Sample records for mathematical knowledge increases

  1. Increasing Your Mathematics and Science Content Knowledge.

    ERIC Educational Resources Information Center

    Thorson, Annette, Ed.

    2002-01-01

    This journal is intended for classroom teachers and provides a collection of essays and instructional materials organized around the theme of mathematics and science content knowledge. Articles include: (1) "Watching Ourselves Learn" (Annette Thorson); (2) "Search Smarter!" (Kimberly S. Roempler); (3) "Teacher Education Materials Project" (Joan…

  2. Pre-service Mathematics Teachers' Knowledge of History of Mathematics and Their Attitudes and Beliefs Towards Using History of Mathematics in Mathematics Education

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    Alpaslan, Mustafa; Işıksal, Mine; Haser, Çiğdem

    2014-01-01

    This study examined pre-service mathematics teachers' knowledge of history of mathematics and their attitudes and beliefs towards using history of mathematics in mathematics education based on year level in teacher education program and gender. The sample included 1,593 freshman, sophomore, junior, and senior pre-service middle school (grades 4-8) mathematics teachers from nine universities in Turkey. Data were collected through Knowledge of History of Mathematics Test and Attitudes and Beliefs towards the Use of History of Mathematics in Mathematics Education Questionnaire. Results indicate that pre-service teachers have moderate knowledge of history of mathematics and positive attitudes and beliefs towards using history of mathematics. Their knowledge scores increase as the year level in teacher education program advanced. Males' knowledge scores are significantly higher than females' scores in the first 2 years. This situation reverses in the last 2 years, but it is not statistically significant. Pre-service teachers have more positive attitudes and availing beliefs towards using history of mathematics as they progress in their teacher education program. Females have greater attitudes and beliefs mean scores than males in each of the years. The results indicate that the teacher education program may have enhanced the pre-service teachers' knowledge of history of mathematics by related courses. However, the moderate knowledge scores indicate that there is a need for revision of these courses. The pre-service teachers' positive attitudes and beliefs towards using history of mathematics stress the importance of teacher education program in order to prepare them for implementing this alternative strategy in the future.

  3. Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

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    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.

  4. How Education Affects Mathematics Teachers' Knowledge: Unpacking Selected Aspects of Teacher Knowledge

    ERIC Educational Resources Information Center

    Koponen, Mika; Asikainen, Mervi A.; Viholainen, Antti; Hirvonen, Pekka E.

    2017-01-01

    It is no surprise that all mathematics teacher education programs attempt to increase future teachers' knowledge, since teachers' knowledge has an effect not only on their teaching but also on their students' achievements. However, measuring the relationship between teachers' knowledge and their education is overly demanding. In this study we…

  5. Integrating pedagogical content knowledge and pedagogical/psychological knowledge in mathematics.

    PubMed

    Harr, Nora; Eichler, Andreas; Renkl, Alexander

    2014-01-01

    In teacher education at universities, general pedagogical and psychological principles are often treated separately from subject matter knowledge and therefore run the risk of not being applied in the teaching subject. In an experimental study (N = 60 mathematics student teachers) we investigated the effects of providing aspects of general pedagogical/psychological knowledge (PPK) and pedagogical content knowledge (PCK) in an integrated or separated way. In both conditions ("integrated" vs. "separated"), participants individually worked on computer-based learning environments addressing the same topic: use and handling of multiple external representations, a central issue in mathematics. We experimentally varied whether PPK aspects and PCK aspects were treated integrated or apart from one another. As expected, the integrated condition led to greater application of pedagogical/psychological aspects and an increase in applying both knowledge types simultaneously compared to the separated condition. Overall, our findings indicate beneficial effects of an integrated design in teacher education.

  6. Integrating pedagogical content knowledge and pedagogical/psychological knowledge in mathematics

    PubMed Central

    Harr, Nora; Eichler, Andreas; Renkl, Alexander

    2014-01-01

    In teacher education at universities, general pedagogical and psychological principles are often treated separately from subject matter knowledge and therefore run the risk of not being applied in the teaching subject. In an experimental study (N = 60 mathematics student teachers) we investigated the effects of providing aspects of general pedagogical/psychological knowledge (PPK) and pedagogical content knowledge (PCK) in an integrated or separated way. In both conditions (“integrated” vs. “separated”), participants individually worked on computer-based learning environments addressing the same topic: use and handling of multiple external representations, a central issue in mathematics. We experimentally varied whether PPK aspects and PCK aspects were treated integrated or apart from one another. As expected, the integrated condition led to greater application of pedagogical/psychological aspects and an increase in applying both knowledge types simultaneously compared to the separated condition. Overall, our findings indicate beneficial effects of an integrated design in teacher education. PMID:25191300

  7. Re-"Conceptualizing" Procedural Knowledge in Mathematics.

    ERIC Educational Resources Information Center

    Star, Jon R.

    Many mathematics educators have lost sight of the critical importance of the mathematical understanding which underlies procedural competence, in part because we do not have a language to refer to this kind of understanding. The modal way of categorizing mathematical knowledge--conceptual and procedural knowledge--is limited in that: (a) it is…

  8. Primary Mathematics Trainee Teacher Confidence and Its Relationship to Mathematical Knowledge

    ERIC Educational Resources Information Center

    Norton, Stephen J.

    2017-01-01

    The purpose of this paper is to examine trainee primary school teachers' confidence in their mathematical content knowledge (MCK) and confidence to teach specific primary mathematics concepts (mathematics pedagogical content knowledge --MPCK) which was correlated to their actual MCK on specific tasks. For this correlational study survey and test…

  9. Mathematical Knowledge: Its Growth through Teaching. Mathematics Education Library, Volume 10.

    ERIC Educational Resources Information Center

    Bishop, Alan J., Ed.; And Others

    This book presents issues concerning relationships between mathematical knowledge and the teaching and learning processes, focusing especially on the genesis of mathematical knowledge in the classroom. The chapter titles are: (1) The Fragility of Knowledge (Guy Brousseau and Michael Otte); (2) The Double Bind as a Didactical Trap (Stieg…

  10. Mathematical knowledge for teaching: Making the tacit more explicit in mathematics teacher education

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    Abdullah, Mohd Faizal Nizam Lee; Vimalanandan, Lena

    2017-05-01

    Teaching practice during school based experiences, afford an opportunity for pre service teachers to put into practice their knowledge for teaching mathematics. Like all knowledge, Mathematical Knowledge for Teaching (MKT) is held in both tacit and explicit form, making it especially difficult to study and map during instruction. This study investigates the tacit and explicit nature of MKT held by pre service teachers in a Malaysian Teacher Education Program and how it impacts the Mathematical Quality of their instruction (MQI). This study of three mathematics pre-service teachers (PSTs), utilised videos of mathematics lessons, reflective debriefs and interviews. The findings suggest that factors such as reflecting, peer-sharing, conferencing with mentors and observing support in making tacit knowledge more explicit during planning and instruction. Implications for preparation of mathematics teachers capable of high Mathematical Quality of Instruction are also discussed.

  11. Knowledge Concerning the Mathematical Horizon: A Close View

    ERIC Educational Resources Information Center

    Guberman, Raisa; Gorev, Dvora

    2015-01-01

    The main objective of this study is to identify components of teachers' mathematical knowledge for teaching, associated with the knowledge of mathematical horizon (KMH) in order to describe this type of knowledge from the viewpoint of elementary school mathematics teachers. The research population of this study consisted of 118 elementary school…

  12. Developing Mathematical Thinking: Changing Teachers' Knowledge and Instruction

    ERIC Educational Resources Information Center

    Brendefur, Jonathan L.; Thiede, Keith; Strother, Sam; Bunning, Kim; Peck, Duane

    2013-01-01

    In the present research, we evaluated the effectiveness of a multi-year professional development program in mathematics for elementary teachers. Each year the program focused on a different domain of mathematics. We found the program increased teachers' knowledge of (a) number and operations, (b) measurement and geometry, and (c) probability and…

  13. Preservice Secondary Mathematics Teachers' Development of Mathematical Knowledge for Teaching and Their Use of Knowledge in Their Instruction

    ERIC Educational Resources Information Center

    Moon, Kyunghee

    2013-01-01

    This study examined how preservice secondary mathematics teachers developed mathematical knowledge for teaching (MKT) around representations and big ideas through mathematics and mathematics education courses. The importance of big ideas and representations in mathematics has been emphasized in national standards as well as in literature. Yet,…

  14. Adapting Technological Pedagogical Content Knowledge Framework to Teach Mathematics

    ERIC Educational Resources Information Center

    Getenet, Seyum Tekeher

    2017-01-01

    The technological pedagogical content knowledge framework is increasingly in use by educational technology researcher as a generic description of the knowledge requirements for teachers using technology in all subjects. This study describes the development of a mathematics specific variety of the technological pedagogical content knowledge…

  15. Finnish Mentor Mathematics Teachers' Views of the Teacher Knowledge Required for Teaching Mathematics

    ERIC Educational Resources Information Center

    Asikainen, Mervi A.; Pehkonen, Erkki; Hirvonen, Pekka E.

    2013-01-01

    Seven Finnish mentor mathematics teachers were interviewed about their views regarding the teacher knowledge required for teaching mathematics. The results of the interviews revealed not only the teachers' spontaneous views of the knowledge base needed for effective mathematics teaching but also their views of the particular types of teacher…

  16. The effects of an intervention to increase liberal arts mathematics and science majors' knowledge of and attitudinal favorability toward the teaching profession

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    Klemballa, Carolyn

    In light of the persistent shortage of qualified mathematics and science teachers and the new teacher qualification provisions of the recently passed No Child Left Behind Act, This study tested the impact of an educational intervention designed to enhance interest in public school teaching careers among undergraduate students who were declared/intended majors in mathematics and/or natural science. Besides salary, research reveals content fear as the biggest roadblock to attracting mathematics and science teachers. Because of this, liberal arts majors in mathematics and science are a target pool of individuals to recruit into teaching. The researcher hypothesized that knowledge and attitudinal favorability would both increase after an intervention about teaching careers and that an increase in one variable would be associated with the other. Also, knowledge and attitudinal favorability would have a greater increase after a more intensive intervention than a less intensive intervention or no intervention. The researcher also hypothesized that if undergraduates were less decided in their career, lower classmen, and female, their attitudes toward the teaching profession would increase the most. One hundred eighty-nine college students, 73 males and 116 females, including 85 freshmen, 67 sophomores, 18 juniors and 19 seniors, at University A and University B were randomly assigned to a workshop, reading, or control group. The workshop group attended a workshop about the teaching profession. The reading group read articles with the same information presented in the workshop. The control group read unrelated articles. The findings from this study indicate that an intervention about teaching does significantly increase both knowledge and attitudinal favorability toward teaching (p < .01). A low significant correlation was found between knowledge and attitudinal favorability (p < .05). Findings also suggested that a more intensive intervention yields a higher increase in

  17. Elementary School Quality: The Mathematics Curriculum and the Role of Local Knowledge.

    ERIC Educational Resources Information Center

    Balfanz, Robert

    This report considers how the mathematical knowledge children develop on their own outside of formal school instruction can be used to increase the distribution and level of mathematical knowledge attained by students in grades K-3. Included are preliminary results of an investigation of the counting and calculating abilities brought to…

  18. Mathematics University Teachers' Perception of Pedagogical Content Knowledge (PCK)

    ERIC Educational Resources Information Center

    Khakbaz, Azimehsadat

    2016-01-01

    Teaching mathematics in university levels is one of the most important fields of research in the area of mathematics education. Nevertheless, there is little information about teaching knowledge of mathematics university teachers. Pedagogical content knowledge (PCK) provides a suitable framework to study knowledge of teachers. The purpose of this…

  19. Causal Connections between Mathematical Language and Mathematical Knowledge: A Dialogic Reading Intervention

    ERIC Educational Resources Information Center

    Purpura, David J.; Napoli, Amy R.; Wehrspann, Elizabeth A.; Gold, Zachary S.

    2017-01-01

    The acquisition of early mathematical knowledge is critical for successful long-term academic development. Mathematical language is one of the strongest predictors of children's early mathematical success. Findings from previous studies have provided correlational evidence supporting the importance of mathematical language to the development of…

  20. Depth of Teachers' Knowledge: Frameworks for Teachers' Knowledge of Mathematics

    ERIC Educational Resources Information Center

    Holmes, Vicki-Lynn

    2012-01-01

    This article describes seven teacher knowledge frameworks and relates these frameworks to the teaching and assessment of elementary teacher's mathematics knowledge. The frameworks classify teachers' knowledge and provide a vocabulary and common language through which knowledge can be discussed and assessed. These frameworks are categorized into…

  1. Prospective Secondary Mathematics Teachers' Perspectives and Mathematical Knowledge for Teaching

    ERIC Educational Resources Information Center

    Karagöz-Akar, Gülseren

    2016-01-01

    This study investigated the relationship between prospective secondary mathematics teachers' perspectives and their mathematical knowledge for teaching in action. Data from two prospective teachers' practice-teachings, one in geometry and one in algebra, their lesson plans and self-reflections were analyzed with Teacher Perspectives and Knowledge…

  2. Didactics and History of Mathematics: Knowledge and Self-Knowledge

    ERIC Educational Resources Information Center

    Fried, Michael N.

    2007-01-01

    The basic assumption of this paper is that mathematics and history of mathematics are both forms of knowledge and, therefore, represent different ways of knowing. This was also the basic assumption of Fried (2001) who maintained that these ways of knowing imply different conceptual and methodological commitments, which, in turn, lead to a conflict…

  3. Pre-Service Teachers' Mathematics Content Knowledge: Implications for How Mathematics Is Taught in Higher Education

    ERIC Educational Resources Information Center

    Lowrie, Tom; Jorgensen, Robyn

    2016-01-01

    This investigation explored pre-service teachers' mathematics content knowledge (MCK) and beliefs associated with mathematics education practices. An Exploratory Factor Analysis, conducted on a beliefs and attitudes questionnaire, produced three common attitude factors associated with (1) inquiry-based teaching; (2) how mathematics knowledge is…

  4. The Relationship of Mathematics Anxiety and Mathematical Knowledge to the Learning of Mathematical Pedagogy by Preservice Elementary Teachers.

    ERIC Educational Resources Information Center

    Battista, Michael T.

    1986-01-01

    Examined how preservice elementary teachers' (N=38) mathematical knowledge and mathematics anxiety affect their success in a mathematics methods course. Also examined the hypothesis that a mathematics methods course can reduce the mathematics anxiety of these teachers. One finding is that mathematics anxiety does not inhibit their learning of…

  5. Knowledge of Curriculum Embedded Mathematics: Exploring a Critical Domain of Teaching

    ERIC Educational Resources Information Center

    Remillard, Janine; Kim, Ok-Kyeong

    2017-01-01

    This paper proposes a framework for identifying the mathematical knowledge teachers activate when using curriculum resources. We use the term "knowledge of curriculum embedded mathematics" (KCEM) to refer to the mathematics knowledge activated by teachers when reading and interpreting mathematical tasks, instructional designs, and…

  6. Considering Indigenous Knowledges and Mathematics Curriculum

    ERIC Educational Resources Information Center

    Sterenberg, Gladys

    2013-01-01

    Across Canada, significant program changes in school mathematics have been made that encourage teachers to consider Aboriginal perspectives. In this article, I investigate one Aboriginal teacher's approaches to integrating Indigenous knowledges and the mandated mathematics curriculum in a Blackfoot First Nation school. Using a framework that…

  7. The Transition from Informal to Formal Mathematical Knowledge: Mediation by Numeral Knowledge

    ERIC Educational Resources Information Center

    Purpura, David J.; Baroody, Arthur J.; Lonigan, Christopher J.

    2013-01-01

    The purpose of the present study was to determine if numeral knowledge--the ability to identify Arabic numerals and connect Arabic numerals to their respective quantities--mediates the relation between informal and formal mathematical knowledge. A total of 206 3- to 5-year-old preschool children were assessed on 6 informal mathematics tasks and 2…

  8. Mathematical Knowledge for Teaching Fraction Multiplication

    ERIC Educational Resources Information Center

    Izsak, Andrew

    2008-01-01

    The present study contrasts mathematical knowledge that two sixth-grade teachers apparently used when teaching fraction multiplication with the Connected Mathematics Project materials. The analysis concentrated on those tasks from the materials that use drawings to represent fractions as length or area quantities. Examining the two teachers'…

  9. Secondary School Mathematics Teachers' Knowledge Levels and Use of History of Mathematics

    ERIC Educational Resources Information Center

    Bütüner, Suphi Önder

    2018-01-01

    This study describes secondary school mathematics teachers' use of history of mathematics in their classes and their knowledge levels in this field. The study population included a total of 58 secondary school mathematics teachers working at the secondary schools located in Yozgat city center, and the sample included 32 mathematics teachers from…

  10. A "Knowledge Quartet" Used to Identify a Second-Year Pre-Service Teacher's Primary Mathematical Content Knowledge

    ERIC Educational Resources Information Center

    Livy, Sharyn

    2010-01-01

    This paper draws on observation of a primary mathematics lesson prepared and taught by a second-year pre-service teacher who lacked mathematical content knowledge. A "knowledge quartet" (Rowland, Turner, Thwaites, & Huckstep, 2009) was used to investigate when and how a pre-service teacher drew on their knowledge of mathematics during primary…

  11. Exploring the Associations Among Nutrition, Science, and Mathematics Knowledge for an Integrative, Food-Based Curriculum.

    PubMed

    Stage, Virginia C; Kolasa, Kathryn M; Díaz, Sebastián R; Duffrin, Melani W

    2018-01-01

    Explore associations between nutrition, science, and mathematics knowledge to provide evidence that integrating food/nutrition education in the fourth-grade curriculum may support gains in academic knowledge. Secondary analysis of a quasi-experimental study. Sample included 438 students in 34 fourth-grade classrooms across North Carolina and Ohio; mean age 10 years old; gender (I = 53.2% female; C = 51.6% female). Dependent variable = post-test-nutrition knowledge; independent variables = baseline-nutrition knowledge, and post-test science and mathematics knowledge. Analyses included descriptive statistics and multiple linear regression. The hypothesized model predicted post-nutrition knowledge (F(437) = 149.4, p < .001; Adjusted R = .51). All independent variables were significant predictors with positive association. Science and mathematics knowledge were predictive of nutrition knowledge indicating use of an integrative science and mathematics curriculum to improve academic knowledge may also simultaneously improve nutrition knowledge among fourth-grade students. Teachers can benefit from integration by meeting multiple academic standards, efficiently using limited classroom time, and increasing nutrition education provided in the classroom. © 2018, American School Health Association.

  12. Deepening Pre-Service Secondary Teachers' Mathematical Content Knowledge through Engaging with Peers' Mathematical Contributions

    ERIC Educational Resources Information Center

    Pournara, C.

    2016-01-01

    Depth and rigour in mathematical knowledge for pre-service secondary school mathematics teachers may be found in particular experiences of learning and doing school-level mathematics. Drawing on two cases from a course on financial mathematics for secondary school teachers, I illustrate opportunities for exploring compound and exponential growth.…

  13. Examining Mathematics Teacher Content Knowledge: Policy and Practice

    ERIC Educational Resources Information Center

    Esprivalo Harrell, Pamela; Eddy, Colleen McLean

    2012-01-01

    This study examines mathematics teacher content knowledge in terms of state and national policymaker recommendations, college coursework and the Mathematics Texas Examination of Educator Standards (TExES) score. Results indicate differences between state and national policy recommendations and college degrees in mathematics. A statistically…

  14. Preschool children's mathematical knowledge: The effect of teacher "math talk.".

    PubMed

    Klibanoff, Raquel S; Levine, Susan C; Huttenlocher, Janellen; Vasilyeva, Marina; Hedges, Larry V

    2006-01-01

    This study examined the relation between the amount of mathematical input in the speech of preschool or day-care teachers and the growth of children's conventional mathematical knowledge over the school year. Three main findings emerged. First, there were marked individual differences in children's conventional mathematical knowledge by 4 years of age that were associated with socioeconomic status. Second, there were dramatic differences in the amount of math-related talk teachers provided. Third, and most important, the amount of teachers' math-related talk was significantly related to the growth of preschoolers' conventional mathematical knowledge over the school year but was unrelated to their math knowledge at the start of the school year. Copyright 2006 APA, all rights reserved.

  15. Can Pedagogical Concerns Eclipse Mathematical Knowledge?

    ERIC Educational Resources Information Center

    Creager, Mark A.; Jacobson, Erik; Aydeniz, Fetiye

    2016-01-01

    Mathematical knowledge for teaching (MKT) is often thought of as a transformed, mutually-influencing mixture of content and pedagogy. However when individuals' MKT does not integrate content and pedagogy, one type of knowledge can supersede the other, sometimes unconsciously. We exemplify this with Emma, a prospective elementary teacher, whose…

  16. 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

  17. Elementary Teachers' Mathematical Knowledge for Teaching Prerequisite Algebra Concepts

    ERIC Educational Resources Information Center

    Welder, Rachael M.; Simonsen, Linda M.

    2011-01-01

    The current study investigated the effects of an undergraduate mathematics content course for pre-service elementary teachers. The participants' content knowledge was quantitatively measured using an instrument comprised of items from the Mathematical Knowledge for Teaching Measures (Hill, Schilling, & Ball, 2004). Using a one-group…

  18. Examination of Pre-Service Mathematics Teachers' Knowledge of Teaching Function Concept

    ERIC Educational Resources Information Center

    Tasdan, Berna Tataroglu; Koyunkaya, Melike Yigit

    2017-01-01

    Teaching of mathematics could be improved with teachers who have a strong mathematical knowledge and have an ability to reflect this knowledge on their teaching. Therefore, it is important to develop mathematics teachers' theoretical and pedagogical knowledge. This study was designed to examine pre-service secondary mathematics teachers' (PSMT)…

  19. Contrasting Knowledge for Elementary and Secondary Mathematics Teaching

    ERIC Educational Resources Information Center

    Rowland, Tim

    2012-01-01

    This paper describes and analyses two mathematics lessons, one with very young pupils, about subtraction, the other for lower secondary school pupils, about gradients [slopes] and graphs. The focus of the analysis is on teacher knowledge, and on the fundamental mathematical and mathematics-pedagogical prerequisites that underpin teaching these…

  20. Preservice Elementary Teachers' Mathematics Content Knowledge and Teacher Efficacy

    ERIC Educational Resources Information Center

    Newton, Kristie Jones; Leonard, Jacqueline; Evans, Brian R.; Eastburn, Julie A.

    2012-01-01

    The purpose of this study was to examine the relationship between mathematics content knowledge and teacher efficacy during an elementary mathematics methods course. A positive moderate relationship between content knowledge and personal teaching efficacy was found, and this relationship was stable during the course. No relationship was found…

  1. Exploring Mathematics Teachers' Pedagogical Content Knowledge in the Context of Knowledge of Students

    ERIC Educational Resources Information Center

    Aksu, Zeki; Kul, Ümit

    2016-01-01

    Functions are one of the basic topics taught in mathematics curriculum at Secondary school level requiring knowledge from the students' past, and uniting mathematical topics. Mathematics teachers have both their own learning experience of functions, as well as their own teaching experience, leading to the question of what level of student…

  2. Comparing the Major Definitions of Mathematics Pedagogical Content Knowledge

    ERIC Educational Resources Information Center

    Johnson, Jeffrey

    2017-01-01

    The purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK). As part of a larger study, nine current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT)--Mathematics assessment and the Cognitively Activating Instruction in Mathematics…

  3. Definitions of Mathematical Knowledge for Teaching: Using These Constructs in Research on Secondary and College Mathematics Teachers

    ERIC Educational Resources Information Center

    Speer, Natasha M.; King, Karen D.; Howell, Heather

    2015-01-01

    The construct "mathematical knowledge for teaching" (MKT) has received considerable attention in the mathematics education community in recent years. The development and refinement of the MKT construct, including the components of common content knowledge (CCK) and specialized content knowledge (SCK), came from research into elementary…

  4. Children's Mathematical Knowledge Prior to Starting School

    ERIC Educational Resources Information Center

    Gervasoni, Ann; Perry, Bob

    2013-01-01

    The introduction of the "Early Years Learning Framework and the Australian Curriculum-Mathematics" in Australian preschools and primary schools has caused early childhood educators to reconsider what may be appropriate levels of mathematics knowledge to expect from children as they start school. This paper reports on initial data from an…

  5. The Microevolution of Mathematical Knowledge: The Case of Randomness.

    ERIC Educational Resources Information Center

    Pratt, Dave; Noss, Richard

    2002-01-01

    Explores the growth of mathematical knowledge and the relationship between abstraction and context. Builds on work to construct a viable model of the micro-evolution of mathematical knowledge in context whose central feature is the visibility of its mechanisms. Illustrates a case study of 10-11-year-old children's construction of meanings for…

  6. Measuring Mathematics Teacher Educators' Knowledge of Technology Integrated Teaching: Instrument Development

    ERIC Educational Resources Information Center

    Getenet, Seyum Tekeher; Beswick, Kim

    2013-01-01

    This study describes the construction of a questionnaire instrument to measure mathematics teacher educators' knowledge for technology integrated mathematics teaching. The study was founded on a reconceptualisation of the generic Technological Pedagogical Content Knowledge framework in the specific context of mathematics teaching. Steps in the…

  7. The Framing Discussion: Connecting Student Experience with Mathematical Knowledge

    ERIC Educational Resources Information Center

    Henning, John E.; Balong, Megan

    2011-01-01

    This article introduces the framing discussion, an informal discussion of a mathematical problem that takes place at the beginning of a lesson or unit. The purpose of the framing discussion is to assess student knowledge, motivate student interest, and to serve as a basis for guiding students to more formal mathematical knowledge. The article…

  8. Knowledge and Knowing in Mathematics and Pedagogy: A Case Study of Mathematics Student Teachers' Epistemological Beliefs

    ERIC Educational Resources Information Center

    Löfström, Erika; Pursiainen, Tuomas

    2015-01-01

    This study focuses on mathematics student teachers' epistemological beliefs in mathematics and education. The study aimed at gaining insight into the challenges that students experience in the consolidation of knowledge in the two disciplines. The case study with three mathematics pre-service teachers utilised mathematical and pedagogical…

  9. On Singapore Prospective Secondary School Teachers' Mathematical Content Knowledge

    ERIC Educational Resources Information Center

    Toh, Tin Lam

    2017-01-01

    This paper reports the performance of one entire cohort of Singapore prospective secondary school mathematics teachers in a mathematics proficiency test. The prospective teachers were admitted to the teacher education program specializing in teaching secondary school mathematics. The strengths of the prospective teachers' content knowledge, their…

  10. Understanding Malaysian Pre-Service Teachers Mathematical Content Knowledge and Pedagogical Content Knowledge

    ERIC Educational Resources Information Center

    Leong, Kwan Eu; Meng, Chew Cheng; Rahim, Suzieleez Syrene Abdul

    2015-01-01

    This article seeks to present findings from the analysis of the TEDS-M reports on the mathematical content knowledge (MCK) and pedagogical content knowledge (PCK) of the pre-service teachers in Malaysia. The main objective of this study was to investigate the level of teaching knowledge attained by the Malaysian pre-service primary and secondary…

  11. Mitigating the Mathematical Knowledge Gap between High School and First Year University Chemical Engineering Mathematics Course

    ERIC Educational Resources Information Center

    Basitere, Moses; Ivala, Eunice

    2015-01-01

    This paper reports on a study carried out at a University of Technology, South Africa, aimed at identifying the existence of the mathematical knowledge gap and evaluating the intervention designed to bridge the knowledge gap amongst students studying first year mathematics at the Chemical Engineering Extended Curriculum Program (ECP). In this…

  12. Processes and Pathways: How Do Mathematics and Science Partnerships Measure and Promote Growth in Teacher Content Knowledge?

    ERIC Educational Resources Information Center

    Moyer-Packenham, Patricia S.; Westenskow, Arla

    2012-01-01

    Intense focus on student achievement results in mathematics and science has brought about claims that K-12 teachers should be better prepared to teach basic concepts in these disciplines. The focus on teachers' mathematics and science content knowledge has been met by efforts to increase teacher knowledge through funded national initiatives…

  13. Prospective Middle Grade Mathematics Teachers' Knowledge of Algebra for Teaching

    ERIC Educational Resources Information Center

    Huang, Rongjin; Kulm, Gerald

    2012-01-01

    This study examined prospective middle grade mathematics teachers' knowledge of algebra for teaching with a focus on knowledge for teaching the concept of function. 115 prospective teachers from an interdisciplinary program for mathematics and science middle teacher preparation at a large public university in the USA participated in a survey. It…

  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. Mathematical knowledge in teaching of fraction concepts using diagrammatical approach

    NASA Astrophysics Data System (ADS)

    Veloo, Palanisamy Kathir; Puteh, Marzita

    2017-05-01

    Teachers need various types of knowledge in order to deliver various fraction concepts at elementary level. In this paper, Balls' framework (2008) or, Mathematical Knowledge for Teaching (MKT) is used as benchmark guideline. This paper investigates and explores component of MKT knowledge among eight experienced teachers of the primary school. Data was collected using paper pencil test, interview and video recording. This paper, narrowed to teacher's knowledge and their practices while teaching of various fractions concepts using diagrammatical approach in present of MKT. The data gathered from teachers were analyzed using thematic analysis techniques. The results indicated that teachers lack various components of MKT knowledge as a proposal by various researchers and assumed that teaching as procedural more than enough due to lack of deep understanding of mathematics and the various types of MKT is not required due to the present of practices in the mathematics classroom.

  16. Pedagogical content knowledge: Knowledge of pedagogy novice teachers in mathematics learning on limit algebraic function

    NASA Astrophysics Data System (ADS)

    Ma'rufi, Budayasa, I. Ketut; Juniati, Dwi

    2017-02-01

    Teacher is one of the key aspects of student's achievement. Teachers should master content material taught, how to teach it, and can interpret the students' thinking so that students easily understand the subject matter. This research was a qualitative research that aimed at describing profile of PCK's teachers in mathematics on limit algebraic functions in terms of the differences of teaching experience. Pedagogical Content Knowledge (PCK) and understanding of teachers is defined as involving the relationship between knowledge of teaching materials, how to transfer the subject matter, and the knowledge of students in mathematics on limit algebraic functions that the subject matter may be understood by students. The PCK components in this research were knowledge of subject matter, knowledge of pedagogy, and knowledge of students. Knowledge of pedagogy defines as knowledge and understanding of teachers about the planning and organization of the learning and teaching strategy of limit algebraic function. The subjects were two mathematics high school teachers who teach in class XI IPS. Data were collected through observation of learning during five meetings and interviews before and after the lesson continued with qualitative data analysis. Focus of this article was to describe novice teacher's knowledge of student in mathematics learning on limit algebraic function. Based on the results of the analysis of qualitative data the data concluded that novice teacher's knowledge of pedagogy in mathematics on limit algebraic function showed: 1) in teaching the definitions tend to identify prior knowledge of the student experience with the material to be studied, but not in the form of a problem, 2) in posing the questions tend to be monotonous non lead and dig, 3) in response to student questions preservice teachers do not take advantage of the characteristics or the potential of other students, 4) in addressing the problem of students, tend to use the drill approach and did

  17. Preservice Secondary Mathematics Teachers' Knowledge of Students

    ERIC Educational Resources Information Center

    Kilic, Hulya

    2011-01-01

    The aim of this paper is to present the nature of preservice secondary mathematics teachers' knowledge of students as emerged from a study investigating the development of their pedagogical content knowledge in a methods course and its associated field experience. Six preservice teachers participated in the study and the data were collected in the…

  18. Technological Pedagogical Content Knowledge of Secondary Mathematics Teachers

    ERIC Educational Resources Information Center

    Handal, Boris; Campbell, Chris; Cavanagh, Michael; Petocz, Peter; Kelly, Nick

    2013-01-01

    The integration of technology, pedagogy, and content in the teaching of secondary mathematics was explored among 280 secondary mathematics teachers in the State of New South Wales, Australia. The study adopted the technological pedagogical content knowledge (TPCK) model through the administration of a 30-item instrument called TPCK-M. The…

  19. Examination of Mathematics Teachers' Pedagogical Content Knowledge of Probability

    ERIC Educational Resources Information Center

    Danisman, Sahin; Tanisli, Dilek

    2017-01-01

    The aim of this study is to explore the probability-related pedagogical content knowledge (PCK) of secondary school mathematics teachers in terms of content knowledge, curriculum knowledge, student knowledge, and knowledge of teaching methods and strategies. Case study design, a qualitative research model, was used in the study, and the…

  20. The Hidden Strand of Mathematical Proficiency: Defining and Assessing for Productive Disposition in Elementary School Teachers' Mathematical Content Knowledge

    ERIC Educational Resources Information Center

    Siegfried, John Zig Michael

    2012-01-01

    Teachers' mathematical content knowledge is one of the most important constructs considered by researchers studying elementary mathematics education (Fennema & Franke, 1992). One component of mathematical content knowledge that is complicated, ill-defined, and oft-ignored is "productive disposition," defined as the…

  1. Early Math Trajectories: Low-Income Children's Mathematics Knowledge From Ages 4 to 11.

    PubMed

    Rittle-Johnson, Bethany; Fyfe, Emily R; Hofer, Kerry G; Farran, Dale C

    2017-09-01

    Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An early math trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from ages 4 to 11. This model includes a broad range of math topics, as well as potential pathways from preschool to middle grades mathematics achievement. In preschool, nonsymbolic quantity, counting, and patterning knowledge predicted fifth-grade mathematics achievement. By the end of first grade, symbolic mapping, calculation, and patterning knowledge were the important predictors. Furthermore, the first-grade predictors mediated the relation between preschool math knowledge and fifth-grade mathematics achievement. Findings support the early math trajectories model among low-income children. © 2016 The Authors. Child Development © 2016 Society for Research in Child Development, Inc.

  2. Evolution of Mathematics Teachers' Pedagogical Knowledge When They Are Teaching through Modeling

    ERIC Educational Resources Information Center

    Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Alacaci, Cengiz; Cakiroglu, Erdinc; Cetinkaya, Bulent

    2017-01-01

    Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students' mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers' knowledge to use modeling in mathematics education and how…

  3. The Development of Mathematical Knowledge for Teaching of Mathematics Teachers in Lesson Analysis Process

    ERIC Educational Resources Information Center

    Baki, Mujgan

    2015-01-01

    This study aims to explore the role of lesson analysis in the development of mathematical knowledge for teaching. For this purpose, a graduate course based on lesson analysis was designed for novice mathematics teachers. Throughout the course the teachers watched videos of group-mates and discussed the issues they identified in terms of…

  4. An Exploration of the Common Content Knowledge of High School Mathematics Teachers

    ERIC Educational Resources Information Center

    Bansilal, Sarah; Brijlall, Deonarain; Mkhwanazi, Thokozani

    2014-01-01

    Many studies point to the problem of poor mathematics content knowledge of mathematics teachers in South Africa. The purpose of this study was to investigate teachers' knowledge of the mathematics they are themselves teaching. Data was generated from the teachers' (n = 253) written responses to test that was a shortened form of a previous Grade 12…

  5. Effects of an Additional Mathematics Content Course on Elementary Teachers' Mathematical Beliefs and Knowledge for Teaching

    ERIC Educational Resources Information Center

    Smith, Marvin E.; Swars, Susan L.; Smith, Stephanie Z.; Hart, Lynn C.; Haardorfer, Regine

    2012-01-01

    This longitudinal study examines the effects of changes in an elementary teacher preparation program on mathematics beliefs and content knowledge for teaching of two groups of prospective teachers (N = 276): (1) those who completed a program with three mathematics content courses and two mathematics methods courses and (2) those who completed a…

  6. The Development of Logico-Mathematical Knowledge in a Block-Building Activity at Ages 1-4

    ERIC Educational Resources Information Center

    Kamii, Constance; Miyakawa, Yoko; Kato, Yasuhiko

    2004-01-01

    To study the developmental interrelationships among various aspects of logico-mathematical knowledge, 80 one- to 4-year-olds were individually asked to build "something tall" with 20 blocks. Percentages of new and significant behaviors increased with age and were analyzed in terms of the development of logico-mathematical relationships. It was…

  7. Middle School Students' Mathematics Knowledge Retention: Online or Face-To-Face Environments

    ERIC Educational Resources Information Center

    Edwards, Clayton M.; Rule, Audrey C.; Boody, Robert M.

    2017-01-01

    Educators seek to develop students' mathematical knowledge retention to increase student efficacy in follow-on classwork, improvement of test scores, attainment of standards, and preparation for careers. Interactive visuals, feedback during problem solving, and incorporation of higher-order thinking skills are known to increase retention, but a…

  8. Building Knowledge Structures by Testing Helps Children with Mathematical Learning Difficulty

    ERIC Educational Resources Information Center

    Zhang, Yiyun; Zhou, Xinlin

    2016-01-01

    Mathematical learning difficulty (MLD) is prevalent in the development of mathematical abilities. Previous interventions for children with MLD have focused on number sense or basic mathematical skills. This study investigated whether mathematical performance of fifth grade children with MLD could be improved by developing knowledge structures by…

  9. Pre-Service Elementary Teachers' Mathematics Content Knowledge: A Predictor of Sixth Graders' Mathematics Performance

    ERIC Educational Resources Information Center

    Shirvani, Hosin

    2015-01-01

    This study examined the knowledge of mathematics content of elementary pre-service teachers at a sixth grade level. The researcher administered a mathematics test for sixth graders mandated by the Texas Education Agency to pre-service teachers; the same test was given to sixth graders in Texas. The study found that pre-service teachers performed…

  10. International Comparisons of Foundation Phase Number Domain Mathematics Knowledge and Practice Standards

    ERIC Educational Resources Information Center

    Human, Anja; van der Walt, Marthie; Posthuma, Barbara

    2015-01-01

    Poor mathematics performance in schools is both a national and an international concern. Teachers ought to be equipped with relevant subject matter knowledge and pedagogical content knowledge as one way to address this problem. However, no mathematics knowledge and practice standards have as yet been defined for the preparation of Foundation Phase…

  11. Theoretical Framework of Researcher Knowledge Development in Mathematics Education

    ERIC Educational Resources Information Center

    Kontorovich, Igor'

    2016-01-01

    The goal of this paper is to present a framework of researcher knowledge development in conducting a study in mathematics education. The key components of the framework are: knowledge germane to conducting a particular study, processes of knowledge accumulation, and catalyzing filters that influence a researcher's decision making. The components…

  12. Assessing Knowledge of Mathematical Equivalence: A Construct-Modeling Approach

    ERIC Educational Resources Information Center

    Rittle-Johnson, Bethany; Matthews, Percival G.; Taylor, Roger S.; McEldoon, Katherine L.

    2011-01-01

    Knowledge of mathematical equivalence, the principle that 2 sides of an equation represent the same value, is a foundational concept in algebra, and this knowledge develops throughout elementary and middle school. Using a construct-modeling approach, we developed an assessment of equivalence knowledge. Second through sixth graders (N = 175)…

  13. The Increase of Critical Thinking Skills through Mathematical Investigation Approach

    NASA Astrophysics Data System (ADS)

    Sumarna, N.; Wahyudin; Herman, T.

    2017-02-01

    Some research findings on critical thinking skills of prospective elementary teachers, showed a response that is not optimal. On the other hand, critical thinking skills will lead a student in the process of analysis, evaluation and synthesis in solving a mathematical problem. This study attempts to perform an alternative solution with a focus on mathematics learning conditions that is held in the lecture room through mathematical investigation approach. This research method was Quasi-Experimental design with pre-test post-test design. Data analysis using a mixed method with Embedded design. Subjects were regular students enrolled in 2014 at the study program of education of primary school teachers. The number of research subjects were 111 students consisting of 56 students in the experimental group and 55 students in the control group. The results of the study showed that (1) there is a significant difference in the improvement of critical thinking ability of students who receive learning through mathematical investigation approach when compared with students studying through expository approach, and (2) there is no interaction effect between prior knowledge of mathematics and learning factors (mathematical investigation and expository) to increase of critical thinking skills of students.

  14. Field Experience and Prospective Teachers' Mathematical Knowledge and Beliefs

    ERIC Educational Resources Information Center

    Jacobson, Erik D.

    2017-01-01

    This study (n = 1,044) used data from the Teacher Education and Development Study in Mathematics (TEDS-M) to examine the relationship between field experience focus (instruction- or exploration-focused), duration, and timing (early or not) and prospective elementary teachers' intertwined knowledge and beliefs about mathematics and mathematics…

  15. Gender Difference in Teachers' Mathematical Knowledge for Teaching in the Context of Single-Sex Classrooms

    ERIC Educational Resources Information Center

    Haroun, Ramzi F.; Ng, Dicky; Abdelfattah, Faisal A.; AlSalouli, Misfer S.

    2016-01-01

    This study examines gender differences of teachers on their mathematical knowledge for teaching in the context of single-sex classrooms in Saudi Arabia. A translated version of the Mathematical Knowledge for Teaching (MKT) instrument (Learning Mathematics for Teaching [LMT], 2008) in Number and Operation Content Knowledge (CK) and Knowledge of…

  16. Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement: An Eight-Year Longitudinal Study

    PubMed Central

    Geary, David C.; Nicholas, Alan; Li, Yaoran; Sun, Jianguo

    2016-01-01

    The contributions of domain-general abilities and domain-specific knowledge to subsequent mathematics achievement were longitudinally assessed (n = 167) through 8th grade. First grade intelligence and working memory and prior grade reading achievement indexed domain-general effects and domain-specific effects were indexed by prior grade mathematics achievement and mathematical cognition measures of prior grade number knowledge, addition skills, and fraction knowledge. Use of functional data analysis enabled grade-by-grade estimation of overall domain-general and domain-specific effects on subsequent mathematics achievement, the relative importance of individual domain-general and domain-specific variables on this achievement, and linear and non-linear across-grade estimates of these effects. The overall importance of domain-general abilities for subsequent achievement was stable across grades, with working memory emerging as the most important domain-general ability in later grades. The importance of prior mathematical competencies on subsequent mathematics achievement increased across grades, with number knowledge and arithmetic skills critical in all grades and fraction knowledge in later grades. Overall, domain-general abilities were more important than domain-specific knowledge for mathematics learning in early grades but general abilities and domain-specific knowledge were equally important in later grades. PMID:28781382

  17. Opportunities to Promote Mathematical Content Knowledge for Primary Teaching

    ERIC Educational Resources Information Center

    Livy, Sharyn; Herbert, Sandra

    2014-01-01

    Understanding the development of pre-service teachers' mathematical content knowledge (MCK) is important for improving primary mathematics' teacher education. This paper reports on a case study, Rose and her opportunities to develop MCK during the four years of her program. Program opportunities to promote MCK when planning and practicing primary…

  18. The Relationship between Mathematical Knowledge of Numbers and Operations and Mathematics Beliefs of Prospective Teachers

    ERIC Educational Resources Information Center

    Stiegelmeyer, Cindy

    2012-01-01

    This study surveyed 82 preservice elementary teachers using items from an instrument designed to predict student achievement based on a teacher's mathematics knowledge for teaching (MKT) in numbers and operations concepts. Additional mathematics beliefs items asked participants to rate their level of agreement with math myths and math anxiety…

  19. Mathematics as an Im/Pure Knowledge System: Symbiosis, (W)Holism and Synergy in Mathematics Education

    ERIC Educational Resources Information Center

    Luitel, Bal Chandra

    2013-01-01

    The problem of culturally decontextualised mathematics education faced by Nepali students, teachers and teacher educators has often been oriented by the view of the nature of "mathematics as a body of pure knowledge," which gives rise to an exclusive emphasis on an ideology of singularity, epistemology of objectivism, language of…

  20. Developing a Leveling Framework of Mathematical Belief and Mathematical Knowledge for Teaching of Indonesian Pre-Service Teachers

    ERIC Educational Resources Information Center

    Novikasari, Ifada; Darhim, Didi Suryadi

    2015-01-01

    This study explored the characteristics of pre-service primary teachers (PSTs) influenced by mathematical belief and mathematical knowledge for teaching (MKT) PSTs'. A qualitative approach was used to investigate the levels of PSTs on mathematical belief and MKT. The two research instruments used in this study were an interview-based task and a…

  1. Theorising about Mathematics Teachers' Professional Knowledge: The Content, Form, Nature, and Course of Teachers' Knowledge

    ERIC Educational Resources Information Center

    Scheiner, Thorsten

    2015-01-01

    The guiding philosophy of this theoretical work lays in the argument that mathematics teachers' professional knowledge is the integration of various knowledge facets derived from different sources including teaching experience and research. This paper goes beyond past trends identifying what the teachers' knowledge is about (content) by providing…

  2. Pedagogical Content Knowledge: Teacher’s Knowledge of Students in Learning Mathematics on Limit of Function Subject

    NASA Astrophysics Data System (ADS)

    Ma'rufi; Ketut Budayasa, I.; Juniati, Dwi

    2018-01-01

    This research aims at describing the profile of high school teacher’s Pedagogical Content Knowledge in learning mathematics from the perspective of teaching experience. Pedagogical Content Knowledge (PCK) covers teacher’s knowledge of subject matter, knowledge of pedagogy, and knowledge of students. The subject of this research was two high school mathematics teachers who have different teaching experience. The data were obtained through interview and observation then analyzed qualitatively. The focus of this research is the novice teacher’s PCK deals with knowledge of students. Knowledge of Student is defined as teacher’s knowledge about the students’ conception and misconception on limit of function material and teacher’s ability to cope with students’ difficulty, mistake, and misconception. The result of this research shows that novice teacher’s ability in analyzing the cause of students’ difficulty, mistake, and misconception was limited. Novice teacher tended to overcome the students’ difficulty, mistake, and misconception by re-explaining the procedure of question completion which is not understood by the students.

  3. Learning to teach upper primary school algebra: changes to teachers' mathematical knowledge for teaching functional thinking

    NASA Astrophysics Data System (ADS)

    Wilkie, Karina J.

    2016-06-01

    A key aspect of learning algebra in the middle years of schooling is exploring the functional relationship between two variables: noticing and generalising the relationship, and expressing it mathematically. This article describes research on the professional learning of upper primary school teachers for developing their students' functional thinking through pattern generalisation. This aspect of algebra learning has been explicitly brought to the attention of upper primary teachers in the recently introduced Australian curriculum. Ten practising teachers participated over 1 year in a design-based research project involving a sequence of geometric pattern generalisation lessons with their classes. Initial and final survey responses and teachers' interactions in regular meetings and lessons were analysed from cognitive and situated perspectives on professional learning, using a theoretical model for the different types of knowledge needed for teaching mathematics. The teachers demonstrated an increase in certain aspects of their mathematical knowledge for teaching algebra as well as some residual issues. Implications for the professional learning of practising and pre-service teachers to develop their mathematics knowledge for teaching functional thinking, and challenges with operationalising knowledge categories for field-based research are presented.

  4. Relationship between mathematics teacher subject matter knowledge, pedagogical content knowledge and professional development needs

    NASA Astrophysics Data System (ADS)

    Tajudin, Nor'ain Mohd; Chinnappan, Mohan; Saad, Noor Shah

    2017-05-01

    Two key variables emerged from the literature review is that Specific Matter Knowledge [SMK] and Pedagogical Content Knowledge [PCK] can influence the mathematics teachers' Professional Development [PD] needs. However, the key variables of SMK and PCK that were being investigated were not defined clearly. Empirical evidence that support relationship between SMK and PD and PCK and PD were not verified. In addition, how does PCK mediate SMK and PD is not clear and somewhat lacking. Therefore, the purpose of this paper was to examine the relationship between primary mathematics teacher's SMK, PCK and PD needs. Results of path analysis with SmartPLS indicated that the direct effect of SMK on PD was mediated via PCK. This data provide support for the claim that PD programs for future teachers of primary mathematics should be driven by a more nuanced understanding of the link between SMK and PCK.

  5. 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…

  6. The challenges facing initial teacher education: Irish prospective elementary teachers' mathematics subject matter knowledge

    NASA Astrophysics Data System (ADS)

    Hourigan, Mairéad; O'Donoghue, John

    2013-01-01

    Given the acknowledged relationship between teachers' knowledge, their teaching and pupil learning, teachers' mathematics subject matter knowledge (MSMK) has received increased attention internationally. As children's early mathematics experiences have been recognized as a critical stage, elementary teachers' MSMK has become a focal point among researchers and policy makers alike. International research findings have uncovered that in many cases, there is a mismatch between what is perceived to be an appropriate MSMK for teaching elementary mathematics and that demonstrated by many qualified and prospective elementary teachers. Following repeated incidences of weak MSMK during interactions with prospective elementary teachers in one Irish College of Education (provider of initial teacher education programme for elementary teachers), this study sought to examine and address the issue purposefully through two cycles of action research. This article focuses on the data collected prospective teachers' MSMK in the initial stage (reconnaissance) of these cycles, i.e. pre-test findings. While considerable differences were evident among the pre-test population, the findings suggest that prior to the intervention stage many participating prospective teachers; regardless of previous mathematics achievements or the level of mathematics study; demonstrate weaknesses and gaps in their 'common' MSMK. Particular difficulties were evident in relation to pre-test items requiring knowledge of rational numbers, conceptual understanding or problem solving. These findings highlight the inadequacy of previous mathematics achievements and indeed minimum entry requirements as predictors of MSMK for teaching. As well as its contribution at a local and national level, the findings provide an Irish perspective on this international issue.

  7. Mathematics Teachers' Knowledge of Student Thinking and Its Evidences in Their Instruction

    ERIC Educational Resources Information Center

    Çelik, Aytug Özaltun; Güzel, Esra Bukova

    2017-01-01

    The aim of this case study is to examine mathematics teachers' knowledge of students' thinking and its evidences in their teaching. The participants were three secondary mathematics teachers. Data were gathered from interviews and observations. While analyzing the data, the framework about teachers' knowledge of students' thinking was used. The…

  8. Mathematical Knowledge for Teaching, Standards-Based Mathematics Teaching Practices, and Student Achievement in the Context of the "Responsive Classroom Approach"

    ERIC Educational Resources Information Center

    Ottmar, Erin R.; Rimm-Kaufman, Sara E.; Larsen, Ross A.; Berry, Robert Q.

    2015-01-01

    This study investigates the effectiveness of the Responsive Classroom (RC) approach, a social and emotional learning intervention, on changing the relations between mathematics teacher and classroom inputs (mathematical knowledge for teaching [MKT] and standards-based mathematics teaching practices) and student mathematics achievement. Work was…

  9. Cortical circuits for mathematical knowledge: evidence for a major subdivision within the brain's semantic networks.

    PubMed

    Amalric, Marie; Dehaene, Stanislas

    2017-02-19

    Is mathematical language similar to natural language? Are language areas used by mathematicians when they do mathematics? And does the brain comprise a generic semantic system that stores mathematical knowledge alongside knowledge of history, geography or famous people? Here, we refute those views by reviewing three functional MRI studies of the representation and manipulation of high-level mathematical knowledge in professional mathematicians. The results reveal that brain activity during professional mathematical reflection spares perisylvian language-related brain regions as well as temporal lobe areas classically involved in general semantic knowledge. Instead, mathematical reflection recycles bilateral intraparietal and ventral temporal regions involved in elementary number sense. Even simple fact retrieval, such as remembering that 'the sine function is periodical' or that 'London buses are red', activates dissociated areas for math versus non-math knowledge. Together with other fMRI and recent intracranial studies, our results indicated a major separation between two brain networks for mathematical and non-mathematical semantics, which goes a long way to explain a variety of facts in neuroimaging, neuropsychology and developmental disorders.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).

  10. Pedagogical Content Knowledge in Mathematical Modelling Instruction

    ERIC Educational Resources Information Center

    Tan, Liang Soon; Ang, Keng Cheng

    2012-01-01

    This paper posits that teachers' pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students' learning…

  11. Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

    ERIC Educational Resources Information Center

    Schwerdtfeger, Sara

    2017-01-01

    This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

  12. Technological pedagogical content knowledge and teaching practice of mathematics trainee teachers

    NASA Astrophysics Data System (ADS)

    Tajudin, Nor'ain Mohd.; Kadir, Noor Zarinawaty Abd.

    2014-07-01

    This study aims to identify the level of technological pedagogical content knowledge (TPCK) of mathematics trainee teachers at Universiti Pendidikan Sultan Idris (UPSI) and explore their teaching practices during practical training at school. The study was conducted in two phases using a mix-method research. In the first phase, a survey method using a questionnaire was carried out on 156 trainee teachers of Bachelor of Mathematics Education (AT14) and Bachelor of Science (Mathematics) with Education (AT48). The instrument used was a questionnaire that measures the level of content knowledge, pedagogy, technology and TPCK of mathematics. Data were analyzed using descriptive statistics, namely the mean. While in the second phase, the interview method involved four trainee teachers were performed. The instrument used was the semi-structured interview protocol to assess the trainee teacher's TPCK integration in their teaching practice. Data were analyzed using the content analysis. The findings showed that the level of knowledge of TPCK among trainee teachers was moderate with overall mean score of 3.60. This level did not show significant differences between the two programs with mean scores of 3.601 for the AT14 group and 3.603 for the AT48 group. However, there was a difference for gender classification such that the female trainees had mean score of 3.58 and male trainees with mean score of 3.72. Although students' TPCK level was moderate, the level of content knowledge (CK), technological knowledge (TK) and pedagogical knowledge (PK), showed a higher level with overall mean scores of 3.75, 3.87 and 3.84 respectively. The findings also showed that in terms of content knowledge, trainee teacher's learning mathematics background was good, but the knowledge of mathematics was limited in the curriculum, philosophy and application aspect. In terms of pedagogical content knowledge, all respondents tend to use lecture and discussion methods in teaching Trigonometry topic

  13. Iterating between lessons on concepts and procedures can improve mathematics knowledge.

    PubMed

    Rittle-Johnson, Bethany; Koedinger, Kenneth

    2009-09-01

    Knowledge of concepts and procedures seems to develop in an iterative fashion, with increases in one type of knowledge leading to increases in the other type of knowledge. This suggests that iterating between lessons on concepts and procedures may improve learning. The purpose of the current study was to evaluate the instructional benefits of an iterative lesson sequence compared to a concepts-before-procedures sequence for students learning decimal place-value concepts and arithmetic procedures. In two classroom experiments, sixth-grade students from two schools participated (N=77 and 26). Students completed six decimal lessons on an intelligent-tutoring systems. In the iterative condition, lessons cycled between concept and procedure lessons. In the concepts-first condition, all concept lessons were presented before introducing the procedure lessons. In both experiments, students in the iterative condition gained more knowledge of arithmetic procedures, including ability to transfer the procedures to problems with novel features. Knowledge of concepts was fairly comparable across conditions. Finally, pre-test knowledge of one type predicted gains in knowledge of the other type across experiments. An iterative sequencing of lessons seems to facilitate learning and transfer, particularly of mathematical procedures. The findings support an iterative perspective for the development of knowledge of concepts and procedures.

  14. Knowledge Base of Mathematics Teacher Educators: A Goals-Knowledge-Practice Approach

    ERIC Educational Resources Information Center

    Veselovsky, Aleksandra

    2017-01-01

    Critical analysis of the literature reveals that many questions about the knowledge and practice of mathematics teacher educators (MTEs) remain in need of further research: how do they know what to teach; how do they learn how to teach teachers; how do they prepare to teach their courses; how does the research on teacher education inform their…

  15. Infusing Mathematics Content into a Methods Course: Impacting Content Knowledge for Teaching

    ERIC Educational Resources Information Center

    Burton, Megan; Daane, C. J.; Giesen, Judy

    2008-01-01

    This study compared content knowledge for teaching mathematics differences between elementary pre-service teachers in a traditional versus an experimental mathematics methods course. The experimental course replaced 20 minutes of traditional methods, each class, with an intervention of elementary mathematics content. The difference between groups…

  16. Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics

    ERIC Educational Resources Information Center

    Wang, Youjun

    2009-01-01

    In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…

  17. Building Knowledge Structures by Testing Helps Children With Mathematical Learning Difficulty.

    PubMed

    Zhang, Yiyun; Zhou, Xinlin

    2016-01-01

    Mathematical learning difficulty (MLD) is prevalent in the development of mathematical abilities. Previous interventions for children with MLD have focused on number sense or basic mathematical skills. This study investigated whether mathematical performance of fifth grade children with MLD could be improved by developing knowledge structures by testing using a web-based curriculum learning system. A total of 142 children with MLD were recruited; half of the children were in the experimental group (using the system), and the other half were in the control group (not using the system). The children were encouraged to use the web-based learning system at home for at least a 15-min session, at least once a week, for one and a half months. The mean accumulated time of testing on the system for children in the experimental group was 56.2 min. Children in the experimental group had significantly higher scores on their final mathematical examination compared to the control group. The results suggest that web-based curriculum learning through testing that promotes the building of knowledge structures for a mathematical course was helpful for children with MLD. © Hammill Institute on Disabilities 2014.

  18. Exploring Connections between Content Knowledge, Pedagogical Content Knowledge, and the Opportunities to Learn Mathematics: Findings from the TEDS-M Dataset

    ERIC Educational Resources Information Center

    Murray, Eileen; Durkin, Kelley; Chao, Theodore; Star, Jon R.; Vig, Rozy

    2018-01-01

    Past work on mathematics teachers' content knowledge (CK) and pedagogical content knowledge (PCK) has resulted in mixed findings about the strength of the relationship between and development of these constructs. The current study uses data from the Teacher Education and Development Study in Mathematics (TEDS-M) to examine the relationship between…

  19. Early Math Trajectories: Low-Income Children's Mathematics Knowledge from Age 4 to 11

    ERIC Educational Resources Information Center

    Rittle-Johnson, Bethany; Fyfe, Emily R.; Hofer, Kerry G.; Farran, Dale C.

    2016-01-01

    Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An Early Math Trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from age 4 to 11. This model includes a broad range of math…

  20. The Relationship Between Teachers' Mathematical Content and Pedagogical Knowledge, Teachers' Perceptions, and Student Achievement

    ERIC Educational Resources Information Center

    Campbell, Patricia F.; Nishio, Masako; Smith, Toni M.; Clark, Lawrence M.; Conant, Darcy L.; Rust, Amber H.; DePiper, Jill Neumayer; Frank, Toya Jones; Griffin, Matthew J.; Choi, Youyoung

    2014-01-01

    This study of early-career teachers identified a significant relationship between upper-elementary teachers' mathematical content knowledge and their students' mathematics achievement, after controlling for student- and teacher-level characteristics. Findings provide evidence of the relevance of teacher knowledge and perceptions for teacher…

  1. Behavioural Intention and Pre-Service Mathematics Teachers' Technological Pedagogical Content Knowledge

    ERIC Educational Resources Information Center

    Gonzalez, Maria Jose; González-Ruiz, Ignacio

    2017-01-01

    Teachers' beliefs, together with sound technological pedagogical content knowledge (TPACK), are directly related to the effective integration of technology in mathematics teaching. This study explored the relationship between pre-service teachers' behavioural intention to use technology to teach mathematics and their TPACK. A case-study analysis…

  2. Determining Quality Teachers: Mathematical Content Knowledge, Perceptions of Teaching Self-Efficacy, and Attitudes toward Mathematics among a Teach for America Cohort

    ERIC Educational Resources Information Center

    Evans, Brian R.

    2010-01-01

    The purpose of this study was to understand the relationships between mathematical content knowledge, perceptions of teaching self-efficacy, and attitudes toward mathematics in one cohort of Teach for America teachers who took the New York State Content Special Test in mathematics at the start of their program, and a mathematics attitude…

  3. Status of Teachers' Proficiency in Mathematical Knowledge for Teaching at Secondary School Level in Kenya

    ERIC Educational Resources Information Center

    Miheso-O'Connor Khakasa, Marguerite; Berger, Margot

    2016-01-01

    Mathematical knowledge for teaching (MKT), defined by Ball ("Elementary Journal," 93, 373-397, 1993) as knowledge that is needed to teach mathematics, has been used as a framework by researchers to interrogate various aspects of teaching and learning mathematics. In this article, which draws from a larger study, we show how an in-depth…

  4. TEDS-M 2008 User Guide for the International Database. Supplement 4: TEDS-M Released Mathematics and Mathematics Pedagogy Knowledge Assessment Items

    ERIC Educational Resources Information Center

    Brese, Falk, Ed.

    2012-01-01

    The goal for selecting the released set of test items was to have approximately 25% of each of the full item sets for mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) that would represent the full range of difficulty, content, and item format used in the TEDS-M study. The initial step in the selection was to…

  5. Investigating First Year Elementary Mathematics Teacher Education Students' Knowledge of Prism

    ERIC Educational Resources Information Center

    Bozkurt, Ali; Koc, Yusuf

    2012-01-01

    The purpose of this study was to investigate first year elementary mathematics teacher education students' knowledge of prism. For this goal, the participants were asked to define the geometric concept of prism. The participants were 158 first year elementary mathematics teacher education students from a public university in Southern Turkey. The…

  6. Relationship between Pedagogical Strategies and Teachers' Content Knowledge of Mathematics

    ERIC Educational Resources Information Center

    Kanyongo, Gibbs Y.; Brown, Launcelot I.

    2013-01-01

    This study employed regression analysis to investigate the relationship between primary school teachers' pedagogical practices and their knowledge of mathematics. The sample composed of 606 Grade 6 mathematics teachers in Namibia, i.e. 304 (50.2%) males and 302 (49.8%) females. The study utilized existing questionnaire data collected by the…

  7. 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

  8. 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

  9. Online Mathematics Homework Increases Student Achievement

    ERIC Educational Resources Information Center

    Roschelle, Jeremy; Feng, Mingyu; Murphy, Robert F.; Mason, Craig A.

    2016-01-01

    In a randomized field trial with 2,850 seventh-grade mathematics students, we evaluated whether an educational technology intervention increased mathematics learning. Assigning homework is common yet sometimes controversial. Building on prior research on formative assessment and adaptive teaching, we predicted that combining an online homework…

  10. The Effects of Different Undergraduate Mathematics Courses on the Content Knowledge and Attitude towards Mathematics of Preservice Elementary Teachers

    ERIC Educational Resources Information Center

    Matthews, Michael E.; Seaman, Walter I.

    2007-01-01

    Preservice elementary teachers have been shown to generally possess poor mathematical knowledge (e.g. Goulding, Rowland, & Barber, 2002) and also strong negative attitudes toward mathematics (e.g. MacNab & Payne, 2004). Recently, national organizations have proposed interventions to address these issues (Conference Board of the…

  11. Science and Mathematics Teacher Candidates' Environmental Knowledge, Awareness, Behavior and Attitudes

    ERIC Educational Resources Information Center

    Yumusak, Ahmet; Sargin, Seyid Ahmet; Baltaci, Furkan; Kelani, Raphael R.

    2016-01-01

    The purpose of this study was to measure science and mathematics teacher candidates' environmental knowledge level, awareness, behavior and environmental attitudes. Four instruments comprising Environmental Sensitivity Scale, environmental Behavior Scale, Environmental Attitudes Scale and Environmental Knowledge Test were administered to a total…

  12. Making Connections in Practice: How Prospective Elementary Teachers Connect to Children's Mathematical Thinking and Community Funds of Knowledge in Mathematics Instruction

    ERIC Educational Resources Information Center

    Aguirre, Julia M.; Turner, Erin E.; Bartell, Tonya Gau; Kalinec-Craig, Crystal; Foote, Mary Q.; Roth McDuffie, Amy; Drake, Corey

    2013-01-01

    This study examines the ways prospective elementary teachers (PSTs) made connections to children's mathematical thinking and children's community funds of knowledge in mathematics lesson plans. We analyzed the work of 70 PSTs from across three university sites associated with an instructional module for elementary mathematics methods courses that…

  13. Rethinking Teacher Preparation: Conceptualizing Skills and Knowledge of Novice Teachers of Secondary Mathematics

    ERIC Educational Resources Information Center

    Cummings, Margarita Borelli

    2010-01-01

    This dissertation examines the extent to which novice secondary mathematics teachers (licensed and currently teaching in Utah) perceive they are prepared to do the work of teaching secondary mathematics. It first examined if novice secondary mathematics teachers' perceptions of their knowledge and skills of doing their work fell into four…

  14. 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.

  15. Using Video as a Stimulus to Reveal Elementary Teachers' Mathematical Knowledge for Teaching

    ERIC Educational Resources Information Center

    Barlow, Angela T.; Gaddy, Angeline K.; Baxter, Wesley A.

    2017-01-01

    The purpose of this article is to explore the usefulness of a video-based tool for measuring teachers' mathematical knowledge for teaching. Unique to this tool is the use of a video featuring a mathematical disagreement that occurred in an elementary classroom. The authors define mathematical disagreements as instances in which students challenge…

  16. What Math Matters? Types of Mathematics Knowledge and Relationships to Methods Course Performance

    ERIC Educational Resources Information Center

    Kajander, Ann; Holm, Jennifer

    2016-01-01

    This study investigated the effect of a departmental focus on enhanced mathematics knowledge for teaching on overall performance in upper elementary mathematics methods courses. The study examined the effect of performance on a new course in mathematics for teaching on performance at the methods course level. In addition, the effect of performance…

  17. Indonesian Primary Teachers' Mathematical Knowledge for Teaching Geometry: Implications for Educational Policy and Teacher Preparation Programs

    ERIC Educational Resources Information Center

    Ng, Dicky

    2011-01-01

    This study examines Indonesian primary teachers' mathematical knowledge for teaching geometry and what factors contribute to this knowledge. A translated and adapted version of the Learning Mathematics for Teaching measures and the Indonesian Educational Survey were used to gather information on teachers' knowledge for teaching geometry and their…

  18. Characterizing the Development of Specialized Mathematical Content Knowledge for Teaching in Algebraic Reasoning and Number Theory

    ERIC Educational Resources Information Center

    Bair, Sherry L.; Rich, Beverly S.

    2011-01-01

    This article characterizes the development of a deep and connected body of mathematical knowledge categorized by Ball and Bass' (2003b) model of Mathematical Knowledge for Teaching (MKT), as Specialized Content Knowledge for Teaching (SCK) in algebraic reasoning and number sense. The research employed multiple cases across three years from two…

  19. The Devalued Student: Misalignment of Current Mathematics Knowledge and Level of Instruction

    ERIC Educational Resources Information Center

    LeMire, Steven D.; Melby, Marcella L.; Haskins, Anne M.; Williams, Tony

    2012-01-01

    Within this study, we investigated the association between 10th-grade students' mathematics performance and their feelings of instructional misalignment between their current mathematics knowledge and educator support. Data from the 2002 Education Longitudinal Study, which included a national sample of 750 public and private high schools in the…

  20. The Relationship between Scores of Mathematics Knowledge and Teaching Practice of Diploma Mathematics Students: A Quest for Quality Assurance

    ERIC Educational Resources Information Center

    Adamu, L. E.

    2015-01-01

    The purpose of the study was to determine the relationship between scores in mathematics knowledge and teaching practice of Diploma mathematics students. A sample of 39 students was used. Two research questions and two hypotheses were asked and formulated respectively. An ex-post facto correlation design was used. The data were analyzed using…

  1. Does Knowing More Advanced Mathematics Ensure Effectiveness of Working towards Demonstrating Specialised Mathematical Content Knowledge of Second-Year Pre-Service Teachers?

    ERIC Educational Resources Information Center

    Livy, Sharyn

    2012-01-01

    The theoretical understanding that underpins a teacher's foundation knowledge draws on their common content knowledge (CCK) and influences their mathematics' teaching (Rowland, Turner, Thwaites, & Huckstep, 2009). Teachers who have specialised content knowledge (SCK) demonstrate a unique kind of content knowledge which is more than knowing the…

  2. First Year Pre-Service Teachers' Mathematical Content Knowledge: Methods of Solution for a Ratio Question

    ERIC Educational Resources Information Center

    Livy, Sharyn; Vale, Colleen

    2011-01-01

    In this article, pre-service teachers' mathematics content knowledge is explored through the analysis of two items about ratio from a Mathematical Competency, Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors and misconceptions in their responses are presented and discussed. Of particular interest was the range…

  3. Towards a Methodology for the Characterization of Teachers' Didactic-Mathematical Knowledge

    ERIC Educational Resources Information Center

    Pino-Fan, Luis R.; Assis, Adriana; Castro, Walter F.

    2015-01-01

    This research study aims at exploring the use of some dimensions and theoretical-methodological tools suggested by the model of Didactic-Mathematical Knowledge (DMK) for the analysis, characterization and development of knowledge that teachers should have in order to efficiently develop within their practice. For this purpose, we analyzed the…

  4. 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…

  5. Investigating Level of Mathematics Knowledge for Students Attending Vocational Schools in Turkey

    ERIC Educational Resources Information Center

    Colakoglu, Nurdan

    2013-01-01

    Students attend mathematics courses in Turkey for totally 11 years, throughout education life ranging from primary school to university, including eight years in primary education and three years in secondary education (four years based on new arrangement); however, level of mathematic knowledge of students is upsetting when they reach university…

  6. [The discussion of the infiltrative model of mathematical knowledge to genetics teaching].

    PubMed

    Liu, Jun; Luo, Pei-Gao

    2011-11-01

    Genetics, the core course of biological field, is an importance major-basic course in curriculum of many majors related with biology. Due to strong theoretical and practical as well as abstract of genetics, it is too difficult to study on genetics for many students. At the same time, mathematics is one of the basic courses in curriculum of the major related natural science, which has close relationship with the establishment, development and modification of genetics. In this paper, to establish the intrinsic logistic relationship and construct the integral knowledge network and to help students improving the analytic, comprehensive and logistic abilities, we applied some mathematical infiltrative model genetic knowledge in genetics teaching, which could help students more deeply learn and understand genetic knowledge.

  7. Faded-example as a Tool to Acquire and Automate Mathematics Knowledge

    NASA Astrophysics Data System (ADS)

    Retnowati, E.

    2017-04-01

    Students themselves accomplish Knowledge acquisition and automation. The teacher plays a role as the facilitator by creating mathematics tasks that assist students in building knowledge efficiently and effectively. Cognitive load caused by learning material presented by teachers should be considered as a critical factor. While the intrinsic cognitive load is related to the degree of complexity of the material learning ones can handle, the extraneous cognitive load is directly caused by how the material is presented. Strategies to present a learning material in computational learning domains like mathematics are a namely worked example (fully-guided task) or problem-solving (discovery task with no guidance). According to the empirical evidence, learning based on problem-solving may cause high-extraneous cognitive load for students who have limited prior knowledge, conversely learn based on worked example may cause high-extraneous cognitive load for students who have mastered the knowledge base. An alternative is a faded example consisting of the partly-completed task. Learning from faded-example can facilitate students who already acquire some knowledge about the to-be-learned material but still need more practice to automate the knowledge further. This instructional strategy provides a smooth transition from a fully-guided into an independent problem solver. Designs of faded examples for learning trigonometry are discussed.

  8. Early Math Trajectories: Low-Income Children's Mathematics Knowledge from Ages 4 to 11

    ERIC Educational Resources Information Center

    Rittle-Johnson, Bethany; Fyfe, Emily R.; Hofer, Kerry G.; Farran, Dale C.

    2017-01-01

    Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An early math trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from ages 4 to 11. This model includes a broad range of math…

  9. Mathematical Knowledge and Skills Expected by Higher Education in Engineering and the Social Sciences: Implications for High School Mathematics Curriculum

    ERIC Educational Resources Information Center

    Basaran, Mehmet; Özalp, Gülümser; Kalender, Ilker; Alacaci, Cengiz

    2015-01-01

    One important function of school mathematics curriculum is to prepare high school students with the knowledge and skills needed for university education. Identifying them empirically will help making sound decisions about the contents of high school mathematics curriculum. It will also help students to make informed choices in course selection at…

  10. Singapore Pre-Service Secondary Mathematics Teachers' Content Knowledge: Findings from an International Comparative Study

    ERIC Educational Resources Information Center

    Toh, Tin Lam; Kaur, Berinderjeet; Koay, Phong Lee

    2013-01-01

    In this article, we explore the mathematical content knowledge of one entire cohort of pre-service teachers (N = 107) through analysing their performance in a Secondary Mathematics Audit that was developed for the International Comparative Studies in Mathematics Teacher Training that was initiated by the University of Plymouth. We study how their…

  11. How students learn to coordinate knowledge of physical and mathematical models in cellular physiology

    NASA Astrophysics Data System (ADS)

    Lira, Matthew

    This dissertation explores the Knowledge in Pieces (KiP) theory to account for how students learn to coordinate knowledge of mathematical and physical models in biology education. The KiP approach characterizes student knowledge as a fragmented collection of knowledge elements as opposed to stable and theory-like knowledge. This dissertation sought to use this theoretical lens to account for how students understand and learn with mathematical models and representations, such as equations. Cellular physiology provides a quantified discipline that leverages concepts from mathematics, physics, and chemistry to understand cellular functioning. Therefore, this discipline provides an exemplary context for assessing how biology students think and learn with mathematical models. In particular, the resting membrane potential provides an exemplary concept well defined by models of dynamic equilibrium borrowed from physics and chemistry. In brief, membrane potentials, or voltages, "rest" when the electrical and chemical driving forces for permeable ionic species are equal in magnitude but opposite in direction. To assess students' understandings of this concept, this dissertation employed three studies: the first study employed the cognitive clinical interview to assess student thinking in the absence and presence of equations. The second study employed an intervention to assess student learning and the affordances of an innovative assessment. The third student employed a human-computer-interaction paradigm to assess how students learn with a novel multi-representational technology. Study 1 revealed that students saw only one influence--the chemical gradient--and that students coordinated knowledge of only this gradient with the related equations. Study 2 revealed that students benefited from learning with the multi-representational technology and that the assessment detected performance gains across both calculation and explanation tasks. Last, Study 3 revealed how students

  12. Technological Pedagogical Content Knowledge of Prospective Mathematics Teacher in Three Dimensional Material Based on Sex Differences

    NASA Astrophysics Data System (ADS)

    Aqib, M. A.; Budiarto, M. T.; Wijayanti, P.

    2018-01-01

    The effectiveness of learning in this era can be seen from 3 factors such as: technology, content, and pedagogy that covered in Technological Pedagogical Content Knowledge (TPCK). This research was a qualitative research which aimed to describe each domain from TPCK include Content Knowledge, Pedagogical Knowledge, Pedagogical Content Knowledge, Technological Knowledge, Technological Content Knowledge, Technological Pedagogical Knowledge and Technological, Pedagogical, and Content Knowledge. The subjects of this research were male and female mathematics college students at least 5th semester who has almost the same ability for some course like innovative learning, innovative learning II, school mathematics I, school mathematics II, computer applications and instructional media. Research began by spreading the questionnaire of subject then continued with the assignment and interview. The obtained data was validated by time triangulation.This research has result that male and female prospective teacher was relatively same for Content Knowledge and Pedagogical Knowledge domain. While it was difference in the Technological Knowledge domain. The difference in this domain certainly has an impact on other domains that has technology components on it. Although it can be minimized by familiarizing the technology.

  13. Integrating the Use of Interdisciplinary Learning Activity Task in Creating Students' Mathematical Knowledge

    ERIC Educational Resources Information Center

    Mahanin, Hajah Umisuzimah Haji; Shahrill, Masitah; Tan, Abby; Mahadi, Mar Aswandi

    2017-01-01

    This study investigated the use of interdisciplinary learning activity task to construct students' knowledge in Mathematics, specifically on the topic of scale drawing application. The learning activity task involved more than one academic discipline, which is Mathematics, English Language, Art, Geography and integrating the Brunei Darussalam…

  14. Investigating Lebanese Grade Seven Biology Teachers Mathematical Knowledge and Skills: A Case Study

    ERIC Educational Resources Information Center

    Raad, Nawal Abou; Chatila, Hanadi

    2016-01-01

    This paper investigates Lebanese grade 7 biology teachers' mathematical knowledge and skills, by exploring how they explain a visual representation in an activity depending on the mathematical concept "Function". Twenty Lebanese in-service biology teachers participated in the study, and were interviewed about their explanation for the…

  15. Eleventh-Grade High School Students' Accounts of Mathematical Metacognitive Knowledge: Explicitness and Systematicity

    ERIC Educational Resources Information Center

    van Velzen, Joke H.

    2016-01-01

    Theoretically, it has been argued that a conscious understanding of metacognitive knowledge requires that this knowledge is explicit and systematic. The purpose of this descriptive study was to obtain a better understanding of explicitness and systematicity in knowledge of the mathematical problem-solving process. Eighteen 11th-grade…

  16. Licensure tests for special education teachers: how well they assess knowledge of reading instruction and mathematics.

    PubMed

    Stotsky, Sandra

    2009-01-01

    To determine the extent to which knowledge of evidence-based reading instruction and mathematics is assessed on licensure tests for prospective special education teachers, this study drew on information provided by Educational Testing Service (ETS), the American Board for Certification of Teacher Excellence, and National Evaluation Systems (now Evaluation Systems group of Pearson). It estimated the percentage of test items on phonemic awareness, phonics, and vocabulary knowledge and on mathematics content. It also analyzed descriptions of ETS's tests of "principles of teaching and learning." Findings imply that prospective special education teachers should be required to take both a dedicated test of evidence-based reading instructional knowledge, as in California, Massachusetts, and Virginia, and a test of mathematical knowledge, as in Massachusetts. States must design their own tests of teaching principles to assess knowledge of evidence-based educational theories.

  17. The Mathematical Content Knowledge of Prospective Teachers in Iceland

    ERIC Educational Resources Information Center

    Johannsdottir, Bjorg

    2013-01-01

    This study focused on the mathematical content knowledge of prospective teachers in Iceland. The sample was 38 students in the School of Education at the University of Iceland, both graduate and undergraduate students. All of the participants in the study completed a questionnaire survey and 10 were interviewed. The choice of ways to measure the…

  18. The Preparation Experiences of Elementary Mathematics Specialists: Examining Influences on Beliefs, Content Knowledge, and Teaching Practices

    ERIC Educational Resources Information Center

    Swars, Susan L.; Smith, Stephanie Z.; Smith, Marvin E.; Carothers, Jody; Myers, Kayla

    2018-01-01

    Many in the field of mathematics education call for elementary schools to have elementary mathematics specialists (EMSs) who provide needed mathematical expertise and support for children and teachers. EMSs serve as a reasonable, immediate alternative to the challenges generated by elementary teachers needing improved mathematical knowledge for…

  19. A Case Study on the Impact of Teacher Mathematical Knowledge on Pedagogical Practices

    ERIC Educational Resources Information Center

    Hughes, Sally

    2016-01-01

    This study explores the implications for mathematical knowledge and pedagogical practices of primary teachers in Papua New Guinea making a shift from a transmission approach to a connectionist approach to teaching mathematics. The research participants were engaged in a professional development program designed to support the teaching and learning…

  20. Focusing on the Interactive Development of Secondary School Teachers' Knowledge of Mathematical Statements

    ERIC Educational Resources Information Center

    Levenson, Esther; Tsamir, Pessia; Tirosh, Dina; Dreyfus, Tommy; Barkai, Ruthi; Tabach, Michal

    2012-01-01

    This paper focuses on the first session of a professional development course revolving around the topic of mathematical statements and their appropriate proving methods. It analyzes the interactive development of the teachers' knowledge by focusing on the relation between the mathematical statements, the instructor, and the teachers. Different…

  1. Sociological Tools in the Study of Knowledge and Practice in Mathematics Teacher Education

    ERIC Educational Resources Information Center

    Parker, Diane; Adler, Jill

    2014-01-01

    In this paper, we put Basil Bernstein's theory of pedagogic discourse to work together with additional theoretical resources to interrogate knowledge and practice in mathematics teacher education. We illustrate this methodology through analysis of an instance of mathematics teacher education pedagogic practice. While the methodology itself is…

  2. Examining Relations between Mathematics Teachers' Instructional Vision and Knowledge and Change in Practice

    ERIC Educational Resources Information Center

    Munter, Charles; Correnti, Richard

    2017-01-01

    This article provides a longitudinal examination of how changes in more than 200 middle-grades mathematics teachers' instructional practices related to their (a) mathematical knowledge for teaching (MKT) and (b) instructional vision. Results of this multilevel regression analysis suggest that MKT and instructional vision are related to instruction…

  3. Examining Prospective Mathematics Teachers' Pedagogical Content Knowledge on Fractions in Terms of Students' Mistakes

    ERIC Educational Resources Information Center

    Sahin, Ömer; Gökkurt, Burçin; Soylu, Yasin

    2016-01-01

    The aim of the study is to examine prospective mathematics teachers' pedagogical content knowledge in terms of knowledge of understanding students and knowledge of instructional strategies which are the subcomponents of pedagogical content knowledge. The participants of this research consist of 98 prospective teachers who are studying in two…

  4. A Framework for Proofs and Refutations in School Mathematics: Increasing Content by Deductive Guessing

    ERIC Educational Resources Information Center

    Komatsu, Kotaro

    2016-01-01

    The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…

  5. A Model of Professional Competences in Mathematics to Update Mathematical and Didactic Knowledge of Teachers

    ERIC Educational Resources Information Center

    Díaz, Verónica; Poblete, Alvaro

    2017-01-01

    This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an…

  6. Middle School Mathematics Teachers' Pedagogical Content Knowledge Regarding Teaching Strategies on Quadrilaterals

    ERIC Educational Resources Information Center

    Akkas, Elif Nur; Türnüklü, Elif

    2014-01-01

    Pedagogical content knowledge is consisted of two components: student knowledge and teaching strategies. Teaching strategies was defined under two sub-headings as strategies for specific topics and specific strategies for any topic. The purpose of this study was to examine the method with which quadrilaterals were taught by mathematics teachers…

  7. Assessing Key Epistemic Features of Didactic-Mathematical Knowledge of Prospective Teachers: The Case of The Derivative

    ERIC Educational Resources Information Center

    Pino-Fan, Luis R.; Godino, Juan D.; Font, Vicenç

    2018-01-01

    In recent years, there has been a growing interest in studying the knowledge that mathematics teachers require in order for their teaching to be effective. However, only a few studies have focused on the design and application of instruments that are capable of exploring different aspects of teachers' didactic-mathematical knowledge about specific…

  8. A model of professional competences in mathematics to update mathematical and didactic knowledge of teachers

    NASA Astrophysics Data System (ADS)

    Díaz, Verónica; Poblete, Alvaro

    2017-07-01

    This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers' competence regarding the didactic strategy used and its results, as well as the students' learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.

  9. The Effect of Teacher Education Programs on Future Elementary Mathematics Teachers' Knowledge: A Five-Country Analysis Using TEDS-M Data

    ERIC Educational Resources Information Center

    Qian, Hong; Youngs, Peter

    2016-01-01

    This article addresses the problem of how opportunities to learn in teacher education programs influence future elementary mathematics teachers' knowledge. This study used data collected for the Teacher Education and Development Study in Mathematics (TEDS-M). TEDS-M measured the mathematics content knowledge (MCK) and the mathematics pedagogical…

  10. Construction of teacher knowledge in context: Preparing elementary teachers to teach mathematics and science

    NASA Astrophysics Data System (ADS)

    Lowery, Maye Norene Vail

    1998-12-01

    The purposes of this study were to further the understanding of how preservice teacher construct teacher knowledge and pedagogical content knowledge of elementary mathematics and science and to determine the extent of that knowledge in a school-based setting. Preservice teachers, university instructors, inservice teachers, and other school personnel were involved in this context-specific study. Evidence of the preservice teachers' knowledge construction (its acquisition, its dimensions, and the social context) was collected through the use of a qualitative methodology. Collected data included individual and group interviews, course documents, artifacts, and preservice teaching portfolios. Innovative aspects of this integrated mathematics and science elementary methods course included standards-based instruction with immediate access to field experiences. Grade-level teams of preservice and inservice teachers planned and implemented lessons in mathematics and science for elementary students. An on-site, portable classroom building served as a mathematics and science teaching and learning laboratory. A four-stage analysis was performed, revealing significant patterns of learning. An ecosystem of learning within a constructivist learning environment was identified to contain three systems: the university system; the school system; and the cohort of learners system. A mega system for the construction of teacher knowledge was revealed in the final analysis. Learning venues were discovered to be the conduits of learning in a situated learning context. Analysis and synthesis of data revealed an extensive acquisition of teacher knowledge and pedagogical content knowledge through identified learning components. Patience, flexibility, and communication were identified as necessities for successful teaching. Learning components included: collaboration with inservice teachers; implementation of discovery learning and hands-on/minds-on learning; small groupwork; lesson planning

  11. Using the "Knowledge Quartet" to Quantify Mathematical Knowledge in Teaching: The Development of a Protocol for Initial Teacher Education

    ERIC Educational Resources Information Center

    Weston, Tracy L.

    2013-01-01

    This study examined trainee teachers' mathematical knowledge in teaching (MKiT) over their final year in a US Initial Teacher Education (ITE) programme. This paper reports on an exploratory methodological approach taken to use the "Knowledge Quartet" to quantify MKiT through the development of a new protocol to code trainees' teaching of…

  12. Characteristics and Impact of the Further Mathematics Knowledge Networks: Analysis of an English Professional Development Initiative on the Teaching of Advanced Mathematics

    ERIC Educational Resources Information Center

    Ruthven, Kenneth

    2014-01-01

    Reports from 13 Further Mathematics Knowledge Networks supported by the National Centre for Excellence in the Teaching of Mathematics [NCETM] are analysed. After summarizing basic characteristics of the networks regarding leadership, composition and pattern of activity, each of the following aspects is examined in greater depth: Developmental aims…

  13. Examination of Lower Secondary Mathematics Teachers' Content Knowledge and Its Connection to Students' Performance

    ERIC Educational Resources Information Center

    Tchoshanov, Mourat; Cruz, Maria D.; Huereca, Karla; Shakirova, Kadriya; Shakirova, Liliana; Ibragimova, Elena N.

    2017-01-01

    This mixed methods study examined an association between cognitive types of teachers' mathematical content knowledge and students' performance in lower secondary schools (grades 5 through 9). Teachers (N = 90) completed the Teacher Content Knowledge Survey (TCKS), which consisted of items measuring different cognitive types of teacher knowledge.…

  14. Embracing "Nepantla": Rethinking "Knowledge" and Its Use in Mathematics Teaching

    ERIC Educational Resources Information Center

    Gutiérrez, Rochelle

    2012-01-01

    Although educational researchers are moving beyond purely psychological and cognitive models of learning to consider the ways in which mathematics teaching might reach a more diverse student population, this work remains in its infancy, and the concept of "knowledge" is rarely questioned. This paper begins with the idea that mathematics…

  15. Examining Change in K-3 Teachers' Mathematical Knowledge, Attitudes, and Beliefs: The Case of Primarily Math

    ERIC Educational Resources Information Center

    Kutaka, T. S.; Ren, L.; Smith, W. M.; Beattie, H. L.; Edwards, C. P.; Green, J. L.; Chernyavskiy, P.; Stroup, W.; Heaton, R. M.; Lewis, W. J.

    2018-01-01

    This study examines the impact of the Primarily Math Elementary Mathematics Specialist program on K-3 teachers' mathematical content knowledge for teaching, attitudes toward learning mathematics, and beliefs about mathematics teaching and learning. Three cohorts of teachers participating in the program were compared to a similar group of…

  16. The Development of Mathematical Knowledge for Teaching for Quantitative Reasoning Using Video-Based Instruction

    ERIC Educational Resources Information Center

    Walters, Charles David

    2017-01-01

    Quantitative reasoning (P. W. Thompson, 1990, 1994) is a powerful mathematical tool that enables students to engage in rich problem solving across the curriculum. One way to support students' quantitative reasoning is to develop prospective secondary teachers' (PSTs) mathematical knowledge for teaching (MKT; Ball, Thames, & Phelps, 2008)…

  17. Creative Reasoning and Shifts of Knowledge in the Mathematics Classroom

    ERIC Educational Resources Information Center

    Hershkowitz, Rina; Tabach, Michal; Dreyfus, Tommy

    2017-01-01

    In the course of the last few years, we have investigated shifts of knowledge among different settings in inquiry-based mathematics classrooms: the individual, the small group and the whole class community. The different theoretical perspectives we used for analysing group work and for analysing whole class discussions, and the empirical data, led…

  18. Connecting Mathematics and Literature: An Analysis of Pre-Service Elementary School Teachers' Changing Beliefs and Knowledge

    ERIC Educational Resources Information Center

    Wilburne, Jane M.; Napoli, Mary

    2008-01-01

    The National Council of Teachers of Mathematics calls for students to see relationships and connections with mathematics (2000). This study examined the influences on eight pre-service elementary school teachers' beliefs and knowledge of teaching mathematics through literature. The semester long project involved both the language arts and…

  19. The Influence of University Courses and Field Experiences on Chinese Elementary Candidates' Mathematical Knowledge for Teaching

    ERIC Educational Resources Information Center

    Youngs, Peter; Qian, Hong

    2013-01-01

    In this article, we draw on survey data to investigate associations between Chinese elementary teaching candidates’ mathematical knowledge for teaching (MKT) and their experiences in mathematics courses, mathematics methods courses, and student teaching. In our study, we found that (a) Chinese teaching candidates' completion of courses in number…

  20. Visual Representation in Mathematics: Special Education Teachers' Knowledge and Emphasis for Instruction

    ERIC Educational Resources Information Center

    van Garderen, Delinda; Scheuermann, Amy; Poch, Apryl; Murray, Mary M.

    2018-01-01

    The use of visual representations (VRs) in mathematics is a strongly recommended practice in special education. Although recommended, little is known about special educators' knowledge of and instructional emphasis about VRs. Therefore, in this study, the authors examined special educators' own knowledge of and their instructional emphasis with…

  1. Measuring and factors influencing mathematics teachers' technological pedagogical and content knowledge (TPACK) in three southernmost provinces, Thailand

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    Adulyasas, Lilla

    2017-08-01

    Technology becomes an important role in teaching and learning mathematics nowadays. Integrating technology in the classroom helps students have better understanding in many of mathematics concepts. One of the major framework for assessing the knowledge of integrating technology with the pedagogy and content in the classroom is Technological Pedagogical and Content Knowledge (TPACK) framework. This study aimed to measure mathematics teachers' TPACK in three southernmost provinces, Thailand and to study on factors influencing their TPACK. A quantitative study was carried out with 210 secondary level mathematics teachers in the three southernmost provinces, Thailand which were random by two stage sampling technique. Data were collected by using a questionnaire to identify the level of mathematics teachers' TPACK and the factors influencing their TPACK. Descriptive statistics, Pearson product moment correlation and multiple regression analysis were used for analysing data. Findings reveal that the mean score of mathematics teachers' TPACK is 3.33 which is in the medium level and the three factors which have positive correlation at .05 level of significant with the level of TPACK are teaching experience factor, individual specialization factor and personal & organization factor. However, there are only two factors influencing mathematics teachers' TPACK. The two factors are individual specialization factor and personal & organization factors. These give better understanding on mathematics teachers' knowledge in integrating technology with the pedagogy and content which will be the important information for improving mathematics teachers' TPACK.

  2. Spaced Retrieval Practice Increases College Students' Short- and Long-Term Retention of Mathematics Knowledge

    ERIC Educational Resources Information Center

    Hopkins, Robin F.; Lyle, Keith B.; Hieb, Jeff L.; Ralston, Patricia A. S.

    2016-01-01

    A major challenge college students face is retaining the knowledge they acquire in their classes, especially in cumulative disciplines such as engineering, where ultimate success depends on long-term retention of foundational content. Cognitive psychologists have recently recommended various techniques educators might use to increase retention.…

  3. A Conceptual Analysis of the Knowledge of Prospective Mathematics Teachers about Degree and Radian

    ERIC Educational Resources Information Center

    Tuna, Abdulkadir

    2013-01-01

    This study examined the knowledge levels of prospective mathematics teachers about the concepts of degree and radian, which are among the angle measuring units that constitute the basis of trigonometry, and the relationships between those concepts. The study group consisted of 93 prospective mathematics teachers attending a state university in…

  4. Preservice Secondary Mathematics Teachers' Statistical Knowledge: A Snapshot of Strengths and Weaknesses

    ERIC Educational Resources Information Center

    Lovett, Jennifer N.; Lee, Hollylynne S.

    2017-01-01

    Amid the implementation of new curriculum standard regarding statistics and new recommendations for preservice secondary mathematics teachers [PSMTs] to teach statistics, there is a need to examine the current state of PSMTs' common statistical knowledge. This study reports on the statistical knowledge 217 PSMTs from a purposeful sample of 18…

  5. Mathematics understanding and anxiety in collaborative teaching

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    Ansari, B. I.; Wahyu, N.

    2017-12-01

    This study aims to examine students’ mathematical understanding and anxiety using collaborative teaching. The sample consists of 51 students in the 7th-grade of MTs N Jeureula, one of the Islamic public junior high schools in Jeureula, Aceh, Indonesia. A test of mathematics understanding was administered to the students twice during the period of two months. The result suggests that there is a significant increase in mathematical understanding in the pre-test and post-test. We categorized the students into the high, intermediate, and low level of prior mathematics knowledge. In the high-level prior knowledge, there is no difference of mathematical understanding between the experiment and control group. Meanwhile, in the intermediate and low level of prior knowledge, there is a significant difference of mathematical understanding between the experiment and control group. The mathematics anxiety is at an intermediate level in the experiment class and at a high level in the control group. There is no interaction between the learning model and the students’ prior knowledge towards the mathematical understanding, but there are interactions towards the mathematics anxiety. It indicates that the collaborative teaching model and the students’ prior knowledge do not simultaneously impacts on the mathematics understanding but the mathematics anxiety.

  6. Mathematics Funds of Knowledge: "Sotmaute" and "Sermaute" Fish in a Torres Strait Islander Community

    ERIC Educational Resources Information Center

    Ewing, Bronwyn

    2012-01-01

    The purpose of this article is to describe a project with one Torres Strait Islander Community. It provides some insights into parents' funds of knowledge that are mathematical in nature, such as sorting shells and giving fish. The idea of funds of knowledge is based on the premise that people are competent and have knowledge that has been…

  7. Content Knowledge, Attitudes, and Self-Efficacy in the Mathematics New York City Teaching Fellows (NYCTF) Program

    ERIC Educational Resources Information Center

    Evans, Brian R.

    2011-01-01

    The purpose of this study was to understand the mathematical content knowledge new teachers have both before and after taking a mathematics methods course in the NYCTF program. Further, the purpose was to understand the attitudes toward mathematics and concepts of self-efficacy that Teaching Fellows had over the course of the semester. The sample…

  8. The Effectiveness of the GeoGebra Software: The Intermediary Role of Procedural Knowledge on Students' Conceptual Knowledge and Their Achievement in Mathematics

    ERIC Educational Resources Information Center

    Zulnaidi, Hutkemri; Zamri, Sharifah Norul Akmar Syed

    2017-01-01

    The aim of this study was to identify the effects of GeoGebra software on students' conceptual and procedural knowledge and the achievement of Form Two students in Mathematics particularly on the topic Function. In addition, this study determined the role of procedural knowledge as a mediator between conceptual knowledge and students' achievement.…

  9. Concept Maps Provide a Window onto Preservice Elementary Teachers' Knowledge in the Teaching and Learning of Mathematics

    ERIC Educational Resources Information Center

    Chichekian, Tanya; Shore, Bruce M.

    2013-01-01

    This collaborative concept-mapping exercise was conducted in a second-year mathematics methods course. Teachers' visual representations of their mathematical content and pedagogical knowledge provided insight into their understanding of how students learn mathematics. We collected 28 preservice student teachers' concept maps and analyzed them by…

  10. Effects of Prior Knowledge in Mathematics on Learner-Interface Interactions in a Learning-by-Teaching Intelligent Tutoring System

    ERIC Educational Resources Information Center

    Bringula, Rex P.; Basa, Roselle S.; Dela Cruz, Cecilio; Rodrigo, Ma. Mercedes T.

    2016-01-01

    This study attempted to determine the influence of prior knowledge in mathematics of students on learner-interface interactions in a learning-by-teaching intelligent tutoring system. One hundred thirty-nine high school students answered a pretest (i.e., the prior knowledge in mathematics) and a posttest. In between the pretest and posttest, they…

  11. Mathematical Knowledge for Teaching the Function Concept and Student Learning Outcomes

    ERIC Educational Resources Information Center

    Hatisaru, Vesife; Erbas, Ayhan Kursat

    2017-01-01

    The purpose of this study was to examine the potential interrelationships between teachers' mathematical knowledge for teaching (MKT) the function concept and their students' learning outcomes of this concept. Data were collected from two teachers teaching in a vocational high school and their students through a function concept test for teachers…

  12. Mathematical Learning Models that Depend on Prior Knowledge and Instructional Strategies

    ERIC Educational Resources Information Center

    Pritchard, David E.; Lee, Young-Jin; Bao, Lei

    2008-01-01

    We present mathematical learning models--predictions of student's knowledge vs amount of instruction--that are based on assumptions motivated by various theories of learning: tabula rasa, constructivist, and tutoring. These models predict the improvement (on the post-test) as a function of the pretest score due to intervening instruction and also…

  13. A Collaborative Inquiry to Promote Pedagogical Knowledge of Mathematics in Practice

    ERIC Educational Resources Information Center

    Moghaddam, Alireza; Sarkar Arani, Mohammad Reza; Kuno, Hiroyuki

    2015-01-01

    The present study attempts to report a collaborative cycle of professional development in teaching elementary school mathematics through lesson study. It explores a practice of lesson study conducted by teachers aiming to improve their knowledge of pedagogy. The study adopts an ethnographic approach to examine how collaborative teaching within an…

  14. Constructing Mathematical Knowledge: Epistemology and Mathematics Education. Studies in Mathematics Education Series: 4.

    ERIC Educational Resources Information Center

    Ernest, Paul, Ed.

    This book illustrates the breadth of theoretical and philosophical perspectives that can be brought to bear on mathematics and education. Part 1, "Constructivism and the Learning of Mathematics," contains the following chapters: (1) "A Radical Constructivist View of Basic Mathematical Concepts" (E. von Glasersfeld); (2) "Interaction and Children's…

  15. Connection between Topic-Specific Teacher Knowledge and Student Performance in Lower Secondary School Mathematics

    ERIC Educational Resources Information Center

    Tchoshanov, Mourat; Quinones, Maria Cruz; Shakirova, Kadriya B.; Ibragimova, Elena N.; Shakirova, Liliana R.

    2017-01-01

    The interpretive cross-case study focused on the examination of connections between teacher and student topic-specific knowledge of lower secondary mathematics. Two teachers were selected for the study using non-probability purposive sampling technique. Teachers completed the Teacher Content Knowledge Survey before teaching a topic on division of…

  16. Operationalizing Levels of Academic Mastery Based on Vygotsky's Theory: The Study of Mathematical Knowledge

    ERIC Educational Resources Information Center

    Nezhnov, Peter; Kardanova, Elena; Vasilyeva, Marina; Ludlow, Larry

    2015-01-01

    The present study tested the possibility of operationalizing levels of knowledge acquisition based on Vygotsky's theory of cognitive growth. An assessment tool (SAM-Math) was developed to capture a hypothesized hierarchical structure of mathematical knowledge consisting of procedural, conceptual, and functional levels. In Study 1, SAM-Math was…

  17. Secondary Pre-Service Teachers' Content Knowledge for State Assessments: Implications for Mathematics Education Programs

    ERIC Educational Resources Information Center

    Wilburne, Jane M.; Long, Michael

    2010-01-01

    Seventy secondary mathematics pre-service teachers from two universities were assessed on their content knowledge, vocabulary knowledge, and their perceived confidence in teaching the content addressed on the eleventh grade state assessment. The results indicate the pre-service teachers had significant content weakness in data analysis, algebra,…

  18. Meta Didactic-Mathematical Knowledge of Teachers: Criteria for the Reflection and Assessment on Teaching Practice

    ERIC Educational Resources Information Center

    Breda, Adriana; Pino-Fan, Luis Roberto; Font, Vicenç

    2017-01-01

    The objective of this study is to demonstrate that the criteria of didactical suitability, proposed by the theoretical framework known as the Onto-Semiotic Approach (OSA) of mathematical knowledge and instruction, are powerful tools for organizing the reflection and assessment of instruction processes carried out by mathematics teachers. To this…

  19. Developing the STS sound pollution unit for enhancing students' applying knowledge among science technology engineering and mathematics

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    Jumpatong, Sutthaya; Yuenyong, Chokchai

    2018-01-01

    STEM education suggested that students should be enhanced to learn science with integration between Science, Technology, Engineering and Mathematics. To help Thai students make sense of relationship between Science, Technology, Engineering and Mathematics, this paper presents learning activities of STS Sound Pollution. The developing of STS Sound Pollution is a part of research that aimed to enhance students' perception of the relationship between Science Technology Engineering and Mathematics. This paper will discuss how to develop Sound Pollution through STS approach in framework of Yuenyong (2006) where learning activities were provided based on 5 stages. These included (1) identification of social issues, (2) identification of potential solutions, (3) need for knowledge, (4) decisionmaking, and (5) socialization stage. The learning activities could be highlighted as following. First stage, we use video clip of `Problem of people about Sound Pollution'. Second stage, students will need to identification of potential solutions by design Home/Factory without noisy. The need of scientific and other knowledge will be proposed for various alternative solutions. Third stage, students will gain their scientific knowledge through laboratory and demonstration of sound wave. Fourth stage, students have to make decision for the best solution of designing safety Home/Factory based on their scientific knowledge and others (e.g. mathematics, economics, art, value, and so on). Finally, students will present and share their Design Safety Home/Factory in society (e.g. social media or exhibition) in order to validate their ideas and redesigning. The paper, then, will discuss how those activities would allow students' applying knowledge of science technology engineering, mathematics and others (art, culture and value) for their possible solution of the STS issues.

  20. Visual Programming: A Programming Tool for Increasing Mathematics Achivement

    ERIC Educational Resources Information Center

    Swanier, Cheryl A.; Seals, Cheryl D.; Billionniere, Elodie V.

    2009-01-01

    This paper aims to address the need of increasing student achievement in mathematics using a visual programming language such as Scratch. This visual programming language facilitates creating an environment where students in K-12 education can develop mathematical simulations while learning a visual programming language at the same time.…

  1. 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

  2. A Case Study of Four Latina/o Pre-Service Teachers in Learning to Teach Mathematics for Understanding and Integrate a Child's Out-of-School Mathematical Knowledge and Experiences

    ERIC Educational Resources Information Center

    Kalinec-Craig, Crystal

    2012-01-01

    This dissertation study examines the experiences of four Latina/o pre-service teachers (PSTs) as they learn about teaching mathematics for understanding (TM4U) and integrating a child's out-of-school mathematical knowledge and experiences during instruction. Studying the knowledge and experiences of Latina/o PSTs is necessary because PSTs…

  3. Argumentative Knowledge Construction in an Online Graduate Mathematics Course: A Case Study

    ERIC Educational Resources Information Center

    Bayazit, Nermin; Clarke, Pier Angeli Junor; Vidakovic, Draga

    2018-01-01

    The authors report on three students' argumentative knowledge construction in an asynchronous online graduate level geometry course designed for in-service secondary mathematics (ISM) teachers. Using Weinberger and Fischer's framework, they analyzed the ISM teachers' (a) geometry autobiography and (b) discussion board posts (both comments and…

  4. Improving Geometric and Trigonometric Knowledge and Skill for High School Mathematics Teachers: A Professional Development Partnership

    ERIC Educational Resources Information Center

    Merrill, Chris; Devine, Kevin L.; Brown, Joshua W.; Brown, Ryan A.

    2010-01-01

    In the summer of 2009, a professional development partnership was established between the Peoria Public School District (PPSD), a local education agency (LEA), and Illinois State University (ISU) to improve geometric and trigonometric knowledge and skill for high school mathematics teachers as part of the Illinois Mathematics and Science…

  5. Using the Mixture Rasch Model to Explore Knowledge Resources Students Invoke in Mathematic and Science Assessments

    ERIC Educational Resources Information Center

    Zhang, Danhui; Orrill, Chandra; Campbell, Todd

    2015-01-01

    The purpose of this study was to investigate whether mixture Rasch models followed by qualitative item-by-item analysis of selected Programme for International Student Assessment (PISA) mathematics and science items offered insight into knowledge students invoke in mathematics and science separately and combined. The researchers administered an…

  6. Exploring the Associations among Nutrition, Science, and Mathematics Knowledge for an Integrative, Food-Based Curriculum

    ERIC Educational Resources Information Center

    Stage, Virginia C.; Kolasa, Kathryn M.; Díaz, Sebastián R.; Duffrin, Melani W.

    2018-01-01

    Background: Explore associations between nutrition, science, and mathematics knowledge to provide evidence that integrating food/nutrition education in the fourth-grade curriculum may support gains in academic knowledge. Methods: Secondary analysis of a quasi-experimental study. Sample included 438 students in 34 fourth-grade classrooms across…

  7. A Study of Students' Conceptual, Procedural Knowledge, Logical Thinking and Creativity during the First Year of Tertiary Mathematics

    ERIC Educational Resources Information Center

    Tularam, Gurudeo Anand; Hulsman, Kees

    2015-01-01

    This study focuses on students in first year environmental science degree programs, where traditionally mathematical emphasis has been much less than within the strict science or math majors. The importance now placed on applied mathematics, however, means that students need to gain more conceptual and quantitative knowledge of mathematics in not…

  8. Schooled Mathematics and Cultural Knowledge.

    ERIC Educational Resources Information Center

    de Abreu, Guida; Cline, Tony

    2003-01-01

    Asserts that recognition of the cultural nature of schooled mathematics requires research that locates these practices in the sociopolitical context and provides an account of the social valorization of mathematical practices and the impact on learning. Using data on students in multiethnic English elementary schools, the article proposes how the…

  9. Survey Team On: Conceptualisation of the Role of Competencies, Knowing and Knowledge in Mathematics Education Research

    ERIC Educational Resources Information Center

    Niss, Mogens; Bruder, Regina; Planas, Núria; Turner, Ross; Villa-Ochoa, Jhony Alexander

    2016-01-01

    This paper presents the outcomes of the work of the ICME 13 Survey Team on "Conceptualisation and the role of competencies, knowing and knowledge in mathematics education research". It surveys a variety of historical and contemporary views and conceptualisations of what it means to master mathematics, focusing on notions such as…

  10. Validity issues in the evaluation of a measure of science and mathematics teacher knowledge

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    Talbot, Robert M., III

    2011-12-01

    This study investigates the reliability and validity of an instrument designed to measure science and mathematics teachers' strategic knowledge . Strategic knowledge is conceptualized as a construct that is related to pedagogical knowledge and is comprised of two dimensions: Flexible Application (FA) and Student Centered Instruction (SCI). The FA dimension describes how a science teacher invokes, applies and modifies her instructional repertoire in a given teaching context. The SCI dimension describes how a science teacher conceives of a given situation as an opportunity for active engagement with the students. The Flexible Application of Student-Centered Instruction (FASCI) survey instrument was designed to measure science teachers' strategic knowledge by eliciting open-ended responses to scenario-based items. This study addresses the following overarching question: What are some potential issues pertaining to the validity of measures of science and mathematics teacher knowledge? Using a validity argument framework, different sources of evidence are identified, collected, and evaluated to examine support for a set or propositions related to the intended score interpretation and instrument use: FASCI scores can be used to compare and distinguish the strategic knowledge of novice science and mathematics teachers in the evaluation of teacher education programs. Three separate but related studies are presented and discussed. These studies focus on the reliability of FASCI scores, the effect of adding specific science content to the scenario-based items, and the observation of strategic knowledge in teaching practice. Serious issues were found with the reliability of scores from the FASCI instrument. It was also found that adding science content to the scenario-based items has an effect on FASCI scores, but not for the reason hypothesized. Finally, it was found that more evidence is needed to make stronger claims about the relationship between FASCI scores and novice

  11. Investigating the Knowledge Needed for Teaching Mathematics: An Exploratory Validation Study Focusing on Teaching Practices

    ERIC Educational Resources Information Center

    Charalambous, Charalambos Y.

    2016-01-01

    Central in the frameworks proposed to capture the knowledge needed for teaching mathematics is the assumption that teachers need more than pure subject-matter knowledge. Validation studies exploring this assumption by recruiting contrasting populations are relatively scarce. Drawing on a sample of 644 Greek-Cypriots preservice and inservice…

  12. Secondary School Advanced Mathematics, Chapter 1, Organizing Geometric Knowledge, Chapter 2, Concepts and Skills in Algebra. Student's Text.

    ERIC Educational Resources Information Center

    Stanford Univ., CA. School Mathematics Study Group.

    This text is the first of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first chapter, devoted to organizing geometric knowledge, deals with the distinction…

  13. Schooled Mathematics and Cultural Knowledge

    ERIC Educational Resources Information Center

    de Abreu, Guida; Cline, Tony

    2003-01-01

    In this article it is argued that due recognition of the cultural nature of schooled mathematics requires an analysis that locates these practices in their social-political context. That analysis will need to provide an account of the social valorisation of mathematical practices and its impact on learning. It is suggested that the link between…

  14. The influence of attention on mathematical knowledge of teachers and lecturers: a comparison

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    Klymchuk, Sergiy; Thomas, Michael O. J.

    2011-10-01

    This article reports on some findings from the project 'Analysing the Transition from Secondary to Tertiary Education in Mathematics'. One of the key variables in the school to university transition is the teacher/lecturer, and here, we deal with the data analysing secondary teachers' and tertiary lecturers' responses to four mathematics questions. Elsewhere, we consider knowledge, preparedness, teaching style, etc., but this article tracks the ability to use mathematical procedures. We hypothesize that this is a function of what we pay attention to, as described in Mason's discipline of noticing. The results reveal that many teachers and lecturers fail to notice the necessary conditions for problems that imply that procedures are not always applicable. Possible reasons for this along with implications for student learning are discussed.

  15. Secondary-Level Student Teachers' Conceptions of Mathematical Proof

    ERIC Educational Resources Information Center

    Varghese, Thomas

    2009-01-01

    Recent reforms in mathematics education have led to an increased emphasis on proof and reasoning in mathematics curricula. The National Council of Teachers of Mathematics highlights the important role that teachers' knowledge and beliefs play in shaping students' understanding of mathematics, their confidence in and outlook on mathematics…

  16. The Building of Pre-Service Primary Teachers' Knowledge of Mathematics Teaching: Interaction and Online Video Case Studies

    ERIC Educational Resources Information Center

    Llinares, Salvador; Valls, Julia

    2009-01-01

    This study explores how preservice primary teachers became engaged in meaning-making mathematics teaching when participating in online discussions within learning environments integrating video-clips of mathematics teaching. We identified different modes of participation in the online discussions and different levels of knowledge-building. The…

  17. A Study of Strengthening Secondary Mathematics Teachers' Knowledge of Statistics and Probability via Professional Development

    ERIC Educational Resources Information Center

    DeVaul, Lina

    2017-01-01

    A professional development program (PSPD) was implemented to improve in-service secondary mathematics teachers' content knowledge, pedagogical knowledge, and self-efficacy in teaching secondary school statistics and probability. Participants generated a teaching resource website at the conclusion of the PSPD program. Participants' content…

  18. Upper Primary School Teachers' Mathematical Knowledge for Teaching Functional Thinking in Algebra

    ERIC Educational Resources Information Center

    Wilkie, Karina J.

    2014-01-01

    This article is based on a project that investigated teachers' knowledge in teaching an important aspect of algebra in the middle years of schooling--functions, relations and joint variation. As part of the project, 105 upper primary teachers were surveyed during their participation in Contemporary Teaching and Learning of Mathematics, a research…

  19. Professional Knowledge Required When Teaching Mathematics for Numeracy in the Multiplicative Domain

    ERIC Educational Resources Information Center

    Mills, Judith

    2015-01-01

    This paper presents findings as part of a wider study that investigated the professional knowledge of teachers when teaching mathematics for numeracy in the primary school classroom. This paper focuses on teachers in action as they taught two lessons on multiplication. It outlines the specific pedagogical categories the teachers used and the…

  20. Emergences and Affordances as Opportunities to Develop Teachers' Mathematical Content Knowledge

    ERIC Educational Resources Information Center

    Julie, Cyril

    2014-01-01

    Teachers' mathematical content knowledge has been under scrutiny for some time. This development is in the wake of learners' unsatisfactory performance in national examinations and international achievement tests. A widely held belief is that one, if not the most important, of the efforts to improve and enhance the performance and…

  1. The Effects of Professional Development on the Knowledge, Attitudes, & Anxiety of Intermediate Teachers of Mathematics

    ERIC Educational Resources Information Center

    McCartney, Kathleen Perry

    2013-01-01

    This study examined the effects of a short-term professional development on the mathematical knowledge, anxiety, and attitudes of intermediate teachers. Participants in the control and experimental groups were pre-tested for knowledge using the eighth grade TCAP Item Sampler. Anxiety was measured through the use of Suinn and Winston's (2003)…

  2. The impact of assumed knowledge entry standards on undergraduate mathematics teaching in Australia

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    King, Deborah; Cattlin, Joann

    2015-10-01

    Over the last two decades, many Australian universities have relaxed their selection requirements for mathematics-dependent degrees, shifting from hard prerequisites to assumed knowledge standards which provide students with an indication of the prior learning that is expected. This has been regarded by some as a positive move, since students who may be returning to study, or who are changing career paths but do not have particular prerequisite study, now have more flexible pathways. However, there is mounting evidence to indicate that there are also significant negative impacts associated with assumed knowledge approaches, with large numbers of students enrolling in degrees without the stated assumed knowledge. For students, there are negative impacts on pass rates and retention rates and limitations to pathways within particular degrees. For institutions, the necessity to offer additional mathematics subjects at a lower level than normal and more support services for under-prepared students impacts on workloads and resources. In this paper, we discuss early research from the First Year in Maths project, which begins to shed light on the realities of a system that may in fact be too flexible.

  3. Developing Mathematics Teacher Knowledge: The Paradidactic Infrastructure of "Open Lesson" in Japan

    ERIC Educational Resources Information Center

    Miyakawa, Takeshi; Winslow, Carl

    2013-01-01

    In this paper, we first present a theoretical approach to study mathematics teacher knowledge and the conditions for developing it, which is firmly rooted in a systemic approach to didactic phenomena at large, namely the anthropological theory of the didactic. Then, a case of open lesson is presented and analysed, using this theoretical approach,…

  4. Building Pre-Service Teacher's Mathematical Knowledge for Teaching of High School Geometry

    ERIC Educational Resources Information Center

    Somayajulu, Ravi Bhamidipati

    2012-01-01

    There were two primary goals of the research conducted for this dissertation study. Firstly, to fill a gap in the research literature and begin a discussion around secondary pre-service teachers Mathematical Knowledge for Teaching (MKT) as it pertains to geometry. Although a multitude of studies exist for elementary teachers' MKT, few exist at the…

  5. Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom

    NASA Astrophysics Data System (ADS)

    Hitt, Fernando

    2011-09-01

    Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the mathematics classroom has not had the expected impact, as it has been its use in everyday life (i.e. cell phone). What about teachers' opinions? Mathematics teachers can be divided into three categories: those with a boundless overflow (enthusiasm) who want to use the technology without worrying much about the construction of mathematical concepts, those who reject outright the use of technology because they think that their use inhibits the development of mathematical skills and others that reflect on the balance that must exist between paper-pencil activities and use of technology. The mathematics teacher, by not having clear examples that support this last option about the balance of paper-pencil activities and technology, opt for one of the extreme positions outlined above. In this article, we show the results of research on a methodology based on collaborative learning (ACODESA) in the training of mathematics teachers in secondary schools and implementation of activities in an environment of paper-pencil and CAS in the mathematics classroom. We also note that with the development of technology on the use of electronic tablets and interactive whiteboards, these activities will take on greater momentum in the near future.

  6. The Impact of a Professional Development Program on Teachers' Mathematical Knowledge for Teaching, Instruction, and Student Achievement

    ERIC Educational Resources Information Center

    Jacob, Robin; Hill, Heather; Corey, Doug

    2017-01-01

    In this paper, we describe findings from a three-year evaluation of a well-developed mathematics professional development program that is commercially available on a wide scale. The professional development is designed to improve teachers' mathematical knowledge for teaching and to enable them to elicit more student thinking and reasoning during…

  7. Mathematics Learning Difficulties in Primary Education: Teachers' Professional Knowledge and the Use of Commercially Available Learning Packages

    ERIC Educational Resources Information Center

    Van Steenbrugge, H.; Valcke, M.; Desoete, A.

    2010-01-01

    The present study builds on teachers' professional knowledge about mathematics learning difficulties. Based on the input of 918 primary school teachers, an attempt is made to develop an overview of difficult curriculum topics in primary school mathematics. The research approach builds on new conceptions about the professional identity of teachers…

  8. The transformation of science and mathematics content knowledge into teaching content by university faculty

    NASA Astrophysics Data System (ADS)

    Flynn, Natalie P.

    This study developed a survey from the existing literature in an attempt to illuminate the processes, tools, insights, and events that allow university science and mathematics content experts (Ph.D.'s) unpack their expertise in order to teach develop and teach undergraduate students. A pilot study was conducted at an urban university in order to refine the survey. The study consisted of 72 science or mathematics Ph.D. faculty members that teach at a research-based urban university. Follow-up interviews were conducted with 21 volunteer faculty to further explore their methods and tools for developing and implementing teaching within their discipline. Statistical analysis of the data revealed: faculty that taught while obtaining their Ph.D. were less confident in their ability to teach successful and faculty that received training in teaching believed that students have difficult to change misconceptions and do not commit enough time to their course. Student centered textbooks ranked the highest among tools used to gain teaching strategies followed by grading of exams and assignments for gaining insights into student knowledge and difficulties. Science and mathematics education literature and university provided education session ranked the lowest in rating scale for providing strategies for teaching. The open-ended survey questions were sub-divided and analyzed by the number of years of experience to identify the development of teaching knowledge over time and revealed that teaching became more interactive, less lecture based, and more engaging. As faculty matured and gained experience they became more aware of student misconceptions and difficulties often changing their teaching to eliminate such issues. As confidence levels increase their teaching included more technology-based tools, became more interactive, incorporated problem based activities, and became more flexible. This change occurred when and if faculty members altered their thinking about their

  9. Teaching Efficacy: Exploring Relationships between Mathematics and Science Self-Efficacy Beliefs, PCK and Domain Knowledge among Preservice Teachers from the United States

    ERIC Educational Resources Information Center

    Thomson, Margareta Maria; DiFrancesca, Daniell; Carrier, Sarah; Lee, Carrie

    2017-01-01

    This mixed-methods study investigated the relationships among preservice teachers' efficacy beliefs, pedagogical content knowledge (PCK) and their domain knowledge (DK) as related to mathematics and science teaching. Quantitative results revealed that participants' PCK was significantly correlated with their mathematics and science efficacy…

  10. Preservice Mathematics Teachers' Views on Distance Education and Their Web Pedagogical Content Knowledge

    ERIC Educational Resources Information Center

    Cagirgan Gulten, Dilek

    2013-01-01

    This research aims to investigate primary preservice mathematics teachers' views on distance education and web pedagogical content knowledge in terms of the subscales of general web, communicative web, pedagogical web, web pedagogical content and attitude towards web based instruction. The research was conducted with 46 senior students in the…

  11. Two-Year Community: Increasing Science Knowledge among High-Risk Student Populations through a Community College Honors/Service-Learning Program

    ERIC Educational Resources Information Center

    Ellerton, Sharon; Carmona, Naydu; Tsimounis, Areti

    2016-01-01

    There is an urgent need to increase K-12 science knowledge and STEM (science, technology, engineering, and mathematics) preparedness for college. State and national data suggest a strong correlation between student performance in STEM subjects and student socioeconomic status, race, and ethnicity. Queensborough Community College (QCC) is situated…

  12. Relations between Mathematical Knowledge for Teaching, Mathematics Instructional Quality, and Student Achievement in the Context of the "Responsive Classroom (RC)" Approach

    ERIC Educational Resources Information Center

    Ottmar, Erin R.; Rimm-Kaufman, Sara E.; Larsen, Ross; Merritt, Eileen G.

    2011-01-01

    Despite over thirty years of theoretically based research investigating "how" teacher mathematical knowledge and instructional practice relate to student learning, it is still largely unclear how these constructs are related, and policy makers and practitioners are still situated in a context with insufficient data to make decisions. Thus, there…

  13. Applying mathematical concepts with hands-on, food-based science curriculum

    PubMed Central

    Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Eugene, Geist; Duffrin, Melani W.

    2015-01-01

    This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the impact of the FoodMASTER Intermediate curriculum on fourth-grade student’s mathematics knowledge. The curriculum is a part of the FoodMASTER Initiative, which is a compilation of programs utilizing food, a familiar and necessary part of everyday life, as a tool to teach mathematics and science. Students exposed to the curriculum completed a 20-item researcher-developed mathematics knowledge exam (Intervention n=288; Control n=194). Overall, the results showed a significant increase in mathematics knowledge from pre- to post-test. These findings suggest that students engaged in food-based science activities provided them with the context in which to apply mathematical concepts to an everyday experience. Therefore, the FoodMASTER approach was successful at improving students’ mathematics knowledge while building a foundation for becoming quantitatively literate adults. PMID:26494927

  14. Applying mathematical concepts with hands-on, food-based science curriculum.

    PubMed

    Roseno, Ashley T; Carraway-Stage, Virginia G; Hoerdeman, Callan; Díaz, Sebastián R; Eugene, Geist; Duffrin, Melani W

    2015-01-01

    This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the impact of the FoodMASTER Intermediate curriculum on fourth-grade student's mathematics knowledge. The curriculum is a part of the FoodMASTER Initiative, which is a compilation of programs utilizing food, a familiar and necessary part of everyday life, as a tool to teach mathematics and science. Students exposed to the curriculum completed a 20-item researcher-developed mathematics knowledge exam (Intervention n=288; Control n=194). Overall, the results showed a significant increase in mathematics knowledge from pre- to post-test. These findings suggest that students engaged in food-based science activities provided them with the context in which to apply mathematical concepts to an everyday experience. Therefore, the FoodMASTER approach was successful at improving students' mathematics knowledge while building a foundation for becoming quantitatively literate adults.

  15. Developing an Assessment Instrument to Measure Early Elementary Teachers' Mathematical Knowledge for Teaching

    ERIC Educational Resources Information Center

    Schoen, Robert C.; Bray, Wendy; Wolfe, Christopher; Tazaz, Amanda M.; Nielsen, Lynne

    2017-01-01

    This study reports on the development and field study of K-TEEM, a web-based assessment instrument designed to measure mathematical knowledge for teaching (MKT) at the early elementary level. The development process involved alignment with early elementary curriculum standards, expert review of items and scoring criteria, cognitive interviews with…

  16. The Impact of Assumed Knowledge Entry Standards on Undergraduate Mathematics Teaching in Australia

    ERIC Educational Resources Information Center

    King, Deborah; Cattlin, Joann

    2015-01-01

    Over the last two decades, many Australian universities have relaxed their selection requirements for mathematics-dependent degrees, shifting from hard prerequisites to assumed knowledge standards which provide students with an indication of the prior learning that is expected. This has been regarded by some as a positive move, since students who…

  17. Developing Mathematical Knowledge for Teaching in a Methods Course: The Case of Function

    ERIC Educational Resources Information Center

    Steele, Michael D.; Hillen, Amy F.; Smith, Margaret S.

    2013-01-01

    This study describes teacher learning in a teaching experiment consisting of a content-focused methods course involving the mathematical knowledge for teaching function. Prospective and practicing teachers in the course showed growth in their ability to define function, to provide examples of functions and link them to the definition, in the…

  18. History of Mathematics: Illuminating Understanding of School Mathematics Concepts for Prospective Mathematics Teachers

    ERIC Educational Resources Information Center

    Clark, Kathleen Michelle

    2012-01-01

    The use of the history of mathematics in teaching has long been considered a tool for enriching students' mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of…

  19. The Acquisition of Mathematics Pedagogical Content Knowledge in University Mathematics Education Courses: Results of a Mixed Methods Study on the Effectiveness of Teacher Education in Germany

    ERIC Educational Resources Information Center

    Buchholtz, Nils Frederik

    2017-01-01

    This paper reports on a longitudinal mixed methods evaluation study on the acquisition and development of mathematical pedagogical content knowledge (MPCK) of future teachers at several German universities. The study is a German supplementary study to the international comparative TEDS-M 2008 study. Besides the pedagogical content knowledge that…

  20. Exploring the Impact of a Standards-Based Mathematics and Pedagogy Class on Preservice Teachers' Beliefs and Subject Matter Knowledge

    ERIC Educational Resources Information Center

    Stohlmann, Micah Stephen

    2012-01-01

    This case study explored the impact of a standards-based mathematics and pedagogy class on preservice elementary teachers' beliefs and conceptual subject matter knowledge of linear functions. The framework for the standards-based mathematics and pedagogy class in this study involved the National Council of Teachers of Mathematics Standards,…

  1. Developing Technological Pedagogical Content Knowledge in Pre-Service Mathematics Teachers through Collaborative Design

    ERIC Educational Resources Information Center

    Agyei, Douglas D.; Voogt, Joke

    2012-01-01

    Although many studies have shown the need to pay attention to teachers' preparation for the integration of technology in classroom practice, most teachers in Ghana have not had any preparation that develops their technological pedagogical content knowledge (TPCK). This paper presents a case study of four pre-service mathematics teachers from the…

  2. Use of Learning Trajectories to Examine Pre-Service Teachers' Mathematics Knowledge for Teaching Area and Perimeter: Emerging Issues

    ERIC Educational Resources Information Center

    Butterfield, Barbara; Forrester, Tricia; McCallum, Faye; Chinnappan, Mohan

    2013-01-01

    A current concern is student learning outcomes and these are largely a function of teachers' knowledge and their practice. This position paper is premised on the notion that certain knowledge is required for the teaching of mathematics. An exploration of literature demonstrates that such professional knowledge development can be supported by…

  3. Increasing Cognitive Inhibition with a Difficult Prior Task: Implications for Mathematical Thinking

    ERIC Educational Resources Information Center

    Attridge, Nina; Inglis, Matthew

    2015-01-01

    Dual-process theories posit two distinct types of cognitive processing: Type 1, which does not use working memory making it fast and automatic, and Type 2, which does use working memory making it slow and effortful. Mathematics often relies on the inhibition of pervasive Type 1 processing to apply new skills or knowledge that require Type 2…

  4. 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…

  5. Rethinking about the Pedagogy for Pedagogical Content Knowledge in the Context of Mathematics Teaching

    ERIC Educational Resources Information Center

    Ozmantar, Mehmet Fatih

    2011-01-01

    This study reconsiders the notion of pedagogy for pedagogical content knowledge (PCK) in the context of teaching mathematics. The perspectives of critical pedagogy are employed for this reconsideration, stressing the operation of historical, social, ideological, political, institutional and cultural forces in the production of pedagogical…

  6. Construction of Mathematical Knowledge Using Graphic Calculators (CAS) in the Mathematics Classroom

    ERIC Educational Resources Information Center

    Hitt, Fernando

    2011-01-01

    Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the mathematics classroom has not had the expected impact, as it has been its use in everyday life (i.e. cell phone). What about teachers' opinions? Mathematics…

  7. Addressing prospective elementary teachers' mathematics subject matter knowledge through action research

    NASA Astrophysics Data System (ADS)

    Hourigan, Mairéad; O'Donoghue, John

    2015-01-01

    There is international dissatisfaction regarding the standard of mathematics subject matter knowledge (MSMK) evident among both qualified and prospective elementary teachers. Ireland is no exception. Following increasing anecdotal evidence of prospective elementary teachers in one Irish College of Education (provider of initial teacher education programme) demonstrating weaknesses in this regard, this study sought to examine and address the issue through two cycles of action research. The examination of the nature of prospective teachers' MSMK (as well as related beliefs in the main study) informed the design and implementation of an intervention to address the issue. A mixed method approach was taken throughout. In both cycles, Shapiro's criteria were used as a conceptual framework for the evaluation of the initiative. This paper focuses on the perceived and actual effects of the intervention on participants' MSMK. As well as its contribution at a local and national level, the study provides an Irish perspective on approaches taken to address the phenomenon internationally.

  8. Mathematical Ability Relies on Knowledge, Too

    ERIC Educational Resources Information Center

    Sweller, John; Clark, Richard E.; Kirschner, Paul A.

    2011-01-01

    Recent "reform" curricula both ignore the absence of supporting data and completely misunderstand the role of problem solving in cognition. If, the argument goes, teachers are not really teaching people mathematics but rather are teaching them some form of general problem solving, then mathematical content can be reduced in importance. According…

  9. Designing Tasks to Examine Mathematical Knowledge for Teaching Statistics for Primary Teachers

    NASA Astrophysics Data System (ADS)

    Siswono, T. Y. E.; Kohar, A. W.; Hartono, S.

    2018-01-01

    Mathematical knowledge for teaching (MKT) is viewed as fuel resources for conducting an orchestra in a teaching and learning process. By understanding MKT, especially for primary teachers, it can predict the success of a goal of an instruction and analyze the weaknesses and improvements of it. To explore what teachers think about subject matters, pedagogical terms, and appropriate curriculum, it needs a task which can be identified the teachers’ MKT including the subject matter knowledge (SMK) and pedagogical content knowledge (PCK). This study aims to design an appropriate task for exploring primary teachers’ MKT for statistics in primary school. We designed six tasks to examine 40 primary teachers’ MKT, of which each respectively represents the categories of SMK (common content knowledge (CCK) and specialised content knowledge (SCK)) and PCK (knowledge of content and students (KCS), knowledge of content and teaching (KCT), and knowledge of content and curriculum (KCC)). While MKT has much attention of numbers of scholars, we consider knowledge of content and culture (KCCl) to be hypothesized in the domains of MKT. Thus, we added one more task examining how the primary teachers used their knowledge of content (KC) regarding to MKT in statistics. Some examples of the teachers’ responses on the tasks are discussed and some refinements of MKT task in statistics for primary teachers are suggested.

  10. Engaging in Problem Posing Activities in a Dynamic Geometry Setting and the Development of Prospective Teachers' Mathematical Knowledge

    ERIC Educational Resources Information Center

    Lavy, Ilana; Shriki, Atara

    2010-01-01

    In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the "What If Not?" (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs'…

  11. Increase Productivity Through Knowledge Management

    NASA Astrophysics Data System (ADS)

    Gavrikova, N. A.; Dolgih, I. N.; Dyrina, E. N.

    2016-04-01

    Increase in competition level requires companies to improve the efficiency of work force use characterized by labor productivity. Professional knowledge of staff and its experience play the key role in it. The results of Extrusion Line operator’s working time analysis are performed in this article. The analysis revealed that the reasons of working time ineffective use connected with inadequate information exchange and knowledge management in the company. Authors suggest the way to solve this problem: the main sources of knowledge in engineering enterprise have been defined, the conditions of success and the stages of knowledge management control have been stated.

  12. Increasing Mathematical Computation Skills for Students with Physical and Health Disabilities

    ERIC Educational Resources Information Center

    Webb, Paula

    2017-01-01

    Students with physical and health disabilities struggle with basic mathematical concepts. The purpose of this research study was to increase the students' mathematical computation skills through implementing new strategies and/or methods. The strategies implemented with the students was utilizing the ten-frame tiles and technology with the purpose…

  13. Using Video Analysis to Support Prospective K-8 Teachers' Noticing of Students' Multiple Mathematical Knowledge Bases

    ERIC Educational Resources Information Center

    Roth McDuffie, Amy; Foote, Mary Q.; Bolson, Catherine; Turner, Erin E.; Aguirre, Julia M.; Bartell, Tonya Gau; Drake, Corey; Land, Tonia

    2014-01-01

    As part of a larger research project aimed at transforming preK-8 mathematics teacher preparation, the purpose of this study was to examine the extent to which prospective teachers notice children's competencies related to children's mathematical thinking, and children's community, cultural, and linguistic funds of knowledge or what…

  14. Widening and Increasing Post-16 Mathematics Participation: Pathways, Pedagogies and Politics

    ERIC Educational Resources Information Center

    Noyes, Andrew; Wake, Geoff; Drake, Pat

    2011-01-01

    This paper explores the potential impact of a national pilot initiative in England aimed at increasing and widening participation in advanced mathematical study through the creation of a new qualification for 16- to 18-year-olds. This proposed qualification pathway--"Use of Mathematics"--sits in parallel with long-established,…

  15. Informing Estimates of Program Effects for Studies of Mathematics Professional Development Using Teacher Content Knowledge Outcomes.

    PubMed

    Phelps, Geoffrey; Kelcey, Benjamin; Jones, Nathan; Liu, Shuangshuang

    2016-10-03

    Mathematics professional development is widely offered, typically with the goal of improving teachers' content knowledge, the quality of teaching, and ultimately students' achievement. Recently, new assessments focused on mathematical knowledge for teaching (MKT) have been developed to assist in the evaluation and improvement of mathematics professional development. This study presents empirical estimates of average program change in MKT and its variation with the goal of supporting the design of experimental trials that are adequately powered to detect a specified program effect. The study drew on a large database representing five different assessments of MKT and collectively 326 professional development programs and 9,365 teachers. Results from cross-classified hierarchical growth models found that standardized average change estimates across the five assessments ranged from a low of 0.16 standard deviations (SDs) to a high of 0.26 SDs. Power analyses using the estimated pre- and posttest change estimates indicated that hundreds of teachers are needed to detect changes in knowledge at the lower end of the distribution. Even studies powered to detect effects at the higher end of the distribution will require substantial resources to conduct rigorous experimental trials. Empirical benchmarks that describe average program change and its variation provide a useful preliminary resource for interpreting the relative magnitude of effect sizes associated with professional development programs and for designing adequately powered trials. © The Author(s) 2016.

  16. Teachers' Understanding of Mathematical Cognition in Childhood: Towards a Shift in Pedagogical Content Knowledge?

    ERIC Educational Resources Information Center

    Henning, Elizabeth

    2013-01-01

    This article about the discourse of pedagogy as related to child cognition in mathematics addresses the issue of what constitutes the main disciplinary content and the pedagogical content knowledge (PCK) of foundation-phase teachers. I argue that, unless child cognition itself is the primary disciplinary content of foundation-phase teacher's…

  17. Socioeconomic Status and Preschoolers' Mathematical Knowledge: The Contribution of Home Activities and Parent Beliefs

    ERIC Educational Resources Information Center

    DeFlorio, Lydia; Beliakoff, Amber

    2015-01-01

    Research Findings: Children from families of lower socioeconomic status (SES) enter kindergarten with less developed mathematical knowledge compared to children from middle SES families. This discrepancy is present at age 3 years and likely stems from differences in the home learning environment. This study reports SES-related differences both in…

  18. Developing an Assessment Instrument to Measure Early Elementary Teachers' Mathematical Knowledge for Teaching

    ERIC Educational Resources Information Center

    Schoen, Robert C.; Bray, Wendy; Wolfe, Christopher; Tazaz, Amanda M.; Nielsen, Lynne

    2017-01-01

    This study reports on the development and field study of K-TEEM, a web-based assessment instrument designed to measure mathematical knowledge for teaching (MKT) at the early elementary level. The development process involved alignment with early elementary curriculum standards, expert review of items and scoring criteria, cognitive interviews with…

  19. What is the Role of Mathematics Education in the Computer Age?

    ERIC Educational Resources Information Center

    Popp, Jerome A.

    1986-01-01

    Proposes that the role of mathematics education be re-examined in terms of an increased emphasis on mathematical knowledge rather than attainment of calculational speed. Offers perspectives on the reform movement in mathematics education and advocates the teaching of the history, logic, and method of mathematical thinking. (ML)

  20. Teacher Knowledge That Supports Student Processes in Learning Mathematics: A Study at All-Female Middle Schools in Saudi Arabia

    ERIC Educational Resources Information Center

    Alsaeed, Maha Saad

    2012-01-01

    Teachers in Saudi Arabia are attempting to advance their teaching in mathematics to address specific reforms by the Ministry of Education. Saudi teachers must improve their students' thinking through engagement in problem solving. This qualitative study investigated how teachers use knowledge of student mathematical learning and how they promote…

  1. Mathematics, Anyone?

    ERIC Educational Resources Information Center

    Reys, Robert; Reys, Rustin

    2011-01-01

    In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…

  2. The Effect of Syllabus on Mathematical Knowledge

    ERIC Educational Resources Information Center

    Belsom, C. G. H.; Elton, L. R. B.

    1974-01-01

    Item analysis of a mathematics preknowledge test given to physics students revealed that significant differences existed on certain items between groups of students who had followed different mathematics syllabuses. (MLH)

  3. Assessing Mathematical Problem Solving Using Comparative Judgement

    ERIC Educational Resources Information Center

    Jones, Ian; Swan, Malcolm; Pollitt, Alastair

    2015-01-01

    There is an increasing demand from employers and universities for school leavers to be able to apply their mathematical knowledge to problem solving in varied and unfamiliar contexts. These aspects are however neglected in most examinations of mathematics and, consequentially, in classroom teaching. One barrier to the inclusion of mathematical…

  4. Food-based Science Curriculum Increases 4th Graders Multidisciplinary Science Knowledge

    PubMed Central

    Hovland, Jana A.; Carraway-Stage, Virginia G.; Cela, Artenida; Collins, Caitlin; Díaz, Sebastián R.; Collins, Angelo; Duffrin, Melani W.

    2013-01-01

    Health professionals and policymakers are asking educators to place more emphasis on food and nutrition education. Integrating these topics into science curricula using hand-on, food-based activities may strengthen students’ understanding of science concepts. The Food, Math, and Science Teaching Enhancement Resource (FoodMASTER) Initiative is a compilation of programs aimed at using food as a tool to teach mathematics and science. Previous studies have shown that students experiencing the FoodMASTER curriculum were very excited about the activities, became increasingly interested in the subject matter of food, and were able to conduct scientific observations. The purpose of this study was to: 1) assess 4th graders food-related multidisciplinary science knowledge, and 2) compare gains in food-related science knowledge after implementation of an integrated, food-based curriculum. During the 2009–2010 school year, FoodMASTER researchers implemented a hands-on, food-based intermediate curriculum in eighteen 4th grade classrooms in Ohio (n=9) and North Carolina (n=9). Sixteen classrooms in Ohio (n=8) and North Carolina (n=8), following their standard science curricula, served as comparison classrooms. Students completed a researcher-developed science knowledge exam, consisting of 13 multiple-choice questions administered pre- and post-test. Only subjects with pre- and post-test scores were entered into the sample (Intervention n=343; Control n=237). No significant differences were observed between groups at pre-test. At post-test, the intervention group scored (9.95±2.00) significantly higher (p=.000) than the control group (8.84±2.37) on a 13-point scale. These findings suggest the FoodMASTER intermediate curriculum is more effective than a standard science curriculum in increasing students’ multidisciplinary science knowledge related to food. PMID:25152539

  5. Connecting mathematics learning through spatial reasoning

    NASA Astrophysics Data System (ADS)

    Mulligan, Joanne; Woolcott, Geoffrey; Mitchelmore, Michael; Davis, Brent

    2018-03-01

    Spatial reasoning, an emerging transdisciplinary area of interest to mathematics education research, is proving integral to all human learning. It is particularly critical to science, technology, engineering and mathematics (STEM) fields. This project will create an innovative knowledge framework based on spatial reasoning that identifies new pathways for mathematics learning, pedagogy and curriculum. Novel analytical tools will map the unknown complex systems linking spatial and mathematical concepts. It will involve the design, implementation and evaluation of a Spatial Reasoning Mathematics Program (SRMP) in Grades 3 to 5. Benefits will be seen through development of critical spatial skills for students, increased teacher capability and informed policy and curriculum across STEM education.

  6. Family Child Care Learning Environments: Caregiver Knowledge and Practices Related to Early Literacy and Mathematics

    ERIC Educational Resources Information Center

    Phillips, Beth M.; Morse, Erika E.

    2011-01-01

    This paper presents findings from a stratified-random survey of family child care providers' backgrounds, caregiving environments, practices, attitudes, and knowledge related to language, literacy, and mathematics development for preschool children. Descriptive results are consistent with prior studies suggesting that home-based providers are…

  7. Teaching Early Knowledge of Whole Number Concepts through Technology: Findings from a Feasibility Study of an iPad Delivered Kindergarten Mathematics Intervention

    ERIC Educational Resources Information Center

    Shanley, Lina; Cary, Mari Strand; Clarke, Ben; Jungjohann, Kathy

    2013-01-01

    Children enter kindergarten with variable levels of mathematics skill and knowledge gained from informal learning opportunities at home, preschool, and daycare. Many perform well once they receive formal mathematics instruction. However, if students do not develop an initial understanding of the most basic aspects of formal mathematics, they are…

  8. Deepening Pre-Service Teachers' Knowledge of Technology, Pedagogy, and Content (TPACK) in an Elementary School Mathematics Methods Course

    ERIC Educational Resources Information Center

    Polly, Drew

    2014-01-01

    This paper presents the findings of a study that examined pre-service teachers' development of knowledge about technology, pedagogy and content (TPACK) during a mathematics pedagogy course focused on elementary school mathematics in the United States. Data sources included work samples from pre-service teachers as well as an open-ended survey…

  9. Teaching Mathematics That Addresses Learners' Multiple Intelligences

    ERIC Educational Resources Information Center

    Gouws, E.; Dicker, A-M.

    2011-01-01

    To meet the demands of our highly technological and globally competitive society, it is becoming increasingly important for all learners in South Africa to obtain skills and knowledge in mathematics. However, South Africa performed the worst of all the countries who participated in the Trends in International Mathematics and Science Study (TIMMS).…

  10. Vamos a Jugar Counters! Learning Mathematics through Funds of Knowledge, Play, and the Third Space

    ERIC Educational Resources Information Center

    Razfar, Aria

    2012-01-01

    Drawing on Cultural Historical Activity Theory (CHAT), funds of knowledge, and third space, this article presents a model for practitioners and researchers to think about how Latina/o, bilingual children develop explicit mathematics strategies through multilingual and multigenerational interactions. Using data collected through fieldwork in an…

  11. Understanding Mathematics and Science Matters. Studies in Mathematical Thinking and Learning Series

    ERIC Educational Resources Information Center

    Romberg, Thomas A., Ed.; Carpenter, Thomas P., Ed.; Dremock, Fae, Ed.

    2005-01-01

    The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world. The National Center for Improving Student Learning in Mathematics…

  12. Increasing mathematical problem-solving performance through relaxation training

    NASA Astrophysics Data System (ADS)

    Sharp, Conni; Coltharp, Hazel; Hurford, David; Cole, Amykay

    2000-04-01

    Two intact classes of 30 undergraduate students enrolled in the same general education mathematics course were each administered the IPSP Mathematics Problem Solving Test and the Mathematics Anxiety Rating Scale at the beginning and end of the semester. Both groups experienced the same syllabus, lectures, course requirements, and assessment techniques; however, one group received relaxation training during an initial class meeting and during the first 5 to 7 minutes of each subsequent class. The group which had received relaxation training had significantly lower mathematics anxiety and significantly higher mathematics performance at the end of the course. The results suggest that relaxation training may be a useful tool for treating anxiety in undergraduate general education mathematics students.

  13. Studying Challenges in Integrating Technology in Secondary Mathematics with Technological Pedagogical and Content Knowledge (TPACK)

    ERIC Educational Resources Information Center

    Stoilescu, Dorian

    2014-01-01

    This paper describes challenges encountered by two secondary mathematics teachers when they try to integrate ICT devices in their classes. These findings are based on using the Technological Pedagogical and Content Knowledge (TPACK) context, the four dimension framework developed by Niess: 1) overarching conceptions of integrating ICT, 2)…

  14. Profile of Metacognition of Mathematics and Mathematics Education Students in Understanding the Concept of Integral Calculus

    NASA Astrophysics Data System (ADS)

    Misu, La; Ketut Budayasa, I.; Lukito, Agung

    2018-03-01

    This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.

  15. Mathematics teaching experiences of elementary preservice teachers with high and low mathematics anxiety during student teaching: A multiple case study

    NASA Astrophysics Data System (ADS)

    Nisbet, Leslie Deanna

    This study investigated the teaching experiences of six elementary preservice teachers (EPTs), three with high mathematics anxiety and three with low mathematics anxiety, during their student teaching semester. The EPTs were selected from an initial pool of 121 EPTs who took the Abbreviated Mathematics Anxiety Scale. The cases were compared in a cross case analysis to highlight mathematics teaching experiences among EPTs. Data sources included EPT and researcher journal entries, interview transcripts, pre-lesson surveys, field notes, lesson plans, and artifacts of observed lessons. Data were coded using Shulman's content knowledge, Graeber's mathematics pedagogical content knowledge, and mathematics anxiety characteristics. Findings revealed both similarities and differences across EPTs as related to four major categories: (a) planning and resources used, (b) role of the cooperating teacher, (c) content knowledge, and (d) pedagogical content knowledge. All EPTs used mostly direct instruction and relied on the course textbook and their respective cooperating teacher as their primary resources for planning. Additionally, across participants, the cooperating teacher influenced EPTs' perceptions of students and teaching. Also, EPTs with high mathematics anxiety were weaker with respect to content knowledge and pedagogical content knowledge. Findings suggest a need to re-design methods courses to address improving the pedagogical content knowledge of EPTs with mathematics anxiety. Findings also suggest a need to develop content specific mathematics courses for EPTs to improve their content knowledge. Future studies could include a longitudinal study to follow highly anxious EPTs who take content specific elementary mathematics courses to observe their content knowledge and mathematics anxiety.

  16. Mathematical learning models that depend on prior knowledge and instructional strategies

    NASA Astrophysics Data System (ADS)

    Pritchard, David E.; Lee, Young-Jin; Bao, Lei

    2008-06-01

    We present mathematical learning models—predictions of student’s knowledge vs amount of instruction—that are based on assumptions motivated by various theories of learning: tabula rasa, constructivist, and tutoring. These models predict the improvement (on the post-test) as a function of the pretest score due to intervening instruction and also depend on the type of instruction. We introduce a connectedness model whose connectedness parameter measures the degree to which the rate of learning is proportional to prior knowledge. Over a wide range of pretest scores on standard tests of introductory physics concepts, it fits high-quality data nearly within error. We suggest that data from MIT have low connectedness (indicating memory-based learning) because the test used the same context and representation as the instruction and that more connected data from the University of Minnesota resulted from instruction in a different representation from the test.

  17. Problem-Based Learning--Buginese Cultural Knowledge Model--Case Study: Teaching Mathematics at Junior High School

    ERIC Educational Resources Information Center

    Cheriani, Cheriani; Mahmud, Alimuddin; Tahmir, Suradi; Manda, Darman; Dirawan, Gufran Darma

    2015-01-01

    This study aims to determine the differences in learning output by using Problem Based Model combines with the "Buginese" Local Cultural Knowledge (PBL-Culture). It is also explores the students activities in learning mathematics subject by using PBL-Culture Models. This research is using Mixed Methods approach that combined quantitative…

  18. Children's Construction of Mathematical Knowledge in Solving Novel Isomorphic Problems in Concrete and Written Form.

    ERIC Educational Resources Information Center

    English, Lyn D.

    1996-01-01

    Presents case study data of low- and high-achieving nine-year olds focusing on construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in strategies for dealing with isomorphic combinatorial problems presented in hands-on and written form. Results showed that achievement level does not predict…

  19. Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) vs. low mathematics achievement

    PubMed Central

    Mazzocco, Michèle M. M.; Myers, Gwen F.; Lewis, Katherine E.; Hanich, Laurie B.; Murphy, Melissa M.

    2014-01-01

    Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions equivalent to “one-half,” and fraction pairs with common denominators) differentiates those with mathematical learning disability (MLD) versus low achievement (LA) or typical achievement (TA) in mathematics, and whether long term learning trajectories of this knowledge also differentiate these groups. We confirmed that although 4th graders with LA (n = 18) or TA (n = 93) are more accurate evaluating one-half vs. non-half fractions (until they reach ceiling performance levels on both types of fractions), children with MLD (n=11) do not show a one-half advantage until Grade 7 and do not reach ceiling performance even by Grade 8. Both the MLD and LA groups have early difficulties with fractions, but by Grade 5 the LA group approaches performance levels of the TA group and deviates from the MLD group. All groups showed a visual model advantage over Arabic number representation of fractions, but this advantage was short lived for the TA group (because ceiling level was achieved across formats), slightly more persistent for the LA group, and persisted through Grade 8 for children with MLD. Thus, difficulties with fractions persist through Grade 8 for many students, but the nature and trajectories of those difficulties varies across children with math difficulties (MLD or LA). PMID:23587941

  20. Interference thinking in constructing students’ knowledge to solve mathematical problems

    NASA Astrophysics Data System (ADS)

    Jayanti, W. E.; Usodo, B.; Subanti, S.

    2018-04-01

    This research aims to describe interference thinking in constructing students’ knowledge to solve mathematical problems. Interference thinking in solving problems occurs when students have two concepts that interfere with each other’s concept. Construction of problem-solving can be traced using Piaget’s assimilation and accommodation framework, helping to know the students’ thinking structures in solving the problems. The method of this research was a qualitative method with case research strategy. The data in this research involving problem-solving result and transcripts of interviews about students’ errors in solving the problem. The results of this research focus only on the student who experience proactive interference, where student in solving a problem using old information to interfere with the ability to recall new information. The student who experience interference thinking in constructing their knowledge occurs when the students’ thinking structures in the assimilation and accommodation process are incomplete. However, after being given reflection to the student, then the students’ thinking process has reached equilibrium condition even though the result obtained remains wrong.

  1. Levels of line graph question interpretation with intermediate elementary students of varying scientific and mathematical knowledge and ability: A think aloud study

    NASA Astrophysics Data System (ADS)

    Keller, Stacy Kathryn

    This study examined how intermediate elementary students' mathematics and science background knowledge affected their interpretation of line graphs and how their interpretations were affected by graph question levels. A purposive sample of 14 6th-grade students engaged in think aloud interviews (Ericsson & Simon, 1993) while completing an excerpted Test of Graphing in Science (TOGS) (McKenzie & Padilla, 1986). Hand gestures were video recorded. Student performance on the TOGS was assessed using an assessment rubric created from previously cited factors affecting students' graphing ability. Factors were categorized using Bertin's (1983) three graph question levels. The assessment rubric was validated by Padilla and a veteran mathematics and science teacher. Observational notes were also collected. Data were analyzed using Roth and Bowen's semiotic process of reading graphs (2001). Key findings from this analysis included differences in the use of heuristics, self-generated questions, science knowledge, and self-motivation. Students with higher prior achievement used a greater number and variety of heuristics and more often chose appropriate heuristics. They also monitored their understanding of the question and the adequacy of their strategy and answer by asking themselves questions. Most used their science knowledge spontaneously to check their understanding of the question and the adequacy of their answers. Students with lower and moderate prior achievement favored one heuristic even when it was not useful for answering the question and rarely asked their own questions. In some cases, if students with lower prior achievement had thought about their answers in the context of their science knowledge, they would have been able to recognize their errors. One student with lower prior achievement motivated herself when she thought the questions were too difficult. In addition, students answered the TOGS in one of three ways: as if they were mathematics word problems

  2. A survey on the effectiveness of using GeoGebra software towards lecturers' conceptual knowledge and procedural mathematics

    NASA Astrophysics Data System (ADS)

    Wan Salleh, Masturah; Sulaiman, Hajar

    2013-04-01

    The use of technology in the teaching of mathematics at the university level has long been introduced; but many among the lecturers, especially those that have taught for many years, still opt for a traditional teaching method, that is, by lecture talk. One reason is that lecturers themselves were not exposed to the technologies available and how it can assist in the teaching and learning procedures (T&L) in mathematics. GeoGebra is a mathematical software which is open and free and has just recently been introduced in Malaysia. Compared with the software Cabri Geometry and Geometer's Sketchpad (GSP), which only focus on geometry, GeoGebra is able to connect geometry, algebra and numerical representation. Realizing this, the researchers have conducted a study to expose the university lecturers on the use of GeoGebra in T&L. The researchers chose to do the research on mathematics lecturers at the Department of Computer Science and Mathematics (JSKM), Universiti Teknologi Mara (UiTM), Penang. The objective of this study is to determine whether an exposure to GeoGebra software can affect the conceptual knowledge and procedural teaching of mathematics at the university level. This study is a combination of descriptive and qualitative. One session was conducted in an open workshop for all the 45 lecturers. From that total, four people were selected as a sample. The sample was selected by using a simple random sampling method. This study used materials in the form of modules during the workshop. In terms of conceptual knowledge, the results showed that the GeoGebra software is appropriate, relevant and highly effective for in-depth understanding of the selected topics. While the procedural aspects of teaching, it can be one of the teaching aids and considerably facilitate the lecturers.

  3. Vicissitudes of Children's Mathematical Knowledge: Implications of Developmental Research for Early Childhood Mathematics Education

    ERIC Educational Resources Information Center

    Sophian, Catherine

    2013-01-01

    Hachey's (2013) article celebrates a revolution that is taking place in early childhood mathematics education, fueled in part by developmental research demonstrating the mathematical capabilities of young children. At the same time, Hachey notes that the mathematics revolution she describes is not yet complete. In this commentary, the author…

  4. Implementation of Pedagogical Content Knowledge (PCK) of Mathematics Teachers in Teaching Practice: A Case Study

    ERIC Educational Resources Information Center

    Maryono; Sutawidjaja, Akbar; Subanji; Irawati, Santi

    2017-01-01

    This study aims to describe the implementation of pedagogical content knowledge (PCK) of mathematics teachers in the teaching practice of the material system of linear equations of two variables (SLETV). The approach used is a qualitative case study. The main instrument is the researchers themselves and the supporting instruments is a vignette…

  5. Comparing Mathematics Achievement Scores: Face-To-Face versus Online Delivery

    ERIC Educational Resources Information Center

    Lenderman, Ami

    2017-01-01

    The purpose of this quantitative study was to explore the relationship between the use of online courseware at Georgia Virtual School as an instructional delivery method and student achievement of 9th and 10th grade mathematics students as measured by Mathematics I and Mathematics II End of Course Test (EOCT) scores. The knowledge of an increase,…

  6. Why (Urban) Mathematics Teachers Need Political Knowledge

    ERIC Educational Resources Information Center

    Gutiérrez, Rochelle

    2013-01-01

    Rochelle Gutiérrez has spent 15 years researching effective, urban high school mathematics departments that served Black, Latin@ and low-income adolescents (see, e.g., Gutiérrez, 1996, 1999a, 1999b, 2000, 2002). These were schools where students took more mathematics than was required by their district; where English learners, recent immigrants,…

  7. Early Predictors of High School Mathematics Achievement

    ERIC Educational Resources Information Center

    Siegler, Robert S.; Duncan, Greg J.; Davis-Kean, Pamela E.; Duckworth, Kathryn; Claessens, Amy; Engel, Mimi; Susperreguy, Maria Ines; Meichu, Chen

    2012-01-01

    Identifying the types of mathematics content knowledge that are most predictive of students' long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students' knowledge of algebra and overall mathematics…

  8. The Nature of Mathematics: A Heuristic Inquiry

    ERIC Educational Resources Information Center

    Pair, Jeffrey David

    2017-01-01

    What is mathematics? What does it mean to be a mathematician? What should students understand about the nature of mathematical knowledge and inquiry? Research in the field of mathematics education has found that students often have naive views about the nature of mathematics. Some believe that mathematics is a body of unchanging knowledge, a…

  9. Spontaneous focusing on numerosity in preschool as a predictor of mathematical skills and knowledge in the fifth grade.

    PubMed

    Nanu, Cristina E; McMullen, Jake; Munck, Petriina; Hannula-Sormunen, Minna M

    2018-05-01

    Previous studies in a variety of countries have shown that there are substantial individual differences in children's spontaneous focusing on numerosity (SFON), and these differences are positively related to the development of early numerical skills in preschool and primary school. A total of 74 5-year-olds participated in a 7-year follow-up study, in which we explored whether SFON measured with very small numerosities at 5 years of age predicts mathematical skills and knowledge, math motivation, and reading in fifth grade at 11 years of age. Results show that preschool SFON is a unique predictor of arithmetic fluency and number line estimation but not of rational number knowledge, mathematical achievement, math motivation, or reading. These results hold even after taking into account age, IQ, working memory, digit naming, and cardinality skills. The results of the current study further the understanding of how preschool SFON tendency plays a role in the development of different formal mathematical skills over an extended period of time. Copyright © 2017 Elsevier Inc. All rights reserved.

  10. Microteaching Lesson Study: Mentor Interaction Structure and Its Relation to Elementary Preservice Mathematics Teacher Knowledge Development

    ERIC Educational Resources Information Center

    Molina, Roxanne V.

    2012-01-01

    This study investigated Microteaching Lesson Study (MLS) and three possible MLS mentor interaction structures during the debriefing sessions in relation to elementary preservice teacher development of knowledge for teaching. One hundred three elementary preservice teachers enrolled in five different sections of a mathematics methods course at a…

  11. Mathematical subtleties and scientific knowledge: Francis Bacon and mathematics, at the crossing of two traditions.

    PubMed

    Mori, Giuliano

    2017-03-01

    This article engages the much-debated role of mathematics in Bacon's philosophy and inductive method at large. The many references to mathematics in Bacon's works are considered in the context of the humanist reform of the curriculum studiorum and, in particular, through a comparison with the kinds of natural and intellectual subtlety as they are defined by many sixteenth-century authors, including Cardano, Scaliger and Montaigne. Additionally, this article gives a nuanced background to the 'subtlety' commonly thought to have been eschewed by Bacon and by Bacon's self-proclaimed followers in the Royal Society of London. The aim of this article is ultimately to demonstrate that Bacon did not reject the use of mathematics in natural philosophy altogether. Instead, he hoped that following the Great Instauration a kind of non-abstract mathematics could be founded: a kind of mathematics which was to serve natural philosophy by enabling men to grasp the intrinsic subtlety of nature. Rather than mathematizing nature, it was mathematics that needed to be 'naturalized'.

  12. High School Teachers' Problem Solving Activities to Review and Extend Their Mathematical and Didactical Knowledge

    ERIC Educational Resources Information Center

    Santos-Trigo, Manuel; Barrera-Mora, Fernando

    2011-01-01

    The study documents the extent to which high school teachers reflect on their need to revise and extend their mathematical and practicing knowledge. In this context, teachers worked on a set of tasks as a part of an inquiring community that promoted the use of different computational tools in problem solving approaches. Results indicated that the…

  13. Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement.

    PubMed

    Mazzocco, Michèle M M; Myers, Gwen F; Lewis, Katherine E; Hanich, Laurie B; Murphy, Melissa M

    2013-06-01

    Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions equivalent to one-half, fraction pairs with common denominators) differentiates those with mathematics learning disability (MLD) versus low achievement (LA) or typical achievement (TA) in mathematics and whether long-term learning trajectories of this knowledge also differentiate these groups. We confirmed that although fourth graders with TA (n=93) were more accurate in evaluating "one-half" fractions than in evaluating "non-half" fractions (until they reached ceiling performance levels on both types of fractions), children with MLD (n=11) did not show a one-half advantage until Grade 7 and did not reach ceiling performance even by Grade 8. Both the MLD and LA groups had early difficulties with fractions, but by Grade 5 the LA group approached performance levels of the TA group and deviated from the MLD group. All groups showed a visual model advantage over Arabic number representation of fractions, but this advantage was short-lived for the TA group (because ceiling level was achieved across formats), whereas it was slightly more persistent for the LA group and persisted through Grade 8 for children with MLD. Thus, difficulties with fractions persist through Grade 8 for many students, but the nature and trajectories of those difficulties vary across children with math difficulties (MLD or LA). Copyright © 2013 Elsevier Inc. All rights reserved.

  14. Kindergarten Children’s Growth Trajectories in Reading and Mathematics: Who Falls Increasingly Behind?

    PubMed Central

    Morgan, Paul L.; Farkas, George; Wu, Qiong

    2015-01-01

    We used a large sample of children (N ≈ 7,400) participating in the Early Childhood Longitudinal Study – Kindergarten Cohort to estimate kindergarten children’s academic achievement growth trajectories in reading and mathematics. We were particularly interested in whether the growth trajectories of children with learning disabilities (LD) or speech language impairments (SLI)—as well as those of other groups of children—were consistent with a cumulative or compensatory developmental cycle. Both LD and SLI children displayed significantly lower levels of kindergarten reading achievement than non-disabled children. However, and over the subsequent five years of elementary school, only children with SLI lagged increasingly behind non-disabled peers in their reading skills growth. We observed a different pattern for mathematics achievement. Children with LD, but not SLI, lagged increasingly behind non-disabled children in their mathematics skills growth. We also observed some consistency in “poor-get-poorer” effects across reading and mathematic achievement for additional population subgroups. Those kindergarten children who were from lower socio-economic status (SES) families, who were African-American, and who more frequently displayed learning-related behaviors problems initially had lower levels of reading and mathematics achievement and also lagged increasingly behind in their acquisition of these skills over time. Some groups of children, including those with SLI, experience a cumulative rather than compensatory cycle of achievement growth. PMID:21856991

  15. A Collective Case Study of the Influence of Teachers' Beliefs and Knowledge on Error-Handling Practices during Class Discussion of Mathematics

    ERIC Educational Resources Information Center

    Bray, Wendy S.

    2011-01-01

    This collective case study examines the influence of 4 third-grade teachers' beliefs and knowledge on their error-handling practices during class discussion of mathematics. Study findings suggest that, although teachers' ways of handling student errors during class discussion of mathematics are clearly linked to both teacher beliefs and teacher…

  16. A Critical Examination of the Technological Pedagogical Content Knowledge Framework: Secondary School Mathematics Teachers Integrating Technology

    ERIC Educational Resources Information Center

    Stoilescu, Dorian

    2015-01-01

    This study explores the Technological Pedagogical Content Knowledge (TPACK) for three experienced mathematics secondary teachers from a Toronto public school. By using a multiple case study, teachers' attitudes, skills, and approaches toward the use of Information and Communications Technology (ICT) in classrooms are described. By being aware of…

  17. Toward Improving the Mathematics Preparation of Elementary Preservice Teachers

    ERIC Educational Resources Information Center

    Cardetti, Fabiana; Truxaw, Mary P.

    2014-01-01

    Research suggests the importance of mathematics knowledge for teaching (MKT) for enabling elementary school teachers to effectively teach mathematics. MKT involves both mathematical content knowledge (M-CK) and mathematical pedagogical content knowledge (M-PCK). However, there is no consensus on how best to prepare elementary preservice teachers…

  18. What do mathematics teachers and teacher trainees know about the history of mathematics?

    NASA Astrophysics Data System (ADS)

    Gazit, Avikam

    2013-06-01

    The aim of this study is to present the findings of a study that examined the knowledge of mathematics teachers and teacher trainees, in different tracks, about the concepts, topics and characters from the history of mathematics. The findings indicate a lack of knowledge concerning most of the topics examined. Only about 40% of the participants knew about the origin of our counting system and the only item that reached above 50% was the item relating to the man who edited the book which is the basis for the plane geometry - Euclid (about 83%). Another meaningful finding was that the group with the highest score was that of mathematics teacher trainees in the accelerated track - a unique training scheme for middle school teachers (65.7%). The group with the lowest score was that of the elementary school mathematics student teachers (19.3%). One obvious conclusion is that we need to strengthen the knowledge of the history of mathematics in teacher training and in-service teachers' advanced studies.

  19. Impact of a Required Pharmaceutical Calculations Course on Mathematics Ability and Knowledge Retention

    PubMed Central

    Buring, Shauna M.; Papas, Elizabeth

    2013-01-01

    Objective. To assess doctor of pharmacy (PharmD) students’ mathematics ability by content area before and after completing a required pharmaceutical calculations course and to analyze changes in scores. Methods. A mathematics skills assessment was administered to 2 cohorts of pharmacy students (class of 2013 and 2014) before and after completing a pharmaceutical calculations course. The posttest was administered to the second cohort 6 months after completing the course to assess knowledge retention. Results. Both cohorts performed significantly better on the posttest (cohort 1, 13% higher scores; cohort 2, 15.9% higher scores). Significant improvement on posttest scores was observed in 6 of the 10 content areas for cohorts 1 and 2. Both cohorts scored lower in percentage calculations on the posttest than on the pretest. Conclusions. A required, 1-credit-hour pharmaceutical calculations course improved PharmD students’ overall ability to perform fundamental and application-based calculations. PMID:23966727

  20. Impact of a required pharmaceutical calculations course on mathematics ability and knowledge retention.

    PubMed

    Hegener, Michael A; Buring, Shauna M; Papas, Elizabeth

    2013-08-12

    To assess doctor of pharmacy (PharmD) students' mathematics ability by content area before and after completing a required pharmaceutical calculations course and to analyze changes in scores. A mathematics skills assessment was administered to 2 cohorts of pharmacy students (class of 2013 and 2014) before and after completing a pharmaceutical calculations course. The posttest was administered to the second cohort 6 months after completing the course to assess knowledge retention. Both cohorts performed significantly better on the posttest (cohort 1, 13% higher scores; cohort 2, 15.9% higher scores). Significant improvement on posttest scores was observed in 6 of the 10 content areas for cohorts 1 and 2. Both cohorts scored lower in percentage calculations on the posttest than on the pretest. A required, 1-credit-hour pharmaceutical calculations course improved PharmD students' overall ability to perform fundamental and application-based calculations.

  1. Conceptions and Images of Mathematics Professors on Teaching Mathematics in School.

    ERIC Educational Resources Information Center

    Pehkonen, Erkki

    1999-01-01

    Clarifies what kind of mathematical beliefs are conveyed to student teachers during their studies. Interviews mathematics professors (n=7) from five Finnish universities who were responsible for mathematics teacher education. Professors estimated that teachers' basic knowledge was poor and old-fashioned, requiring improvement, and they emphasized…

  2. Early Career Mathematics Teachers' General Pedagogical Knowledge and Skills: Do Teacher Education, Teaching Experience, and Working Conditions Make a Difference?

    ERIC Educational Resources Information Center

    König, Johannes; Blömeke, Sigrid; Kaiser, Gabriele

    2015-01-01

    We examined several facets of general pedagogical knowledge and skills of early career mathematics teachers, asking how they are associated with characteristics of teacher education, teaching experience, and working conditions. Declarative general pedagogical knowledge (GPK) was assessed via a paper-and-pencil test, while early career teachers'…

  3. Technological pedagogical content knowledge of junior high school mathematics teachers in teaching linear equation

    NASA Astrophysics Data System (ADS)

    Wati, S.; Fitriana, L.; Mardiyana

    2018-04-01

    Linear equation is one of the topics in mathematics that are considered difficult. Student difficulties of understanding linear equation can be caused by lack of understanding this concept and the way of teachers teach. TPACK is a way to understand the complex relationships between teaching and content taught through the use of specific teaching approaches and supported by the right technology tools. This study aims to identify TPACK of junior high school mathematics teachers in teaching linear equation. The method used in the study was descriptive. In the first phase, a survey using a questionnaire was carried out on 45 junior high school mathematics teachers in teaching linear equation. While in the second phase, the interview involved three teachers. The analysis of data used were quantitative and qualitative technique. The result PCK revealed teachers emphasized developing procedural and conceptual knowledge through reliance on traditional in teaching linear equation. The result of TPK revealed teachers’ lower capacity to deal with the general information and communications technologies goals across the curriculum in teaching linear equation. The result indicated that PowerPoint constitutes TCK modal technological capability in teaching linear equation. The result of TPACK seems to suggest a low standard in teachers’ technological skills across a variety of mathematics education goals in teaching linear equation. This means that the ability of teachers’ TPACK in teaching linear equation still needs to be improved.

  4. A case study of pedagogy of mathematics support tutors without a background in mathematics education

    NASA Astrophysics Data System (ADS)

    Walsh, Richard

    2017-01-01

    This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to these tutors' provision of mathematics support to first and second year undergraduate engineering students and second year undergraduate science students. It was found that tutors are lacking in various pedagogical skills which are needed for high-quality learning amongst service mathematics students (e.g. engineering/science/technology students), a demographic which have low levels of mathematics upon entering university. Tutors teach their support classes in a very fast didactic way with minimal opportunities for students to ask questions or to attempt problems. It was also found that this teaching method is even more so exaggerated in mandatory departmental mathematics tutorials that students take as part of their mathematics studies at tertiary level. The implications of the findings on mathematics tutor training at tertiary level are also discussed.

  5. Learning from Lessons: Studying the Construction of Teacher Knowledge Catalysed by Purposefully-Designed Experimental Mathematics Lessons

    ERIC Educational Resources Information Center

    Clarke, Doug; Clarke, David; Roche, Anne; Chan, Man Ching Esther

    2015-01-01

    A central premise of this project is that teachers learn from the act of teaching a lesson and that this learning is evident in the planning and teaching of a subsequent lesson. In this project, the knowledge construction of mathematics teachers was examined utilising multi-camera research techniques during lesson planning, classroom interactions…

  6. Examining the Relationship between Thinking Styles and Technological Pedagogical Content Knowledge of the Candidate Mathematics Teachers

    ERIC Educational Resources Information Center

    Canbolat, Nuran; Erdogan, Ahmet; Yazlik, Derya Ozlem

    2016-01-01

    The aim of this research is measuring the technological pedagogical content knowledge of the candidate elementary mathematics teachers, identifying the thinking styles of the same candidates and finding out that whether there is a correlation or not. The research has the characteristics of a basic research to add new information to the scientific…

  7. International Perspectives on the Nature of Mathematical Knowledge for Secondary Teaching: Progress and Dilemmas. Research Forum

    ERIC Educational Resources Information Center

    Doerr, Helen M.; Wood, Terry

    2004-01-01

    This research forum addresses the question: what is the nature of the mathematical knowledge that is needed for secondary teaching? Six international contributors: (1) Australia (Kaye Stacey); (2) Brazil (Marcelo Borba); (3) Israel (Ruhama Even); (4) Norway (Bodil Kleve and Barbara Jaworski); (5) Taiwan (Fou-Lai Lin); and (6) USA (Helen Doerr)…

  8. A Framework for Teachers' Knowledge of Mathematical Reasoning

    ERIC Educational Resources Information Center

    Herbert, Sandra

    2014-01-01

    Exploring and developing primary teachers' understanding of mathematical reasoning was the focus of the "Mathematical Reasoning Professional Learning Research Program." Twenty-four primary teachers were interviewed after engagement in the first stage of the program incorporating demonstration lessons focused on reasoning conducted in…

  9. Epistemological Beliefs of Prospective Preschool Teachers and Their Relation to Knowledge, Perception, and Planning Abilities in the Field of Mathematics: A Process Model

    ERIC Educational Resources Information Center

    Dunekacke, Simone; Jenßen, Lars; Eilerts, Katja; Blömeke, Sigrid

    2016-01-01

    Teacher competence is a multi-dimensional construct that includes beliefs as well as knowledge. The present study investigated the structure of prospective preschool teachers' mathematics-related beliefs and their relation to content knowledge and pedagogical content knowledge. In addition, prospective preschool teachers' perception and planning…

  10. Bridging CAGD knowledge into CAD/CG applications: Mathematical theories as stepping stones of innovations

    NASA Astrophysics Data System (ADS)

    Gobithaasan, R. U.; Miura, Kenjiro T.; Hassan, Mohamad Nor

    2014-07-01

    Computer Aided Geometric Design (CAGD) which surpasses the underlying theories of Computer Aided Design (CAD) and Computer Graphics (CG) has been taught in a number of Malaysian universities under the umbrella of Mathematical Sciences' faculty/department. On the other hand, CAD/CG is taught either under the Engineering or Computer Science Faculty. Even though CAGD researchers/educators/students (denoted as contributors) have been enriching this field of study by means of article/journal publication, many fail to convert the idea into constructive innovation due to the gap that occurs between CAGD contributors and practitioners (engineers/product/designers/architects/artists). This paper addresses this issue by advocating a number of technologies that can be used to transform CAGD contributors into innovators where immediate impact in terms of practical application can be experienced by the CAD/CG practitioners. The underlying principle of solving this issue is twofold. First would be to expose the CAGD contributors on ways to turn mathematical ideas into plug-ins and second is to impart relevant CAGD theories to CAD/CG to practitioners. Both cases are discussed in detail and the final section shows examples to illustrate the importance of turning mathematical knowledge into innovations.

  11. Mathematics Teachers' Level of Knowledge and Practice on the Implementation of Higher-Order Thinking Skills (HOTS)

    ERIC Educational Resources Information Center

    Abdullah, Abdul Halim; Mokhtar, Mahani; Halim, Noor Dayana Abd; Ali, Dayana Farzeeha; Tahir, Lokman Mohd; Kohar, Umar Haiyat Abdul

    2017-01-01

    This study aims to identify the level of knowledge and practice on the implementation of higher-order thinking skills (HOTS) among mathematics teachers at a secondary school in the district of Terengganu. The study focused on the aspects of curriculum, pedagogy and assessment and compared them with demographic factors of the respondents. It used…

  12. Scrutinizing a Survey-Based Measure of Science and Mathematics Teacher Knowledge: Relationship to Observations of Teaching Practice

    NASA Astrophysics Data System (ADS)

    Talbot, Robert M.

    2017-12-01

    There is a clear need for valid and reliable instrumentation that measures teacher knowledge. However, the process of investigating and making a case for instrument validity is not a simple undertaking; rather, it is a complex endeavor. This paper presents the empirical case of one aspect of such an instrument validation effort. The particular instrument under scrutiny was developed in order to determine the effect of a teacher education program on novice science and mathematics teachers' strategic knowledge (SK). The relationship between novice science and mathematics teachers' SK as measured by a survey and their SK as inferred from observations of practice using a widely used observation protocol is the subject of this paper. Moderate correlations between parts of the observation-based construct and the SK construct were observed. However, the main finding of this work is that the context in which the measurement is made (in situ observations vs. ex situ survey) is an essential factor in establishing the validity of the measurement itself.

  13. What do Mathematics Teachers and Teacher Trainees Know about the History of Mathematics?

    ERIC Educational Resources Information Center

    Gazit, Avikam

    2013-01-01

    The aim of this study is to present the findings of a study that examined the knowledge of mathematics teachers and teacher trainees, in different tracks, about the concepts, topics and characters from the history of mathematics. The findings indicate a lack of knowledge concerning most of the topics examined. Only about 40% of the participants…

  14. Using Differentiated Instruction to Increase Mathematics Achievement in Elementary Students

    ERIC Educational Resources Information Center

    Faulkner, Jennifer H.

    2013-01-01

    As evidenced by the poor mathematics performance in American schools, specifically in the school district in the current study, providing identical educational opportunities for diverse students does not necessarily increase academic achievement for everyone. Differentiation is an instructional method that has been found to be successful in…

  15. Young children's core symbolic and nonsymbolic quantitative knowledge in the prediction of later mathematics achievement.

    PubMed

    Geary, David C; vanMarle, Kristy

    2016-12-01

    At the beginning of preschool (M = 46 months of age), 197 (94 boys) children were administered tasks that assessed a suite of nonsymbolic and symbolic quantitative competencies as well as their executive functions, verbal and nonverbal intelligence, preliteracy skills, and their parents' education level. The children's mathematics achievement was assessed at the end of preschool (M = 64 months). We used a series of Bayesian and standard regression analyses to winnow this broad set of competencies down to the core subset of quantitative skills that predict later mathematics achievement, controlling other factors. This knowledge included children's fluency in reciting the counting string, their understanding of the cardinal value of number words, and recognition of Arabic numerals, as well as their sensitivity to the relative quantity of 2 collections of objects. The results inform theoretical models of the foundations of children's early quantitative development and have practical implications for the design of early interventions for children at risk for poor long-term mathematics achievement. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

  16. Task Modification and Knowledge Utilization by Korean Prospective Mathematics Teachers

    ERIC Educational Resources Information Center

    Lee, Kyeong-Hwa; Lee, Eun-Jung; Park, Min-Sun

    2016-01-01

    It has been asserted that mathematical tasks play a critical role in the teaching and learning of mathematics. Modification of tasks included in intended curriculum materials, such as textbooks, can be an effective activity for prospective teachers to understand the role of mathematical tasks in the teaching and learning of mathematics; designing…

  17. Secondary Mathematics Teachers' Beliefs, Attitudes, Knowledge Base, and Practices in Meeting the Needs of English Language Learners

    ERIC Educational Resources Information Center

    Gann, Linda

    2013-01-01

    The research centered on secondary mathematics teachers' beliefs, attitudes, knowledge base, and practices in meeting the academic and language needs of English language learners. Using socio-cultural theory and social practice theory to frame the study, the research design employed a mixed methods approach incorporating self-reported surveys,…

  18. Iterating between Lessons on Concepts and Procedures Can Improve Mathematics Knowledge

    ERIC Educational Resources Information Center

    Rittle-Johnson, Bethany; Koedinger, Kenneth

    2009-01-01

    Background: Knowledge of concepts and procedures seems to develop in an iterative fashion, with increases in one type of knowledge leading to increases in the other type of knowledge. This suggests that iterating between lessons on concepts and procedures may improve learning. Aims: The purpose of the current study was to evaluate the…

  19. Evaluating the Effects of Mastery Learning in Postsecondary Developmental Mathematics

    ERIC Educational Resources Information Center

    Bradley, Kirk

    2016-01-01

    The purpose of this study was to determine which academic and affective student factors were significant to student success in a mastery learning program in developmental mathematics and to determine if the mastery learning program led to increased mathematical knowledge retention and success in the subsequent math course. The first phase of the…

  20. Classroom Stress Promotes Motivated Forgetting of Mathematics Knowledge

    ERIC Educational Resources Information Center

    Ramirez, Gerardo; McDonough, Ian M.; Jin, Ling

    2017-01-01

    The ability to retain educationally relevant content in a readily accessible state in memory is critical for students at all stages in schooling. We hypothesized that a high degree of stress in mathematics courses can threaten students' mathematics self-concept and lead to a motivation to forget course content. We tested the aforementioned…

  1. Exploring Turkish Mathematics Teachers' Content Knowledge of Quadrilaterals

    ERIC Educational Resources Information Center

    Butuner, Suphi Onder; Filiz, Mehmet

    2017-01-01

    The aim of this research was to examine mathematics teachers' performances in defining special types of quadrilaterals, identifying their family and hierarchically classifying them. In this vein, 33 of 58 primary school mathematics teachers working in the province of Yozgat, Turkey were voluntarily recruited for this survey, and they were asked to…

  2. "Prime Online": Developing Grades 3-5 Teachers' Content Knowledge for Teaching Mathematics in an Online Professional Development Program

    ERIC Educational Resources Information Center

    Pape, Stephen J.; Prosser, Sherri K.; Griffin, Cynthia C.; Dana, Nancy Fichtman; Algina, James; Bae, Jungah

    2015-01-01

    This study sought to identify components of an asynchronous online teacher professional development program, "Prime Online," that potentially affected participants' mathematical knowledge for teaching (MKT). Twenty-three third- through fifth-grade general education and special education teachers completed a yearlong online teacher…

  3. Noticing numeracy now! Examining changes in preservice teachers' noticing, knowledge, and attitudes

    NASA Astrophysics Data System (ADS)

    Fisher, Molly H.; Thomas, Jonathan; Schack, Edna O.; Jong, Cindy; Tassell, Janet

    2018-06-01

    This study examined the impact of an intervention, focused on professional noticing of children's conceptual development in whole number and arithmetic reasoning, on preservice elementary teachers' (PSETs') professional noticing skills, attitudes toward mathematics, and mathematical knowledge for teaching mathematics. A video-based professional noticing module, situated in the pedagogies of practice framework, was used with 224 PSETs from five universities. Comparison data was also collected with similar groups not participating in the instructional module. Through pre- and post-assessments, findings indicated that PSETs can develop sound professional noticing skills as a result of participation in a video-based module. The impact on attitudes toward mathematics was less convincing as significant changes were revealed in intervention as well as comparison groups. We hypothesized the potential for professional noticing of children's mathematical thinking to serve as a mechanism for increasing the capabilities of PSETs to negotiate the complexities of mathematics teaching and learning; however, mathematics knowledge for teaching showed no significant increase for either group.

  4. Persistent Genetic and Family-Wide Environmental Contributions to Early Number Knowledge and Later Achievement in Mathematics.

    PubMed

    Garon-Carrier, Gabrielle; Boivin, Michel; Kovas, Yulia; Feng, Bei; Brendgen, Mara; Vitaro, Frank; Séguin, Jean R; Tremblay, Richard E; Dionne, Ginette

    2017-12-01

    This study investigated the stable and transient genetic and environmental contributions to individual differences in number knowledge in the transition from preschool (age 5) to Grade 1 (age 7) and to the predictive association between early number knowledge and later math achievement (age 10-12). We conducted genetic simplex modeling across these three time points. Genetic variance was transmitted from preschool number knowledge to late-elementary math achievement; in addition, significant genetic innovation (i.e., new influence) occurred at ages 10 through 12 years. The shared and nonshared environmental contributions decreased during the transition from preschool to school entry, but shared and nonshared environment contributed to the continuity across time from preschool number knowledge to subsequent number knowledge and math achievement. There was no new environmental contribution at time points subsequent to preschool. Results are discussed in light of their practical implications for children who have difficulties with mathematics, as well as for preventive intervention.

  5. Freedom Quilts: Mathematics on the Underground Railroad

    ERIC Educational Resources Information Center

    Neumann, Maureen D.

    2005-01-01

    A mathematics activity is presented which is a lesson frequently taught to upper elementary school students. It helps the students to see the connection of mathematics with a real-world activity, appreciate the mathematical knowledge required of quilt makers, reinforce their knowledge of the geometrical properties of different shapes and bring…

  6. Mathematics Teacher TPACK Standards and Development Model

    ERIC Educational Resources Information Center

    Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis

    2009-01-01

    What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…

  7. What Math Knowledge Does Teaching Require?

    ERIC Educational Resources Information Center

    Thames, Mark Hoover; Ball, Deborah Loewenberg

    2010-01-01

    No one would argue with the claim that teaching mathematics requires mathematics knowledge. However, a clear description of such knowledge needed for teaching has been surprisingly elusive. To differentiate teachers' levels of mathematical knowledge, numerous studies have examined whether a teacher has a certification in math or a degree as well…

  8. An Analysis of Mathematics Interventions: Increased Time-on-Task Compared with Computer-Assisted Mathematics Instruction

    ERIC Educational Resources Information Center

    Calhoun, James M., Jr.

    2011-01-01

    Student achievement is not progressing on mathematics as measured by state, national, and international assessments. Much of the research points to mathematics curriculum and instruction as the root cause of student failure to achieve at levels comparable to other nations. Since mathematics is regarded as a gate keeper to many educational…

  9. Professional Communities in the Context of Teachers' Professional lives: A Case of Mathematics Specialists

    ERIC Educational Resources Information Center

    Nickerson, Susan D.; Moriarty, Gail

    2005-01-01

    We describe an urban school initiative aimed at teachers' professional development with the goal of increasing their mathematics content knowledge and helping them improve their practice. In the lowest performing schools, mathematics specialists were employed to teach only mathematics in upper-elementary grades (ages 9-12). One aspect of this…

  10. Increasing Mathematics and Science Achievement for Culturally Diverse Students through Teaching Training

    NASA Technical Reports Server (NTRS)

    Mahon, Lee

    1997-01-01

    The purpose of this proposal was to field test and evaluate a Teacher Training program that would prepare teachers to increase the motivation and achievement of culturally diverse students in the areas of science and mathematics. Designed as a three year program, this report covers the first two years of the training program at the Ronald McNair School in the Ravenswood School district, using the resources of the NASA Ames Research Center and the California Framework for Mathematics and Science.

  11. Mathematics/Arithmetic Knowledge-Based Way of Thinking and Its Maintenance Needed for Engineers

    NASA Astrophysics Data System (ADS)

    Harada, Shoji

    Examining curriculum among universities revealed that no significant difference in math class or related subjects can be seen. However, amount and depth of those studies, in general, differed depending on content of curriculum and the level of achievement at entrance to individual university. Universalization of higher education shows that students have many problems in learning higher level of traditional math and that the memory of math they learned quickly fades away after passing in exam. It means that further development of higher math knowledgebased engineer after graduation from universities. Under these circumstances, the present author, as one of fun of math, propose how to maintain way of thinking generated by math knowledge. What necessary for engineer is to pay attention to common books, dealing with elementary mathematics or arithmetic- related matters. This surely leads engineer to nourish math/arithmetic knowledge-based way of thinking.

  12. Assessing Understanding through Reading and Writing in Mathematics

    ERIC Educational Resources Information Center

    Adu-Gyamfi, Kwaku; Bosse, Michael J.; Faulconer, Johna

    2010-01-01

    The mathematics education community recognizes the integrality of reading and writing in learning and communicating mathematics knowledge. Unfortunately, many students have yet to significantly experience this integrality in their mathematics classrooms despite the power these tools offer teachers for assessing student knowledge. This paper…

  13. An Intelligent Tutor-Assisted Mathematics Intervention Program for Students with Learning Difficulties

    ERIC Educational Resources Information Center

    Xin, Yan Ping; Tzur, Ron; Hord, Casey; Liu, Jia; Park, Joo Young; Si, Luo

    2017-01-01

    The Common Core Mathematics Standards have raised expectations for schools and students in the United States. These standards demand much deeper content knowledge from teachers of mathematics and their students. Given the increasingly diverse student population in today's classrooms and shortage of qualified special education teachers,…

  14. Utah's New Mathematics Core

    ERIC Educational Resources Information Center

    Utah State Office of Education, 2011

    2011-01-01

    Utah has adopted more rigorous mathematics standards known as the Utah Mathematics Core Standards. They are the foundation of the mathematics curriculum for the State of Utah. The standards include the skills and understanding students need to succeed in college and careers. They include rigorous content and application of knowledge and reflect…

  15. Examining Elementary Pre-Service Teachers' Capacity to Use Children's Mathematical Understanding to Select and Pose Mathematical Tasks

    ERIC Educational Resources Information Center

    Gichobi, Mary N.

    2013-01-01

    The need to design teacher preparation programs to ensure that pre-service teachers (PSTs) are prepared and equipped with knowledge, skills and practices to increase the chances that they will become effective novice mathematics teachers is of prime importance. Teacher educators are facing lingering challenges, since teacher education is…

  16. Developing Pre-Service Teachers' Technological Pedagogical Content Knowledge for Teaching Mathematics with the Geometer's Sketchpad through Lesson Study

    ERIC Educational Resources Information Center

    Meng, Chew Cheng; Sam, Lim Chap

    2013-01-01

    The purpose of this study was to develop pre-service secondary teachers' technological pedagogical content knowledge (TPACK) for teaching mathematics with The Geometer's Sketchpad (GSP) through Lesson Study (LS). Specifically, a single-group pretest-posttest design was employed to examine whether there was a significant difference in the…

  17. Activating Junior Secondary School Students' Prior Knowledge for the Development of Vocabulary, Concepts and Mathematics through Instructional Strategies

    ERIC Educational Resources Information Center

    Oyinloye, Olu; Popoola, Abiodun A.

    2013-01-01

    This paper investigates the activation of students' prior knowledge for the development of vocabulary, concepts and mathematics. It has been observed that many secondary school students are not performing well in the examination conducted by the West African Examinations Council and National Examinations Council of Nigeria. The situation became…

  18. Teaching Mathematics in Geography Degrees

    ERIC Educational Resources Information Center

    Bennett, Robert

    1978-01-01

    Examines ways of developing college students' motivation for mathematical training; describes the type of mathematical knowledge required in the geography discipline; and explores an applied approach to mathematics teaching based on a systems concept. For journal availability, see SO 506 224. (Author/AV)

  19. Mathematics in the Early Years.

    ERIC Educational Resources Information Center

    Copley, Juanita V., Ed.

    Noting that young children are capable of surprisingly complex forms of mathematical thinking and learning, this book presents a collection of articles depicting children discovering mathematical ideas, teachers fostering students' informal mathematical knowledge, adults asking questions and listening to answers, and researchers examining…

  20. Increasing Awareness of Practice through Interaction across Communities: The Lived Experiences of a Mathematician and Mathematics Teacher Educator

    ERIC Educational Resources Information Center

    Bleiler, Sarah K.

    2015-01-01

    Collaborations between mathematicians and mathematics teacher educators are increasingly being expected, and realized, within the context of mathematics teacher education. Most research related to collaborative efforts between members of the mathematics and mathematics education communities has focused on the products, rather than the process of…

  1. An Investigation of the Mathematics-Vocabulary Knowledge of First-Grade Students

    ERIC Educational Resources Information Center

    Powell, Sarah R.; Nelson, Gena

    2017-01-01

    Competency with mathematics requires use of numerals and symbols as well as an understanding and use of mathematics vocabulary (e.g., "add," "more," "triangle"). Currently, no measures exist in which the primary function is to gauge mathematics-vocabulary understanding. We created a 64-item mathematics-vocabulary…

  2. Reflective Awareness in Mathematics Teachers' Learning and Teaching

    ERIC Educational Resources Information Center

    Chapman, Olive

    2015-01-01

    The nature of mathematics teachers' knowledge specific to teaching mathematics [MTK] is of ongoing concern in mathematics education research. This article contributes to our under-standing of this knowledge with particular focus on reflective awareness. It discusses MTK based on ways it has been used in research. It highlights reflective awareness…

  3. The Influence of the Pedagogical Content Knowledge Framework on Research in Mathematics Education: A Review across Grade Bands

    ERIC Educational Resources Information Center

    Matthews, Mary Elizabeth

    2013-01-01

    This literature review examines the models, theories, and research in mathematics education that are informed by Lee S. Shulman's construct, Pedagogical Content Knowledge. The application of the concept differs in nature and volume across levels of schooling. The research includes substantial work at the elementary level, fewer studies at the…

  4. Developing a Pedagogically Useful Content Knowledge in Elementary Mathematics.

    ERIC Educational Resources Information Center

    Peck, Donald M.; Connell, Michael L.

    Elementary school teacher candidates typically enter their professional training with deficiencies in their conceptual understanding of the topics of elementary school mathematics and with a reliance upon procedural (algorithmic) approaches to the solutions of mathematical problems. If elementary school teacher candidates are expected to teach…

  5. Understanding Understanding Mathematics. Artificial Intelligence Memo No. 488.

    ERIC Educational Resources Information Center

    Michener, Edwina Rissland

    This document is concerned with the important extra-logical knowledge that is often outside of traditional discussions in mathematics, and looks at some of the ingredients and processes involved in the understanding of mathematics. The goal is to develop a conceptual framework in which to talk about mathematical knowledge and to understand the…

  6. Professional Development for Mathematics Teachers: Using Task Design and Analysis

    ERIC Educational Resources Information Center

    Lee, Hea-Jin; Özgün-Koca, S. Asli

    2016-01-01

    This study is based on a Task Design and Analysis activity from a year-long professional development program. The activity was designed to increase teacher growth in several areas, including knowledge of mathematics, understanding of students' cognitive activity, knowledge of good questions, and ability to develop and improve high quality tasks.…

  7. Using Problem Solving to Assess Young Children's Mathematics Knowledge

    ERIC Educational Resources Information Center

    Charlesworth, Rosalind; Leali, Shirley A.

    2012-01-01

    Mathematics problem solving provides a means for obtaining a view of young children's understanding of mathematics as they move through the early childhood concept development sequence. Assessment information can be obtained through observations and interviews as children develop problem solutions. Examples of preschool, kindergarten, and primary…

  8. The Development of Beginning Mathematics Teacher Pedagogical Content Knowledge

    ERIC Educational Resources Information Center

    Lannin, John K.; Webb, Matthew; Chval, Kathryn; Arbaugh, Fran; Hicks, Sarah; Taylor, Cynthia; Bruton, Rebecca

    2013-01-01

    Recent research efforts (Schmidt et al. in "The preparation gap: teacher education for middle school mathematics in six countries," MSU Center for Research in Mathematics and Science Education, 2007) demonstrate that teacher development programs in high-performing countries offer experiences that are designed to develop both mathematical…

  9. Make a Drawing. Effects of Strategic Knowledge, Drawing Accuracy, and Type of Drawing on Students' Mathematical Modelling Performance

    ERIC Educational Resources Information Center

    Rellensmann, Johanna; Schukajlow, Stanislaw; Leopold, Claudia

    2017-01-01

    Drawing strategies are widely used as a powerful tool for promoting students' learning and problem solving. In this article, we report the results of an inferential mediation analysis that was applied to investigate the roles that strategic knowledge about drawing and the accuracy of different types of drawings play in mathematical modelling…

  10. Learning to Leverage Children's Multiple Mathematical Knowledge Bases in Mathematics Instruction

    ERIC Educational Resources Information Center

    Turner, Erin E.; Foote, Mary Q.; Stoehr, Kathleen Jablon; McDuffie, Amy Roth; Aguirre, Julia Maria; Bartell, Tonya Gau; Drake, Corey

    2016-01-01

    In this article, the authors explore prospective elementary teachers' engagement with and reflection on activities they conducted to learn about a single child from their practicum classroom. Through these activities, prospective teachers learned about their child's mathematical thinking and the interests, competencies, and resources she or he…

  11. Connecting Advanced and Secondary Mathematics

    ERIC Educational Resources Information Center

    Murray, Eileen; Baldinger, Erin; Wasserman, Nicholas; Broderick, Shawn; White, Diana

    2017-01-01

    There is an ongoing debate among scholars in understanding what mathematical knowledge secondary teachers should have in order to provide effective instruction. We explore connections between advanced and secondary mathematics as an entry point into this debate. In many cases, advanced mathematics is considered relevant for secondary teachers…

  12. Assessment and Learning of Mathematics.

    ERIC Educational Resources Information Center

    Leder, Gilah C., Ed.

    This book addresses the link between student learning of mathematics, the teaching method adopted in the mathematics classroom, and the assessment procedures used to determine and measure student knowledge. Fifteen chapters address issues that include a review of different models of mathematics learning and assessment practices, three contrasting…

  13. Enhancing Students’ Interest through Mathematics Learning

    NASA Astrophysics Data System (ADS)

    Azmidar, A.; Darhim, D.; Dahlan, J. A.

    2017-09-01

    A number of previous researchers indicated that students’ mathematics interest still low because most of them have perceived that mathematics is very difficult, boring, not very practical, and have many abstract theorems that were very hard to understand. Another cause is the teaching and learning process used, which is mechanistic without considering students’ needs. Learning is more known as the process of transferring the knowledge to the students. Let students construct their own knowledge with the physical and mental reflection that is done by activity in the new knowledge. This article is literature study. The purpose of this article is to examine the Concrete-Pictorial-Abstract approach in theoretically to improve students’ mathematics interest. The conclusion of this literature study is the Concrete-Pictorial-Abstract approach can be used as an alternative to improve students’ mathematics interest.

  14. Distributed Leadership: Key to Improving Primary Students' Mathematical Knowledge

    ERIC Educational Resources Information Center

    Larson, Matthew R.; Smith, Wendy M.

    2013-01-01

    The purpose of this article is to present the findings of a quantitative study focused on primary mathematics teachers who participated in an intensive professional development program and then had leadership responsibility for the implementation of a new primary mathematics curriculum in their district. The study examines the effect of the…

  15. An Analysis of the Changes in Ability and Knowledge of Students Taking A-Level Physics and Mathematics over a 35 Year Period

    ERIC Educational Resources Information Center

    Barham, Peter J.

    2012-01-01

    New undergraduate students arriving to study physics at the University of Bristol from 1975 onwards have all taken the same test of their knowledge and understanding of physics and mathematics. Many of the questions test knowledge of material that has been in the A-level syllabus for maths or physics throughout this period. The ability of incoming…

  16. Mathematical Connections and Their Relationship to Mathematics Knowledge for Teaching Geometry

    ERIC Educational Resources Information Center

    Eli, Jennifer A.; Mohr-Schroeder, Margaret J.; Lee, Carl W.

    2013-01-01

    Effective competition in a rapidly growing global economy places demands on a society to produce individuals capable of higher-order critical thinking, creative problem solving, connection making, and innovation. We must look to our teacher education programs to help prospective middle grades teachers build the mathematical habits of mind that…

  17. Improving of prospective elementary teachers' reasoning: Learning geometry through mathematical investigation

    NASA Astrophysics Data System (ADS)

    Sumarna, Nana; Sentryo, Izlan

    2017-08-01

    This research applies mathematical investigation approach in teaching geometry to improve mathematical reasoning abilities of prospective elementary teachers. Mathematical investigation in this study involved non-routine tasks through a mathematical investigation process, namely through a series of activities as an attribute of mathematical investigation. Developing the ability of mathematical reasoning of research subjects obtained through capability of research subjects in the analysis, generalization, synthesis, justify, and resolve non-routine, which is operationally constructed as an indicator of research and is used as a criterion for measuring the ability of mathematical reasoning. Research design using Quasi-Experimental design. Based on this type, the researchers apply a pre-and posttest design, which is divided into two study groups: control group and the treatment group. The number of research subjects were 111 students consisting of 56 students in the experimental group and 55 students in the control group. The conclusion of this study stated that (1) Investigation of mathematics as an approach to learning is able to give a positive response to the increasing ability of mathematical reasoning, and (2) There is no interaction effect of the factors of learning and prior knowledge of mathematics to the increased ability of mathematical reasoning.

  18. Technology Focus: Enhancing Conceptual Knowledge of Linear Programming with a Flash Tool

    ERIC Educational Resources Information Center

    Garofalo, Joe; Cory, Beth

    2007-01-01

    Mathematical knowledge can be categorized in different ways. One commonly used way is to distinguish between procedural mathematical knowledge and conceptual mathematical knowledge. Procedural knowledge of mathematics refers to formal language, symbols, algorithms, and rules. Conceptual knowledge is essential for meaningful understanding of…

  19. An Exploration of the Relevance of the Pedagogy and Academic Content Knowledge That Are Offered to Prospective Science and Mathematics Teachers in Tanzania Teachers' Colleges

    ERIC Educational Resources Information Center

    Mungure, Daudi Mika

    2016-01-01

    This paper explored the Relevance of the Pedagogy and Academic Content Knowledge that are offered to Prospective Science and Mathematics Teachers in Tanzania Teachers' colleges. Morogoro Teachers' College and Kleruu Teachers' college were used as a case study. The performance in science and mathematics subjects in form four National examinations…

  20. Using Analogies to Facilitate Conceptual Change in Mathematics Learning

    ERIC Educational Resources Information Center

    Vamvakoussi, Xenia

    2017-01-01

    The problem of adverse effects of prior knowledge in mathematics learning has been amply documented and theorized by mathematics educators as well as cognitive/developmental psychologists. This problem emerges when students' prior knowledge about a mathematical notion comes in contrast with new information coming from instruction, giving rise to…

  1. Mathematics and Structural Learning. Final Report.

    ERIC Educational Resources Information Center

    Scandura, Joseph M.

    This report contains four papers describing research based on the view of mathematical knowledge as a hierarchy of "rules." The first paper: "The Role of Rules in Behavior" was abstracted in ED 040 036 (October 1970). The second paper: "A Theory of Mathematical Knowledge" defends the thesis that rules are the basic building blocks of mathematical…

  2. A Study of the Correlation between STEM Career Knowledge, Mathematics Self-Efficacy, Career Interests, and Career Activities on the Likelihood of Pursuing a STEM Career among Middle School Students

    ERIC Educational Resources Information Center

    Blotnicky, Karen A.; Franz-Odendaal, Tamara; French, Frederick; Joy, Phillip

    2018-01-01

    Background: A sample of 1448 students in grades 7 and 9 was drawn from public schools in Atlantic Canada to explore students' knowledge of science and mathematics requirements for science, technology, engineering, and mathematics (STEM) careers. Also explored were their mathematics self-efficacy (MSE), their future career interests, their…

  3. An analysis of the changes in ability and knowledge of students taking A-level physics and mathematics over a 35 year period

    NASA Astrophysics Data System (ADS)

    Barham, Peter J.

    2012-03-01

    New undergraduate students arriving to study physics at the University of Bristol from 1975 onwards have all taken the same test of their knowledge and understanding of physics and mathematics. Many of the questions test knowledge of material that has been in the A-level syllabus for maths or physics throughout this period. The ability of incoming students to answer these questions declined significantly in the 1990s with average scores falling from around 75% up to 1990 to below 50% after 2000 against a background of increasing A-level grades of the entrants to the programme. It is suggested that changes in teaching and examination methods have caused students to be less able to carry out multi-stage calculations and that the introduction of modular examinations may have encouraged a culture where students tend to forget material learnt in previous modules.

  4. Promoting Social Change through Writing: A Quantitative Study of Research-Based Best Practices in Eighth-Grade Mathematics

    ERIC Educational Resources Information Center

    Bettencourt, Connie Lynn

    2009-01-01

    Studies report that U.S. students rank among the lowest in the area of mathematical knowledge of all industrialized countries. Schools in the United States are producing graduates ill-prepared to be successful at jobs which require mathematical competency. To increase mathematical understanding, this study examined the inclusion of writing in…

  5. Mathematics and the surgeon.

    PubMed Central

    Crank, J.

    1976-01-01

    The surgeon uses elementary mathematics just as much as any other educated layman. In his professional life, however, much of the knowledge and skill on which he relies has had a mathematical strand in its development, possibly woven into the supporting disciplines such as physics, chemistry, biology, and bioengineering. The valves and limitations of mathematical models are examined briefly in the general medical field and particularly in relation to the surgeon. Arithmetic and statistics are usually regarded as the most immediately useful parts of mathematics. Examples are cited, however, of medical postgraduate work which uses other highly advanced mathematical techniques. The place of mathematics in postgraduate and postexperience teaching courses is touched on. The role of a mathematical consultant in the medical team is discussed. PMID:942167

  6. Asking Questions in First-Grade Mathematics Classes: Potential Influences on Mathematical Thought.

    ERIC Educational Resources Information Center

    Perry, Michelle; And Others

    1993-01-01

    Types of questions asked in first-grade mathematics classes in Japan, Taiwan, and the United States were investigated. Observations of 311 lessons by 16 Japanese, 20 Taiwanese, and 33 U.S. teachers suggest that the kinds of questions asked in Taiwan and Japan contribute to more sophisticated mathematical knowledge. (SLD)

  7. Measuring Computer Science Knowledge Level of Hungarian Students Specialized in Informatics with Romanian Students Attending a Science Course or a Mathematics-Informatics Course

    ERIC Educational Resources Information Center

    Kiss, Gabor

    2012-01-01

    An analysis of Information Technology knowledge of Hungarian and Romanian students was made with the help of a self developed web based Informatics Test. The goal of this research is an analysis of the Computer Science knowledge level of Hungarian and Romanian students attending a Science course or a Mathematics-Informatics course. Analysed was…

  8. Cognitive Correlates of Performance in Advanced Mathematics

    ERIC Educational Resources Information Center

    Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

    2012-01-01

    Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…

  9. The Role of Mathematical Knowledge in Children's Understanding of Geographical Concepts.

    ERIC Educational Resources Information Center

    Kaplan, Rochelle G.

    This study examines the relationship between children's procedural and conceptual understanding of mathematics and their accuracy in reporting and interpreting geography text material containing mathematical information. It was hypothesized that (1) children's misconceptions or lack of experience with particular mathematical content areas would be…

  10. 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…

  11. Multilingualism in indigenous mathematics education: an epistemic matter

    NASA Astrophysics Data System (ADS)

    Parra, Aldo; Trinick, Tony

    2017-12-01

    An investigation into an aspect of indigenous education provides the opportunity to forefront an epistemological discussion about mathematical knowledge. This paper analyses indigenous peoples' educational experiences in Colombia and Aotearoa/New Zealand of mathematics education, focusing on, among other things, sociolinguistic issues such as language planning. In these experiences, researchers, teachers and local communities, working together, elaborated their respective languages to create a corpus of lexicon that has enabled the teaching of Western mathematics. An analysis using decolonial theory is made, showing how this corpus development works to enable the teaching of [Western] mathematics resulted in investigations into culture, language and mathematics that revealed an interplay among knowledge and power. Such analysis raises issues about the epistemology of mathematics and the politics of knowledge, analogous with current discussions on multilingualism in mathematics education and in ethnomathematics. The paper concludes that mathematics educators can explore and take advantage of the sociolinguistic and epistemological issues that arise when an indigenous language is elaborated in a short period of time in comparison to other languages which have been developed incrementally over hundreds of years and thus much more difficult to critique.

  12. Examining Fourth-Grade Mathematics Writing: Features of Organization, Mathematics Vocabulary, and Mathematical Representations

    ERIC Educational Resources Information Center

    Hebert, Michael A.; Powell, Sarah R.

    2016-01-01

    Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…

  13. Characterizing the Use of Mathematical Knowledge in Boundary-Crossing Situations at Work

    ERIC Educational Resources Information Center

    Kent, Phillip; Noss, Richard; Guile, David; Hoyles, Celia; Bakker, Arthur

    2007-01-01

    The first aim of this article is to present a characterization of the techno-mathematical literacies needed for effective practice in modern, technology-rich workplaces that are both highly automated and increasingly focused on flexible response to customer needs. The second aim is to introduce an epistemological dimension to activity theory,…

  14. Developing an Instrument for Measuring Teachers' Mathematics Content Knowledge on Ratio and Proportion: A Case of Indonesian Primary Teachers

    ERIC Educational Resources Information Center

    Ekawati, Rooselyna; Lin, Fou-Lai; Yang, Kai-Lin

    2015-01-01

    In this study, we developed an instrument for assessing teachers' mathematics content knowledge (MCK) on ratio and proportion and examined the profile of Indonesian primary teacher's MCK on this topic. The MCK items were administered to 271 Indonesian in-service primary teachers with a variety of educational backgrounds and teaching experiences.…

  15. Development Mathematic Assessment to Increase Mathematical Prerequisite Ability on The Student with Learning Disabilities in Inclusive Elementary School

    NASA Astrophysics Data System (ADS)

    Robiansyah, S. T. U.; Nanang, F.; Hidayat

    2018-01-01

    The purpose of this study was to introduce about mathematic assessment is a process of obtaining data or information about the mastery of a student's mathematical skills as an ingredient in preparing a learning program. With this mathematics assessment can be known obstacles, difficulties and needs of students especially in the field of mathematic, so that the learning program will be in accordance with the potential students because it is tailored to what is required of students. This research study was conducted at elementary school of inclusive precisely at SDN Sukagalih I Bandung City based learning in setting of inclusive education. This research study is motivated by the existence of a first-grade student who has disabilities learning in mathematics, the ability of the mathematical prerequisite mastery of the classification of objects by color. The results of the research can provide a profile picture of student data information, the data obtained from the results of the development of systematic and formal mathematical assessment. After doing the development of mathematics assessment then the teacher gets important related information: 1. process the analysis of students’ learning needs, especially in the field of mathematics, 2. preparing the learning program planning according to student learning needs, 3. Designing procedural of method remedial program.

  16. University Students’ Conceptual Knowledge of Randomness and Probability in the Contexts of Evolution and Mathematics

    PubMed Central

    Fiedler, Daniela; Tröbst, Steffen; Harms, Ute

    2017-01-01

    Students of all ages face severe conceptual difficulties regarding key aspects of evolution—the central, unifying, and overarching theme in biology. Aspects strongly related to abstract “threshold” concepts like randomness and probability appear to pose particular difficulties. A further problem is the lack of an appropriate instrument for assessing students’ conceptual knowledge of randomness and probability in the context of evolution. To address this problem, we have developed two instruments, Randomness and Probability Test in the Context of Evolution (RaProEvo) and Randomness and Probability Test in the Context of Mathematics (RaProMath), that include both multiple-choice and free-response items. The instruments were administered to 140 university students in Germany, then the Rasch partial-credit model was applied to assess them. The results indicate that the instruments generate reliable and valid inferences about students’ conceptual knowledge of randomness and probability in the two contexts (which are separable competencies). Furthermore, RaProEvo detected significant differences in knowledge of randomness and probability, as well as evolutionary theory, between biology majors and preservice biology teachers. PMID:28572180

  17. An appraisal of an online tutorial system for the teaching and learning of engineering physics in conjunction with contextual physics and mathematics, and relevant mathematics

    NASA Astrophysics Data System (ADS)

    Bhathal, Ragbir

    2016-09-01

    The number of students entering engineering schools in Australian universities has increased tremendously over the last few years because of the Australian Federal Government's policy of increasing the participation rates of Higher School Certificate students and students from low social economic status backgrounds in the tertiary sector. They now come with a diverse background of skills, motivations and prior knowledge. It is imperative that new methods of teaching and learning be developed. This paper describes an online tutorial system used in conjunction with contextual physics and mathematics, and the revision of the relevant mathematical knowledge at the appropriate time before a new topic is introduced in the teaching and learning of engineering physics. Taken as a whole, this study shows that students not only improved their final examination results but there was also an increase in the retention rate of first-year engineering students which has financial implications for the university.

  18. Discrete mathematics in deaf education: a survey of teachers' knowledge and use.

    PubMed

    Pagliaro, Claudia M; Kritzer, Karen L

    The study documents what deaf education teachers know about discrete mathematics topics and determines if these topics are present in the mathematics curriculum. Survey data were collected from 290 mathematics teachers at center and public school programs serving a minimum of 120 students with hearing loss, grades K-8 or K-12, in the United States. Findings indicate that deaf education teachers are familiar with many discrete mathematics topics but do not include them in instruction because they consider the concepts too complicated for their students. Also, regardless of familiarity level, deaf education teachers are not familiar with discrete mathematics terminology; nor is their mathematics teaching structured to provide opportunities to apply the real-world-oriented activities used in discrete mathematics instruction. Findings emphasize the need for higher expectations of students with hearing loss, and for reform in mathematics curriculum and instruction within deaf education.

  19. Improving students’ mathematical representational ability through RME-based progressive mathematization

    NASA Astrophysics Data System (ADS)

    Warsito; Darhim; Herman, T.

    2018-01-01

    This study aims to determine the differences in the improving of mathematical representation ability based on progressive mathematization with realistic mathematics education (PMR-MP) with conventional learning approach (PB). The method of research is quasi-experiments with non-equivalent control group designs. The study population is all students of class VIII SMPN 2 Tangerang consisting of 6 classes, while the sample was taken two classes with purposive sampling technique. The experimental class is treated with PMR-MP while the control class is treated with PB. The instruments used are test of mathematical representation ability. Data analysis was done by t-test, ANOVA test, post hoc test, and descriptive analysis. The result of analysis can be concluded that: 1) there are differences of mathematical representation ability improvement between students treated by PMR-MP and PB, 2) no interaction between learning approach (PMR-MP, PB) and prior mathematics knowledge (PAM) to improve students’ mathematical representation; 3) Students’ mathematical representation improvement in the level of higher PAM is better than medium, and low PAM students. Thus, based on the process of mathematization, it is very important when the learning direction of PMR-MP emphasizes on the process of building mathematics through a mathematical model.

  20. SKOPE-IT (Shareable Knowledge Objects as Portable Intelligent Tutors): Overlaying Natural Language Tutoring on an Adaptive Learning System for Mathematics

    ERIC Educational Resources Information Center

    Nye, Benjamin D.; Pavlik, Philip I., Jr.; Windsor, Alistair; Olney, Andrew M.; Hajeer, Mustafa; Hu, Xiangen

    2018-01-01

    Background: This study investigated learning outcomes and user perceptions from interactions with a hybrid intelligent tutoring system created by combining the AutoTutor conversational tutoring system with the Assessment and Learning in Knowledge Spaces (ALEKS) adaptive learning system for mathematics. This hybrid intelligent tutoring system (ITS)…

  1. Orienteering in Knowledge Spaces: The Hyperbolic Geometry of Wikipedia Mathematics

    PubMed Central

    Leibon, Gregory; Rockmore, Daniel N.

    2013-01-01

    In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example of the pages of Wikipedia devoted to Mathematics, or “The MathWiki.” The applicability of these ideas extends beyond Wikipedia to provide a natural framework for visual search and to prescribe a natural mode of navigation for any kind of “knowledge space” in which higher order concepts aggregate various instances of information. Other examples would include genre or author organization of cultural objects such as books, movies, documents or even merchandise in an online store. PMID:23844017

  2. Orienteering in knowledge spaces: the hyperbolic geometry of Wikipedia Mathematics.

    PubMed

    Leibon, Gregory; Rockmore, Daniel N

    2013-01-01

    In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example of the pages of Wikipedia devoted to Mathematics, or "The MathWiki." The applicability of these ideas extends beyond Wikipedia to provide a natural framework for visual search and to prescribe a natural mode of navigation for any kind of "knowledge space" in which higher order concepts aggregate various instances of information. Other examples would include genre or author organization of cultural objects such as books, movies, documents or even merchandise in an online store.

  3. Guide to Mathematics Released Items: Understanding Scoring

    ERIC Educational Resources Information Center

    Partnership for Assessment of Readiness for College and Careers, 2017

    2017-01-01

    The Partnership for Assessment of Readiness for College and Careers (PARCC) mathematics items measure critical thinking, mathematical reasoning, and the ability to apply skills and knowledge to real-world problems. Students are asked to solve problems involving the key knowledge and skills for their grade level as identified by the Common Core…

  4. Multiple Proof Approaches and Mathematical Connections

    ERIC Educational Resources Information Center

    Jiang, Zhonghong; O'Brien, George E.

    2012-01-01

    One of the most rewarding accomplishments of working with preservice secondary school mathematics teachers is helping them develop conceptually connected knowledge and see mathematics as an integrated whole rather than isolated pieces. To help students see and use the connections among various mathematical topics, the authors have paid close…

  5. Strategy Choices in Simple and Complex Addition: Contributions of Working Memory and Counting Knowledge for Children with Mathematical Disability

    ERIC Educational Resources Information Center

    Geary, David C.; Hoard, Mary K.; Byrd-Craven, Jennifer; DeSoto, M. Catherine

    2004-01-01

    Groups of first-grade (mean age = 82 months), third-grade (mean age = 107 months), and fifth-grade (mean age = 131 months) children with a learning disability in mathematics (MD, n=58) and their normally achieving peers (n = 91) were administered tasks that assessed their knowledge of counting principles, working memory, and the strategies used to…

  6. Narrative assessment: making mathematics learning visible in early childhood settings

    NASA Astrophysics Data System (ADS)

    Anthony, Glenda; McLachlan, Claire; Lim Fock Poh, Rachel

    2015-09-01

    Narratives that capture children's learning as they go about their day-to-day activities are promoted as a powerful assessment tool within early childhood settings. However, in the New Zealand context, there is increasing concern that learning stories—the preferred form of narrative assessment—currently downplay domain knowledge. In this paper, we draw on data from 13 teacher interviews and samples of 18 children's learning stories to examine how mathematics is made visible within learning stories. Despite appreciating that mathematics is embedded in a range of everyday activities within the centres, we found that the nature of a particular activity appeared to influence `how' and `what' the teachers chose to document as mathematics learning. Many of the teachers expressed a preference to document and analyse mathematics learning that occurred within explicit mathematics activities rather than within play that involves mathematics. Our concern is that this restricted documentation of mathematical activity could potentially limit opportunities for mathematics learning both in the centre and home settings.

  7. How Are the Mathematical Identities of Low Achieving South African Eleventh Graders Related to Their Ability to Solve Mathematical Tasks?

    ERIC Educational Resources Information Center

    Cranfield, Corvell

    2013-01-01

    The construct of mathematical identity has recently been widely used in mathematics education with the intention to understand how students relate to and engage (or disengage) with mathematics. Grootenboer and Zevenbergen (2008) define mathematical identity as the students' knowledge, abilities, skills, beliefs, dispositions, attitudes and…

  8. The Development of Mathematical Knowledge for Teaching for Quantitative Reasoning Using Video-Based Instruction

    NASA Astrophysics Data System (ADS)

    Walters, Charles David

    Quantitative reasoning (P. W. Thompson, 1990, 1994) is a powerful mathematical tool that enables students to engage in rich problem solving across the curriculum. One way to support students' quantitative reasoning is to develop prospective secondary teachers' (PSTs) mathematical knowledge for teaching (MKT; Ball, Thames, & Phelps, 2008) related to quantitative reasoning. However, this may prove challenging, as prior to entering the classroom, PSTs often have few opportunities to develop MKT by examining and reflecting on students' thinking. Videos offer one avenue through which such opportunities are possible. In this study, I report on the design of a mini-course for PSTs that featured a series of videos created as part of a proof-of-concept NSF-funded project. These MathTalk videos highlight the ways in which the quantitative reasoning of two high school students developed over time. Using a mixed approach to grounded theory, I analyzed pre- and postinterviews using an extant coding scheme based on the Silverman and Thompson (2008) framework for the development of MKT. This analysis revealed a shift in participants' affect as well as three distinct shifts in their MKT around quantitative reasoning with distances, including shifts in: (a) quantitative reasoning; (b) point of view (decentering); and (c) orientation toward problem solving. Using the four-part focusing framework (Lobato, Hohensee, & Rhodehamel, 2013), I analyzed classroom data to account for how participants' noticing was linked with the shifts in MKT. Notably, their increased noticing of aspects of MKT around quantitative reasoning with distances, which features prominently in the MathTalk videos, seemed to contribute to the emergence of the shifts in MKT. Results from this study link elements of the learning environment to the development of specific facets of MKT around quantitative reasoning with distances. These connections suggest that vicarious experiences with two students' quantitative

  9. How to build a course in mathematical-biological modeling: content and processes for knowledge and skill.

    PubMed

    Hoskinson, Anne-Marie

    2010-01-01

    Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments.

  10. Impact of the Course Teaching and Learning of Mathematics on Preservice Grades 7 and 8 Mathematics Teachers in Singapore

    ERIC Educational Resources Information Center

    Kaur, Berinderjeet

    2017-01-01

    This paper explores the impact of the course "Teaching and Learning of Mathematics (Grades 7 and 8)" for the preparation of pre-service secondary mathematics teachers. It examines how pre-service teachers perceived mathematical problem solving and communicating mathematical knowledge before and after the course. The main objective of the…

  11. Using Mathematics in Science: Working with Your Mathematics Department

    ERIC Educational Resources Information Center

    Lyon, Steve

    2014-01-01

    Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…

  12. Overcoming Challenges of Being an In-Field Mathematics Teacher in Indigenous Secondary School Classrooms

    ERIC Educational Resources Information Center

    Sandhu, Satwant; Kidman, Gillian; Cooper, Tom

    2013-01-01

    Queensland rural and remote schools have difficulty in attracting experienced, in-field mathematics teachers. Thus, when such teachers arrive, much is expected of them to increase the mathematics knowledge of students. This paper looks at one such teacher who, against the high expectations placed upon him as an in-field teacher, experienced…

  13. Mathematics from High School to Community College: Using Existing Tools to Increase College-Readiness Now. Policy Brief 14-1

    ERIC Educational Resources Information Center

    Jaffe, Louise

    2014-01-01

    The adoption and implementation of the Common Core State Standards and Smarter Balanced assessments in mathematics are intended to provide all students in California with the knowledge and skills required to transition from high school to college-level coursework. This implementation will take time. Concurrent with these efforts, policymakers and…

  14. Provocative Mathematics Questions: Drawing Attention to a Lack of Attention

    ERIC Educational Resources Information Center

    Klymchuk, Sergiy

    2015-01-01

    The article investigates the role of attention in the reflective thinking of school mathematics teachers. It analyses teachers' ability to pay attention to detail and "use" their mathematical knowledge. The vast majority of teachers can be expected to have an excellent knowledge of mathematical techniques. The question examined here is…

  15. The Effects of Teacher Collaboration in Grade 9 Applied Mathematics

    ERIC Educational Resources Information Center

    Egodawatte, Gunawardena; McDougall, Douglas; Stoilescu, Dorian

    2011-01-01

    The current emphasis of many mathematics education reform documents is on the need to change the environment of mathematics classrooms from the transmission of knowledge by the teacher to the transaction of knowledge between the teacher and the students which promotes mathematical investigation and exploration. In this article, we discuss the…

  16. A day of immersive physiology experiments increases knowledge and excitement towards physiology and scientific careers in Native American students.

    PubMed

    Becker, Bryan K; Schiller, Alicia M; Zucker, Irving H; Eager, Eric A; Bronner, Liliana P; Godfrey, Maurice

    2017-03-01

    Underserved minority groups are disproportionately absent from the pursuit of careers in science, technology, engineering, and mathematics (STEM) fields. One such underserved population, Native Americans, are particularly underrepresented in STEM fields. Although recent advocacy and outreach designed toward increasing minority involvement in health care-related occupations have been mostly successful, little is known about the efficacy of outreach programs in increasing minority enthusiasm toward careers in traditional scientific professions. Furthermore, very little is known about outreach among Native American schools toward increasing involvement in STEM. We collaborated with tribal middle and high schools in South Dakota and Nebraska through a National Institutes of Health Science Education Partnership Award to hold a day-long physiology, activity-based event to increase both understanding of physiology and enthusiasm to scientific careers. We recruited volunteer biomedical scientists and trainees from the University of Nebraska Medical Center, Nebraska Wesleyan University, and University of South Dakota. To evaluate the effectiveness of the day of activities, 224 of the ~275-300 participating students completed both a pre- and postevent evaluation assessment. We observed increases in both students self-perceived knowledge of physiology and enthusiasm toward scientific career opportunities after the day of outreach activities. We conclude that activity-based learning opportunities in underserved populations are effective in increasing both knowledge of science and interest in scientific careers. Copyright © 2017 the American Physiological Society.

  17. Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

    ERIC Educational Resources Information Center

    Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

    2016-01-01

    Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

  18. Changes in Elementary Mathematics Teachers' Understanding of Cognitive Demand: When Adapting, Creating, and Using Mathematical Performance Tasks

    ERIC Educational Resources Information Center

    Jamieson, Thad Spencer

    2015-01-01

    The use of mathematics performance tasks can provide a window into how a student is applying mathematics to various situations, how they are reasoning mathematically and how they are applying conceptual knowledge through problem solving and critical thinking. The purpose of this study was to investigate, according to the elementary mathematics…

  19. "Concreteness Fading" Promotes Transfer of Mathematical Knowledge

    ERIC Educational Resources Information Center

    McNeil, Nicole M.; Fyfe, Emily R.

    2012-01-01

    Recent studies have suggested that educators should avoid concrete instantiations when the goal is to promote transfer. However, concrete instantiations may benefit transfer in the long run, particularly if they are "faded" into more abstract instantiations. Undergraduates were randomly assigned to learn a mathematical concept in one of three…

  20. Development of a Performance Assessment Task and Rubric to Measure Prospective Secondary School Mathematics Teachers' Pedagogical Content Knowledge and Skills

    ERIC Educational Resources Information Center

    Koirala, Hari P.; Davis, Marsha; Johnson, Peter

    2008-01-01

    The purpose of this paper is to share a performance assessment task and rubric designed to assess secondary school mathematics preservice teachers' pedagogical content knowledge and skills. The assessment task and rubric were developed in collaboration with five education faculty, four arts and sciences faculty, and four high school teachers over…

  1. Is Constructivist Learning Environment Really Effective on Learning and Long-Term Knowledge Retention in Mathematics? Example of the Infinity Concept

    ERIC Educational Resources Information Center

    Narli, Serkan

    2011-01-01

    This study investigates the long-term effects of instructing Cantor set theory using constructivist learning approach on student knowledge retention. The participants included 60 first-year secondary mathematics pre-service teachers. Students were divided into two classes one of which was taught via traditional lecture (n = 30) and the other was…

  2. Didactic Transposition in Mathematics Textbooks.

    ERIC Educational Resources Information Center

    Kang, Wan; Kilpatrick, Jeremy

    1992-01-01

    Didactic transposition theory asserts that bodies of knowledge are designed not to be taught but to be used. Discusses didactic transposition, the transposition of knowledge regarded as a tool to be used to knowledge as something to be learned in mathematics textbooks. (14 references) (MDH)

  3. Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

    ERIC Educational Resources Information Center

    Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

    2017-01-01

    This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

  4. Impact of Summer Recess on Mathematics Learning Retention

    ERIC Educational Resources Information Center

    Hornack, David

    2016-01-01

    School administrators across the nation are actively searching for solutions to increase student achievement due in part to the significant amount of knowledge that is lost annually each summer. Mathematical computation skills are especially at-risk. This quantitative research study was designed to investigate the impact of summer recess also…

  5. Increasing Student Learning in Mathematics with the Use of Collaborative Teaching Strategies

    ERIC Educational Resources Information Center

    Di Fatta, Jenna; Garcia, Sarah; Gorman, Stephanie

    2009-01-01

    Three teacher researchers conducted this action research project to increase their 54 high school students' achievements in mathematics. The teacher researchers had noticed a trend of low scores on teacher-made chapter tests and non-completion of daily homework. Standardized tests showed that most students scored below average on the mathematics…

  6. Public knowledge about AIDS increasing.

    PubMed

    Campbell, M J; Waters, W E

    1987-04-04

    In response to concern over the perceived limited effectiveness of Department of Health and Social Security (UK) advertising campaigns to inform the public of the basic facts of Acquired Immunodeficiency Syndrome (AIDS), a prospective questionnaire study was undertaken in Southampton, England to test the effectiveness of government education prior to a January, 1987 government television/leaflet advertising campaign. 300 questionnaires about AIDS were mailed in December of 1986 to a sample drawn from electoral rolls. The response rate was 61%. Most of the questions were drawn from material covered in the campaign. The results seemed to indicate a small overall increase in knowledge about AIDS. Some changes from a June survey were noted, e.g.: more people were aware that AIDS is a virus for which there is no cure and that it is not readily transmitted by sharing washing, eating or drinking utensils; more people believed that the statement that women are at greater risk for catching AIDS is false. Respondents were generally favorable to the government's continued use of television, even with explicit language, and to its use of the schools, for AIDS education. Many were not aware of the dangers to intravenous drug users or of the symptoms of AIDS. Other surveys have shown an increasing knowledge of AIDS dangers. It is possible that television coverage of the problem will continue to be necessary, in order that less literate populations be reached. Further AIDS health education in general is needed.

  7. Mathematical Investigations for Supporting Pre-Service Primary Teachers Repeating a Mathematics Education Course

    ERIC Educational Resources Information Center

    Bailey, Judy

    2014-01-01

    Preparing to become an effective primary school mathematics teacher is a challenging and complex task; and is influenced by one's past experiences, personal knowledge of, and beliefs and attitudes towards mathematics. This paper examines the experiences of a small group of pre-service teachers who did not pass their first year mathematics…

  8. What We Are Learning about Mathematics Interventions and Conducting Research on Mathematics Interventions

    ERIC Educational Resources Information Center

    Gersten, Russell

    2016-01-01

    In this commentary, the author reflects on four studies that have greatly expanded the knowledge base on effective interventions in mathematics, and he provides four rigorous experimental studies of approaches for students likely to experience difficulties learning mathematics over a large grade-level span (pre-K to 4th grade). All of the…

  9. Affective Influences in the Knowledge of Mathematics.

    ERIC Educational Resources Information Center

    Gomez-Chacon, Ines Maria

    2000-01-01

    Proposes a model to study the interaction between cognition and affect in mathematics. Develops important dimensions related to affect and cognition. Explains the importance of taking into account such dimensions in this kind of research, referring to students who are failing academically through a case study. (Contains 21 references.) (Author/ASK)

  10. The Predominance of Procedural Knowledge in Fractions

    ERIC Educational Resources Information Center

    Forrester, Tricia; Chinnappan, Mohan

    2010-01-01

    Teachers play a crucial role in the mathematical learning outcomes of their students. The quality of teachers' mathematical knowledge has been of interest to key stakeholders and several lines of inquiry have been running in an effort to better understand the kinds of knowledge that mathematics teachers need to acquire and use to drive their…

  11. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop (March 19-21, 1999).

    ERIC Educational Resources Information Center

    National Academy of Sciences - National Research Council, Washington, DC. Mathematical Sciences Education Board.

    The Mathematics Teacher Preparation Content Workshop, held March 19-21, 1999, focused on two questions: (1) What is the mathematical knowledge teachers need to know in order to teach well? and (2) How can teachers develop the mathematical knowledge they need to teach well? Chapters include: (1) "Knowledge of Fundamental Mathematics for Teaching"…

  12. Pre-K Mathematics. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2007

    2007-01-01

    "Pre-K Mathematics" is a supplemental curriculum designed to develop informal mathematical knowledge and skills in preschool children. Mathematical content is organized into seven units. Specific mathematical concepts and skills from each unit are taught in the classroom through teacher-guided, small-group activities with concrete…

  13. Clinical Assessment in Mathematics: Learning the Craft.

    ERIC Educational Resources Information Center

    Hunting, Robert P.; Doig, Brian A.

    1997-01-01

    Discusses a professional development program called Clinical Approaches to Mathematics Assessment. Argues for the advanced training of mathematics teachers who understand knowledge construction processes of students; can use clinical tools for evaluating a student's unique mathematical "fingerprint"; and can create or adapt problems, tasks, or…

  14. Students' Relationships with Mathematics: Affect and Identity

    ERIC Educational Resources Information Center

    Ingram, Naomi

    2015-01-01

    In this paper, an examination of students' relationships with mathematics is informed by affective research into internal mathematical structures and identity research into students' narratives. By analysing the perceptions of a class of 31 adolescents, five interacting elements emerged: students' views, feelings, mathematical knowledge,…

  15. Early Career Teachers, Mathematics and Technology: Device Conflict and Emerging Mathematical Knowledge

    ERIC Educational Resources Information Center

    Attard, Catherine; Orlando, Joanne

    2014-01-01

    Information and communication technologies (ICT) are positioned in policy/syllabus documents as an essential resource in the teaching of mathematics. Given their youth and lifelong experience with technology, early career teachers (ECTs) are expected to excel in their use of ICT; however, we are not clear on the viability of these expectations and…

  16. The Effects of Modern Mathematics Computer Games on Mathematics Achievement and Class Motivation

    ERIC Educational Resources Information Center

    Kebritchi, Mansureh; Hirumi, Atsusi; Bai, Haiyan

    2010-01-01

    This study examined the effects of a computer game on students' mathematics achievement and motivation, and the role of prior mathematics knowledge, computer skill, and English language skill on their achievement and motivation as they played the game. A total of 193 students and 10 teachers participated in this study. The teachers were randomly…

  17. An Investigation of Teachers' Noticing, Cognitive Demand, and Mathematical Knowledge for Teaching: Video Reflections in an Elementary Mathematics Context

    ERIC Educational Resources Information Center

    Coddington, Lorelei R.

    2014-01-01

    In the past decade, mathematics performance by all students, especially minority students in low socioeconomic schools, has shown limited improvement nationwide (NCES, 2011). Traditionally in the United States, mathematics has consisted of arithmetic and computational fluency; however, mathematics researchers widely believe that this method of…

  18. Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement: An Eight-Year Longitudinal Study

    ERIC Educational Resources Information Center

    Geary, David C.; Nicholas, Alan; Li, Yaoran; Sun, Jianguo

    2017-01-01

    The contributions of domain-general abilities and domain-specific knowledge to subsequent mathematics achievement were longitudinally assessed (n = 167) through 8th grade. First grade intelligence and working memory and prior grade reading achievement indexed domain-general effects, and domain-specific effects were indexed by prior grade…

  19. Physics and Mathematics as Interwoven Disciplines in Science Education

    NASA Astrophysics Data System (ADS)

    Galili, Igal

    2018-03-01

    The relationship between physics and mathematics is reviewed upgrading the common in physics classes' perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.

  20. The Transformation of Mathematics in On-Line Courses

    ERIC Educational Resources Information Center

    Borba, Marcelo C.

    2005-01-01

    This paper presents some research findings regarding the changes in the mathematics produced by mathematics teachers in on-line distance courses. Predicated on the belief that knowledge is generated by collectives of humans-with-media, and that different technologies modify the nature of the knowledge generated, we have sought to understand how…

  1. Building a Knowledge Base: Understanding Prospective Elementary Teachers' Mathematical Content Knowledge

    ERIC Educational Resources Information Center

    Thanheiser, Eva; Browning, Christine; Edson, Alden J.; Kastberg, Signe; Lo, Jane-Jane

    2013-01-01

    This survey of the literature summarizes and reflects on research findings regarding elementary preservice teachers' (PSTs') mathematics conceptions and the development thereof. Despite the current focus on teacher education, peer-reviewed journals offer a surprisingly sparse insight in these areas. The limited research that exists…

  2. Considering the Role of K-2 Teachers' Mathematical Knowledge for Teaching Place Value in Mathematics Intervention

    ERIC Educational Resources Information Center

    Juenke, Carl W.

    2017-01-01

    A significant number of students receive special education services for mathematics learning disabilities, however, many additional students need mathematics intervention to support their learning in the regular education classroom. A Response to Intervention (RtI) model has been identified as effective in addressing these students' needs;…

  3. Investigating the Relevance and Importance of Mathematical Content Knowledge Areas for Beginning Elementary School Teachers. Research Memorandum No. RM-16-10

    ERIC Educational Resources Information Center

    Martin-Raugh, Michelle P.; Reese, Clyde M.; Howell, Heather; Tannenbaum, Richard J.; Steinberg, Jonathan H.; Xu, Jun

    2016-01-01

    The purpose of this report is to explore the content-related validity evidence supporting the mathematics components of the "ETS"® National Observational Teaching Exam (NOTE) assessment series, a kindergarten through 6th grade teacher licensure assessment. To establish the content knowledge required for the effective teaching of…

  4. Provoking Contingent Moments: Knowledge for "Powerful Teaching" at the Horizon

    ERIC Educational Resources Information Center

    Hurst, Chris

    2017-01-01

    Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content…

  5. [Mathematics - astronomy - astrology special library].

    PubMed

    Gluch, Sibylle

    2011-01-01

    About 1560 Elector August of Saxony created an unusual library--one distinguished within its period by both its specialization and location. Situated within the Kunstkammer this library was mostly dedicated to the mathematical sciences and related disciplines. It contained works by the most important authors on mathematics, astronomy, and astrology from the classical, medieval, and early modern periods. This essay traces the formation and composition of August's library, and examines its function: What kind of relationship existed between the library and the Kunstkammer? In what way did the library mirror the interests of the Elector, and to what extend does it permit inferences regarding the Elector's knowledge of mathematics? From the analysis August emerges not as a specialist with a deep understanding of mathematics, but as a particular aficionado of mathematical applications. As a practitioner and general follower of the mathematical arts he took part in a far-reaching intellectual network the center of which lay in the University of Wittenberg. Here, Melanchthon had effectively strengthened the importance of the mathematical disciplines within the university curriculum. He regarded mathematics as the foremost science, arguing that before all other disciplines its method enabled man to recognize the harmonic order of the world, and to discern divine providence. Thus, mathematics offered consoling stability and support in an often seemingly chaotic world torn by religious controversies. This kind of esteem for the mathematical sciences did not presuppose expert knowledge. Hence, the fact that August does not appear to have read the mathematical books he collected does not come as a contradiction. On the contrary, for August it sufficed to recognize the potential of the mathematical sciences, which he brought into life through the creation of a specialized library that developed a rhetoric of its own. The collection of his Kunstkammer library spoke of a

  6. An Objectivist Critique of Relativism in Mathematics Education

    NASA Astrophysics Data System (ADS)

    Rowlands, Stuart; Graham, Ted; Berry, John

    Many constructivists tag as `absolutist' references to mathematics as an abstract body of knowledge, and stake-out the moral high-ground with the argument that mathematics is not only utilised oppressively but that mathematics is, in-itself, oppressive. With much reference to Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that if mathematics is a social-cultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. This paper argues that mathematics, albeit a social-cultural creation that is mutable and fallible, is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Ernest (1998) has attempted to express social constructivism as a philosophy of mathematics and has included the category of logical necessity in his elaboration of the objectivity of mathematics. We argue that this inclusion of logical necessity not only represents a U-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.

  7. A Case Study of Pedagogy of Mathematics Support Tutors without a Background in Mathematics Education

    ERIC Educational Resources Information Center

    Walsh, Richard

    2017-01-01

    This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to…

  8. The Effects of STEM PBL on Students' Mathematical and Scientific Vocabulary Knowledge

    ERIC Educational Resources Information Center

    Bilgin, Ali; Boedeker, Peter; Capraro, Robert M.; Capraro, Mary M.

    2015-01-01

    Vocabulary is at the surface level of language usage; thus, students need to develop mathematical and scientific vocabulary to be able to explicitly communicate their mathematical and scientific reasoning with others. The National Council of Teachers of Mathematics (NCTM) and the National Science Teachers Association (NSTA) have both created…

  9. The Challenge of Learning Physics Before Mathematics: A Case Study of Curriculum Change in Taiwan

    NASA Astrophysics Data System (ADS)

    Chiu, Mei-Shiu

    2016-12-01

    The aim of this study was to identify challenges in implementing a physics-before- 10 mathematics curriculum. Obviously, students need to learn necessary mathematics skills in order to develop advanced physics knowledge. In the 2010 high school curriculum in Taiwan, however, grade 11 science students study two-dimensional motion in physics without prior learning experiences of trigonometry in mathematics. The perspectives of three curriculum developers, 22 mathematics and physics teachers, two principals, and 45 science students were obtained by interview. The results of qualitative data analysis revealed six challenges and suggested likely solutions. The national level includes political and social challenges, resolved by respecting teachers as professionals; the teacher level includes knowledge and teaching challenges, resolved by increasing teacher trans-literal capacities; and the student level includes learning and justice challenges, resolved by focusing on students' diverse developments in cross-domain learning.

  10. The Impact of Sustained, Standards-Based Professional Learning on Second and Third Grade Teachers' Content and Pedagogical Knowledge in Integrated Mathematics

    ERIC Educational Resources Information Center

    Bailey, Lora B.

    2010-01-01

    This 3 year longitudinal study reports the feasibility of an "Improving Teacher Quality: No Child Left Behind" project for impacting teachers' content and pedagogical knowledge in mathematics in nine Title I elementary schools in the southeastern United States. Data were collected for 3 years to determine the impact of standards and…

  11. Longitudinal associations between reading and mathematics achievement.

    PubMed

    Grimm, Kevin J

    2008-01-01

    The association between early reading skills and changes in mathematics was examined in a large, low-income sample to determine whether students who have a greater level of reading skills in early elementary school exhibit more rapid gains in tests of mathematics. The longitudinal associations between third grade reading comprehension and changes in three components of mathematics achievement (Problem Solving and Data Interpretation, Mathematical Concepts and Estimation, Mathematical Computation) from third through eighth grade were examined. Latent growth models were fit to the repeated assessments of each mathematics component and the students' third grade reading and global mathematics scores were included as predictors of the intercept and slope. Gender, poverty status, and ethnicity were included in the models as control variables. The results showed males and African-American students tended to have shallower rates of change than females and non-African-American/non-Hispanic students. In terms of the effect of reading on changes in mathematics, third grade reading comprehension was found to be a positive significant predictor of change for each component of mathematics, suggesting students with a greater level of reading achievement in early elementary school change more rapidly in mathematics skills controlling for prior mathematics skills and student characteristics. The largest effects were shown for the Problem Solving and Data Interpretation test, a test focused on the applications of mathematics knowledge, and the Mathematical Concepts and Estimation test. Negligible effects were found for changes in Mathematical Computation. Thus, early reading comprehension was shown to be related to a conceptual understanding of mathematics and the application of mathematics knowledge. These findings lend support for the notion that early reading skills are important for success in mathematics.

  12. Brazilian Peasant Mathematics, School Mathematics and Adult Education

    ERIC Educational Resources Information Center

    Knijnik, Gelsa

    2007-01-01

    The paper analyzes adult mathematics education from a cultural perspective. Specifically, its purpose is to broaden our comprehension about this field of knowledge using as a theoretical tool-box an Ethnomathematics perspective founded on post-modern thought, post-structuralism theorizations and Wittgenstein's work developed in his book…

  13. Magnitude knowledge: the common core of numerical development.

    PubMed

    Siegler, Robert S

    2016-05-01

    The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic numbers, (2) connecting small symbolic numbers to their non-symbolic referents, (3) extending understanding from smaller to larger whole numbers, and (4) accurately representing the magnitudes of rational numbers. The present review identifies substantial commonalities, as well as differences, in these four aspects of numerical development. With both whole and rational numbers, numerical magnitude knowledge is concurrently correlated with, longitudinally predictive of, and causally related to multiple aspects of mathematical understanding, including arithmetic and overall math achievement. Moreover, interventions focused on increasing numerical magnitude knowledge often generalize to other aspects of mathematics. The cognitive processes of association and analogy seem to play especially large roles in this development. Thus, acquisition of numerical magnitude knowledge can be seen as the common core of numerical development. © 2016 John Wiley & Sons Ltd.

  14. Mario Bunge's Philosophy of Mathematics: An Appraisal

    ERIC Educational Resources Information Center

    Marquis, Jean-Pierre

    2012-01-01

    In this paper, I present and discuss critically the main elements of Mario Bunge's philosophy of mathematics. In particular, I explore how mathematical knowledge is accounted for in Bunge's systemic emergent materialism.

  15. Implementing an Effective Mathematics Fact Fluency Practice Activity

    ERIC Educational Resources Information Center

    Riccomini, Paul J.; Stocker, James D., Jr.; Morano, Stephanie

    2017-01-01

    Proficiency in mathematics involves the seamless synchronization of conceptual understanding, procedural knowledge, computational fluency, and problem solving (NMAP, 2008). Clearly, fluency with mathematics facts is one element embedded within mathematical proficiency and important for students with disabilities to develop. As more and more…

  16. Mentoring to Alleviate Anxiety in Pre-Service Primary Mathematics Teachers: An Orientation towards Improvement Rather than Evaluation

    ERIC Educational Resources Information Center

    Perkins, Timothy

    2015-01-01

    Increasing numbers of primary pre-service teachers (PSTs) enrolled in Education degrees in Australia enter university with insufficient mathematical content knowledge (Livy & Vale, 2011) and low confidence levels about their ability to teach and do the mathematics required for their intended role as classroom teachers (Wilson, 2009). Mentoring…

  17. Going beyond the lesson: Self-generating new factual knowledge in the classroom

    PubMed Central

    Esposito, Alena G.; Bauer, Patricia J.

    2016-01-01

    For children to build a knowledge base, they must integrate and extend knowledge acquired across separate episodes of new learning. Children’s performance was assessed in a task requiring them to self-generate new factual knowledge from the integration of novel facts presented through separate lessons in the classroom. Whether self-generation performance predicted academic outcomes in reading comprehension and mathematics was also examined. The 278 participating children were in grades K-3 (mean age 7.7 years; range 5.5–10.3 years). Children self-generated new factual knowledge through integration in the classroom; age-related increases were observed. Self-generation performance predicted both reading comprehension and mathematics academic outcomes, even when controlling for caregiver education. PMID:27728784

  18. Discrete Mathematics in Deaf Education: A Survey of Teachers' Knowledge and Use

    ERIC Educational Resources Information Center

    Pagliaro, C.; Kritzer, K. L.

    2005-01-01

    The study documents what deaf education teachers know about discrete mathematics topics and determines if these topics are present in the mathematics curriculum. Survey data were collected from 290 mathematics teachers at center and public school programs serving a minimum of 120 students with hearing loss, grades K-8 or K-12, in the United…

  19. Increasing the Diversity of Teachers in Mathematics and Science Partnerships

    ERIC Educational Resources Information Center

    Moyer-Packenham, Patricia S.; Parker, Jana L.; Kitsantas, Anastasia; Bolyard, Johnna J.; Huie, Faye

    2009-01-01

    This study examines teacher diversity in a federally-funded mathematics and science partnership program. Each of the partnerships in the program provided preservice and/or inservice education for teachers in mathematics, science, or both. Researchers used qualitative and quantitative methods to examine the effect of strategies implemented by the…

  20. Operation STEM: Increasing Success and Improving Retention among Mathematically Underprepared Students in STEM

    ERIC Educational Resources Information Center

    Carver, Susan D.; Van Sickle, Jenna; Holcomb, John P.; Jackson, Debbie K.; Resnick, Andrew H.; Duffy, Stephen F.; Sridhar, Nigamanth; Marquard, Antoinette M.; Quinn, Candice M.

    2017-01-01

    In 2012, Cleveland State University implemented a comprehensive program, called Operation STEM (OpSTEM), funded by two National Science Foundation grants, federal work study, and Cleveland State University. Its goal is to increase retention and graduation rates among Science, Technology, Engineering, and Mathematics (STEM) students by helping them…

  1. Results of a Comprehension Test in Mathematics

    ERIC Educational Resources Information Center

    Debrenti, Edith

    2013-01-01

    In higher education the main subjects build on the knowledge acquired in high school. Research shows that students entering universities have acquired basic knowledge to different extents. It is very important to be able to apply mathematical knowledge directly. Students often treat practical knowledge separately from theoretical knowledge. They…

  2. Knowledge Growth: Applied Models of General and Individual Knowledge Evolution

    ERIC Educational Resources Information Center

    Silkina, Galina Iu.; Bakanova, Svetlana A.

    2016-01-01

    The article considers the mathematical models of the growth and accumulation of scientific and applied knowledge since it is seen as the main potential and key competence of modern companies. The problem is examined on two levels--the growth and evolution of objective knowledge and knowledge evolution of a particular individual. Both processes are…

  3. How Do Kindergarteners Express Their Mathematics Understanding?

    ERIC Educational Resources Information Center

    Johns, Kyoko

    2015-01-01

    This article describes how kindergarten students represent their understanding of mathematical knowledge. The study examines the students' use of oral expressions, drawings, written language, and gestures when communicating mathematically with their classmates and teacher.

  4. Science, technology, engineering, mathematics (STEM) as mathematics learning approach in 21st century

    NASA Astrophysics Data System (ADS)

    Milaturrahmah, Naila; Mardiyana, Pramudya, Ikrar

    2017-08-01

    This 21st century demands competent human resources in science, technology, engineering design and mathematics so that education is expected to integrate the four disciplines. This paper aims to describe the importance of STEM as mathematics learning approach in Indonesia in the 21st century. This paper uses a descriptive analysis research method, and the method reveals that STEM education growing in developed countries today can be a framework for innovation mathematics in Indonesia in the 21st century. STEM education integrate understanding of science, math skills, and the available technology with the ability to perform engineering design process. Implementation of mathematics learning with STEM approach makes graduates trained in using of mathematics knowledge that they have to create innovative products that are able to solve the problems that exist in society.

  5. Interest in mathematics and science among students having high mathematics aptitude

    NASA Astrophysics Data System (ADS)

    Ely, Jane Alice

    The study investigates why men and women differ in their interest in mathematics and science and in the pursuit of careers in mathematics and science. The most persistent gender differential in educational standard testing is the scores in mathematics achievement. The mean Scholastic Aptitude Test (Mathematics) scores for women are consistently below that of men by about 40 points. One result of this gender differential in mathematics is that few women entertain a career requiring a robust knowledge of higher mathematics (i.e. engineering, computing, or the physical sciences). A large body of literature has been written attempting to explain why this is happening. Biological, cultural, structural and psychological explanations have been suggested and empirically examined. Controlling for mathematical ability is one method of sorting out these explanations. Eliminating mathematical ability as a factor, this dissertation reports the results of a study of men and women college students who all had high mathematics ability. Thus, any differences we found among them would have to be a result of other variables. Using a Mathematics Placement Exam and the SAT-M, forty-two students (12 males and 30 females) with high scores in both were interviewed. Student were asked about their experiences in high school and college mathematics, their career choices, and their attitudes toward mathematics. The findings, that there were no gender differences in the course selection, attitudes towards mathematics, and career choice, differed from my initial expectations. This negative finding suggests that women with high ability in mathematics are just as likely as men to pursue interests in mathematics and related courses in college and in selecting careers.

  6. Strategies Employed by Middle School Principals Successful in Increasing and Sustaining the Mathematics Achievement of African American Students

    ERIC Educational Resources Information Center

    Clark, Rebecca

    2013-01-01

    This study approaches the problem of African American mathematics achievement from a strength-based perspective, identifying practices implemented by middle school principals successful in increasing and sustaining the mathematics achievement of African American students. The study was designed to answer questions regarding both school-wide…

  7. Mathematical Modelling as a Professional Task

    ERIC Educational Resources Information Center

    Frejd, Peter; Bergsten, Christer

    2016-01-01

    Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…

  8. Need for Equipping Student Teachers with Language of Mathematics

    ERIC Educational Resources Information Center

    Gafoor, K. Abdul; Sarabi, M. K.

    2015-01-01

    The significance of curriculum in building up language of mathematics which enables learners to construct and communicate knowledge of mathematics has not received due attention even as the pedagogical challenges faced by the students in learning mathematics have been discussed for years. Learning language of mathematics is not only valuable in…

  9. Competence with Fractions Predicts Gains in Mathematics Achievement

    PubMed Central

    Bailey, Drew H.; Hoard, Mary K.; Nugent, Lara; Geary, David C.

    2012-01-01

    Competence with fractions predicts later mathematics achievement, but the co-developmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this co-development through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grade (n = 212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted one year gains in mathematics achievement (β = .14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (β = .03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, and central executive span and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. PMID:22832199

  10. Competence with fractions predicts gains in mathematics achievement.

    PubMed

    Bailey, Drew H; Hoard, Mary K; Nugent, Lara; Geary, David C

    2012-11-01

    Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grades (N=212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted 1-year gains in mathematics achievement (ß=.14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (ß=.03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, central executive span, and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. Copyright © 2012 Elsevier Inc. All rights reserved.

  11. Mathematics for Physicists and Engineers.

    ERIC Educational Resources Information Center

    Organisation for Economic Cooperation and Development, Paris (France).

    The text is a report of the OEEC Seminar on "The Mathematical Knowledge Required by the Physicist and Engineer" held in Paris, 1961. There are twelve major papers presented: (1) An American Parallel (describes the work of the Panel on Physical Sciences and Engineering of the Committee on the Undergraduate Program in Mathematics of the Mathematical…

  12. Main Road Extraction from ZY-3 Grayscale Imagery Based on Directional Mathematical Morphology and VGI Prior Knowledge in Urban Areas

    PubMed Central

    Liu, Bo; Wu, Huayi; Wang, Yandong; Liu, Wenming

    2015-01-01

    Main road features extracted from remotely sensed imagery play an important role in many civilian and military applications, such as updating Geographic Information System (GIS) databases, urban structure analysis, spatial data matching and road navigation. Current methods for road feature extraction from high-resolution imagery are typically based on threshold value segmentation. It is difficult however, to completely separate road features from the background. We present a new method for extracting main roads from high-resolution grayscale imagery based on directional mathematical morphology and prior knowledge obtained from the Volunteered Geographic Information found in the OpenStreetMap. The two salient steps in this strategy are: (1) using directional mathematical morphology to enhance the contrast between roads and non-roads; (2) using OpenStreetMap roads as prior knowledge to segment the remotely sensed imagery. Experiments were conducted on two ZiYuan-3 images and one QuickBird high-resolution grayscale image to compare our proposed method to other commonly used techniques for road feature extraction. The results demonstrated the validity and better performance of the proposed method for urban main road feature extraction. PMID:26397832

  13. Connecting Mathematics Learning through Spatial Reasoning

    ERIC Educational Resources Information Center

    Mulligan, Joanne; Woolcott, Geoffrey; Mitchelmore, Michael; Davis, Brent

    2018-01-01

    Spatial reasoning, an emerging transdisciplinary area of interest to mathematics education research, is proving integral to all human learning. It is particularly critical to science, technology, engineering and mathematics (STEM) fields. This project will create an innovative knowledge framework based on spatial reasoning that identifies new…

  14. Prospective Mathematics Teachers' Attitudes Towards Learning Mathematics with Technology

    ERIC Educational Resources Information Center

    Ipek, A. Sabri; Berigel, Muhammed; Albayrak, Mustafa

    2007-01-01

    Role of technology which is an important tool for new approaches in learning mathematics is rapidly increasing at focus point of learning mathematics with new designs. One of the biggest factors at learning and instructing technology based mathematic education is attitudes of mathematics teachers towards technology. At this study, attitudes of…

  15. Learning over Time: Learning Trajectories in Mathematics Education

    ERIC Educational Resources Information Center

    Maloney, Alan P., Ed.; Confrey, Jere, Ed.; Nguyen, Kenny H., Ed.

    2014-01-01

    The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics--how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings--and how to use these insights to improve instruction and student learning. In this…

  16. The Microevolution of Mathematical Representations in Children's Activity.

    ERIC Educational Resources Information Center

    Meira, Luciano

    1995-01-01

    Discusses children's design of mathematical representations on paper. Suggests that the design of displays during problem solving shapes one's mathematical activity and sense making in crucial ways, and that knowledge of mathematical representations is not simply recalled and applied to problem solving, but also emerges out of one's interactions…

  17. Preservice Mathematics Teachers' Perceptions of Drama Based Instruction

    ERIC Educational Resources Information Center

    Bulut, Neslihan

    2016-01-01

    The purpose of this study was to determine the perceptions of pre-service mathematics teachers related to drama-based instruction. For this purpose, effects of a drama-based mathematics course on senior class pre-service mathematics teachers' knowledge about drama-based instruction and teacher candidates' competencies for developing and…

  18. Mathematical Problem Solving Ability of Eleventh Standard Students

    ERIC Educational Resources Information Center

    Priya, J. Johnsi

    2017-01-01

    There is a general assertion among mathematics instructors that learners need to acquire problem solving expertise, figure out how to communicate using mathematics knowledge and aptitude, create numerical reasoning and thinking, to see the interconnectedness amongst mathematics and other subjects. Based on this perspective, the present study aims…

  19. Investigating Engineering Practice Is Valuable for Mathematics Learning

    ERIC Educational Resources Information Center

    Goold, Eileen

    2015-01-01

    While engineering mathematics curricula often prescribe a fixed body of mathematical knowledge, this study takes a different approach; second-year engineering students are additionally required to investigate and document an aspect of mathematics used in engineering practice. A qualitative approach is used to evaluate the impact that students'…

  20. Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

    ERIC Educational Resources Information Center

    Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

    2014-01-01

    Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

  1. Mathematical Making in Teacher Preparation: What Knowledge Is Brought to Bear?

    ERIC Educational Resources Information Center

    Greenstein, Steven; Seventko, Justin

    2017-01-01

    In this paper, we describe an experience within mathematics teacher preparation that engages preservice teachers (PSTs) in Making and design practices that we hypothesized would inform their conceptual and pedagogical thinking. With a focus on the design of new tools to support mathematics teaching and learning, this Learning by Design experience…

  2. How Mathematics Propels the Development of Physical Knowledge

    ERIC Educational Resources Information Center

    Schwartz, Daniel L.; Martin, Taylor; Pfaffman, Jay

    2005-01-01

    Three studies examined whether mathematics can propel the development of physical understanding. In Experiment 1, 10-year-olds solved balance scale problems that used easy-to-count discrete quantities or hard-to-count continuous quantities. Discrete quantities led to age typical performances. Continuous quantities caused performances like those of…

  3. Mathematical Knowledge of Technology and Design Student Teachers: Diagnosis and Remediation

    ERIC Educational Resources Information Center

    Bell, Irene Teresa; Gibson, Ken

    2009-01-01

    This research examines how e-assessment and e-resources were used to assess and support the mathematics of Technology and Design students undertaking a B.Ed. (post-primary) teacher education course. The students participated in two similar tests in order to ascertain if their mathematical difficulties were in the underlying concepts of the…

  4. Construction of the mathematical concept of pseudo thinking students

    NASA Astrophysics Data System (ADS)

    Anggraini, D.; Kusmayadi, T. A.; Pramudya, I.

    2018-05-01

    Thinking process is a process that begins with the acceptance of information, information processing and information calling in memory with structural changes that include concepts or knowledges. The concept or knowledge is individually constructed by each individual. While, students construct a mathematical concept, students may experience pseudo thinking. Pseudo thinking is a thinking process that results in an answer to a problem or construction to a concept “that is not true”. Pseudo thinking can be classified into two forms there are true pseudo and false pseudo. The construction of mathematical concepts in students of pseudo thinking should be immediately known because the error will have an impact on the next construction of mathematical concepts and to correct the errors it requires knowledge of the source of the error. Therefore, in this article will be discussed thinking process in constructing of mathematical concepts in students who experience pseudo thinking.

  5. The written mathematical communication profile of prospective math teacher in mathematical proving

    NASA Astrophysics Data System (ADS)

    Pantaleon, K. V.; Juniati, D.; Lukito, A.; Mandur, K.

    2018-01-01

    Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.

  6. Design of capability measurement instruments pedagogic content knowledge (PCK) for prospective mathematics teachers

    NASA Astrophysics Data System (ADS)

    Aminah, N.; Wahyuni, I.

    2018-05-01

    The purpose of this study is to find out how the process of designing a tool of measurement Pedagogical Content Knowledge (PCK) capabilities, especially for prospective mathematics teachers are valid and practical. The design study of this measurement appliance uses modified Plomp development step, which consists of (1) initial assessment stage, (2) design stage at this stage, the researcher designs the measuring grille of PCK capability, (3) realization stage that is making measurement tool ability of PCK, (4) test phase, evaluation, and revision that is testing validation of measurement tools conducted by experts. Based on the results obtained that the design of PCK capability measurement tool is valid as indicated by the assessment of expert validator, and the design of PCK capability measurement tool, shown based on the assessment of teachers and lecturers as users of states strongly agree the design of PCK measurement tools can be used.

  7. State and trait effects on individual differences in children's mathematical development.

    PubMed

    Bailey, Drew H; Watts, Tyler W; Littlefield, Andrew K; Geary, David C

    2014-11-01

    Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. © The Author(s) 2014.

  8. State and Trait Effects on Individual Differences in Children's Mathematical Development

    PubMed Central

    Bailey, Drew H.; Watts, Tyler W.; Littlefield, Andrew K.; Geary, David C.

    2015-01-01

    Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. PMID:25231900

  9. Student Comprehension of Mathematics through Astronomy

    ERIC Educational Resources Information Center

    Search, Robert

    2016-01-01

    The purpose of this study is to examine how knowledge of astronomy can enhance college-level learning situations involving mathematics. The fundamental symbiosis between mathematics and astronomy was established early in the 17th century when Johannes Kepler deduced the 3 basic laws of planetary motion. This mutually harmonious relationship…

  10. Compendium for Research in Mathematics Education

    ERIC Educational Resources Information Center

    Cai, Jinfa, Ed.

    2017-01-01

    This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five…

  11. Early mathematics development and later achievement: Further evidence

    NASA Astrophysics Data System (ADS)

    Aubrey, Carol; Godfrey, Ray; Dahl, Sarah

    2006-05-01

    There is a growing international recognition of the importance of the early years of schooling as well as an interest being shown in the relationship of early education to later achievement. This article focuses on a cohort of English pupils who have been tracked through primary school during the first five years of the new National Numeracy Strategy. It reports a limited longitudinal study of young children's early mathematical development, initially within three testing cycles: at the mid-point and towards the end of their reception year (at five years-of-age) and again at the mid-point of Year 1 (at six years-ofage). These cycles were located within the broader context of progress through to the end of Key Stage 1 (at seven years) and Key Stage 2 (at eleven years) on the basis of national standardised assessment tests (SATs). Results showed that children who bring into school early mathematical knowledge do appear to be advantaged in terms of their mathematical progress through primary school. Numerical attainment increases in importance across the primary years and practical problem solving remains an important element of this. This finding is significant given the current emphasis on numerical calculation in the English curriculum. It is concluded that without active intervention, it is likely that children with little mathematical knowledge at the beginning of formal schooling will remain low achievers throughout their primary years and, probably, beyond.

  12. South Dakota Middle School Mathematics Teachers' Perceptions of Teaching Competencies

    ERIC Educational Resources Information Center

    Bleecker, Heather A.

    2017-01-01

    This quantitative research study investigates South Dakota middle school (grades 5-8) mathematics teachers' perceptions of teaching competencies including general pedagogical knowledge (GPK) and mathematical pedagogical content knowledge (MPCK). The study also considered how teacher characteristics relate to teacher competencies. The study…

  13. Primary Mathematics Teacher Education Encountering Difficult Terrain: A Personal Perspective

    ERIC Educational Resources Information Center

    Norton, Stephen

    2016-01-01

    This paper is a case study in preparing prospective primary teachers to teach mathematics at one Australian university. The paper describes the content knowledge of prospective teachers, pre and post a final mathematics curriculum subject. The teaching approach which attempts to account for both content and pedagogical content knowledge is…

  14. First-Year Students' Beliefs about Context Problems in Mathematics in University Science Programmes

    ERIC Educational Resources Information Center

    Drobnic Vidic, Andreja

    2015-01-01

    Mathematics-related beliefs play an important role in the willingness to engage in academic activities in mathematics education. Such beliefs might not be consistent with the beliefs students hold about context problems that require sufficient mathematical knowledge and the application of such knowledge to various real-life situations. This study…

  15. The Influence of Relational Knowledge and Executive Function on Preschoolers' Repeating Pattern Knowledge

    ERIC Educational Resources Information Center

    Miller, Michael R.; Rittle-Johnson, Bethany; Loehr, Abbey M.; Fyfe, Emily R.

    2016-01-01

    Children's knowledge of repeating patterns (e.g., ABBABB) is a central component of early mathematics, but the developmental mechanisms underlying this knowledge are currently unknown. We sought clarity on the importance of relational knowledge and executive function (EF) to preschoolers' understanding of repeating patterns. One hundred…

  16. Exploring Wind Power: Improving Mathematical Thinking through Digital Fabrication

    ERIC Educational Resources Information Center

    Tillman, Daniel A.; An, Song A.; Cohen, Jonathan D.; Kjellstrom, William; Boren, Rachel L.

    2014-01-01

    This mixed methods study examined the impacts of digital fabrication activities that were integrated into contextualized mathematics education. The study investigated the students' mathematics content knowledge and attitudes. Data analysis yielded two key findings regarding our intervention combined with the other mathematics activities resulted…

  17. The Relationship between Agriculture Knowledge Bases for Teaching and Sources of Knowledge

    ERIC Educational Resources Information Center

    Rice, Amber H.; Kitchel, Tracy

    2015-01-01

    The purpose of this study was to describe the agriculture knowledge bases for teaching of agriculture teachers and to see if a relationship existed between years of teaching experience, sources of knowledge, and development of pedagogical content knowledge (PCK), using quantitative methods. A model of PCK from mathematics was utilized as a…

  18. ONTIC: A Knowledge Representation System for Mathematics

    DTIC Science & Technology

    1987-01-01

    rrrPrL rr.t - ~ jr V 1.2. O.NTIC ASA FORMAL LANGUAGE 11 (IS zr) :I. (EXISTS-SOME r) (EXISTS ((xI 71) (U2 T2 ) ... ) ( li . X2, -.) . (FORALL ((xl 71) (x2...language. Jonathan Rees spent j.. about a month defining various mathematical concepts in Ontic. Starting with onlv the fundamental notions described...novelty of the Ontic system lies in the way that the above four inference mechanisms are brought together. Ontic integrates constraint prop- agation

  19. Knowledge and Attitudes of Ugandan Preservice Science and Mathematics Teachers toward Global and Ugandan Science--and Technology-Based Problems and/or Threats

    ERIC Educational Resources Information Center

    Robinson, Michael; Tibanyendera, Basil; Seltzer-Kelly, Debbie

    2007-01-01

    This article reports the effects of a science, technology, and society (STS) teaching approach on the knowledge and attitudes of preservice science and mathematics teachers in Uganda toward global science and technology-based problems and/or threats. The responses of a baseline or control group (N = 50) and an experimental group (N = 50) to five…

  20. Developmental Foundations of Children's Fraction Magnitude Knowledge.

    PubMed

    Mou, Yi; Li, Yaoran; Hoard, Mary K; Nugent, Lara D; Chu, Felicia W; Rouder, Jeffrey N; Geary, David C

    2016-01-01

    The conceptual insight that fractions represent magnitudes is a critical yet daunting step in children's mathematical development, and the knowledge of fraction magnitudes influences children's later mathematics learning including algebra. In this study, longitudinal data were analyzed to identify the mathematical knowledge and domain-general competencies that predicted 8 th and 9 th graders' (n=122) knowledge of fraction magnitudes and its cross-grade gains. Performance on the fraction magnitude measures predicted 9 th grade algebra achievement. Understanding and fluently identifying the numerator-denominator relation in 7 th grade emerged as the key predictor of later fraction magnitudes knowledge in both 8 th and 9 th grades. Competence at using fraction procedures, knowledge of whole number magnitudes, and the central executive contributed to 9 th but not 8 th graders' fraction magnitude knowledge, and knowledge of whole number magnitude contributed to cross-grade gains. The key results suggest fluent processing of numerator-denominator relations presages students' understanding of fractions as magnitudes and that the integration of whole number and fraction magnitudes occurs gradually.

  1. The Early Childhood Mathematics Education Revolution

    ERIC Educational Resources Information Center

    Hachey, Alyse C.

    2013-01-01

    Research Findings: We are in the midst of a revolution. Prior to the onset of the 21st century, mathematics education in the United States was deemphasized (Geary, 1996), and mathematics as an instructional subject has traditionally been considered above the preschool and kindergarten levels. However, the old regime--the knowledge and philosophies…

  2. Early numerical foundations of young children's mathematical development.

    PubMed

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

    2015-04-01

    This study focused on the relative contributions of the acuity of the approximate number system (ANS) and knowledge of quantitative symbols to young children's early mathematical learning. At the beginning of preschool, 191 children (Mage=46 months) were administered tasks that assessed ANS acuity and explicit knowledge of the cardinal values represented by number words, and their mathematics achievement was assessed at the end of the school year. Children's executive functions, intelligence, and preliteracy skills and their parents' educational levels were also assessed and served as covariates. Both the ANS and cardinality tasks were significant predictors of end-of-year mathematics achievement with and without control of the covariates. As simultaneous predictors and with control of the covariates, cardinality remained significantly related to mathematics achievement, but ANS acuity did not. Mediation analyses revealed that the relation between ANS acuity and mathematics achievement was fully mediated by cardinality, suggesting that the ANS may facilitate children's explicit understanding of cardinal value and in this way may indirectly influence early mathematical learning. Copyright © 2015 Elsevier Inc. All rights reserved.

  3. MATHEMATICS CLUSTERS IN SELECTED AREAS OF VOCATIONAL EDUCATION, REPORT NUMBER 8.

    ERIC Educational Resources Information Center

    RAHMLOW, HAROLD F.; WINCHELL, LEONARD

    IDENTIFICATIONS WERE MADE OF THE MATHEMATICAL KNOWLEDGES COMMONLY USED IN OCCUPATIONS MOST READILY SUITABLE FOR NONCOLLEGE-BOUND YOUTH. TASK ITEMS FROM QUESTIONNAIRES USED IN OFFICE OCCUPATIONS, GENERAL MERCHANDISING, BUILDING TRADES, ELECTRONICS, FOOD SERVICE, CHILD CARE, AND AGRICULTURE STUDIES WERE EXAMINED FOR MATHEMATICAL KNOWLEDGE CONTENT.…

  4. Spreadsheets as a Transparent Resource for Learning the Mathematics of Annuities

    ERIC Educational Resources Information Center

    Pournara, Craig

    2009-01-01

    The ability of mathematics teachers to decompress mathematics and to move between representations are two key features of mathematical knowledge that is usable for teaching. This article reports on four pre-service secondary mathematics teachers learning the mathematics of annuities. In working with spreadsheets students began to make sense of…

  5. Early Predictors of Middle School Fraction Knowledge

    PubMed Central

    Bailey, Drew H.; Siegler, Robert S.; Geary, David C.

    2014-01-01

    Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic proficiency, domain general cognitive abilities, parental income and education, race, and gender. Similarly, knowledge of whole number arithmetic in first grade predicted knowledge of fraction arithmetic in middle school, controlling for whole number magnitude knowledge in first grade and the other control variables. In contrast, neither type of early whole number knowledge uniquely predicted middle school reading achievement. We discuss the implications of these findings for theories of numerical development and for improving mathematics learning. PMID:24576209

  6. Understanding the Technological, Pedagogical, and Mathematical Issues That Emerge as Secondary Mathematics Teachers Design Lessons That Integrate Technology

    ERIC Educational Resources Information Center

    Gonzalez, Marggie Denise

    2016-01-01

    This multiple case study examines four groups of secondary mathematics teachers engaged in a Lesson Study approach to professional development where they planned and taught lessons that integrate technology. Informed by current literature, a framework was developed to focus on the dimensions of teacher's knowledge to teach mathematics with…

  7. Lexicography and Mathematics Learning: A Case Study of "Variable."

    ERIC Educational Resources Information Center

    Frawley, William

    1992-01-01

    Lexicography is shown to offer some useful new tools to researchers in mathematics education. The paper examines the relationship between the sublanguage of mathematics and the acquisition of mathematical knowledge, and also the use of definitions in research and curriculum design. An Explanatory Combinatorial Dictionary is advocated for improving…

  8. 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.)

  9. Differences in the Mathematics-Vocabulary Knowledge of Fifth-Grade Students with and without Learning Difficulties

    ERIC Educational Resources Information Center

    Forsyth, Suzanne R.; Powell, Sarah R.

    2017-01-01

    The purpose of this pilot study was to explore the impact of mathematics and reading learning difficulties on the mathematics-vocabulary understanding of fifth-grade students. Students (n = 114) completed three measures: mathematics computation, general vocabulary, and mathematics vocabulary. Based on performance on the mathematics computation and…

  10. Readiness, Behavior, and Foundational Mathematics Course Success

    ERIC Educational Resources Information Center

    Li, Kevin; Zelenka, Richard; Buonaguidi, Larry; Beckman, Robert; Casillas, Alex; Crouse, Jill; Allen, Jeff; Hanson, Mary Ann; Acton, Tara; Robbins, Steve

    2013-01-01

    This study examines the effects of math readiness and student course behavior (e.g., attendance, participation, homework completion) on knowledge gain and course success using two samples of students enrolled in foundational skills (noncredit-bearing) mathematics courses. As hypothesized, entering student mathematics readiness and course behavior…

  11. Promoting Mathematical Connections Using Three-Dimensional Manipulatives

    ERIC Educational Resources Information Center

    Safi, Farshid; Desai, Siddhi

    2017-01-01

    "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…

  12. Mathematics Program for Grades K-12

    ERIC Educational Resources Information Center

    Montgomery County Public Schools, 2013

    2013-01-01

    In the 21st century, a deep understanding of mathematics, and the ability to apply that understanding, is more important than it has ever been. In Montgomery County (Maryland) Public Schools (MCPS), and across the country, mathematics instruction is changing to provide students with the skills and knowledge they need for success in college and the…

  13. Mathematical anxiety is linked to reduced cognitive reflection: a potential road from discomfort in the mathematics classroom to susceptibility to biases

    PubMed Central

    2014-01-01

    Background When asked to solve mathematical problems, some people experience anxiety and threat, which can lead to impaired mathematical performance (Curr Dir Psychol Sci 11:181–185, 2002). The present studies investigated the link between mathematical anxiety and performance on the cognitive reflection test (CRT; J Econ Perspect 19:25–42, 2005). The CRT is a measure of a person’s ability to resist intuitive response tendencies, and it correlates strongly with important real-life outcomes, such as time preferences, risk-taking, and rational thinking. Methods In Experiments 1 and 2 the relationships between maths anxiety, mathematical knowledge/mathematical achievement, test anxiety and cognitive reflection were analysed using mediation analyses. Experiment 3 included a manipulation of working memory load. The effects of anxiety and working memory load were analysed using ANOVAs. Results Our experiments with university students (Experiments 1 and 3) and secondary school students (Experiment 2) demonstrated that mathematical anxiety was a significant predictor of cognitive reflection, even after controlling for the effects of general mathematical knowledge (in Experiment 1), school mathematical achievement (in Experiment 2) and test anxiety (in Experiments 1–3). Furthermore, Experiment 3 showed that mathematical anxiety and burdening working memory resources with a secondary task had similar effects on cognitive reflection. Conclusions Given earlier findings that showed a close link between cognitive reflection, unbiased decisions and rationality, our results suggest that mathematical anxiety might be negatively related to individuals’ ability to make advantageous choices and good decisions. PMID:25179230

  14. Mathematical anxiety is linked to reduced cognitive reflection: a potential road from discomfort in the mathematics classroom to susceptibility to biases.

    PubMed

    Morsanyi, Kinga; Busdraghi, Chiara; Primi, Caterina

    2014-09-01

    When asked to solve mathematical problems, some people experience anxiety and threat, which can lead to impaired mathematical performance (Curr Dir Psychol Sci 11:181-185, 2002). The present studies investigated the link between mathematical anxiety and performance on the cognitive reflection test (CRT; J Econ Perspect 19:25-42, 2005). The CRT is a measure of a person's ability to resist intuitive response tendencies, and it correlates strongly with important real-life outcomes, such as time preferences, risk-taking, and rational thinking. In Experiments 1 and 2 the relationships between maths anxiety, mathematical knowledge/mathematical achievement, test anxiety and cognitive reflection were analysed using mediation analyses. Experiment 3 included a manipulation of working memory load. The effects of anxiety and working memory load were analysed using ANOVAs. Our experiments with university students (Experiments 1 and 3) and secondary school students (Experiment 2) demonstrated that mathematical anxiety was a significant predictor of cognitive reflection, even after controlling for the effects of general mathematical knowledge (in Experiment 1), school mathematical achievement (in Experiment 2) and test anxiety (in Experiments 1-3). Furthermore, Experiment 3 showed that mathematical anxiety and burdening working memory resources with a secondary task had similar effects on cognitive reflection. Given earlier findings that showed a close link between cognitive reflection, unbiased decisions and rationality, our results suggest that mathematical anxiety might be negatively related to individuals' ability to make advantageous choices and good decisions.

  15. Can Mathematics be Justified by Natural Logic?

    NASA Astrophysics Data System (ADS)

    Schreiber, Lothar; Sommer, Hanns

    2010-11-01

    Charles Darwin claimed that the forms and the behaviour of living beings can be explained from their will to survive. But what are the consequences of this idea for humans knowledge, their theories of nature and their mathematics?. We discuss the view that even Plato's objective world of mathematical objects does not exist absolutely, without the intentions of mathematicians. Using Husserl's Phenomenological Method, cognition can be understood as a process by which meaning is deduced from empirical data relative to intentions. Thereby the essential structure of any cognition process can be detected and this structure is mirrored in logic. A natural logic becomes the direct result of cognition. Only in a second step, mathematics is obtained by abstraction from natural logic. In this way mathematics gains a well-defined foundation and is no longer part of a dubious 'a-priori knowledge' (Kant). This access to mathematics offers a new look on many old problems, e.g. the Petersburg problem and the problem 'P = NP?'. We demonstrate that this new justification of mathematics has also important applications in Artificial Intelligence. Our method provides a procedure to construct an adequate logic to solve most efficiently the problems of a given problem class. Thus, heuristics can be tailor-made for the necessities of applications.

  16. The Integration of technology in teaching mathematics

    NASA Astrophysics Data System (ADS)

    Muhtadi, D.; Wahyudin; Kartasasmita, B. G.; Prahmana, R. C. I.

    2017-12-01

    This paper presents the Transformation of Technological Pedagogical and Content Knowledge (TPACK) of three pre-service math teacher. They participate in technology-based learning modules aligned with teaching practice taught school and became characteristic of teaching method by using the mathematical software. ICT-based learning environment has been the demands in practice learning to build a more effective approach to the learning process of students. Also, this paper presents the results of research on learning mathematics in middle school that shows the influence of design teaching on knowledge of math content specifically.

  17. On the Social Nature of Mathematical Reasoning

    ERIC Educational Resources Information Center

    Roth, Wolff-Michael

    2016-01-01

    It has become a truism to state that mathematical knowledge or "meaning" and the norms and practices of (school) mathematical communities are negotiated and socially constructed before individuals construct (internalize) them for themselves. In this study I suggest that the social in existing conceptualizations is based on a trivial…

  18. Improvement of Self-regulated Learning in Mathematics through a Hypermedia Application: Differences based on Academic Performance and Previous Knowledge.

    PubMed

    Cueli, Marisol; Rodríguez, Celestino; Areces, Débora; García, Trinidad; González-Castro, Paloma

    2017-12-04

    Self-regulation on behalf of the student is crucial in learning Mathematics through hypermedia applications and is an even greater challenge in these IT environments. Two aims are formulated. First, to analyze the effectiveness of a hypermedia tool in improving perceived knowledge of self-regulatory strategies and the perceived usage of the planning, executing and assessment strategy on behalf of students with low, medium and high levels of academic performance. Second, to analyze the effectiveness of the hypermedia tool in improving perceived usage of the strategy for planning, monitoring and evaluating on behalf of students with a perceived knowledge (low, medium and high). Participants were 624 students (aged 10-13), classified into a treatment group (TG; 391) and a comparative group (CG; 233). They completed a questionnaire on perceived knowledge (Perceived Knowledge of Self-Regulatory Strategies) and another one on perceived usage of the strategy for planning, performing and evaluating (Inventory of Self-regulatory Learning Processes). Univariate covariance analyses (ANCOVAs) and Student-t tests were used. ANCOVA results were not statistically significant. However, the linear contrast indicated a significant improvement in perceived knowledge of strategies among the TG with low, medium and high academic performance (p ≤ .001). Results are discussed in the light of past and future research.

  19. Expertise in Mathematics Instruction: Subject Matter Knowledge.

    ERIC Educational Resources Information Center

    Leinhardt, Gaea; Smith, Donald

    The relationship between expert teachers' classroom behavior and their subject matter knowledge is an area of research that has not been examined extensively. To begin that study, one topic, fraction knowledge, was explored in depth as it occurred in natural teaching settings. Fractions are one of the more difficult topics in elementary…

  20. An Ideology Critique of the Use-Value of Mathematics

    ERIC Educational Resources Information Center

    Pais, Alexandre

    2013-01-01

    The idea that mathematics is needed for our mundane everyday activities has raised the question of how people deal with mathematics outside the school walls. Much has been written in mathematics education research about the possibility of transferring knowledge from and into school. Whereas the majority of this literature commends the possibility…

  1. A Study of Mathematics Infusion in Middle School Technology Education Classes

    ERIC Educational Resources Information Center

    Burghardt, M. David; Hecht, Deborah; Russo, Maria; Lauckhardt, James; Hacker, Michael

    2010-01-01

    The present study examined the impact of introducing a mathematics infused engineering/technology education (ETE) curriculum on students' mathematics content knowledge and attitudes toward mathematics. The purpose of the present study was to: (a) compare the effects of a mathematics infused ETE curriculum and a control curriculum on student…

  2. Understanding the Chinese Approach to Creative Teaching in Mathematics Classrooms

    ERIC Educational Resources Information Center

    Niu, Weihua; Zhou, Zheng; Zhou, Xinlin

    2017-01-01

    Using Amabile's componential theory of creativity as a framework, this paper analyzes how Chinese mathematics teachers achieve creative teaching through acquiring in-depth domain-specific knowledge in mathematics, developing creativity-related skills, as well as stimulating student interest in learning mathematics, through well-crafted,…

  3. Reading Stories to Learn Math: Mathematics Vocabulary Instruction for Children with Early Numeracy Difficulties

    ERIC Educational Resources Information Center

    Hassinger-Das, Brenna; Jordan, Nancy C.; Dyson, Nancy

    2015-01-01

    The present study involved examining whether a storybook reading intervention targeting mathematics vocabulary, such as "equal," "more," and "less," and associated number concepts would increase at-risk children's vocabulary knowledge and number competencies. Children with early numeracy difficulties (N = 124) were…

  4. Mathematical Abstraction: Constructing Concept of Parallel Coordinates

    NASA Astrophysics Data System (ADS)

    Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

    2017-09-01

    Mathematical abstraction is an important process in teaching and learning mathematics so pre-service mathematics teachers need to understand and experience this process. One of the theoretical-methodological frameworks for studying this process is Abstraction in Context (AiC). Based on this framework, abstraction process comprises of observable epistemic actions, Recognition, Building-With, Construction, and Consolidation called as RBC + C model. This study investigates and analyzes how pre-service mathematics teachers constructed and consolidated concept of Parallel Coordinates in a group discussion. It uses AiC framework for analyzing mathematical abstraction of a group of pre-service teachers consisted of four students in learning Parallel Coordinates concepts. The data were collected through video recording, students’ worksheet, test, and field notes. The result shows that the students’ prior knowledge related to concept of the Cartesian coordinate has significant role in the process of constructing Parallel Coordinates concept as a new knowledge. The consolidation process is influenced by the social interaction between group members. The abstraction process taken place in this group were dominated by empirical abstraction that emphasizes on the aspect of identifying characteristic of manipulated or imagined object during the process of recognizing and building-with.

  5. 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,…

  6. Correlation between performance in physics and prior mathematics knowledge

    NASA Astrophysics Data System (ADS)

    Hudson, H. T.; Rottmann, Ray M.

    The final grade of 1403 students enrolled in the first semester of the introductory, pre-professional physics course has been correlated with performance on a precourse diagnostic test of mathematical skills. The students were from a total of eight different sections taught by six separate instructors over a three year time span. The student population has been separated into two groups, those who completed the course (913 students) and those who dropped (490 students). The drops were assigned a projected final gradebased on performance up to date of withdrawal. The Pearson product-moment correlation for students who completed the course is 0.418 and correlation for the drops is 0.232. Both correlations are significant at the p < 0.001 level. This study suggests that prior mathematical ability is a primary influence on performance in the course, and has a secondary influence on the tendency to drop out of the course.

  7. Developmental Foundations of Children’s Fraction Magnitude Knowledge

    PubMed Central

    Mou, Yi; Li, Yaoran; Hoard, Mary K.; Nugent, Lara D.; Chu, Felicia W.; Rouder, Jeffrey N.; Geary, David C.

    2016-01-01

    The conceptual insight that fractions represent magnitudes is a critical yet daunting step in children’s mathematical development, and the knowledge of fraction magnitudes influences children’s later mathematics learning including algebra. In this study, longitudinal data were analyzed to identify the mathematical knowledge and domain-general competencies that predicted 8th and 9th graders’ (n=122) knowledge of fraction magnitudes and its cross-grade gains. Performance on the fraction magnitude measures predicted 9th grade algebra achievement. Understanding and fluently identifying the numerator-denominator relation in 7th grade emerged as the key predictor of later fraction magnitudes knowledge in both 8th and 9th grades. Competence at using fraction procedures, knowledge of whole number magnitudes, and the central executive contributed to 9th but not 8th graders’ fraction magnitude knowledge, and knowledge of whole number magnitude contributed to cross-grade gains. The key results suggest fluent processing of numerator-denominator relations presages students’ understanding of fractions as magnitudes and that the integration of whole number and fraction magnitudes occurs gradually. PMID:27773965

  8. Primary Trait Analysis to Assess a Learner-Centered, Upper-Level Mathematics Course

    ERIC Educational Resources Information Center

    Alsardary, Salar; Pontiggia, Laura; Hamid, Mohammed; Blumberg, Phyllis

    2011-01-01

    This study presents a primary trait analysis of a learner-centered, discrete mathematics course based on student-to-student instruction. The authors developed a scoring rubric for the primary traits: conceptual knowledge, procedural knowledge, application of understanding, and mathematical communication skills. Eleven students took an exam…

  9. From Preface to Practice: A Narrative Study of Women Learning to Teach Mathematics

    ERIC Educational Resources Information Center

    Stoehr, Kathleen Jablon

    2014-01-01

    My dissertation research explored the experiences of mathematics anxieties in women elementary preservice teachers while learning mathematics as K-12 students and while learning to teach mathematics. Previous studies conducted in mathematics teacher education have emphasized the importance of preservice teachers' mathematical knowledge for…

  10. Challenges in Measuring Teachers' Knowledge

    ERIC Educational Resources Information Center

    Fauskanger, Janne

    2015-01-01

    Mathematical knowledge for teaching (MKT) measures have been widely adopted by researchers. Critics have debated the value of such measures and questioned the type of knowledge that these access. This article reports on a study where the challenges in measuring teachers' knowledge were illuminated through investigating relationships between the…

  11. Strategies to Increase Representation of Students with Disabilities in Science, Technology, Engineering and Mathematics (STEM)

    ERIC Educational Resources Information Center

    White, Jeffry L.; Massiha, G. H.

    2015-01-01

    As a nation wrestles with the need to train more professionals, persons with disabilities are undereducated and underrepresented in science, technology, engineering, and mathematics (STEM). The following project was proposed to increase representation of students with disabilities in the STEM disciplines. The program emphasizes an integrated…

  12. Which Preschool Mathematics Competencies Are Most Predictive of Fifth Grade Achievement?

    PubMed Central

    Nguyen, Tutrang; Watts, Tyler W.; Duncan, Greg J.; Clements, Douglas H.; Sarama, Julie S.; Wolfe, Christopher; Spitler, Mary Elaine

    2016-01-01

    In an effort to promote best practices regarding mathematics teaching and learning at the preschool level, national advisory panels and organizations have emphasized the importance of children’s emergent counting and related competencies, such as the ability to verbally count, maintain one-to-one correspondence, count with cardinality, subitize, and count forward or backward from a given number. However, little research has investigated whether the kind of mathematical knowledge promoted by the various standards documents actually predict later mathematics achievement. The present study uses longitudinal data from a primarily low-income and minority sample of children to examine the extent to which preschool mathematical competencies, specifically basic and advanced counting, predict fifth grade mathematics achievement. Using regression analyses, we find early numeracy abilities to be the strongest predictors of later mathematics achievement, with advanced counting competencies more predictive than basic counting competencies. Our results highlight the significance of preschool mathematics knowledge for future academic achievement. PMID:27057084

  13. Which Preschool Mathematics Competencies Are Most Predictive of Fifth Grade Achievement?

    PubMed

    Nguyen, Tutrang; Watts, Tyler W; Duncan, Greg J; Clements, Douglas H; Sarama, Julie S; Wolfe, Christopher; Spitler, Mary Elaine

    In an effort to promote best practices regarding mathematics teaching and learning at the preschool level, national advisory panels and organizations have emphasized the importance of children's emergent counting and related competencies, such as the ability to verbally count, maintain one-to-one correspondence, count with cardinality, subitize, and count forward or backward from a given number. However, little research has investigated whether the kind of mathematical knowledge promoted by the various standards documents actually predict later mathematics achievement. The present study uses longitudinal data from a primarily low-income and minority sample of children to examine the extent to which preschool mathematical competencies, specifically basic and advanced counting, predict fifth grade mathematics achievement. Using regression analyses, we find early numeracy abilities to be the strongest predictors of later mathematics achievement, with advanced counting competencies more predictive than basic counting competencies. Our results highlight the significance of preschool mathematics knowledge for future academic achievement.

  14. Measuring Technological and Content Knowledge of Undergraduate Primary Teachers in Mathematics

    NASA Astrophysics Data System (ADS)

    Doukakis, Spyros; Chionidou-Moskofoglou, Maria; Mangina-Phelan, Eleni; Roussos, Petros

    Twenty-five final-year undergraduate students of primary education who were attending a course on mathematics education participated in a research project during the 2009 spring semester. A repeated measures experimental design was used. Quantitative data on students' computer attitudes, self-efficacy in ICT, attitudes toward educational software, and self-efficacy in maths were collected. Data analysis showed a statistically non-significant improvement on participants' computer attitudes and self-efficacy in ICT and ES, but a significant improvement of self-efficacy in mathematics.

  15. Developing Mathematical Knowledge through Social Justice Pedagogy with Young Adult Arab Women

    ERIC Educational Resources Information Center

    Tanko, Mohammed Goma; Atweh, Bill

    2012-01-01

    The study involved a group of Middle Eastern Muslim women learning mathematics through social justice pedagogy. The findings suggest that the involvement of students in social justice issues has not lead into a decline in their opportunity to learn mathematical content as set in the course. However, this approach has helped them to develop…

  16. The Priorities and Challenges of Primary Teachers' Knowledge in Their Mathematics Planning

    ERIC Educational Resources Information Center

    Davidson, Aylie

    2016-01-01

    There is growing consensus that the process of planning mathematics lessons is as complex as teaching them, yet there is limited research on this. This paper reports on one aspect of a project examining issues in primary teachers' mathematics planning. The results, taken from a questionnaire completed by 62 primary teachers, indicate that when…

  17. Developing Mathematical Content Knowledge for Teaching: One Preservice Teacher and Her Planning

    ERIC Educational Resources Information Center

    Wilson, Susanna

    2016-01-01

    This paper describes how a new pre-service teacher engaged with mathematical content in order to learn it for teaching, during practicum. The results show that the PST learned mathematical content by initiating and carrying out a preparation phase prior to planning. This phase involved searching through internet sites and making notes that were…

  18. How Young Students Communicate Their Mathematical Problem Solving in Writing

    ERIC Educational Resources Information Center

    Teledahl, Anna

    2017-01-01

    This study investigates young students' writing in connection to mathematical problem solving. Students' written communication has traditionally been used by mathematics teachers in the assessment of students' mathematical knowledge. This study rests on the notion that this writing represents a particular activity which requires a complex set of…

  19. Elementary Preservice Teachers' Mathematical Knowledge for Teaching: Using Situated Case Studies and Educative Experiences to Examine and Improve the Development of MKT in Teacher Education

    ERIC Educational Resources Information Center

    Johnson, Tracy L.

    2011-01-01

    This study examined pre-service teachers' development of mathematical knowledge for teaching (MKT) over their final year in a university based teacher education program. This was done through analyzing written reflections, focus group interviews, individual interviews, teaching observations, and post-observation interviews as well as through the…

  20. Foundation Content Knowledge: What Do Pre-Service Teachers Need to Know?

    ERIC Educational Resources Information Center

    Linsell, Chris; Anakin, Megan

    2013-01-01

    The mathematics content knowledge of pre-service teachers is a growing area of inquiry. This topic requires further theoretical development due to the limited applicability of current cognitive and practice-oriented frameworks of mathematics content knowledge to beginning pre-service teachers. Foundation content knowledge is an integrated,…

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