-routine problems and type of profiles they present in the classroom and during problem…

  7. Engaging Future Teachers in Problem-Based Learning with the Park City Mathematics Institute Problems

    ERIC Educational Resources Information Center

    Pilgrim, Mary E.

    2014-01-01

    Problem-based learning (PBL) is a pedagogical technique recommended for K-12 mathematics classrooms. However, the mathematics courses in future teachers' degree programs are often lecture based. Students typically learn about problem-based learning in theory, but rarely get to experience it first-hand in their mathematics courses. The premise…

  8. Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills

    ERIC Educational Resources Information Center

    Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

    2015-01-01

    How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

  9. Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem

    ERIC Educational Resources Information Center

    Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova

    2017-01-01

    The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…

  10. Developing Instruction Materials Based on Joyful PBL to Improve Students Mathematical Representation Ability

    ERIC Educational Resources Information Center

    Minarni, Ani; Napitupulu, E. Elvis

    2017-01-01

    Solving problem either within mathematics or beyond is one of the ultimate goal students learn mathematics. It is since mathematics takes role tool as well as vehicle to develop problem solving ability. One of the supporting components to problem solving is mathematical representation ability (MRA). Nowadays, many teachers and researchers find out…

  11. Using the Wonder of Inequalities between Averages for Mathematics Problems Solving

    ERIC Educational Resources Information Center

    Shaanan, Rachel Mogilevsky; Gordon, Moshe Stupel

    2016-01-01

    The study presents an introductory idea of using mathematical averages as a tool for enriching mathematical problem solving. Throughout students' activities, a research was conducted on their ability to solve mathematical problems, and how to cope with a variety of mathematical tasks, in a variety of ways, using the skills, tools and experiences…

  12. A Critical Discourse Analysis of Practical Problems in a Foundation Mathematics Course at a South African University

    ERIC Educational Resources Information Center

    le Roux, Kate; Adler, Jill

    2016-01-01

    Mathematical problems that make links to the everyday and to disciplines other than mathematics--variously referred to as practical, realistic, real-world or applied problems in the literature--feature in school and undergraduate mathematics reforms aimed at increasing mathematics participation in contexts of inequity and diversity. In this…

  13. An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

    ERIC Educational Resources Information Center

    Bukova-Guzel, Esra

    2011-01-01

    This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

  14. Can Television Enhance Children's Mathematical Problem Solving?

    ERIC Educational Resources Information Center

    Fisch, Shalom M.; And Others

    1994-01-01

    A summative evaluation of "Square One TV," an educational mathematics series produced by the Children's Television Workshop, shows that children who regularly viewed the program showed significant improvement in solving unfamiliar, complex mathematical problems, and viewers showed improvement in their mathematical problem-solving ability…

  15. An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving

    NASA Astrophysics Data System (ADS)

    Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani

    2016-02-01

    Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.

  16. Individualized Math Problems in Ratio and Proportion. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume contains problems involving ratio and proportion. Some…

  17. Individualized Math Problems in Whole Numbers. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this set require computations involving whole numbers.…

  18. Individualized Math Problems in Graphs and Tables. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems involving the construction and interpretation of graphs and…

  19. Individualized Math Problems in Simple Equations. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require solution of linear equations, systems…

  20. Individualized Math Problems in Trigonometry. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require the use of trigonometric and inverse…

  1. Individualized Math Problems in Decimals. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    THis is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume concern use of decimals and are related to the…

  2. Individualized Math Problems in Volume. Oregon Vo-Tech Mathematics Problem Sets.

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

    This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this booklet require the computation of volumes of solids,…

  3. Analysis of Secondary School Students’ Algebraic Thinking and Math-Talk Learning Community to Help Students Learn

    NASA Astrophysics Data System (ADS)

    Nurhayati, D. M.; Herman, T.; Suhendra, S.

    2017-09-01

    This study aims to determine the difficulties of algebraic thinking ability of students in one of secondary school on quadrilateral subject and to describe Math-Talk Learning Community as the alternative way that can be done to overcome the difficulties of the students’ algebraic thinking ability. Research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and twenty three students as the sample that was chosen by purposive sampling technique. Data of algebraic thinking were collected through essay test. The results showed the percentage of achievement of students’ algebraic thinking’s indicators on three aspects: a) algebra as generalized arithmetic with the indicators (conceptually based computational strategies and estimation); b) algebra as the language of mathematics (meaning of variables, variable expressions and meaning of solution); c) algebra as a tool for functions and mathematical modelling (representing mathematical ideas using equations, tables, or words and generalizing patterns and rules in real-world contexts) is still low. It is predicted that because the secondary school students was not familiar with the abstract problem and they are still at a semi-concrete stage where the stage of cognitive development is between concrete and abstract. Based on the percentage achievement of each indicators, it can be concluded that the level of achievement of student’s mathematical communication using conventional learning is still low, so students’ algebraic thinking ability need to be improved.

  4. The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

    NASA Astrophysics Data System (ADS)

    Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

    2017-05-01

    This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

  5. Tense and Aspect in Word Problems about Motion: Diagram, Gesture, and the Felt Experience of Time

    ERIC Educational Resources Information Center

    de Freitas, Elizabeth; Zolkower, Betina

    2015-01-01

    Word problems about motion contain various conjugated verb forms. As students and teachers grapple with such word problems, they jointly operationalize diagrams, gestures, and language. Drawing on findings from a 3-year research project examining the social semiotics of classroom interaction, we show how teachers and students use gesture and…

  6. Redefining the Whole: Common Errors in Elementary Preservice Teachers' Self-Authored Word Problems for Fraction Subtraction

    ERIC Educational Resources Information Center

    Dixon, Juli K.; Andreasen, Janet B.; Avila, Cheryl L.; Bawatneh, Zyad; Deichert, Deana L.; Howse, Tashana D.; Turner, Mercedes Sotillo

    2014-01-01

    A goal of this study was to examine elementary preservice teachers' (PSTs) ability to contextualize and decontextualize fraction subtraction by asking them to write word problems to represent fraction subtraction expressions and to choose prewritten word problems to support given fraction subtraction expressions. Three themes emerged from the…

  7. Assessing the Effect of Language Demand in Bundles of Math Word Problems

    ERIC Educational Resources Information Center

    Banks, Kathleen; Jeddeeni, Ahmad; Walker, Cindy M.

    2016-01-01

    Differential bundle functioning (DBF) analyses were conducted to determine whether seventh and eighth grade second language learners (SLLs) had lower probabilities of answering bundles of math word problems correctly that had heavy language demands, when compared to non-SLLs of equal math proficiency. Math word problems on each of four test forms…

  8. When Best Intentions Go Awry: The Failures of Concrete Representations to Help Solve Probability Word Problems

    ERIC Educational Resources Information Center

    Beitzel, Brian D.; Staley, Richard K.; DuBois, Nelson F.

    2011-01-01

    Previous research has cast doubt on the efficacy of utilizing external representations as an aid to solving word problems. The present study replicates previous findings that concrete representations hinder college students' ability to solve probability word problems, and extends those findings to apply to a multimedia instructional context. Our…

  9. Word Frequency, Function Words and the Second Gavagai Problem

    ERIC Educational Resources Information Center

    Hochmann, Jean-Remy

    2013-01-01

    The classic gavagai problem exemplifies the difficulty to identify the referent of a novel word uttered in a foreign language. Here, we consider the reverse problem: identifying the referential part of a label. Assuming "gavagai" indicates a rabbit in a foreign language, it may very well mean ""a" rabbit" or ""that" rabbit". How can a learner know…

  10. The Impact of Metacognitive Strategies and Self-Regulating Processes of Solving Math Word Problems

    ERIC Educational Resources Information Center

    Vula, Eda; Avdyli, Rrezarta; Berisha, Valbona; Saqipi, Blerim; Elezi, Shpetim

    2017-01-01

    This empirical study investigates the impact of metacognitive strategies and self-regulating processes in learners' achievement on solving math word problems. It specifically analyzes the impact of the linguistic factor and the number of steps and arithmetical operations that learners need to apply during the process of solving math word problems.…

  11. Model Drawing Strategy for Fraction Word Problem Solving of Fourth-Grade Students with Learning Disabilities

    ERIC Educational Resources Information Center

    Sharp, Emily; Shih Dennis, Minyi

    2017-01-01

    This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…

  12. Additive Relations Word Problems in the South African Curriculum and Assessment Policy Standard at Foundation Phase

    ERIC Educational Resources Information Center

    Roberts, Nicky

    2016-01-01

    Drawing on a literature review of classifications developed by each of Riley, Verschaffel and Carpenter and their respective research groups, a refined typology of additive relations word problems is proposed and then used as analytical tool to classify the additive relations word problems in South African Curriculum and Assessment Policy Standard…

  13. Building a Career Mathematics File: Challenging Students to Find the Importance of Mathematics in a Variety of Occupations

    ERIC Educational Resources Information Center

    Keleher, Lori A.

    2006-01-01

    The Career Mathematics file is an occupational problem-solving system, which includes a wide range of mathematical problems and solutions, collected from various resources and helps students establish connections between mathematics and their environment. The study shows that the problems given can be used as realistic examples to study and…

  14. An Investigation of Relationships between Students' Mathematical Problem-Posing Abilities and Their Mathematical Content Knowledge

    ERIC Educational Resources Information Center

    Van Harpen, Xianwei Y.; Presmeg, Norma C.

    2013-01-01

    The importance of students' problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students' mathematical content knowledge could be highly…

  15. Creativity and Mathematical Problem Posing: An Analysis of High School Students' Mathematical Problem Posing in China and the USA

    ERIC Educational Resources Information Center

    Van Harpen, Xianwei Y.; Sriraman, Bharath

    2013-01-01

    In the literature, problem-posing abilities are reported to be an important aspect/indicator of creativity in mathematics. The importance of problem-posing activities in mathematics is emphasized in educational documents in many countries, including the USA and China. This study was aimed at exploring high school students' creativity in…

  16. Recent Trends in Japanese Mathematics Textbooks for Elementary Grades: Supporting Teachers to Teach Mathematics through Problem Solving

    ERIC Educational Resources Information Center

    Takahashi, Akihiko

    2016-01-01

    Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over…

  17. The way adults with orientation to mathematics teaching cope with the solution of everyday real-world problems

    NASA Astrophysics Data System (ADS)

    Gazit, Avikam; Patkin, Dorit

    2012-03-01

    The article aims to check the way adults, some who are practicing mathematics teachers at elementary school, some who are academicians making a career change to mathematics teachers at junior high school and the rest who are pre-service mathematics teachers at elementary school, cope with the solution of everyday real-world problems of buying and selling. The findings show that even adults with mathematical background tend to make mistakes in solving everyday real-world problems. Only about 70% of the adults who have an orientation to mathematics solved the sample problem correctly. The lowest percentage of success was demonstrated by the academicians making a career change to junior high school mathematics teachers whereas the highest percentage of success was manifested by pre-service elementary school mathematics teachers. Moreover, the findings illustrate that life experience of the practicing mathematics teachers and, mainly, of the academicians making a career change, who were older than the pre-service teachers, did not facilitate the solution of such a real-world problem. Perhaps the reason resides in the process of mathematics teaching at school, which does not put an emphasis on the solution of everyday real-world problems.

  18. Teaching with Technology: Exploring the Use of Robotics to Teach Mathematics

    ERIC Educational Resources Information Center

    Attard, Catherine

    2012-01-01

    In this article, the author explores the value of using simple robotics such as BeeBots and ProBots to enhance the teaching and learning of mathematics in the primary classroom. Before making the decision to use such technologies, it is important that they be evaluated in terms of their affordances and constraints. In other words, teachers need to…

  19. Deictics and the Construction of Mathematics and Science Knowledge in the Secondary School Classroom

    ERIC Educational Resources Information Center

    Hansen-Thomas, Holly; Langman, Juliet

    2017-01-01

    Taking a Teacher Language Awareness (TLA) perspective, this paper examines how the concept of deixis is employed in oral discourse in two secondary science and mathematics classes in the southwestern part of the US. Drawing on audio and videotaped data from two classrooms, we examine how verbal deixis, or words and phrases that cannot be fully…

  20. Representations in Problem Solving: A Case Study with Optimization Problems

    ERIC Educational Resources Information Center

    Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

    2009-01-01

    Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

  1. Mathematical Modelling in the Early School Years

    ERIC Educational Resources Information Center

    English, Lyn D.; Watters, James J.

    2005-01-01

    In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…

  2. Three-dimensional electrical impedance tomography: a topology optimization approach.

    PubMed

    Mello, Luís Augusto Motta; de Lima, Cícero Ribeiro; Amato, Marcelo Britto Passos; Lima, Raul Gonzalez; Silva, Emílio Carlos Nelli

    2008-02-01

    Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

  3. Exploring Primary Student's Problem-Solving Ability by Doing Tasks Like PISA's Question

    ERIC Educational Resources Information Center

    Novita, Rita; Zulkardi; Hartono, Yusuf

    2012-01-01

    Problem solving plays an important role in mathematics and should have a prominent role in the mathematics education. The term "problem solving" refers to mathematics tasks that have the potential to provide intellectual challenges for enhancing students' mathematical understanding and development. In addition, the contextual problem…

  4. On the Relationships between (Relatively) Advanced Mathematical Knowledge and (Relatively) Advanced Problem-Solving Behaviours

    ERIC Educational Resources Information Center

    Koichu, Boris

    2010-01-01

    This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

  5. Pose and Solve Varignon Converse Problems

    ERIC Educational Resources Information Center

    Contreras, José N.

    2014-01-01

    The activity of posing and solving problems can enrich learners' mathematical experiences because it fosters a spirit of inquisitiveness, cultivates their mathematical curiosity, and deepens their views of what it means to do mathematics. To achieve these goals, a mathematical problem needs to be at the appropriate level of difficulty,…

  6. Applications: Students, the Mathematics Curriculum and Mathematics Textbooks

    ERIC Educational Resources Information Center

    Kilic, Cigdem

    2013-01-01

    Problem posing is one of the most important topics in a mathematics education. Through problem posing, students gain mathematical abilities and concepts and teachers can evaluate their students and arrange adequate learning environments. The aim of the present study is to investigate Turkish primary school teachers' opinions about problem posing…

  7. ABC Problem in Elementary Mathematics Education: Arithmetic "before" Comprehension

    ERIC Educational Resources Information Center

    Boote, Stacy K.; Boote, David N.

    2018-01-01

    Mathematical habits of prospective teachers affect problem comprehension and success and expose their beliefs about mathematics. Prospective elementary teachers (PSTs) (n = 121) engaged in a problem solving activity each week in class. Data were collected from PSTs enrolled in an undergraduate elementary mathematics methods course at a…

  8. Students' and Teachers' Conceptual Metaphors for Mathematical Problem Solving

    ERIC Educational Resources Information Center

    Yee, Sean P.

    2017-01-01

    Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

  9. Pre-Service Class Teacher' Ability in Solving Mathematical Problems and Skills in Solving Daily Problems

    ERIC Educational Resources Information Center

    Aljaberi, Nahil M.; Gheith, Eman

    2016-01-01

    This study aims to investigate the ability of pre-service class teacher at University of Petrain solving mathematical problems using Polya's Techniques, their level of problem solving skills in daily-life issues. The study also investigates the correlation between their ability to solve mathematical problems and their level of problem solving…

  10. Optical character recognition of handwritten Arabic using hidden Markov models

    NASA Astrophysics Data System (ADS)

    Aulama, Mohannad M.; Natsheh, Asem M.; Abandah, Gheith A.; Olama, Mohammed M.

    2011-04-01

    The problem of optical character recognition (OCR) of handwritten Arabic has not received a satisfactory solution yet. In this paper, an Arabic OCR algorithm is developed based on Hidden Markov Models (HMMs) combined with the Viterbi algorithm, which results in an improved and more robust recognition of characters at the sub-word level. Integrating the HMMs represents another step of the overall OCR trends being currently researched in the literature. The proposed approach exploits the structure of characters in the Arabic language in addition to their extracted features to achieve improved recognition rates. Useful statistical information of the Arabic language is initially extracted and then used to estimate the probabilistic parameters of the mathematical HMM. A new custom implementation of the HMM is developed in this study, where the transition matrix is built based on the collected large corpus, and the emission matrix is built based on the results obtained via the extracted character features. The recognition process is triggered using the Viterbi algorithm which employs the most probable sequence of sub-words. The model was implemented to recognize the sub-word unit of Arabic text raising the recognition rate from being linked to the worst recognition rate for any character to the overall structure of the Arabic language. Numerical results show that there is a potentially large recognition improvement by using the proposed algorithms.

  11. Optical character recognition of handwritten Arabic using hidden Markov models

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Aulama, Mohannad M.; Natsheh, Asem M.; Abandah, Gheith A.

    2011-01-01

    The problem of optical character recognition (OCR) of handwritten Arabic has not received a satisfactory solution yet. In this paper, an Arabic OCR algorithm is developed based on Hidden Markov Models (HMMs) combined with the Viterbi algorithm, which results in an improved and more robust recognition of characters at the sub-word level. Integrating the HMMs represents another step of the overall OCR trends being currently researched in the literature. The proposed approach exploits the structure of characters in the Arabic language in addition to their extracted features to achieve improved recognition rates. Useful statistical information of the Arabic language ismore » initially extracted and then used to estimate the probabilistic parameters of the mathematical HMM. A new custom implementation of the HMM is developed in this study, where the transition matrix is built based on the collected large corpus, and the emission matrix is built based on the results obtained via the extracted character features. The recognition process is triggered using the Viterbi algorithm which employs the most probable sequence of sub-words. The model was implemented to recognize the sub-word unit of Arabic text raising the recognition rate from being linked to the worst recognition rate for any character to the overall structure of the Arabic language. Numerical results show that there is a potentially large recognition improvement by using the proposed algorithms.« less

  12. Language affects symbolic arithmetic in children: the case of number word inversion.

    PubMed

    Göbel, Silke M; Moeller, Korbinian; Pixner, Silvia; Kaufmann, Liane; Nuerk, Hans-Christoph

    2014-03-01

    Specific language influences have been observed in basic numerical tasks such as magnitude comparison, transcoding, and the number line estimation task. However, so far language influences in more complex calculations have not been reported in children. In this translingual study, 7- to 9-year-old German- and Italian-speaking children were tested on a symbolic addition task. Whereas the order of tens and units in Italian number words follows the order of the Arabic notation, the order is inverted in German number words. For both language groups, addition problems were more difficult when a carry operation was needed, that is, when a manipulation within the place-value structure of the Arabic number system was particularly important. Most important, this carry effect was more pronounced in response latencies for children speaking German, a language with inverted verbal mapping of the place-value structure. In addition, independent of language group, the size of the carry effect was significantly related to verbal working memory. The current study indicates that symbolic arithmetic and the carry effect in particular are modulated by language-specific characteristics. Our results underline the fact that the structure of the language of instruction is an important factor in children's mathematical education and needs to be taken into account even for seemingly nonverbal symbolic Arabic tasks. Copyright © 2013 Elsevier Inc. All rights reserved.

  13. The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

    ERIC Educational Resources Information Center

    Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

    2016-01-01

    Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

  14. Investigating Mathematics Teachers Candidates' Knowledge about Problem Solving Strategies through Problem Posing

    ERIC Educational Resources Information Center

    Ünlü, Melihan

    2017-01-01

    The aim of the study was to determine mathematics teacher candidates' knowledge about problem solving strategies through problem posing. This qualitative research was conducted with 95 mathematics teacher candidates studying at education faculty of a public university during the first term of the 2015-2016 academic year in Turkey. Problem Posing…

  15. Problem Posing and Solving with Mathematical Modeling

    ERIC Educational Resources Information Center

    English, Lyn D.; Fox, Jillian L.; Watters, James J.

    2005-01-01

    Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

  16. The Impact of Problem Posing on Elementary Teachers' Beliefs about Mathematics and Mathematics Teaching

    ERIC Educational Resources Information Center

    Barlow, Angela T.; Cates, Janie M.

    2006-01-01

    This study investigated the impact of incorporating problem posing in elementary classrooms on the beliefs held by elementary teachers about mathematics and mathematics teaching. Teachers participated in a year-long staff development project aimed at facilitating the incorporation of problem posing into their classrooms. Beliefs were examined via…

  17. Leveling of Critical Thinking Abilities of Students of Mathematics Education in Mathematical Problem Solving

    ERIC Educational Resources Information Center

    Rasiman

    2015-01-01

    This research aims to determine the leveling of critical thinking abilities of students of mathematics education in mathematical problem solving. It includes qualitative-explorative study that was conducted at University of PGRI Semarang. The generated data in the form of information obtained problem solving question and interview guides. The…

  18. Problem Solving in Swedish Mathematics Textbooks for Upper Secondary School

    ERIC Educational Resources Information Center

    Brehmer, Daniel; Ryve, Andreas; Van Steenbrugge, Hendrik

    2016-01-01

    The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their…

  19. Adolescent Mathematical Problem Solving: The Role of Metacognition, Strategies and Beliefs.

    ERIC Educational Resources Information Center

    Fitzpatrick, Corine

    Mathematical problem solving has been the focus of much concern. This study investigated the relationship of various cognitive factors, attributions, and gender to the solution of mathematics problems by 100 high school seniors. The independent variables examined in this study included: (1) mathematics knowledge as measured by a score on the…

  20. An Astronomical Problem in a Japanese Traditional Mathematical Text: The 49th Problem of the Kenki-sanpo of Takebe Katahiro

    NASA Astrophysics Data System (ADS)

    Ôhashi, Yukio

    During the Edo period (Tokugawa-shogunate period) (1603-1867), there was a mathematical tradition now called "Wasan" which was primarily based on Chinese mathematics, but Japanese mathematicians also created new devices. It was quite popular, and common people could enjoy solving mathematical problems through Wasan regardless of their social status. Some astronomical problems were also treated there.

  1. Coping Strategies Applied to Comprehend Multistep Arithmetic Word Problems by Students with Above-Average Numeracy Skills and Below-Average Reading Skills

    ERIC Educational Resources Information Center

    Nortvedt, Guri A.

    2011-01-01

    This article discusses how 13-year-old students with above-average numeracy skills and below-average reading skills cope with comprehending word problems. Compared to other students who are proficient in numeracy and are skilled readers, these students are more disadvantaged when solving single-step and multistep arithmetic word problems. The…

  2. A process for reaching standardization of word processing software for Sandia National Laboratories (Albuquerque) secretaries

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hudson, S.R.

    1989-04-01

    In the summer of 1986, a number of problems being experienced by Sandia secretaries due to multiple word processing packages being used were brought to the attention of Sandia's upper management. This report discusses how these problems evolved, how management chose to correct the problem, and how standardization of word processing for Sandia secretaries was achieved. 11 refs.

  3. Problem Solvers: Problem--Jesse's Train

    ERIC Educational Resources Information Center

    James, Julie; Steimle, Alice

    2014-01-01

    Persevering in problem solving and constructing and critiquing mathematical arguments are some of the mathematical practices included in the Common Core State Standards for Mathematics (CCSSI 2010). To solve unfamiliar problems, students must make sense of the situation and apply current knowledge. Teachers can present such opportunities by…

  4. Research and Implementation of Tibetan Word Segmentation Based on Syllable Methods

    NASA Astrophysics Data System (ADS)

    Jiang, Jing; Li, Yachao; Jiang, Tao; Yu, Hongzhi

    2018-03-01

    Tibetan word segmentation (TWS) is an important problem in Tibetan information processing, while abbreviated word recognition is one of the key and most difficult problems in TWS. Most of the existing methods of Tibetan abbreviated word recognition are rule-based approaches, which need vocabulary support. In this paper, we propose a method based on sequence tagging model for abbreviated word recognition, and then implement in TWS systems with sequence labeling models. The experimental results show that our abbreviated word recognition method is fast and effective and can be combined easily with the segmentation model. This significantly increases the effect of the Tibetan word segmentation.

  5. Mathematically Gifted High School Students' Approaches to Developing Visual Proofs (VP) and Preliminary Ideas about VP

    ERIC Educational Resources Information Center

    Ugurel, Isikhan; Morali, H. Sevgi; Karahan, Ozge; Boz, Burcak

    2016-01-01

    The purpose of this study is to describe the procedure and examples of visual proofs (VP-or proof without words) developed by gifted mathematics secondary school students after their experiences. The participants of this study are three male 9th grade students enrolled in a private science high school. In the first stage of the research a briefing…

  6. Evansville: A City on the Ohio River. An Interdisciplinary Unit for Grade 3: Language Arts, Mathematics, Science, Social Studies.

    ERIC Educational Resources Information Center

    Evansville-Vanderburgh School Corp., IN.

    This grade 3 interdisciplinary resource unit uses Evansville, Indiana and the Ohio River as its focus for social studies, language arts, mathematics, and science lessons. Text, pictures, and maps are provided to teach social studies lessons in history, geography, and map skills, and the student exercises include tests on vocabulary words and map…

  7. Categorization and analysis of explanatory writing in mathematics

    NASA Astrophysics Data System (ADS)

    Craig, Tracy S.

    2011-10-01

    The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to mathematical problem-solving processes. The rationale for the study was the recognized importance of mathematical problem-solving, the widely acknowledged challenge of teaching problem-solving skills directly and the evidence in the literature that writing in mathematics provides a tool for learning. The study was carried out in a first-year mathematics course at the University of Cape Town, South Africa. Students' written submissions were categorized and analysed through use of an adaptation of a journal entry classification scheme. The scheme successfully observed positive changes over the experimental period in students' level of engagement with the mathematical material and with their stance towards knowledge.

  8. Improving of Junior High School Visual Thinking Representation Ability in Mathematical Problem Solving by CTL

    ERIC Educational Resources Information Center

    Surya, Edy; Sabandar, Jozua; Kusumah, Yaya S.; Darhim

    2013-01-01

    The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…

  9. Processes involved in solving mathematical problems

    NASA Astrophysics Data System (ADS)

    Shahrill, Masitah; Putri, Ratu Ilma Indra; Zulkardi, Prahmana, Rully Charitas Indra

    2018-04-01

    This study examines one of the instructional practices features utilized within the Year 8 mathematics lessons in Brunei Darussalam. The codes from the TIMSS 1999 Video Study were applied and strictly followed, and from the 183 mathematics problems recorded, there were 95 problems with a solution presented during the public segments of the video-recorded lesson sequences of the four sampled teachers. The analyses involved firstly, identifying the processes related to mathematical problem statements, and secondly, examining the different processes used in solving the mathematical problems for each problem publicly completed during the lessons. The findings revealed that for three of the teachers, their problem statements coded as `using procedures' ranged from 64% to 83%, while the remaining teacher had 40% of his problem statements coded as `making connections.' The processes used when solving the problems were mainly `using procedures', and none of the problems were coded as `giving results only'. Furthermore, all four teachers made use of making the relevant connections in solving the problems given to their respective students.

  10. Linguistica matematica, statistica linguistica e linguistica applicata. Una nota storica sui lessici di frequenza e l'educazione linguistica (Mathematical Linguistics, Linguistic Statistics, and Applied Linguistics. An Historical Note on Word Frequencies and Linguistic Education)

    ERIC Educational Resources Information Center

    Elia, Annibale

    1977-01-01

    This article traces the history of several themes in applied linguistics and to show the relationships between linguistic theory and the sciences concerned with the learning and teaching of languages. Interest in word frequency statistics is discussed in particular. (Text is in Italian.) (CFM)

  11. A new fractional nonlocal model and its application in free vibration of Timoshenko and Euler-Bernoulli beams

    NASA Astrophysics Data System (ADS)

    Rahimi, Zaher; Sumelka, Wojciech; Yang, Xiao-Jun

    2017-11-01

    The application of fractional calculus in fractional models (FMs) makes them more flexible than integer models inasmuch they can conclude all of integer and non-integer operators. In other words FMs let us use more potential of mathematics to modeling physical phenomena due to the use of both integer and fractional operators to present a better modeling of problems, which makes them more flexible and powerful. In the present work, a new fractional nonlocal model has been proposed, which has a simple form and can be used in different problems due to the simple form of numerical solutions. Then the model has been used to govern equations of the motion of the Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT). Next, free vibration of the Timoshenko and Euler-Bernoulli simply-supported (S-S) beam has been investigated. The Galerkin weighted residual method has been used to solve the non-linear governing equations.

  12. Obstacles Related to Structuring for Mathematization Encountered by Students When Solving Physics Problems

    ERIC Educational Resources Information Center

    Niss, Martin

    2017-01-01

    This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called "structuring for mathematization," where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report the results of an analysis of four…

  13. Incorporating the Common Core's Problem Solving Standard for Mathematical Practice into an Early Elementary Inclusive Classroom

    ERIC Educational Resources Information Center

    Fletcher, Nicole

    2014-01-01

    Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem…

  14. Promoting Access to Common Core Mathematics for Students with Severe Disabilities through Mathematical Problem Solving

    ERIC Educational Resources Information Center

    Spooner, Fred; Saunders, Alicia; Root, Jenny; Brosh, Chelsi

    2017-01-01

    There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…

  15. Strategies to Support Students' Mathematical Modeling

    ERIC Educational Resources Information Center

    Jung, Hyunyi

    2015-01-01

    An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

  16. Contributions of Domain-General Cognitive Resources and Different Forms of Arithmetic Development to Pre-Algebraic Knowledge

    PubMed Central

    Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Powell, Sarah R.; Schumacher, Robin F.; Hamlett, Carol L.; Vernier, Emily; Namkung, Jessica M.; Vukovic, Rose K.

    2012-01-01

    The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n=279; mean age=7.59 yrs) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems at start of 2nd grade and on calculations, word problems, and pre-algebraic knowledge at end of 3rd grade. Multilevel path analysis, controlling for instructional effects associated with the sequence of classrooms in which students were nested across grades 2–3, indicated arithmetic calculations and word problems are foundational to pre-algebraic knowledge. Also, results revealed direct contributions of nonverbal reasoning and oral language to pre-algebraic knowledge, beyond indirect effects that are mediated via arithmetic calculations and word problems. By contrast, attentive behavior, phonological processing, and processing speed contributed to pre-algebraic knowledge only indirectly via arithmetic calculations and word problems. PMID:22409764

  17. The stability issues in problems of mathematical modeling

    NASA Astrophysics Data System (ADS)

    Mokin, A. Yu.; Savenkova, N. P.; Udovichenko, N. S.

    2018-03-01

    In the paper it is briefly considered various aspects of stability concepts, which are used in physics, mathematics and numerical methods of solution. The interrelation between these concepts is described, the questions of preliminary stability research before the numerical solution of the problem and the correctness of the mathematical statement of the physical problem are discussed. Examples of concrete mathematical statements of individual physical problems are given: a nonlocal problem for the heat equation, the Korteweg-de Fries equation with boundary conditions at infinity, the sine-Gordon equation, the problem of propagation of femtosecond light pulses in an area with a cubic nonlinearity.

  18. Working memory components that predict word problem solving: Is it merely a function of reading, calculation, and fluid intelligence?

    PubMed

    Fung, Wenson; Swanson, H Lee

    2017-07-01

    The purpose of this study was to assess whether the differential effects of working memory (WM) components (the central executive, phonological loop, and visual-spatial sketchpad) on math word problem-solving accuracy in children (N = 413, ages 6-10) are completely mediated by reading, calculation, and fluid intelligence. The results indicated that all three WM components predicted word problem solving in the nonmediated model, but only the storage component of WM yielded a significant direct path to word problem-solving accuracy in the fully mediated model. Fluid intelligence was found to moderate the relationship between WM and word problem solving, whereas reading, calculation, and related skills (naming speed, domain-specific knowledge) completely mediated the influence of the executive system on problem-solving accuracy. Our results are consistent with findings suggesting that storage eliminates the predictive contribution of executive WM to various measures Colom, Rebollo, Abad, & Shih (Memory & Cognition, 34: 158-171, 2006). The findings suggest that the storage component of WM, rather than the executive component, has a direct path to higher-order processing in children.

  19. Capturing student mathematical engagement through differently enacted classroom practices: applying a modification of Watson's analytical tool

    NASA Astrophysics Data System (ADS)

    Patahuddin, Sitti Maesuri; Puteri, Indira; Lowrie, Tom; Logan, Tracy; Rika, Baiq

    2018-04-01

    This study examined student mathematical engagement through the intended and enacted lessons taught by two teachers in two different middle schools in Indonesia. The intended lesson was developed using the ELPSA learning design to promote mathematical engagement. Based on the premise that students will react to the mathematical tasks in the forms of words and actions, the analysis focused on identifying the types of mathematical engagement promoted through the intended lesson and performed by students during the lesson. Using modified Watson's analytical tool (2007), students' engagement was captured from what the participants' did or said mathematically. We found that teachers' enacted practices had an influence on student mathematical engagement. The teacher who demonstrated content in explicit ways tended to limit the richness of the engagement; whereas the teacher who presented activities in an open-ended manner fostered engagement.

  20. Profile of male-field dependent (FD) prospective teacher's reflective thinking in solving contextual mathematical problem

    NASA Astrophysics Data System (ADS)

    Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko

    2017-08-01

    Reflective thinking is an important component in the world of education, especially in professional education of teachers. In learning mathematics, reflective thinking is one way to solve mathematical problem because it can improve student's curiosity when student faces a mathematical problem. Reflective thinking is also a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. There are many factors which give impact toward the student's reflective thinking when student solves mathematical problem. One of them is cognitive style. For this reason, reflective thinking and cognitive style are important things in solving contextual mathematical problem. This research paper describes aspect of reflective thinking in solving contextual mathematical problem involved solution by using some mathematical concept, namely linear program, algebra arithmetic operation, and linear equations of two variables. The participant, in this research paper, is a male-prospective teacher who has Field Dependent. The purpose of this paper is to describe aspect of prospective teachers' reflective thinking in solving contextual mathematical problem. This research paper is a descriptive by using qualitative approach. To analyze the data, the researchers focus in four main categories which describe prospective teacher's activities using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.

Some links on this page may take you to non-federal websites. Their policies may differ from this site.
Top