elementary mathematical logic: Topics by Science.gov

Sample records for elementary mathematical logic

Preservice Elementary Teachers' Understanding of Logical Inference

ERIC Educational Resources Information Center

Hauk, Shandy; Judd, April Brown; Tsay, Jenq Jong; Barzilai, Harel; Austin, Homer

2009-01-01

This article reports on the logical reasoning efforts of five prospective elementary school teachers as they responded to interview prompts involving nonsense, natural, and mathematical representations of conditional statements. The interview participants evinced various levels of reliance on personal relevance, linguistic contextualization, and…
Lakatos' Proofs and Refutations Comes Alive in an Elementary Classroom.

ERIC Educational Resources Information Center

Atkins, Sandra L.

1997-01-01

Presents an alternative pedagogy implicit in Imre Lakatos's "Proofs and Refutations: The Logic of Mathematical Discovery." Lakatos reveals that learning mathematics is a discourse-laden activity in which it is acceptable, if not preferable, to refute conjecture. Provides examples of using a Lakatosian approach in an elementary classroom.…
Signs of In/Equality: A History of Representation and Reform in Elementary School Mathematics from the 1950s to the Present

ERIC Educational Resources Information Center

Diaz, Jennifer DeNet

2014-01-01

This study begins with the assumption that the equal sign (=) in elementary school mathematics is not merely a symbol of mathematical logic. Rather, as the equal sign (=) appears in the school math curriculum, it orders children's thinking about equality by assigning identities to things of the world--as expressions of equivalences and…
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…
Brain Stretchers Book 4--Advanced.

ERIC Educational Resources Information Center

Anderson, Carolyn

This book provides puzzles, games, and mathematical activities for students in elementary grades. Number concepts and arithmetic are common topics. These classic math, logic, and word-problem activities encourage students to become flexible, creative thinkers while teaching them to draw valid conclusions based on logic and evidence. Each activity…
Exploring Logical Reasoning and Mathematical Proof in Grade 6 Elementary School Students

ERIC Educational Resources Information Center

Flegas, Konstantinos; Charalampos, Lemonidis

2013-01-01

Research and classroom experience reveal that the construction of mathematical proofs is difficult for all students. While many contemporary mathematics curricula recognize the importance of teaching reasoning and proof, in Greece these concepts are introduced at the secondary education level. In this study, we will attempt to investigate a group…
An Alternative Version of Conditional Probabilities and Bayes' Rule: An Application of Probability Logic

ERIC Educational Resources Information Center

Satake, Eiki; Amato, Philip P.

2008-01-01

This paper presents an alternative version of formulas of conditional probabilities and Bayes' rule that demonstrate how the truth table of elementary mathematical logic applies to the derivations of the conditional probabilities of various complex, compound statements. This new approach is used to calculate the prior and posterior probabilities…
Cognitive and attitudinal predictors related to graphing achievement among pre-service elementary teachers

NASA Astrophysics Data System (ADS)

Szyjka, Sebastian P.

The purpose of this study was to determine the extent to which six cognitive and attitudinal variables predicted pre-service elementary teachers' performance on line graphing. Predictors included Illinois teacher education basic skills sub-component scores in reading comprehension and mathematics, logical thinking performance scores, as well as measures of attitudes toward science, mathematics and graphing. This study also determined the strength of the relationship between each prospective predictor variable and the line graphing performance variable, as well as the extent to which measures of attitude towards science, mathematics and graphing mediated relationships between scores on mathematics, reading, logical thinking and line graphing. Ninety-four pre-service elementary education teachers enrolled in two different elementary science methods courses during the spring 2009 semester at Southern Illinois University Carbondale participated in this study. Each subject completed five different instruments designed to assess science, mathematics and graphing attitudes as well as logical thinking and graphing ability. Sixty subjects provided copies of primary basic skills score reports that listed subset scores for both reading comprehension and mathematics. The remaining scores were supplied by a faculty member who had access to a database from which the scores were drawn. Seven subjects, whose scores could not be found, were eliminated from final data analysis. Confirmatory factor analysis (CFA) was conducted in order to establish validity and reliability of the Questionnaire of Attitude Toward Line Graphs in Science (QALGS) instrument. CFA tested the statistical hypothesis that the five main factor structures within the Questionnaire of Attitude Toward Statistical Graphs (QASG) would be maintained in the revised QALGS. Stepwise Regression Analysis with backward elimination was conducted in order to generate a parsimonious and precise predictive model. This procedure allowed the researcher to explore the relationships among the affective and cognitive variables that were included in the regression analysis. The results for CFA indicated that the revised QALGS measure was sound in its psychometric properties when tested against the QASG. Reliability statistics indicated that the overall reliability for the 32 items in the QALGS was .90. The learning preferences construct had the lowest reliability (.67), while enjoyment (.89), confidence (.86) and usefulness (.77) constructs had moderate to high reliabilities. The first four measurement models fit the data well as indicated by the appropriate descriptive and statistical indices. However, the fifth measurement model did not fit the data well statistically, and only fit well with two descriptive indices. The results addressing the research question indicated that mathematical and logical thinking ability were significant predictors of line graph performance among the remaining group of variables. These predictors accounted for 41% of the total variability on the line graph performance variable. Partial correlation coefficients indicated that mathematics ability accounted for 20.5% of the variance on the line graphing performance variable when removing the effect of logical thinking. The logical thinking variable accounted for 4.7% of the variance on the line graphing performance variable when removing the effect of mathematics ability.
Actualizacion Matematica, AM-2 (Modernizing Mathematics, AM-2).

ERIC Educational Resources Information Center

[Parot, Jean Jacques

This document presents a series of exercises designed to help elementary school children develop skills in mathematics and logic. By means of stories, games, questions, and illustrations, the first set of exercises presents the idea of number systems with bases other than 10. Similar means are used to explain the concept of exponents and to teach…
The Effects of Arts Education on Emotional Literacy.

ERIC Educational Resources Information Center

Wallace, Rebecca Rockwell

Human potential includes at least seven intelligences--only two, linguistics and mathematics/logic, typically are taught in elementary schools. Researchers in the field of multiple intelligences believe the arts represent the other intelligences, i.e.: music, spatial reasoning, kinesthetic, interpersonal, and intrapersonal. A study explored the…
Parent and Teacher Opinions of Eight Different Ways of Thinking and Learning

ERIC Educational Resources Information Center

Maycock, George

2017-01-01

Parents and teachers at seven elementary schools were surveyed to determine their opinions of the importance of Gardner's eight different ways of thinking and learning. Parent and teacher opinions were highest in the four areas of logical-mathematical, intrapersonal, linguistic and interpersonal, which were all rated very important. Next in…
Magic SEED? A New Approach to Teaching Math Produces Some Eye-Popping Results.

ERIC Educational Resources Information Center

Shore, Debra

1991-01-01

Project SEED is a successful program that teaches elementary school students advanced math. Specialists conduct 45-minute lessons, asking questions designed to help students discover mathematical logic. Students respond with a system of SEED hand signals which allow everyone to participate and be monitored at once. (SM)
Proposing and Testing a Model to Explain Traits of Algebra Preparedness

ERIC Educational Resources Information Center

Venenciano, Linda; Heck, Ronald

2016-01-01

Early experiences with theoretical thinking and generalization in measurement are hypothesized to develop constructs we name here as logical reasoning and preparedness for algebra. Based on work of V. V. Davydov (1975), the Measure Up (MU) elementary grades experimental mathematics curriculum uses quantities of area, length, volume, and mass to…
Teaching Fifth Grade Mathematical Concepts: Effects of Word Problems Used with Traditional Methods.

ERIC Educational Resources Information Center

Coy, Jessica

The view of the researcher is that students in the upper elementary to middle school range need to increase their problem-solving skills by making logical deductions and organizing and structuring their thoughts through the use of word problems. Giving children a daily word problem challenged and introduced them to the lesson. This activity…
An Alternative Teaching Method of Conditional Probabilities and Bayes' Rule: An Application of the Truth Table

ERIC Educational Resources Information Center

Satake, Eiki; Vashlishan Murray, Amy

2015-01-01

This paper presents a comparison of three approaches to the teaching of probability to demonstrate how the truth table of elementary mathematical logic can be used to teach the calculations of conditional probabilities. Students are typically introduced to the topic of conditional probabilities--especially the ones that involve Bayes' rule--with…
Academic Achievement from Using the Learning Medium Via a Tablet Device Based on Multiple Intelligences in Grade 1 Elementary Student.

PubMed

Nuallaong, Winitra; Nuallaong, Thanya; Preechadirek, Nongluck

2015-04-01

To measure academic achievement of the multiple intelligence-based learning medium via a tablet device. This is a quasi-experimental research study (non-randomized control group pretest-posttest design) in 62 grade 1 elementary students (33 males and 29 females). Thirty-one students were included in an experimental group using purposive sampling by choosing a student who had highest multiple intelligence test scores in logical-mathematic. Then, this group learned by the new learning medium via a tablet which the application matched to logical-mathematic multiple intelligence. Another 31 students were included in a control group using simple random sampling and then learning by recitation. Both groups did pre-test and post-test vocabulary. Thirty students in the experimental group and 24 students in the control group increased post-test scores (odds ratio = 8.75). Both groups made significant increasing in post-test scores. The experimental group increased 9.07 marks (95% CI 8.20-9.93) significantly higher than the control group which increased 4.39 marks (95% CI 3.06-5.72) (t = -6.032, df = 51.481, p < 0.001). Although learning from either multiple intelligence-based learning medium via a tablet or recitation can contribute academic achievement, learningfrom the new medium contributed more achievement than recitation. The new learning medium group had higher post-test scores 8.75 times than the recitation group. Therefore, the new learning medium is more effective than the traditional recitation in terms of academic achievement. This study has limitations because samples came from the same school. However, the previous study in Thailand did notfind a logical-mathematical multiple intelligence difference among schools. In the future, long-term research to find how the new learning medium affects knowledge retention will support the advantage for life-long learning.
Iterants, Fermions and Majorana Operators

NASA Astrophysics Data System (ADS)

Kauffman, Louis H.

Beginning with an elementary, oscillatory discrete dynamical system associated with the square root of minus one, we study both the foundations of mathematics and physics. Position and momentum do not commute in our discrete physics. Their commutator is related to the diffusion constant for a Brownian process and to the Heisenberg commutator in quantum mechanics. We take John Wheeler's idea of It from Bit as an essential clue and we rework the structure of that bit to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We show how the dynamical system for the square root of minus one is essentially the dynamics of a distinction whose self-reference leads to both the fusion algebra and the operator algebra for the Majorana Fermion. In the course of this, we develop an iterant algebra that supports all of matrix algebra and we end the essay with a discussion of the Dirac equation based on these principles.
Cognitive correlates of performance in advanced mathematics.

PubMed

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

2012-03-01

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). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.
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…
Experimentation of cooperative learning model Numbered Heads Together (NHT) type by concept maps and Teams Games Tournament (TGT) by concept maps in terms of students logical mathematics intellegences

NASA Astrophysics Data System (ADS)

Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

2017-06-01

This research is aimed to find out the effect of learning model towards learning achievement in terms of students’ logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students’ achievements with NHT learning model by Concept Maps were better than students’ achievements with TGT model by Concept Maps and Direct Learning model. The students’ achievements with TGT model by Concept Maps were better than the students’ achievements with Direct Learning model. 2) The students’ achievements that exposed high logical mathematics intelligences were better than students’ medium and low logical mathematics intelligences. The students’ achievements that exposed medium logical mathematics intelligences were better than the students’ low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.

Students’ logical-mathematical intelligence profile

NASA Astrophysics Data System (ADS)

Arum, D. P.; Kusmayadi, T. A.; Pramudya, I.

2018-04-01

One of students’ characteristics which play an important role in learning mathematics is logical-mathematical intelligence. This present study aims to identify profile of students’ logical-mathematical intelligence in general and specifically in each indicator. It is also analyzed and described based on students’ sex. This research used qualitative method with case study strategy. The subjects involve 29 students of 9th grade that were selected by purposive sampling. Data in this research involve students’ logical-mathematical intelligence result and interview. The results show that students’ logical-mathematical intelligence was identified in the moderate level with the average score is 11.17 and 51.7% students in the range of the level. In addition, the level of both male and female students are also mostly in the moderate level. On the other hand, both male and female students’ logical-mathematical intelligence is strongly influenced by the indicator of ability to classify and understand patterns and relationships. Furthermore, the ability of comparison is the weakest indicator. It seems that students’ logical-mathematical intelligence is still not optimal because more than 50% students are identified in moderate and low level. Therefore, teachers need to design a lesson that can improve students’ logical-mathematical intelligence level, both in general and on each indicator.
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…
Math Is Like a Lion Hunting a Sleeping Gazelle: Preservice Elementary Teachers' Metaphors of Mathematics

ERIC Educational Resources Information Center

Latterell, Carmen M.; Wilson, Janelle L.

2016-01-01

Preservice elementary teachers hold a variety of beliefs about mathematics and mathematics learning, which influence their teaching. Previous research has shown that preservice elementary teachers believe that mathematics is doing arithmetic. However, it is unclear if preservice elementary teachers truly believe that mathematics is only…
The Relationships among Mathematics Teaching Efficacy, Mathematics Self-Efficacy, and Mathematical Beliefs for Elementary Pre-Service Teachers

ERIC Educational Resources Information Center

Briley, Jason S.

2012-01-01

Ninety-five elementary pre-service teachers enrolled in a mathematics content course for elementary school teachers completed 3 surveys to measure mathematics teaching efficacy, mathematics self-efficacy, and mathematical beliefs. The pre-service teachers who reported stronger beliefs in their capabilities to teach mathematics effectively were…
Mathematics Anxiety: One Size Does Not Fit All

ERIC Educational Resources Information Center

Stoehr, Kathleen Jablon

2017-01-01

Mathematics educators agree elementary teachers should possess confidence and competence in teaching mathematics. Many prospective elementary teachers (particularly women) pursue careers in elementary teaching despite personal repeated experiences of mathematics anxiety. Previous studies of mathematics anxiety have tended to focus on physical…
On the Importance of Set-Based Meanings for Categories and Connectives in Mathematical Logic

ERIC Educational Resources Information Center

Dawkins, Paul Christian

2017-01-01

Based on data from a series of teaching experiments on standard tools of mathematical logic, this paper characterizes a range of student meanings for mathematical properties and logical connectives. Some observed meanings inhibited students' adoption of logical structure, while others greatly facilitated it. "Reasoning with predicates"…
Preservice Elementary Mathematics Teachers' Level of Relating Mathematical Concepts in Daily Life Contexts

ERIC Educational Resources Information Center

Akkus, Oylum

2008-01-01

The purpose of this study was to investigate preservice elementary mathematics teachers' ability of relating mathematical concepts and daily life context. Two research questions were set; what is the preservice elementary mathematics teachers' level of relating mathematical concepts and daily life context regarding to their education year and…
Elementary Pre-Service Teachers' Mathematics Anxiety and Mathematics Teaching Anxiety

ERIC Educational Resources Information Center

Haciomeroglu, Guney

2014-01-01

The present study examined the structure of elementary pre-service teachers' mathematics anxiety and mathematics teaching anxiety by asking whether the two systems of anxiety are related. The Turkish Mathematics Anxiety Rating Scale Short Version and the Mathematics Teaching Anxiety Scale were administered to 260 elementary pre-service teachers.…
Elementary Mathematics Leaders

ERIC Educational Resources Information Center

Fennell, Francis; Kobett, Beth McCord; Wray, Jonathan A.

2013-01-01

Elementary school mathematics leaders often come to the realization that their position, however titled and determined, although dedicated to addressing needs in math teaching and learning, also entails and directly involves leadership. Elementary school math specialists/instructional leaders (referenced here as elementary mathematics leaders, or…
Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.

ERIC Educational Resources Information Center

Suppes, Patrick

This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…
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…
Reciprocal Relationships between Mathematics Anxiety and Attitude towards Mathematics in Elementary Students

ERIC Educational Resources Information Center

Haciomeroglu, Guney

2017-01-01

This current study examined the reciprocal relationship between anxiety and attitude towards mathematics in elementary students. Two instruments (attitudes towards mathematics inventory short form [ATMI-Short Form] and the Revised Fennema-Sherman Mathematics Anxiety Scale [Revised-FSMAS]) were administered to 310 fourth grade elementary students.…
THRESHOLD LOGIC IN ARTIFICIAL INTELLIGENCE

DTIC Science & Technology

COMPUTER LOGIC, ARTIFICIAL INTELLIGENCE , BIONICS, GEOMETRY, INPUT OUTPUT DEVICES, LINEAR PROGRAMMING, MATHEMATICAL LOGIC, MATHEMATICAL PREDICTION, NETWORKS, PATTERN RECOGNITION, PROBABILITY, SWITCHING CIRCUITS, SYNTHESIS
Comparison of learning models based on mathematics logical intelligence in affective domain

NASA Astrophysics Data System (ADS)

Widayanto, Arif; Pratiwi, Hasih; Mardiyana

2018-04-01

The purpose of this study was to examine the presence or absence of different effects of multiple treatments (used learning models and logical-mathematical intelligence) on the dependent variable (affective domain of mathematics). This research was quasi experimental using 3x3 of factorial design. The population of this research was VIII grade students of junior high school in Karanganyar under the academic year 2017/2018. Data collected in this research was analyzed by two ways analysis of variance with unequal cells using 5% of significance level. The result of the research were as follows: (1) Teaching and learning with model TS lead to better achievement in affective domain than QSH, teaching and learning with model QSH lead to better achievement in affective domain than using DI; (2) Students with high mathematics logical intelligence have better achievement in affective domain than students with low mathematics logical intelligence have; (3) In teaching and learning mathematics using learning model TS, students with moderate mathematics logical intelligence have better achievement in affective domain than using DI; and (4) In teaching and learning mathematics using learning model TS, students with low mathematics logical intelligence have better achievement in affective domain than using QSH and DI.
Precision in the Teaching, Learning, and Communication of Elementary School Mathematics: A Reply to Wilson's "Elementary School Mathematics Priorities"

ERIC Educational Resources Information Center

Maher, Carolyn; Weber, Keith

2009-01-01

In "Elementary School Mathematics Priorities," Wilson (2009 [this issue]) presents a list of five core concepts that students should master in elementary school so that they can succeed in algebra. As researchers in mathematics education, the authors enthusiastically endorse Wilson's recommendations. Learning algebra is key to further study of…
Growth Processes and Formal Logic. Comments on History and Mathematics Regarded as Combined Educational Tools

ERIC Educational Resources Information Center

Seltman, Muriel; Seltman, P. E. J.

1978-01-01

The authors stress the importance of bringing together the causal logic of history and the formal logic of mathematics in order to humanize mathematics and make it more accessible. An example of such treatment is given in a discussion of the centrality of Euclid and the Euclidean system to mathematics development. (MN)
How Do Higher-Education Students Use Their Initial Understanding to Deal with Contextual Logic-Based Problems in Discrete Mathematics?

ERIC Educational Resources Information Center

Lubis, Asrin; Nasution, Andrea Arifsyah

2017-01-01

Mathematical reasoning in logical context has now received much attention in the mathematics curriculum documents of many countries, including Indonesia. In Indonesia, students start formally learning about logic when they pursue to senior-high school. Before, they previously have many experiences to deal with logic, but the earlier assignments do…
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…
Elementary Mathematics: Not so Elementary

ERIC Educational Resources Information Center

Scillieri, Elissa Mains

2012-01-01

International tests indicate that United States students have been outscored by other countries in the area of mathematics. Researchers warn that elementary mathematics curricula and instruction in this country is not designed around helping students achieve mathematics proficiency. Much of this could also be attributed to the weak development and…
From the University to the Classroom: Prospective Elementary Mathematics Specialists' Pedagogical Shifts

ERIC Educational Resources Information Center

Myers, Kayla D.; Swars, Susan L.; Smith, Stephanie Z.

2016-01-01

This project focuses on the development of prospective Elementary Mathematics Specialists (EMSs) in a K-5 Mathematics Endorsement Program. Program courses emphasized elementary mathematics content and pedagogy while providing opportunities for participants to evidence their learning through classroom teaching practice, all in an attempt to…

ABC Problem in Elementary Mathematics Education: Arithmetic "before" Comprehension

ERIC Educational Resources Information Center

Boote, Stacy K.; Boote, David N.

2018-01-01

Mathematical habits of prospective teachers affect problem comprehension and success and expose their beliefs about mathematics. Prospective elementary teachers (PSTs) (n = 121) engaged in a problem solving activity each week in class. Data were collected from PSTs enrolled in an undergraduate elementary mathematics methods course at a…
Music-Themed Mathematics Education as a Strategy for Improving Elementary Preservice Teachers' Mathematics Pedagogy and Teaching Self-Efficacy

ERIC Educational Resources Information Center

An, Song A.; Tillman, Daniel A.; Paez, Carlos R.

2015-01-01

This study investigated the effects upon elementary preservice teachers' mathematics teaching self-efficacy and interdisciplinary lesson design strategies, which resulted from an educational intervention that emphasized integrated music-mathematics instruction. The participating elementary preservice teachers (n = 152) were recruited for this…
Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic

ERIC Educational Resources Information Center

Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.

2016-01-01

Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…
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…
Mathematics Anxiety and Preservice Elementary Teachers' Confidence to Teach Mathematics and Science

ERIC Educational Resources Information Center

Bursal, Murat; Paznokas, Lynda

2006-01-01

Sixty-five preservice elementary teachers' math anxiety levels and confidence levels to teach elementary mathematics and science were measured. The confidence scores of subjects in different math anxiety groups were compared and the relationships between their math anxiety levels and confidence levels to teach mathematics and science were…
Elementary Pre-Service Teachers: Can They Experience Mathematics Teaching Anxiety without Having Mathematics Anxiety?

ERIC Educational Resources Information Center

Brown, Amy Bingham; Westenskow, Arla; Moyer-Packenham, Patricia S.

2011-01-01

Elementary pre-service teachers report high levels of mathematics anxiety (MA), but the construct less widely addressed is their mathematics teaching anxiety (MTA). This study investigated the frequency with which MA stemming from prior experiences leads to MTA. Fifty-three elementary pre-service teachers' written reflections were analyzed, using…
The Impact of Problem Posing on Elementary Teachers' Beliefs about Mathematics and Mathematics Teaching

ERIC Educational Resources Information Center

Barlow, Angela T.; Cates, Janie M.

2006-01-01

This study investigated the impact of incorporating problem posing in elementary classrooms on the beliefs held by elementary teachers about mathematics and mathematics teaching. Teachers participated in a year-long staff development project aimed at facilitating the incorporation of problem posing into their classrooms. Beliefs were examined via…
Could Elementary Mathematics Textbooks Help Give Attention to Reasons in the Classroom?

ERIC Educational Resources Information Center

Newton, Douglas P.; Newton, Lynn D.

2007-01-01

Trainee teachers, new and non-specialist teachers of elementary mathematics have a tendency to avoid thought about reasons in mathematics. Instead, they tend to favour the development of computational skill through the rote application of procedures, routines and algorithms. Could elementary mathematics textbooks serve as models of practice and…
Prospective Elementary Teachers' Perceptions of Gender Differences in Children's Attitudes toward Mathematics

ERIC Educational Resources Information Center

Schwartz, Catherine S.; Sinicrope, Rose

2013-01-01

Prospective elementary teachers hold preconceived ideas about elementary school students' attitudes toward mathematics. We found that there exists a gender bias with prospective teachers expecting girls to have negative attitudes toward mathematics and boys more likely to have positive attitudes toward mathematics. We found that these…
Think Pair Share Using Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Afthina, H.; Mardiyana; Pramudya, I.

2017-09-01

This research aims to determine the impact of mathematics learning applying Think Pair Share (TPS) using Realistic Mathematics Education (RME) viewed from mathematical-logical intelligence in geometry learning. Method that used in this research is quasi experimental research The result of this research shows that (1) mathematics achievement applying TPS using RME approach gives a better result than those applying direct learning model; (2) students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low one, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one; (3) there is no interaction between learning model and the level of students’ mathematical-logical intelligence in giving a mathematics achievement. The impact of this research is that TPS model using RME approach can be applied in mathematics learning so that students can learn more actively and understand the material more, and mathematics learning become more meaningful. On the other hand, internal factors of students must become a consideration toward the success of students’ mathematical achievement particularly in geometry material.
Linear {GLP}-algebras and their elementary theories

NASA Astrophysics Data System (ADS)

Pakhomov, F. N.

2016-12-01

The polymodal provability logic {GLP} was introduced by Japaridze in 1986. It is the provability logic of certain chains of provability predicates of increasing strength. Every polymodal logic corresponds to a variety of polymodal algebras. Beklemishev and Visser asked whether the elementary theory of the free {GLP}-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable [1]. For every positive integer n we solve the corresponding question for the logics {GLP}_n that are the fragments of {GLP} with n modalities. We prove that the elementary theory of the free {GLP}_n-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable for all n. We introduce the notion of a linear {GLP}_n-algebra and prove that all free {GLP}_n-algebras generated by the constants \\mathbf{0}, \\mathbf{1} are linear. We also consider the more general case of the logics {GLP}_α whose modalities are indexed by the elements of a linearly ordered set α: we define the notion of a linear algebra and prove the latter result in this case.
Listening to Early Career Teachers: How Can Elementary Mathematics Methods Courses Better Prepare Them to Utilize Standards-Based Practices in Their Classrooms?

ERIC Educational Resources Information Center

Coester, Lee Anne

2010-01-01

This study was designed to gather input from early career elementary teachers with the goal of finding ways to improve elementary mathematics methods courses. Multiple areas were explored including the degree to which respondents' elementary mathematics methods course focused on the NCTM Process Standards, the teachers' current standards-based…
A Proposed System for Differentiating Elementary Mathematics for Exceptionally Able Students.

ERIC Educational Resources Information Center

Sirr, Palma M.

1984-01-01

A pilot mathematics project for one exceptionally able elementary student expanded to include other students and schools. Project activities included a needs assessment and development of a learning center approach and materials to differentiate the core elementary mathematics curriculum. (CL)
A New Approach to Teaching Mathematics

DTIC Science & Technology

1994-02-01

We propose a new approach to teaching discrete math : First, teach logic as a powerful and versatile tool for discovering and communicating truths...using logic in other areas of study. Our experiences in teaching discrete math at Cornell shows that such success is possible. Propositional logic, Predicate logic, Discrete mathematics.
Adapting Math Instruction to Support Prospective Elementary Teachers

ERIC Educational Resources Information Center

LeSage, Ann

2012-01-01

Purpose: Elementary teachers' understanding of mathematics is a significant contributor to student success with mathematics. Consequently, teacher educators are frequently charged with the responsibility of supporting the development of prospective elementary teachers' mathematics content knowledge as they re-learn concepts in ways they are…
An Analysis of Problem-Posing Tasks in Chinese and US Elementary Mathematics Textbooks

ERIC Educational Resources Information Center

Cai, Jinfa; Jiang, Chunlian

2017-01-01

This paper reports on 2 studies that examine how mathematical problem posing is integrated in Chinese and US elementary mathematics textbooks. Study 1 involved a historical analysis of the problem-posing (PP) tasks in 3 editions of the most widely used elementary mathematics textbook series published by People's Education Press in China over 3…
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…
Examining Mathematics Anxiety in Elementary Classroom Teachers

ERIC Educational Resources Information Center

McAnallen, Rachel R.

2010-01-01

Test anxiety and mathematics anxiety have been found to relate to mathematics performance in both children and adults. This study investigated mathematics anxiety in elementary teachers and whether those who experience mathematics anxiety also have professional anxiety about teaching mathematics. A researcher-developed instrument called the…
The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory

NASA Astrophysics Data System (ADS)

Frey, Kimberly

The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum mathematics in a sense which parallels the foundational role of classical set theory in classical mathematics. One immediate application of the quantum set theory we develop is to provide a foundation on which to construct quantum natural numbers, which are the quantum analog of the classical counting numbers. It turns out that in a special class of models, there exists a 1-1 correspondence between the quantum natural numbers and bounded observables in quantum theory whose eigenvalues are (ordinary) natural numbers. This 1-1 correspondence is remarkably satisfying, and not only gives us great confidence in our quantum set theory, but indicates the naturalness of such models for quantum theory itself. We go on to develop a Peano-like arithmetic for these new "numbers," as well as consider some of its consequences. Finally, we conclude by summarizing our results, and discussing directions for future work.
Guiding Reinvention of Conventional Tools of Mathematical Logic: Students' Reasoning about Mathematical Disjunctions

ERIC Educational Resources Information Center

Dawkins, Paul Christian; Cook, John Paul

2017-01-01

Motivated by the observation that formal logic answers questions students have not yet asked, we conducted exploratory teaching experiments with undergraduate students intended to guide their reinvention of truth-functional definitions for basic logical connectives. We intend to reframe the relationship between reasoning and logic by showing how…

Professional Vision: Elementary School Principals' Perceptions of Mathematics Instruction

ERIC Educational Resources Information Center

Schoen, Robert C.

2010-01-01

This study explored 78 elementary school principals' perceptions of classroom mathematics instruction in an effort to build understanding of the professional vision (Goodwin, 1994) of elementary school principals as it relates to mathematics instruction. This study also tested the theory of Leadership Content Knowledge (Stein & Nelson, 2003)…
A Multi-Method Investigation of Mathematics Motivation for Elementary Age Students

ERIC Educational Resources Information Center

Linder, Sandra M.; Smart, Julie B.; Cribbs, Jennifer

2015-01-01

This paper presents the results of a multi-method study examining elementary students with high self-reported levels of mathematics motivation. Second- through fifth-grade students at a Title One school in the southeastern United States completed the Elementary Mathematics Motivation Instrument (EMMI), which examines levels of mathematics…
Reflective Field Experiences for Success in Teaching Elementary Mathematics

ERIC Educational Resources Information Center

Robards, Shirley N.

2009-01-01

In this paper, the author discusses the major components of a junior level pedagogy course for elementary education majors learning to teach mathematics. The course reviews content and knowledge of the teacher candidates and introduces methods and materials for teaching elementary mathematics using the Standards or benchmarks from the National…
Information-processing differences and laterality of students from different colleges and disciplines.

PubMed

Monfort, M; Martin, S A; Frederickson, W

1990-02-01

1023 college students were assessed for hemispheric brain dominance using the paper-and-pencil test, the Human Information Processing Survey. Analysis of scores of students majoring in Advertising, Interior Design, Music, Journalism, Art, Oral Communication, and Architecture suggested a preference for right-brain hemispheric processing, while scores of students majoring in Accounting, Management, Finance, Computer Science, Mathematics, Nursing, Funeral Service, Criminal Justice, and Elementary Education suggested a preference for left-hemispheric strategies for processing information. The differential effects of hemispheric processing in an educational system emphasizing the left-hemispheric activities of structured logic and sequential processing suggests repression of the intellectual development of those students who may be genetically favorable to right-hemispheric processing.
Contributions from sociology of science to mathematics education in Brazil: logic as a system of beliefs

NASA Astrophysics Data System (ADS)

de Andrade, Thales Haddad Novaes; Vilela, Denise Silva

2013-09-01

In Brazil, mathematics education was associated with Jean Piaget's theory. Scholars in the field of education appropriated Piaget's work in different ways, but usually emphasized logical aspects of thought, which probably lead to an expansion of mathematics education influenced by psychology. This study attempts to extend the range of interlocutions and pose a dialogue between the field of mathematics education in Brazil and the sociology of science proposed by David Bloor. The main point of Bloor's theory is that logical-mathematical knowledge is far from being true and universal and is socially conditioned. In particular we will be discussing the first principle of the strong program, which deals with conditions that generate beliefs promoted by education policies in Brazil, such as the MEC/USAID treaties. In this case the "naturalization of logic" was stimulated by a widespread diffusion of both Piaget studies and the Modern Mathematics Movement.
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…
Mathematical Inqu[ee]ry: Beyond "Add-Queers-and-Stir" Elementary Mathematics Education

ERIC Educational Resources Information Center

Rands, Kathleen

2009-01-01

While elementary educators have developed queer pedagogies and perspectives in many subjects from reading to music, science to English as a second language, queer perspectives on elementary mathematics education are remarkably absent. This article differentiates between two common uses of the term "queer" and delineates two sets of approaches…
Mathematics Anxiety and Beliefs of Turkish Pre-Service Elementary Teachers

ERIC Educational Resources Information Center

Uysal, Figen; Dede, Yüksel

2016-01-01

The purpose of this study was to investigate the relationship between pre-service elementary teachers' mathematics teaching beliefs and mathematics anxiety. The participants of the study consist of 96 pre-service elementary teachers from a department of primary education in a state university in Turkey during the 2010-2011 spring term. Mathematics…
Explorations in Elementary Mathematical Modeling

ERIC Educational Resources Information Center

Shahin, Mazen

2010-01-01

In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…
The Investigation of Elementary Mathematics Teacher Candidates' Problem Solving Skills According to Various Variables

ERIC Educational Resources Information Center

Kaya, Deniz; Izgiol, Dilek; Kesan, Cenk

2014-01-01

The aim was to determine elementary mathematics teacher candidates' problem solving skills and analyze problem solving skills according to various variables. The data were obtained from total 306 different grade teacher candidates receiving education in Department of Elementary Mathematics Education, Buca Faculty of Education, Dokuz Eylul…
Logic for Physicists

NASA Astrophysics Data System (ADS)

Pereyra, Nicolas A.

2018-06-01

This book gives a rigorous yet 'physics-focused' introduction to mathematical logic that is geared towards natural science majors. We present the science major with a robust introduction to logic, focusing on the specific knowledge and skills that will unavoidably be needed in calculus topics and natural science topics in general (rather than taking a philosophical-math-fundamental oriented approach that is commonly found in mathematical logic textbooks).
Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

ERIC Educational Resources Information Center

Wickstrom, Megan H.

2017-01-01

This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…
The Mathematics Teacher Development with Peer Tutoring Program.

ERIC Educational Resources Information Center

Duffie, William B.; Guida, Frank V.

This project addresses the problem of inadequate mathematics high school teacher staffing and the shortage of mathematics specialists in the elementary school. Regular elementary school teachers interested in becoming certified as high school mathematics teachers, and who had taken at least three college-level mathematics courses, were invited to…
"Mathematics Is Like a Lion": Elementary Students' Beliefs about Mathematics

ERIC Educational Resources Information Center

Markovits, Zvia; Forgasz, Helen

2017-01-01

The aim of this study was to explore the beliefs of elementary school students about mathematics and about themselves as mathematics learners. The participants, Israeli grade 4 and grade 6 students, completed questionnaires. Using an "animal metaphor" to tap beliefs, some students perceived mathematics as difficult and complicated, while…
Getting Ready for the Profession: Prospective Teachers' Noticing Related to Teacher Actions

ERIC Educational Resources Information Center

Osmanoglu, Aslihan; Isiksal, Mine; Koc, Yusuf

2015-01-01

The aim of this study was to investigate what the prospective elementary mathematics teachers noticed and how their noticing changed in an environment in which they discuss on video cases. To achieve this aim, we asked senior elementary mathematics prospective teachers to watch and discuss videos depicting real elementary mathematics classrooms.…
A Plan for Improving Mathematics Instruction in California Elementary Schools. Final Report of the Mathematics Education Task Force.

ERIC Educational Resources Information Center

Hoffman, Joseph R.; Tardif, Robert F.

In a project designed to improve elementary school instruction in mathematics, the California Department of Education collected achievement and profile data from 67 elementary schools. Schools were classified according to size, socioeconomic status, minority representation and mobility of students, city size, and type of community. Profile data…
TEACHING OF ADVANCED MATHEMATICAL CONCEPTS TO CULTURALLY DISADVANTAGED ELEMENTARY SCHOOL CHILDREN.

ERIC Educational Resources Information Center

RUPLEY, WILLIAM H.

THE SUCCESS OF DISCOVERY MATHEMATICS TEACHING IN THE ELEMENTARY SCHOOL WAS TESTED OVER A 1-YEAR PERIOD. THE PROJECT WAS INTENDED TO SEE IF A TRAINED MATHEMATICIAN WORKING AT AN ELEMENTARY SCHOOL WITH DISADVANTAGED CHILDREN COULD (1) MOTIVATE THE CHILDREN TO BE INTERESTED IN SCHOOL WORK BY INTERESTING THEM IN MATHEMATICS AND (2) COMMUNICATE WITH…
An Evaluation of Elementary School Mathematics Programs Utilizing the Mini-Calculator.

ERIC Educational Resources Information Center

Campbell, Patricia; Virgin, A. E.

The purpose of this study was to compare the achievement, attitudes, and teaching/learning experiences in mathematics programs of two groups of elementary-school students in grades 5 and 6. Approximately 150 students in each of two elementary schools were given as a pretest a standardized mathematics achievement test and a questionnaire regarding…
Does Teaching Geometry with Augmented Reality Affect the Technology Acceptance of Elementary School Mathematics Teacher Candidates?

ERIC Educational Resources Information Center

Önal, Nezih; Ibili, Emin; Çaliskan, Erkan

2017-01-01

The purpose of this research is to determine the impact of augmented reality technology and geometry teaching on elementary school mathematics teacher candidates' technology acceptance and to examine participants' views on augmented reality. The sample of the research was composed of 40 elementary school mathematics teacher candidates who were…
A Case Study on Mathematical Literacy of Prospective Elementary School Teachers

ERIC Educational Resources Information Center

Suharta, I. Gusti Putu; Suarjana, I. Made

2018-01-01

The purpose of this study is to describe Mathematical Literacy (ML) of Prospective Elementary School Teachers with attention to aspects of mathematical skills and gender. The type of research is qualitative with the research design of Case Study. Respondents are assigned 12 Prospective Elementary School Teachers, consisting of 6 men and 6 women.…

Mathematical, Logical, and Formal Methods in Information Retrieval: An Introduction to the Special Issue.

ERIC Educational Resources Information Center

Crestani, Fabio; Dominich, Sandor; Lalmas, Mounia; van Rijsbergen, Cornelis Joost

2003-01-01

Discusses the importance of research on the use of mathematical, logical, and formal methods in information retrieval to help enhance retrieval effectiveness and clarify underlying concepts of information retrieval. Highlights include logic; probability; spaces; and future research needs. (Author/LRW)
Logic via Computer Programming.

ERIC Educational Resources Information Center

Wieschenberg, Agnes A.

This paper proposed the question "How do we teach logical thinking and sophisticated mathematics to unsophisticated college students?" One answer among many is through the writing of computer programs. The writing of computer algorithms is mathematical problem solving and logic in disguise and it may attract students who would otherwise stop…
Elementary Teachers Integrate Music Activities into Regular Mathematics Lessons: Effects on Students' Mathematical Abilities

ERIC Educational Resources Information Center

An, Song; Capraro, Mary Margaret; Tillman, Daniel A.

2013-01-01

This article presents exploratory research investigating the way teachers integrate music into their regular mathematics lessons as well as the effects of music-mathematics interdisciplinary lessons on elementary school students' mathematical abilities of modeling, strategy and application. Two teachers and two classes of first grade and third…
Factors Influencing Elementary Mathematics Teachers' Beliefs in Reform-Based Teaching

ERIC Educational Resources Information Center

Sawyer, Amanda Gantt

2017-01-01

I investigated a reform based teachers' beliefs about the nature of mathematics, teaching mathematics, and learning mathematics, and the factors leading to their formation. I interviewed and observed a reform-based elementary mathematics teacher with 13 years' experience teaching first grade. She held a Platonist/problem solver view of…
The Impact of Advanced Curriculum on the Achievement of Mathematically Promising Elementary Students

ERIC Educational Resources Information Center

Gavin, M. Katherine; Casa, Tutita M.; Adelson, Jill L.; Carroll, Susan R.; Sheffield, Linda Jensen

2009-01-01

The primary aim of Project M[superscript 3]: Mentoring Mathematical Minds was to develop and field test advanced units for mathematically promising elementary students based on exemplary practices in gifted and mathematics education. This article describes the development of the units and reports on mathematics achievement results for students in…
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…
Exploring the Relationship between Questioning, Enacted Mathematical Tasks, and Mathematical Discourse in Elementary School Mathematics

ERIC Educational Resources Information Center

Martin, Christie; Polly, Drew; McGee, Jen; Wang, Chuang; Lambert, Richard; Pugalee, David

2015-01-01

This study examined the mathematical discourse of elementary school teachers and their students while participating in a year-long professional development project focused on implementing reform-based mathematics curriculum. The teacher participants included 12 teachers, two from each grade level from Kindergarten through Grade 5. Field notes were…
Content Analysis of Jordanian Elementary Textbooks during 1970-2013 as Case Study

ERIC Educational Resources Information Center

Abed, Eman Rasmi; Al-Absi, Mohammad Mustafa

2015-01-01

This study aims to determine types of mathematic disciplines (in term of topics) in Jordanian Elementary textbooks. This study evaluates mathematics text books especially in the period between 1970 and 2013 and identifies types and quantities of mathematics. To examine the relative quantity of mathematics, branches of mathematics, presentation…
Exploring Collective Mathematical Creativity in Elementary School

ERIC Educational Resources Information Center

Levenson, Esther

2011-01-01

This study combines theories related to collective learning and theories related to mathematical creativity to investigate the notion of collective mathematical creativity in elementary school classrooms. Collective learning takes place when mathematical ideas and actions, initially stemming from an individual, are built upon and reworked,…
Flipping Preservice Elementary Teachers' Mathematics Anxieties

ERIC Educational Resources Information Center

Dove, Anthony; Dove, Emily

2017-01-01

In preparing future elementary educators in mathematics, helping them overcome their anxieties of mathematics and teaching mathematics is paramount. This study examined how different instructional practices (in-class lecture, flipped learning with teacher-created videos, flipped classroom with Khan Academy videos) compared in improving students'…
Critical Issues in Reforming Elementary Teacher Preparation in Mathematics and Science. Conference Proceedings (Greeley, Colorado, October 10-13, 1991).

ERIC Educational Resources Information Center

Gardner, April L., Ed.; Cochran, Kathryn F., Ed.

The purpose of the conference reported in this document was to bring together national leaders in teacher education to disseminate findings and innovations in the reform of elementary teacher preparation in mathematics and science. The proceedings begin with a presentation of invited addresses: "New Curricula in Elementary Mathematics: What…
Pre-Service Elementary School and Secondary Mathematics Teachers' Van Hiele Levels and Gender Differences

ERIC Educational Resources Information Center

Halat, Erdogan

2008-01-01

The aim of this study was to find and compare the pre-service elementary school and secondary mathematic teachers' reasoning stages in geometry. There were a total of 281 pre-service teachers, 125 elementary school teachers and 156 secondary mathematics teachers, involved in the study. The researcher employed a multiple-choice geometry test. This…
Predicting the Quality of Elementary Mathematics Teachers Utilizing Pre-Graduation Data Collected from Teacher Preparation Programs

ERIC Educational Resources Information Center

Robertson, Mary Amos

2016-01-01

In order to change the direction of mathematics education, the training of elementary teachers in the United States needs to be of equal or higher quality than top preforming countries. However, pre-service elementary teachers in the United States fall behind their peers in other countries in mathematical content knowledge and mathematical…
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.
A Constructivist Computational Platform to Support Mathematics Education in Elementary School

ERIC Educational Resources Information Center

Garcia, I.; Pacheco, C.

2013-01-01

Many courses for elementary school are based upon teacher presentation and explanation of basic topics, rather than allowing students to develop their own knowledge. This traditional model may turn elementary-level lessons into an extremely theoretical, boring and non-effective process. In this context, research in mathematics elementary education…
One Point of View: Elementary School Mathematics Specialists: Where Are They?

ERIC Educational Resources Information Center

Dossey, John A.

1984-01-01

A plea is made for the mathematics education community to support the need for elementary school mathematics specialists. Roles of such specialists in primary as well as intermediate grades are listed. (MNS)
Preservice Teachers' Perceptions of the Integration of Mathematics, Reading, and Writing.

ERIC Educational Resources Information Center

Reinke, Kathryn; Mokhtari, Kouider; Willner, Elizabeth

1997-01-01

Examined the perceptions of preservice elementary teachers enrolled in reading, mathematics, and integrating reading and mathematics methods courses about integrating mathematics, reading, and writing instruction at the elementary/middle school level. Surveys indicated that all students were generally positive about instructional integration. They…
The Mathematical Preparation of Prospective Elementary Teachers: Reflections from Solving an "Interesting Problem"

ERIC Educational Resources Information Center

Ellis, Mark W.; Contreras, Jose; Martinez-Cruz, Armando M.

2009-01-01

Problem solving tasks offer valuable opportunities to strengthen prospective elementary teachers' knowledge of and disposition toward mathematics, providing them with new experiences doing mathematics. Mathematics educators can influence future instruction by modeling effective pedagogical strategies that engage students in making sense of…
"I Finally Get It!": Developing Mathematical Understanding during Teacher Education

ERIC Educational Resources Information Center

Holm, Jennifer; Kajander, Ann

2012-01-01

A deep conceptual understanding of elementary mathematics as appropriate for teaching is increasingly thought to be an important aspect of elementary teacher capacity. This study explores preservice teachers' initial mathematical understandings and how these understandings developed during a mathematics methods course for upper elementary…
Elementary General and Special Education Teachers' Mathematics Skills and Efficacy

ERIC Educational Resources Information Center

Flores, Margaret M.; Thornton, Jennifer; Franklin, Toni M.; Hinton, Vanessa M.; Strozier, Shaunita

2014-01-01

The purpose of this study was to extend the literature regarding elementary teachers' beliefs about mathematics instruction to include special education teachers by surveying special education and general education teachers' mathematics teaching efficacy. In addition, the researchers' surveyed teachers' mathematics skills. The participants (n =…

"When Mathematical Activity Moves You": An Exploration of the Design and Use of Purposefully Embodied Mathematical Activities, Models, Contexts, and Environments

ERIC Educational Resources Information Center

Campbell, William James

2017-01-01

This dissertation describes a mathematics curriculum and instruction design experiment involving a series of embodied mathematical activities conducted in two Colorado elementary schools Activities designed for this experiment include multi-scalar number line models focused on supporting students' understanding of elementary mathematics. Realistic…
The Relationship between Preservice Elementary Mathematics Teachers' Beliefs and Metacognitive Awareness

ERIC Educational Resources Information Center

Hart, Lynn Cecilia; Memnun, Dilek Sezgin

2015-01-01

The purpose of this study was to examine the metacognitive awareness and the beliefs about mathematics teaching and learning of preservice elementary mathematics teachers and to explore the relationship between the two. The Metacognitive Awareness Instrument (MAI) and the Mathematics Beliefs Instrument (MBI) were implemented with 118 elementary…
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…
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…
Prospective Elementary Teachers' Aesthetic Experience and Relationships to Mathematics

ERIC Educational Resources Information Center

Chen, Rong-Ji

2017-01-01

Previous research has adopted various approaches to examining teachers' and students' relationships to mathematics. The current study extended this line of research and investigated six prospective elementary school teachers' experiences in mathematics and how they saw themselves as learners of mathematics. One-on-one interviews with the…
Building the Wall Brick by Brick: One Prospective Teacher's Experiences with Mathematics Anxiety

ERIC Educational Resources Information Center

Stoehr, Kathleen Jablon

2017-01-01

Mathematics education researchers have investigated mathematics anxiety in prospective elementary teachers. While many of these studies have focused on the bodily sensations and emotions of mathematics anxiety, particularly those felt in assessment situations, opportunities remain to investigate how prospective elementary teachers interpret their…
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.)
Teaching Proofs and Algorithms in Discrete Mathematics with Online Visual Logic Puzzles

ERIC Educational Resources Information Center

Cigas, John; Hsin, Wen-Jung

2005-01-01

Visual logic puzzles provide a fertile environment for teaching multiple topics in discrete mathematics. Many puzzles can be solved by the repeated application of a small, finite set of strategies. Explicitly reasoning from a strategy to a new puzzle state illustrates theorems, proofs, and logic principles. These provide valuable, concrete…
Calculator Logic Systems and Mathematical Understandings.

ERIC Educational Resources Information Center

Burrows, Enid R.

This monograph is aimed at helping the reader understand the built-in logic of various calculator operating systems. It is an outgrowth of workshop contacts with in-service and pre-service teachers of mathematics and is in response to their request for a book on the subject of calculator logic systems and calculator algorithms. The mathematical…
Words to Argue By

ERIC Educational Resources Information Center

Pourciau, Bruce

2018-01-01

In a first proof-oriented mathematics course, students will often ask questions--for example, "What is this problem asking me to do?" or "What would a proof of this even look like"--that have more to do with logic than mathematics. The logical structure of a proof is a dance involving those basic logical forms--such as "p…
Elementary School Teachers' Perceptions toward ICT: The Case of Using Magic Board for Teaching Mathematics

ERIC Educational Resources Information Center

Yuan, Yuan; Lee, Chun-Yi

2012-01-01

This study aims at investigating elementary school teachers' perceptions toward to the use of ICT. Magic Board, an interactive web-based environment which provides a set of virtual manipulatives for elementary mathematics, is used as the case of ICT. After participating in Magic Board workshops, 250 elementary school teachers in Taiwan responded…
Quantum non-objectivity from performativity of quantum phenomena

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei; Schumann, Andrew

2014-12-01

We analyze the logical foundations of quantum mechanics (QM) by stressing non-objectivity of quantum observables, which is a consequence of the absence of logical atoms in QM. We argue that the matter of quantum non-objectivity is that, on the one hand, the formalism of QM constructed as a mathematical theory is self-consistent, but, on the other hand, quantum phenomena as results of experimenters’ performances are not self-consistent. This self-inconsistency is an effect of the language of QM differing greatly from the language of human performances. The former is the language of a mathematical theory that uses some Aristotelian and Russellian assumptions (e.g., the assumption that there are logical atoms). The latter language consists of performative propositions that are self-inconsistent only from the viewpoint of conventional mathematical theory, but they satisfy another logic that is non-Aristotelian. Hence, the representation of quantum reality in linguistic terms may be different: the difference between a mathematical theory and a logic of performative propositions. To solve quantum self-inconsistency, we apply the formalism of non-classical self-referent logics.
Lamp control using the principles of mathematical logic

NASA Astrophysics Data System (ADS)

Yudianto, E.; Firmansyah, F. F.; Akbar, P. S. B. S.; Nisyak, R.; Maudi, F. A.; Saputri, A. N.

2018-03-01

Along with the rapid development of technology, there are so many innovations on tools that can facilitate human’s work, one of which is a remote lamp controller. This light controller can provide convenience and comfort for people in turning on or off lights, especially they are traveling. The way remote light controller is used applies the principle of mathematical logic, particularly biimplication. The principle of mathematical logic (biimplication) on this light controller is applied to GSM module (gprs) and SMS.
The Assessment of Mathematical Logic: Abstract Patterns and Familiar Contexts

ERIC Educational Resources Information Center

Teppo, Anne R.; Esty, Warren W.; Kirkpatrick, Kay

2003-01-01

Undergraduate students' written exams were analyzed from a freshman-level mathematics course that emphasized, among other topics, the study of mathematical logic. Findings indicate that on questions related to the negation of a conditional sentence, students performed much better when given natural-language contexts than they did on questions…
Why physics needs mathematics

NASA Astrophysics Data System (ADS)

Rohrlich, Fritz

2011-12-01

Classical and the quantum mechanical sciences are in essential need of mathematics. Only thus can the laws of nature be formulated quantitatively permitting quantitative predictions. Mathematics also facilitates extrapolations. But classical and quantum sciences differ in essential ways: they follow different laws of logic, Aristotelian and non-Aristotelian logics, respectively. These are explicated.
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…
The Effect of an Integrated Science and Mathematics Content-Based Course on Science and Mathematics Teaching Efficacy of Preservice Elementary Teachers

ERIC Educational Resources Information Center

Moseley, Christine; Utley, Juliana

2006-01-01

The purpose of this study was to determine the effect of an earth systems science course (integrated mathematics and science content) on preservice elementary teachers' mathematics and science teaching efficacy. Paired t-tests revealed that the personal mathematics and science teaching efficacy and science teaching outcome expectancy significantly…
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…
(Re)Envisioning Mathematics Education: Examining Equity and Social Justice in an Elementary Mathematics Methods Course

ERIC Educational Resources Information Center

Koestler, Courtney

2010-01-01

In this dissertation, I present my attempts at designing an elementary mathematics methods course to support prospective teachers in developing an understanding of how to teach all students in learning powerful mathematics. To do this, I introduced them to teaching mathematics for equity and social justice by discussing ways to support students'…
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…

Motivating Prospective Elementary School Teachers to Learn Mathematics by Focusing upon Children's Mathematical Thinking

ERIC Educational Resources Information Center

Philipp, Randolph A.

2008-01-01

Elementary school children in the United States are not developing acceptable levels of mathematical proficiency (National Center for Education Statistics, 1999), and a major concern of teacher educators is that teachers lack the depth and flexibility of mathematical understanding and the corresponding beliefs they need to teach for proficiency…
Questions To Ask and Issues To Consider While Supervising Elementary Mathematics Student Teachers.

ERIC Educational Resources Information Center

Philip, Randolph A.

2000-01-01

Presents four questions to consider when supervising elementary mathematics teachers, who come with many preconceptions about teaching and learning mathematics: What mathematical concepts, procedures, or algorithms are you teaching? Are the concepts and procedures part of a unit? What types of questions do you pose? and What understanding of…
SPATIAL VISUALIZATION ABILITIES OF CENTRAL WASHINGTON STATE COLLEGE PROSPECTIVE ELEMENTARY AND SECONDARY TEACHERS OF MATHEMATICS.

ERIC Educational Resources Information Center

MARTIN, BERNARD LOYAL

INVESTIGATED WAS THE EXTENT TO WHICH STUDENTS COMPLETING PLANNED MATHEMATICS EDUCATION PROGRAMS (1) WERE PROFICIENT IN SPATIAL VISUALIZATION ABILITIES, AND (2) HAD DEVELOPED MATHEMATICAL UNDERSTANDINGS. THE EFFECTS OF THE MATHEMATICS CURRICULA UPON SUCH DEVELOPMENT WERE INVESTIGATED BY COMPARING GROUP MEAN TEST SCORES OF PROSPECTIVE ELEMENTARY AND…
Teaching and Learning K-8 Mathematics and Science through Inquiry: Program Reviews and Recommendations.

ERIC Educational Resources Information Center

Linn, Marcia C.; Kessel, Cathy; Lee, Kristen; Levenson, Janet; Spitulnik, Michelle; Slotta, James D.

This report offers guidance for those shaping policy and designing elementary and middle school science and mathematics courses that prepare students to be lifelong users of scientific and mathematical ideas. We have reviewed programs designed to improve elementary and middle school students' understanding of science and mathematics by…
Making the Grade in Mathematics: Elementary School Mathematics in the United States, Taiwan, and Japan.

ERIC Educational Resources Information Center

Stevenson, Harold W.; And Others

Over the last decade, it has been reported that American students lag behind their Asian counterparts as early as the first grade. This study investigated variables influencing elementary school students' mathematics achievement in Japan, Taiwan, and America. Children's mathematics achievement and cognitive abilities were tested. Children,…
Reading and Reflecting: Elementary Preservice Teachers' Conceptions about Teaching Mathematics for Equity

ERIC Educational Resources Information Center

Jackson, Christa; Jong, Cindy

2017-01-01

Teaching mathematics for equity is critical because it provides opportunities for all students, especially those who have been traditionally marginalised, to learn mathematics that is rigorous and relevant to their lives. This article reports on our work, as mathematics teacher educators, on exposing and engaging 60 elementary preservice teachers…
The Influence of Building Block Play on Mathematics Achievement and Logical and Divergent Thinking in Italian Primary School Mathematics Classes

ERIC Educational Resources Information Center

Pirrone, Concetta; Tienken, Christopher H.; Pagano, Tatiana; Di Nuovo, Santo

2018-01-01

In an experimental study to explain the effect of structured Building Block Play with LEGO™ bricks on 6-year-old student mathematics achievement and in the areas of logical thinking, divergent thinking, nonverbal reasoning, and mental imagery, students in the experimental group scored significantly higher (p = 0.05) in mathematics achievement and…
Profile of mathematical reasoning ability of 8th grade students seen from communicational ability, basic skills, connection, and logical thinking

NASA Astrophysics Data System (ADS)

Sumarsih; Budiyono; Indriati, D.

2018-04-01

This research aims to understand the students’ weaknesses in mathematical reasoning ability in junior secondary school. A set of multiple choice tests were used to measure this ability involve components mathematical communication, basic skills, connection, and logical thinking. A total of 259 respondents were determined by stratified cluster random sampling. Data were analyzed using one-way Anova test with Fobs = 109.5760 and F = 3.0000. The results show that students’ ability from schools with high National Exam in mathematics category was the best and followed by medium and low category. Mathematical connection is the most difficult component performed by students. In addition, most students also have difficulty in expressing ideas and developing logical arguments.
Executive functioning predicts reading, mathematics, and theory of mind during the elementary years.

PubMed

Cantin, Rachelle H; Gnaedinger, Emily K; Gallaway, Kristin C; Hesson-McInnis, Matthew S; Hund, Alycia M

2016-06-01

The goal of this study was to specify how executive functioning components predict reading, mathematics, and theory of mind performance during the elementary years. A sample of 93 7- to 10-year-old children completed measures of working memory, inhibition, flexibility, reading, mathematics, and theory of mind. Path analysis revealed that all three executive functioning components (working memory, inhibition, and flexibility) mediated age differences in reading comprehension, whereas age predicted mathematics and theory of mind directly. In addition, reading mediated the influence of executive functioning components on mathematics and theory of mind, except that flexibility also predicted mathematics directly. These findings provide important details about the development of executive functioning, reading, mathematics, and theory of mind during the elementary years. Copyright © 2016 Elsevier Inc. All rights reserved.
Towards An Engineering Discipline of Computational Security

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

Mili, Ali; Sheldon, Frederick T; Jilani, Lamia Labed

2007-01-01

George Boole ushered the era of modern logic by arguing that logical reasoning does not fall in the realm of philosophy, as it was considered up to his time, but in the realm of mathematics. As such, logical propositions and logical arguments are modeled using algebraic structures. Likewise, we submit that security attributes must be modeled as formal mathematical propositions that are subject to mathematical analysis. In this paper, we approach this problem by attempting to model security attributes in a refinement-like framework that has traditionally been used to represent reliability and safety claims. Keywords: Computable security attributes, survivability, integrity,more » dependability, reliability, safety, security, verification, testing, fault tolerance.« less
Mathematics Anxiety and Learning Styles: What Is the Relationship in Elementary Preservice Teachers?

ERIC Educational Resources Information Center

Sloan, Tina; Daane, C. J.; Giesen, Judy

2002-01-01

Investigates the relationship between elementary preservice teachers' (n=72) mathematics anxiety levels and learning style preferences. Findings reveal a low but significant positive correlation between mathematics anxiety and a global (right-brain dominant) learning style. (Author/MM)
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…
Elementary Mathematics Teachers' Beliefs and Practices: Understanding the Influence of Teaching in a STEAM Setting

ERIC Educational Resources Information Center

Negreiros, Melissa

2017-01-01

Many elementary mathematics teachers hold beliefs about the teaching and learning of mathematics and enact practices that are not aligned with the recommendations of reform efforts in the field of mathematics education (Stigler & Hiebert, 2009). For standards-based reform to gain any significant success, many teachers will have to alter the…
Structure and Typical Profiles of Elementary Teacher Students' View of Mathematics

ERIC Educational Resources Information Center

Hannula, Markku S.; Kaasila, Raimo; Laine, Anu; Pehkonen, Erkki

2005-01-01

The elementary school teachers' view of mathematics is important because it will influence the way they will teach mathematics. Based on a survey study in three Finnish universities we explored the structure of student teachers view of mathematics and also the different belief profiles that they had. The core of student teachers' view consisted of…
Equity in Standards-Based Elementary Mathematics Classrooms. Weaving Gender Equity into Math Reform.

ERIC Educational Resources Information Center

Perez, Christina

This article discusses the issue of equity in standards-based elementary mathematics classrooms. It is argued that while some of the gaps in mathematics achievement have slowly diminished (e.g., differences in mathematics grades and participation rates between girls and boys in K-12 education have decreased), others remain intractable. Other…
The Way Adults with Orientation to Mathematics Teaching Cope with the Solution of Everyday Real-World Problems

ERIC Educational Resources Information Center

Gazit, Avikam; Patkin, Dorit

2012-01-01

The article aims to check the way adults, "some who are" practicing mathematics teachers at elementary school, "some who are" academicians making a career change to mathematics teachers at junior high school and the "rest who are" pre-service mathematics teachers at elementary school, cope with the solution of…
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…
Investigating Alignment between Elementary Mathematics Teacher Education and Graduates' Teaching of Mathematics for Conceptual Understanding

ERIC Educational Resources Information Center

Jansen, Amanda; Berk, Dawn; Meikle, Erin

2017-01-01

In this article, Amanda Jansen, Dawn Berk, and Erin Meikle investigate the impact of mathematics teacher education on teaching practices. In their study they interviewed six first-year teachers who graduated from the same elementary teacher education program and who were oriented toward teaching mathematics conceptually. They observed each teacher…
Using Representations, Decomposition, and Approximations of Practices to Support Prospective Elementary Mathematics Teachers' Practice of Organizing Discussions

ERIC Educational Resources Information Center

Tyminski, Andrew M.; Zambak, V. Serbay; Drake, Corey; Land, Tonia J.

2014-01-01

This paper examines a series of instructional activities that provide prospective elementary teachers with an opportunity to engage in one of the more difficult practices to learn within mathematics teaching--organizing a mathematical discussion. Within a mathematics methods course, representations and decomposition of practice built from the Five…
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…

How Wide Is a Squid Eye? Integrating Mathematics into Public Library Programs for the Elementary Grades

ERIC Educational Resources Information Center

Kliman, Marlene; Jaumot-Pascual, Nuria; Martin, Valerie

2013-01-01

Although public library programs for the elementary grades offer explorations in a wide range of topics in which mathematics plays a role, are all too rare: Mathematics offerings are typically limited to homework help. Participating in out-of-school activities that embed mathematics in authentic ways bolsters children's skill development,…
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…
Combining fuzzy mathematics with fuzzy logic to solve business management problems

NASA Astrophysics Data System (ADS)

Vrba, Joseph A.

1993-12-01

Fuzzy logic technology has been applied to control problems with great success. Because of this, many observers fell that fuzzy logic is applicable only in the control arena. However, business management problems almost never deal with crisp values. Fuzzy systems technology--a combination of fuzzy logic, fuzzy mathematics and a graphical user interface--is a natural fit for developing software to assist in typical business activities such as planning, modeling and estimating. This presentation discusses how fuzzy logic systems can be extended through the application of fuzzy mathematics and the use of a graphical user interface to make the information contained in fuzzy numbers accessible to business managers. As demonstrated through examples from actual deployed systems, this fuzzy systems technology has been employed successfully to provide solutions to the complex real-world problems found in the business environment.
Embracing Curriculum Compacting: Teacher Candidates Supporting Differentiated Instruction in Elementary Mathematics

ERIC Educational Resources Information Center

Livers, Stefanie D.; Paxton, Minda; O'Grady, Nicole; Tontillo, Michael

2018-01-01

This article discusses a collaborative effort to implement curriculum compacting activities with elementary students in conjunction with developing teacher candidates' abilities to teach mathematics. This endeavor included a partnership between a university and a local elementary school. All stakeholders benefited from this project: The elementary…
Professional Learning for Cultural Mathematics in Papua New Guinea's Elementary Schools

ERIC Educational Resources Information Center

Owens, Kay; Edmonds-Wathen, Cris; Kravia, Geori; Sakopa, Priscilla

2014-01-01

A design of principles for teacher professional learning was developed to improve the teaching of "Cultural Mathematics" in elementary schools in Papua New Guinea. The design's appropriateness for PNG elementary schools is the focus of the research implemented through week-long workshops using technology enhancement. Implementation has…
Integrative Pre-Service Elementary Teacher Training: The Role of Interdisciplinary Collaborative Mathematics

ERIC Educational Resources Information Center

Chiatula, Victoria Oliaku

2015-01-01

This primer summarizes interdisciplinary collaborative mathematics as an integrative approach to train pre-service elementary teachers to teach math utilizing Junior Achievement USA (JA) educational programs within an elementary Math Methods course. The primer provides a JA historical background/program overview, summarizes the interdisciplinary…
Formal logic rewrite system bachelor in teaching mathematical informatics

NASA Astrophysics Data System (ADS)

Habiballa, Hashim; Jendryscik, Radek

2017-07-01

The article presents capabilities of the formal rewrite logic system - Bachelor - for teaching theoretical computer science (mathematical informatics). The system Bachelor enables constructivist approach to teaching and therefore it may enhance the learning process in hard informatics essential disciplines. It brings not only detailed description of formal rewrite process but also it can demonstrate algorithmical principles for logic formulae manipulations.
Addressing Priorities for Elementary School Mathematics

ERIC Educational Resources Information Center

Venenciano, Linda; Dougherty, Barbara

2014-01-01

Findings from international assessments present an opportunity to reconsider mathematics education across the grades. If concepts taught in elementary grades lay the foundation for continued study, then children's introduction to school mathematics deserves particular attention. We consider Davydov's theory (1966), which sequences…
Preservice Teachers' Perceptions about Teaching Mathematics through Music

ERIC Educational Resources Information Center

An, Song A.; Tillman, Daniel; Shaheen, Andrea; Boren, Rachel

2014-01-01

This study examined preservice teachers' perceptions about teaching elementary level mathematics lessons integrated with music. It also sought to determine how preservice teachers would strategize the integration of music activities when introducing elementary level mathematics lessons. The participants, 53 undergraduate preservice teachers at a…
Cortical Bases of Elementary Deductive Reasoning: Inference, Memory, and Metadeduction

ERIC Educational Resources Information Center

Reverberi, Carlo; Shallice, Tim; D'Agostini, Serena; Skrap, Miran; Bonatti, Luca L.

2009-01-01

Elementary deduction is the ability of unreflectively drawing conclusions from explicit or implicit premises, on the basis of their logical forms. This ability is involved in many aspects of human cognition and interactions. To date, limited evidence exists on its cortical bases. We propose a model of elementary deduction in which logical…
Health Clinic Environments in Georgia Elementary Schools

ERIC Educational Resources Information Center

Simpson, Susan Rogers

2005-01-01

Schools seem to be the logical place to serve the health needs of students, since children spend a majority of their time there. Design standards were not available for health clinics in Georgia elementary schools; therefore, this study examined key characteristics of an elementary school clinic in order to determine the importance of each design…
Contributions from Sociology of Science to Mathematics Education in Brazil: Logic as a System of Beliefs

ERIC Educational Resources Information Center

Novaes de Andrade, Thales Haddad; Vilela, Denise Silva

2013-01-01

In Brazil, mathematics education was associated with Jean Piaget's theory. Scholars in the field of education appropriated Piaget's work in different ways, but usually emphasized logical aspects of thought, which probably lead to an expansion of mathematics education influenced by psychology. This study attempts to extend the range of…
Manipulative Use and Elementary School Students' Mathematics Learning

ERIC Educational Resources Information Center

Uribe-Flórez, Lida J.; Wilkins, Jesse L. M.

2017-01-01

Using data from the Early Childhood Longitudinal Study (ECLS) 1998/1999, we examine the relationship between elementary students' (K-5) manipulative use and mathematics learning. Using a cross-sectional correlational analysis, we found no relationship between manipulative use and student mathematics "achievement". However, using a…
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…
Examining Preservice Elementary Mathematics Teachers' Understandings about Irrational Numbers

ERIC Educational Resources Information Center

Guven, Bulent; Cekmez, Erdem; Karatas, Ilhan

2011-01-01

The purpose of this study is to provide an account of preservice elementary mathematics teachers' understandings about irrational numbers. Three dimensions of preservice mathematics teachers' understandings are examined: defining rational and irrational numbers, placing rational and irrational numbers on the number line, and operations with…
Prospective Elementary Teachers' Beliefs about Collaborative Problem Solving and Dialogue in Mathematics

ERIC Educational Resources Information Center

Xenofontos, Constantinos; Kyriakou, Artemis

2017-01-01

This study is concerned with prospective elementary teachers' beliefs about collaborative problem solving and dialogue in mathematics classrooms. Participants (n = 16) attended an undergraduate module titled "Problem Solving in Primary Mathematics", which was specifically designed to provide them with opportunities in collaborative…
"Hence"--An Iconoclastic Study of Logic, Language and Argumentation.

ERIC Educational Resources Information Center

Van der Auwera, Johan

An analysis of the role of the word "hence" and its near-synonyms examines the relationship between logic as a science, as a natural language, and as argumentation. The analysis is done in the context of elementary propositional logic. The first section is a limited discussion of the standard logician's treatment relegating "hence" to the realm of…
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…
Investigating Mathematics Self-Efficacy Beliefs of Elementary Pre-Service Teachers in a Reform-Based Mathematics Methods Course

ERIC Educational Resources Information Center

Setra, Abdelghani

2017-01-01

For the last thirty years research has unfailingly shown that teacher efficacy has a positive impact on student outcomes, making teacher efficacy an critical element in quality mathematics instruction. The purpose of this study is to examine the impact of a math methods course on the mathematics teaching efficacy beliefs of elementary pre-service…
Recent Trends in Japanese Mathematics Textbooks for Elementary Grades: Supporting Teachers to Teach Mathematics through Problem Solving

ERIC Educational Resources Information Center

Takahashi, Akihiko

2016-01-01

Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over…

Does Math Achievement "h'APP'en" when iPads and Game-Based Learning Are Incorporated into Fifth-Grade Mathematics Instruction?

ERIC Educational Resources Information Center

Carr, Jennie M.

2012-01-01

After 10 years of No Child Left Behind standards-focused education, mathematics scores have improved only marginally for elementary-aged students. Students who developed a solid conceptual mathematics foundation at the elementary level succeeded later in higher-level mathematics courses; thus, educators have sought ways to increase mathematics…
MIPS to the "4", Mathematics Improves Promotes Students. A Program of Mathematics for the Elementary Math Laboratory. Limited Edition.

ERIC Educational Resources Information Center

Wichita Unified School District 259, KS.

This book is a guide for the reinforcement of the elementary mathematics laboratory program. It uses a hands-on and activity approach with maximum involvement of the students. Reinforcement strategies for the first three phases (concrete, semiconcrete, and semiabstract) of each mathematics concept are suggested. Also included are specific job…
The Effect of Instruction through Mathematical Modelling on Modelling Skills of Prospective Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Ciltas, Alper; Isik, Ahmet

2013-01-01

The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…
Strategies for Teaching Elementary and Junior High Students.

ERIC Educational Resources Information Center

Consuegra, Gerard F.

1980-01-01

Discusses the applications of Piaget's theory of cognitive development to elementary and junior high school science teaching. Topics include planning concrete experiences, inductive and hypothetical deductive reasoning, measurement concepts, combinatorial logic, scientific experimentation and reflexive thinking. (SA)
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…
Collaborating to Improve Inquiry-Based Teaching in Elementary Science and Mathematics Methods Courses

ERIC Educational Resources Information Center

Magee, Paula A.; Flessner, Ryan

2012-01-01

This study examines the effect of promoting inquiry-based teaching (IBT) through collaboration between a science methods course and mathematics methods course in an elementary teacher education program. During the collaboration, preservice elementary teacher (PST) candidates experienced 3 different types of inquiry as a way to foster increased…
Preservice Teachers' Knowledge of Interdisciplinary Pedagogy: The Case of Elementary Mathematics-Science Integrated Lessons

ERIC Educational Resources Information Center

An, Song A.

2017-01-01

The purpose of the study is to explore how elementary preservice teachers' mathematics-science integrated teaching strategies changed as a result of participating in exemplary interdisciplinary activities with multiple themes across school curricula. The participating elementary preservice teachers (n = 28) were recruited for this study from the…
The Emphasis of Inquiry Instructional Strategies: Impact on Preservice Teachers' Mathematics Efficacy

ERIC Educational Resources Information Center

Althauser, Krista L.

2018-01-01

Using a Mixed Methods approach, this study investigated changes in levels of self-efficacy among elementary preservice teachers following a semester course on teaching elementary students' mathematics. Participants in this study included 347 preservice elementary teachers at a mid-size regional university who had just completed an elementary…
Elementary Teachers' Thinking about a Good Mathematics Lesson

ERIC Educational Resources Information Center

Li, Yeping

2011-01-01

In an effort to gain a better understanding of Chinese classroom teaching culture, this study aimed to examine elementary teachers' views about a good mathematics lesson in China. Through analyzing 57 teachers' essays collected from 7 elementary schools in 2 provinces, it is found that Chinese teachers emphasized the most about students and their…
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…
Professional Development in Elementary School Mathematics

ERIC Educational Resources Information Center

Scoggins, C.

2010-01-01

This study was an investigation of mathematics instruction and professional development at a rural elementary school. The Department of Education in a southern U.S. state implemented a new curriculum in 2007 that required major changes in mathematics instruction. The problems were that teachers engaged in different levels of training and many…
Elementary Mathematics Specialists: Ensuring the Intersection of Research and Practice

ERIC Educational Resources Information Center

McGatha, Maggie B.

2017-01-01

This paper provides a historical overview of the role and impact of elementary mathematics specialists as well as current implications and opportunities for the field. Furthermore, suggestions are offered for the mathematics education field for ensuring the intersection of practice and research. [For complete proceedings, see ED581294.
Model Eliciting Activities: Fostering 21st Century Learners

ERIC Educational Resources Information Center

Stohlmann, Micah

2013-01-01

Real world mathematical modeling activities can develop needed and valuable 21st century skills. The knowledge and skills to become adept at mathematical modeling need to develop over time and students in the elementary grades should have experiences with mathematical modeling. For this to occur elementary teachers need to have positive…
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…
The Mathematics Education of Elementary Teachers: Issues and Strategies for Content Courses

ERIC Educational Resources Information Center

Hart, Lynn C., Ed.; Oesterle, Susan, Ed.; Auslander, Susan Swars, Ed.; Kajander, Ann, Ed.

2016-01-01

This book is an edited volume addressing specific issues of significance for individuals involved with the undergraduate mathematics content preparation of prospective elementary teachers (PSTs). Teaching mathematics content courses to this group of students presents unique challenges. While some PSTs enter their teacher preparation with weak…
Elementary Administrators' Mathematics Supervision and Self-Efficacy Development

ERIC Educational Resources Information Center

Johnson, Kelly M. Gomez

2017-01-01

Mathematics curriculum reform is changing the content and resources in today's elementary classrooms as well as the culture of mathematics teaching and learning. Administrators face the challenge of leading large-scale curricular change efforts with limited prior knowledge or experiences with reform curricula structures. Administrators, as the…
Elementary School Mathematics Teacher Trainees' Metacognitive Awareness Levels: Turkey Case

ERIC Educational Resources Information Center

Memnun, Dilek Sezgin; Hart, Lynn Cecilia

2012-01-01

The aim of this research is to determine the metacognitive awareness levels of elementary mathematics teacher trainees and to investigate whether their awareness differs according to gender and class level. We also investigate the relationship between the metacognitive awareness levels of trainee mathematics teacher's and their overall performance…
Improving Elementary Mathematics and Science Teaching and Learning: Lessons from a School-University Partnership

ERIC Educational Resources Information Center

Norman, Patricia J.; Nordine, Jeffrey

2016-01-01

The challenges of teaching elementary mathematics and science, particularly in urban settings, have been well documented. While evidence exists that sustained professional development in mathematics and science can promote inquiry-oriented instruction and bolster student achievement, little has been written about the particular challenges…
An Investigation of Elementary Preservice Teachers' Self-Efficacy for Teaching Mathematics

ERIC Educational Resources Information Center

Giles, Rebecca McMahon; Byrd, Kelly O.; Bendolph, Angelia

2016-01-01

Research has consistently shown that teacher efficacy is related to a variety of desirable student outcomes, thus, making teacher efficacy an important factor in high quality mathematics instruction. The purpose of this study was to determine elementary preservice teachers' self-efficacy beliefs related to teaching mathematics. Forty-one…
Scott Foresman-Addison Wesley Elementary Mathematics. What Works Clearinghouse Intervention Report. Updated

ERIC Educational Resources Information Center

What Works Clearinghouse, 2013

2013-01-01

"Scott Foresman-Addison Wesley Elementary Mathematics" is a core mathematics curriculum for students in prekindergarten through grade 6. The program aims to improve students' understanding of key math concepts through problem-solving instruction, hands-on activities, and math problems that involve reading and writing. The curriculum…

Efficacy of Two Mathematics Interventions for Enhancing Fluency with Elementary Students

ERIC Educational Resources Information Center

Mong, Michael D.; Mong, Kristi W.

2010-01-01

An alternating treatments design was used to evaluate two curriculum-based mathematics interventions designed to enhance fluency with three elementary school students. Results indicate that both the Math to Mastery (MTM) intervention and the Cover, Copy, Compare (CCC) intervention were effective at increasing mathematics fluency, as measured by…
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.
A perceptual account of symbolic reasoning

PubMed Central

Landy, David; Allen, Colin; Zednik, Carlos

2014-01-01

People can be taught to manipulate symbols according to formal mathematical and logical rules. Cognitive scientists have traditionally viewed this capacity—the capacity for symbolic reasoning—as grounded in the ability to internally represent numbers, logical relationships, and mathematical rules in an abstract, amodal fashion. We present an alternative view, portraying symbolic reasoning as a special kind of embodied reasoning in which arithmetic and logical formulae, externally represented as notations, serve as targets for powerful perceptual and sensorimotor systems. Although symbolic reasoning often conforms to abstract mathematical principles, it is typically implemented by perceptual and sensorimotor engagement with concrete environmental structures. PMID:24795662
Variability in Anxiety for Teaching Mathematics among Pre-service Elementary School Teachers Enrolled in a Mathematics Course.

ERIC Educational Resources Information Center

Levine, Gavrielle

This investigation traced changes in anxiety for teaching mathematics (ATM) among pre-service elementary school teachers (n=36) enrolled in a mathematics methods course by analyzing their weekly journal entries. Journal entries were coded for high level of ATM (ATM-high) or absence of ATM (ATM-absent) during the first class session, as well as…
Comparing the Effects of Elementary Music and Visual Arts Lessons on Standardized Mathematics Test Scores

ERIC Educational Resources Information Center

King, Molly Elizabeth

2016-01-01

The purpose of this quantitative, causal-comparative study was to compare the effect elementary music and visual arts lessons had on third through sixth grade standardized mathematics test scores. Inferential statistics were used to compare the differences between test scores of students who took in-school, elementary, music instruction during the…
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…
Beliefs about Using Technology in the Mathematics Classroom: Interviews with Pre-Service Elementary Teachers

ERIC Educational Resources Information Center

Lin, Cheng-Yao

2008-01-01

This study explored the efficacy of web-based workshops in topics in elementary school mathematics in fostering teachers' confidence and competence in using instructional technology, and thereby promoting more positive attitudes toward using computers and Internet resources in the mathematics classroom. It consisted of in-depth interviews of…
Developing the Practice of Teacher Questioning through a K-2 Elementary Mathematics Field Experience

ERIC Educational Resources Information Center

Schwartz, Catherine

2015-01-01

This article presents findings from research on a field experience designed to help elementary preservice teachers learn the practice of teacher questioning during formal and informal interviews to analyze student mathematical thinking in K-2 classrooms. The practice of teacher questioning is framed as choosing a mathematical goal, analyzing…
Early Career Elementary Mathematics Teachers' Noticing Related to Language and Language Learners

ERIC Educational Resources Information Center

Turner, Erin Elizabeth; McDuffie, Amy Roth; Sugimoto, Amanda Tori; Stoehr, Kathleen Jablon; Witters, Angela; Aguirre, Julia; Bartell, Tonya; Drake, Corey; Foote, Mary Q.

2016-01-01

There has been limited attention to early career teachers' (ECTs) understandings and practices related to language in teaching and learning mathematics. In this qualitative case study, we drew upon frameworks for teacher noticing to study the language practices of six early career elementary and middle school mathematics teachers. We describe…
Mathematics for the Elementary School, Unit 15, Addition and Linear Translations.

ERIC Educational Resources Information Center

Clark, Julia, Ed.; Myers, Donald E., Ed.

The Minnesota School Mathematics and Science Teaching (MINNEMAST) Project is characterized by its emphasis on the coordination of mathematics and science in the elementary school curriculum. Units are planned to provide children with activities in which they learn various concepts from both subject areas. Each subject is used to support and…
Scott Foresman-Addison Wesley Elementary Mathematics. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2010

2010-01-01

"Scott Foresman-Addison Wesley Elementary Mathematics" is a core curriculum for students at all ability levels in prekindergarten through grade 6. The program supports students' understanding of key math concepts and skills and covers a range of mathematical content across grades. The What Works Clearinghouse (WWC) reviewed 12 studies on…
Do Pre-Service Elementary School Teachers Still Have Mathematics Anxiety? Some Factors and Correlates

ERIC Educational Resources Information Center

Çatlioglu, Hakan; Gürbüz, Ramazan; Birgin, Osman

2014-01-01

This study aims to provide new evidence from Turkish pre-service elementary school (PES) teachers and to identify some correlations and factors associated with mathematics anxiety (MA). 480 Turkish PES teachers participated in this study. Data was collected using a "Personal Information Form," "Mathematics Anxiety Scale," and…
Coaches' and Principals' Conceptualizations of the Roles of Elementary Mathematics Coaches

ERIC Educational Resources Information Center

Salkind, Gwenanne M.

2010-01-01

Many schools employ coaches to support mathematics instruction and student learning. This research study investigated the roles of coaches from five school districts in Virginia. Participants included 125 elementary mathematics coaches and 59 principals. Results from cross-sectional surveys revealed that most coaches did not have a degree in…
Fostering Elementary Students' Mathematics Disposition through Music-Mathematics Integrated Lessons

ERIC Educational Resources Information Center

An, Song A.; Tillman, Daniel A.; Boren, Rachel; Wang, Junjun

2014-01-01

Two classes of third grade students (n = 56) from an elementary school located on the western coast of the United States participated in this research study. A pretest-posttest control group design was utilized to examine changes between two groups of participating students' in mathematics achievement and dispositions, including beliefs about…
Mentoring Mathematical Minds: An Innovative Program to Develop Math Talent

ERIC Educational Resources Information Center

Gavin, M. Katherine; Casa, Tutita M.; Adelson, Jill L.

2006-01-01

Meeting the needs of mathematically talented elementary students has always been a real challenge due to the lack of appropriate curricular resources and training for teachers. Mathematics is not generally a strength area for elementary or gifted/talented teachers; rather, their talents and interests often lie in the language arts realm. This is…
Examining Elementary School Teachers' Enactment of Mathematical Tasks and Questions

ERIC Educational Resources Information Center

Polly, Drew

2016-01-01

Researchers have linked teachers' use of mathematical tasks and questions to students' achievement in mathematics, and also have documented that the types of tasks and questions posed might change throughout the year in grades that include high-stakes tests of student achievement. This qualitative research study explored 3 elementary school…
Professional Development of Mathematics Teachers Implementing Probabilistic Simulations in Elementary School Classrooms

ERIC Educational Resources Information Center

de Oliveira Souza, Leandro; Lopes, Celi Espasandin; de Oliveira Mendonça, Luzinete

2014-01-01

The inclusion of statistics and probability in the mathematics curriculum has always generated challenges to mathematics teachers of elementary schools. This article discusses activities that promote the professional development of such teachers. We present part of a doctoral research study of 16 teachers in which we discuss two case studies of…
A Case Study of Two Groups of Elementary Prospective Teachers' Experiences in Distinct Mathematics Content Courses

ERIC Educational Resources Information Center

Auslander, Susan Swars; Smith, Stephanie Z.; Smith, Marvin E.; Hart, Lynn C.; Carothers, Jody

2016-01-01

This multiple case study examined two groups of elementary prospective teachers (n=12) completing distinct mathematics content courses. Data were collected via two belief surveys, one content knowledge assessment, and individual interviews. The findings revealed differences in specialized content knowledge and mathematical beliefs between the two…
Perceptual Preferences of Mathematically Deficient Elementary Students: Implications for Instruction.

ERIC Educational Resources Information Center

McCoy, Leah P.

Two groups of elementary school students were tested and compared on learning style perceptual preference. One group was comprised of 11 students identified as being in need of remedial instruction in mathematics. The other group consisted of eight average/above average students experiencing slight or no difficulties in mathematics. Grade levels…
Elementary-School Mathematics Instruction and Achievement of Fourth-Grade Students in Japan: Findings from the TIMSS 2007 Assessment

ERIC Educational Resources Information Center

House, J. Daniel

2009-01-01

Research findings indicate that specific instructional strategies, such as the use of real-world examples and independent learning activities, are positively related to mathematics achievement. This study was designed to investigate relationships between classroom instructional strategies and mathematics achievement of elementary-school students…

The Training of Elementary School Teachers in Mathematics in the Countries Represented in the International Commission on the Teaching of Mathematics. Bulletin, 1915, No. 39. Whole Number 666

ERIC Educational Resources Information Center

Kandel, I. L.

1915-01-01

The accompanying report deals with the mathematical training of prospective teachers in elementary schools as described in the reports submitted by the International Commission of the Teaching of Mathematics to the Fifth International Congress of Mathematicians, held at Cambridge, England, in August, 1912. A comparative study of the facts…
Preparing Tomorrow's Teachers: Are New Mexico's Education School Graduates Ready to Teach Reading and Mathematics in Elementary Classrooms?

ERIC Educational Resources Information Center

Greenberg, Julie; Jacobs, Sandi

2009-01-01

As a follow up to National Council on Teacher Quality (NCTQ's) national studies of how well elementary teachers are prepared to teach reading and mathematics, NCTQ looks at preparation in both subjects in all undergraduate teacher preparation programs in New Mexico. This analysis evaluated New Mexico's eight undergraduate elementary teacher…
Implementation of Technology in an Elementary Mathematics Lesson: The Experiences of Pre-Service Teachers at One University

ERIC Educational Resources Information Center

Herron, Julie

2010-01-01

This study examined pre-service teachers' responses to implementing technology into elementary mathematics lessons. Instructional Architect (IA) was the web-base technology used by the pre-service teachers. Four themes emerged from the data: (a) insights into technology, (b) struggles with technology, (c) access to the mathematics and (d) learning…
Student Growth in Elementary Mathematics: A Cross Level Investigation

ERIC Educational Resources Information Center

Kim, Seong Hee

2012-01-01

The primary purpose of this study is to examine the effect of knowledge for teaching mathematics and teaching practice on student mathematics achievement growth. Thirty two teachers and 299 fourth grade students in three elementary schools from one school district in urban area participated in the study. Most of them are Hispanic in origin and…
Learning without Boundaries: Developing Mobile Learning Scenarios for Elementary and Middle School Language Arts & Mathematics

ERIC Educational Resources Information Center

Evans, Michael A.; Gracanin, Denis

2009-01-01

This article provides an overview to a collaborative knowledge building project using iPod Touches in elementary and secondary language arts and mathematics classrooms, working with 4 teachers and over 80 students. The interactive technologies for embodied Learning in Reading and Mathematics (iteL*RM) project intends to facilitate student…
Who's Wrong? Tasks Fostering Understanding of Mathematical Relationships in Word Problems in Elementary Students

ERIC Educational Resources Information Center

Savard, Annie; Polotskaia, Elena

2017-01-01

Mathematical relationships are crucial elements to consider for learning mathematics. However, too often students pay more attention to the calculations to be done rather than the reasons for doing them. Relying on the relational paradigm to support elementary school students, we proposed two specially designed tasks to help students recognize and…
The Development of a Mathematics Self-Report Inventory for Turkish Elementary Students

ERIC Educational Resources Information Center

Akin, Ayça; Güzeller, Cem Oktay; Evcan, Sinem Sezer

2016-01-01

The purpose of the current study is to develop a mathematics self-report inventory (MSRI) to measure Turkish elementary students' mathematics expectancy beliefs and task values based on the expectancy-value theory of achievement motivation. In Study-1 (n = 1,315), exploratory factor analysis (EFA) and reliability analysis are used to evaluate the…
Self-Contained versus Departmentalized Settings in Urban Elementary Schools: An Analysis of Fifth-Grade Student Mathematics Performance

ERIC Educational Resources Information Center

Jack, Diamond Marie

2014-01-01

Student achievement in mathematics, particularly in urban areas, is a consistent concern in the United States. Research suggests that teachers either are under qualified or have a negative perception of themselves as mathematics teachers. Departmentalization on the elementary level is an organizational structure that may benefit urban students and…
Using Science to Promote Preservice Teacher Understanding of Problem Solving in Mathematics

ERIC Educational Resources Information Center

Tobias, Jennifer M.; Ortiz, Enrique

2007-01-01

Preservice elementary teachers need to be given the experiences of integrating mathematics with other subjects. They need to go into the classroom with the understanding that mathematics is not an isolated topic. This article describes a paper airplane activity that was presented in a class of preservice elementary education teachers to show how…
Transitioning to the Common Core State Standards for Mathematics: A Mixed Methods Study of Elementary Teachers' Experiences and Perspectives

ERIC Educational Resources Information Center

Swars, Susan Lee; Chestnutt, Cliff

2016-01-01

This mixed methods study explored elementary teachers' (n = 73) experiences with and perspectives on the recently implemented Common Core State Standards for Mathematics (CCSS-Mathematics) at a high-needs, urban school. Analysis of the survey, questionnaire, and interview data reveals the findings cluster around: familiarity with and preparation…
The Nature of Feedback Given to Elementary Student Teachers from University Supervisors after Observations of Mathematics Lessons

ERIC Educational Resources Information Center

Schwartz, Catherine; Walkowiak, Temple A.; Poling, Lisa; Richardson, Kerri; Polly, Drew

2018-01-01

This research explores the frequency and nature of mathematics-specific feedback given to elementary student teachers by university supervisors across a collection of post-lesson observation forms. Approximately one-third of the forms (n = 250) analysed from five large universities had no comments related to mathematics. Forms that did have…
Digital Fabrication as an Instructional Technology for Supporting Upper Elementary and Middle School Science and Mathematics Education

ERIC Educational Resources Information Center

Tillman, Daniel

2012-01-01

The purpose of this three-paper manuscript dissertation was to study digital fabrication as an instructional technology for supporting elementary and middle school science and mathematics education. Article one analyzed the effects of digital fabrication activities that were designed to contextualize mathematics education at a summer mathematics…
Prospective elementary teachers' conceptions of multidigit number: exemplifying a replication framework for mathematics education

NASA Astrophysics Data System (ADS)

Jacobson, Erik; Simpson, Amber

2018-04-01

Replication studies play a critical role in scientific accumulation of knowledge, yet replication studies in mathematics education are rare. In this study, the authors replicated Thanheiser's (Educational Studies in Mathematics 75:241-251, 2010) study of prospective elementary teachers' conceptions of multidigit number and examined the main claim that most elementary pre-service teachers think about digits incorrectly at least some of the time. Results indicated no statistically significant difference in the distribution of conceptions between the original and replication samples and, moreover, no statistically significant differences in the distribution of sub-conceptions among prospective teachers with the most common conception. These results suggest confidence is warranted both in the generality of the main claim and in the utility of the conceptions framework for describing prospective elementary teachers' conceptions of multidigit number. The report further contributes a framework for replication of mathematics education research adapted from the field of psychology.
Computational logic: its origins and applications.

PubMed

Paulson, Lawrence C

2018-02-01

Computational logic is the use of computers to establish facts in a logical formalism. Originating in nineteenth century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms, techniques and technologies. One strand of work follows the 'logic for computable functions (LCF) approach' pioneered by Robin Milner, where proofs can be constructed interactively or with the help of users' code (which does not compromise correctness). A refinement of LCF, called Isabelle, retains these advantages while providing flexibility in the choice of logical formalism and much stronger automation. The main application of these techniques has been to prove the correctness of hardware and software systems, but increasingly researchers have been applying them to mathematics itself.
Mathematicians and the Selection Task

ERIC Educational Resources Information Center

Inglis, Matthew; Simpson, Adrian

2004-01-01

Learning to think logically and present ideas in a logical fashion has always been considered a central part of becoming a mathematician. In this paper we compare the performance of three groups: mathematics undergraduates, mathematics staff and history undergraduates (representative of a "general population"). These groups were asked to solve…
From boring to scoring - a collaborative serious game for learning and practicing mathematical logic for computer science education

NASA Astrophysics Data System (ADS)

Schäfer, Andreas; Holz, Jan; Leonhardt, Thiemo; Schroeder, Ulrik; Brauner, Philipp; Ziefle, Martina

2013-06-01

In this study, we address the problem of low retention and high dropout rates of computer science university students in early semesters of the studies. Complex and high abstract mathematical learning materials have been identified as one reason for the dropout rate. In order to support the understanding and practicing of core mathematical concepts, we developed a game-based multitouch learning environment in which the need for a suitable learning environment for mathematical logic was combined with the ability to train cooperation and collaboration in a learning scenario. As application domain, the field of mathematical logic had been chosen. The development process was accomplished along three steps: First, ethnographic interviews were run with 12 students of computer science revealing typical problems with mathematical logic. Second, a multitouch learning environment was developed. The game consists of multiple learning and playing modes in which teams of students can collaborate or compete against each other. Finally, a twofold evaluation of the environment was carried out (user study and cognitive walk-through). Overall, the evaluation showed that the game environment was easy to use and rated as helpful: The chosen approach of a multiplayer game supporting competition, collaboration, and cooperation is perceived as motivating and "fun."
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.

PubMed

Dridi, G; Julien, R; Hliwa, M; Joachim, C

2015-08-28

The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.
Rebounding droplet-droplet collisions on superhydrophobic surfaces: from the phenomenon to droplet logic.

PubMed

Mertaniemi, Henrikki; Forchheimer, Robert; Ikkala, Olli; Ras, Robin H A

2012-11-08

When water droplets impact each other while traveling on a superhydrophobic surface, we demonstrate that they are able to rebound like billiard balls. We present elementary Boolean logic operations and a flip-flop memory based on these rebounding water droplet collisions. Furthermore, bouncing or coalescence can be easily controlled by process parameters. Thus by the controlled coalescence of reactive droplets, here using the quenching of fluorescent metal nanoclusters as a model reaction, we also demonstrate an elementary operation for programmable chemistry. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Exploring the Reasons for Using Electric Books and Technologic Pedagogical and Content Knowledge of Taiwanese Elementary Mathematics and Science Teachers

ERIC Educational Resources Information Center

Chen, Ho-Yuan; Jang, Syh-Jong

2013-01-01

This study highlights trends and features of E-books and their versatility of this tool in elementary educational settings. There has been little quantitative research employed to examine teachers' reasons for using or not using E-books. The purpose of this study was to examine elementary school mathematics and science teachers' reasons for using…
The Impacts of Mathematical Representations Developed through Webquest and Spreadsheet Activities on the Motivation of Pre-Service Elementary School Teachers

ERIC Educational Resources Information Center

Halat, Erdogan; Peker, Murat

2011-01-01

The purpose of this study was to compare the influence of instruction using WebQuest activities with the influence of an instruction using spreadsheet activities on the motivation of pre-service elementary school teachers in mathematics teaching course. There were a total of 70 pre-service elementary school teachers involved in this study. Thirty…

Use of Spreadsheet Simulations in University Chemistry Education

ERIC Educational Resources Information Center

Lim, Kieran F.

2006-01-01

Students who are strong in logical-mathematical intelligence have a natural advantage in learning and understanding chemistry, which is full of abstractions that are remote from the material world. Simulations provide more-inclusive learning activities for students who are weak in logical-mathematical intelligence. A second advantage of using…
One-Year Integrated Mathematics and Mathematics Methods Course for Prospective Elementary School Teachers.

ERIC Educational Resources Information Center

Springer, George

This guide describes the content of a proposed mathematics course for prospective elementary school teachers. It is the result of a two-year study at Indiana University in which three existing courses were integrated and coordinated. For each unit of instruction, there are (1) remarks for motivation of study, (2) remarks on methods of teaching,…
Development and Evaluation of a Case-Based Digital Learning Tool about Children's Mathematical Thinking for Elementary School Teachers (L-TEST)

ERIC Educational Resources Information Center

Olkun, Sinan; Altun, Arif; Deryakulu, Deniz

2009-01-01

It is important for teachers of mathematics to know how pupils react to certain mathematical situations and what these reactions imply, in order to design more effective instructional environments based on their learning needs. This study reports the development processes of a digital learning tool (Learning Tool for Elementary School Teachers…
Investigation of Prospective Primary Mathematics Teachers' Perceptions and Images for Quadrilaterals

ERIC Educational Resources Information Center

Turnuklu, Elif; Gundogdu Alayli, Funda; Akkas, Elif Nur

2013-01-01

The object of this study was to show how prospective elementary mathematics teachers define and classify the quadrilaterals and to find out their images. This research was a qualitative study. It was conducted with 36 prospective elementary mathematics teachers studying at 3rd and 4th years in an educational faculty. The data were collected by…
Nurturing Mathematical Promise in a Regular Elementary Classroom: Exploring the Role of the Teacher and Classroom Environment

ERIC Educational Resources Information Center

Dimitriadis, Christos

2016-01-01

This article presents findings from a case study of an in-classroom program based on ability grouping for Year 2 (ages 6-7) primary (elementary) children identified as high ability in mathematics. The study examined the role of classroom setting, classroom environment, and teacher's approach in realizing and developing mathematical promise. The…
Teaching Early Mathematics with PLATO[R] Software: An Overview of the New PLATO Elementary Mathematics Curricula and How To Use Them. Technical Paper.

ERIC Educational Resources Information Center

Quinn, Bill; Foshay, Rob; Morris, Barbara

The "PLATO[R] Math Expeditions" and "PLATO[R] Projects for the Real World" curricula are designed to implement effective, research-based instructional practices. "Math Expeditions" is designed to give elementary grade users the mathematics skills and practice needed to solve real-life problems. Across the eight…
Assessment of Training Programs for Elementary Mathematics Teachers on Developed Curricula and Attitudes towards Teaching in Najran-Saudi Arabia

ERIC Educational Resources Information Center

Aly, Hassan Shawky; Abdulhakeem, Hassan Daker

2016-01-01

This study aimed at assessing the training programs for Mathematics teachers at elementary stage on developed Curricula and attitudes toward teaching at Najran educational administration in Saudi Arabia. To achieve this objective, two instruments were developed, one of them measures the opinions of Mathematics teachers about the training programs…
Philosophic Heuristic Instruction (PHI)--III.

ERIC Educational Resources Information Center

Coole, Walter A.

This publication contains a course outline, syllabus, and self-study units finished and partly tested in the Open Classroom, an auto-tutorial learning laboratory at Skagit Valley College (Washington). This self-contained course in elementary formal logic is designed for use in conjunction with Kalish and Montague's "Logic--Techniques of…
Rule-following as an Anticipatory Act: Interaction in Second Person and an Internal Measurement Model of Dialogue

NASA Astrophysics Data System (ADS)

Takahashi, Tatsuji; Gunji, Yukio-Pegio

2008-10-01

We pursue anticipation in second person or normative anticipation. As the first step, we make the three concepts second person, internal measurement and asynchroneity clearer by introducing the velocity of logic νl and the velocity of communication νc, in the context of social communication. After proving anticipatory nature of rule-following or language use in general via Kripke's "rule-following paradox," we present a mathematical model expressing the internality essential to second person, taking advantage of equivalences and differences in the formal language theory. As a consequence, we show some advantages of negatively considered concepts and arguments by concretizing them into an elementary and explicit formal model. The time development of the model shows a self-organizing property which never results if we adopt a third person stance.
Primary students' conceptions of living things

NASA Astrophysics Data System (ADS)

Legaspi, Britt Anne

Elementary school teachers are pressed for time throughout the instructional day to teach all curricular areas as expected by states and districts because of the current focus on reading and mathematics. Thus, foundational science concepts may be overlooked. For example, students' understandings of living and nonliving things may be overlooked by teachers, yet is useful in understanding the nature of living things. In this qualitative study, K-3 grade students were asked to sort objects as either living or nonliving and to give rationales for their choices. It was found that K-3 students readily used physical characteristics, such as having body parts, and physical abilities, such as being able to move, as criteria for living things. Students in grades 1 through 3 were able to articulate their reasons with more adult-like logic based on Jean Piaget' s research on developmental stages.
Computational logic: its origins and applications

PubMed Central

2018-01-01

Computational logic is the use of computers to establish facts in a logical formalism. Originating in nineteenth century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms, techniques and technologies. One strand of work follows the ‘logic for computable functions (LCF) approach’ pioneered by Robin Milner, where proofs can be constructed interactively or with the help of users’ code (which does not compromise correctness). A refinement of LCF, called Isabelle, retains these advantages while providing flexibility in the choice of logical formalism and much stronger automation. The main application of these techniques has been to prove the correctness of hardware and software systems, but increasingly researchers have been applying them to mathematics itself. PMID:29507522
The way adults with orientation to mathematics teaching cope with the solution of everyday real-world problems

NASA Astrophysics Data System (ADS)

Gazit, Avikam; Patkin, Dorit

2012-03-01

The article aims to check the way adults, some who are practicing mathematics teachers at elementary school, some who are academicians making a career change to mathematics teachers at junior high school and the rest who are pre-service mathematics teachers at elementary school, cope with the solution of everyday real-world problems of buying and selling. The findings show that even adults with mathematical background tend to make mistakes in solving everyday real-world problems. Only about 70% of the adults who have an orientation to mathematics solved the sample problem correctly. The lowest percentage of success was demonstrated by the academicians making a career change to junior high school mathematics teachers whereas the highest percentage of success was manifested by pre-service elementary school mathematics teachers. Moreover, the findings illustrate that life experience of the practicing mathematics teachers and, mainly, of the academicians making a career change, who were older than the pre-service teachers, did not facilitate the solution of such a real-world problem. Perhaps the reason resides in the process of mathematics teaching at school, which does not put an emphasis on the solution of everyday real-world problems.
Some Observations of Mathematics Teaching in Japanese Elementary and Junior High Schools.

ERIC Educational Resources Information Center

Becker, Jerry P.; And Others

1990-01-01

Discussed is the educational system in the nation of Japan with a special emphasis on elementary mathematics instruction. The amount of time spent on various subjects, observations in Japanese classrooms, Juku, and the use of technology are discussed. (CW)
Mathematical Induction: Deductive Logic Perspective

ERIC Educational Resources Information Center

Dogan, Hamide

2016-01-01

Many studies mentioned the deductive nature of Mathematical Induction (MI) proofs but almost all fell short in explaining its potential role in the formation of the misconceptions reported in the literature. This paper is the first of its kind looking at the misconceptions from the perspective of the abstract of the deductive logic from one's…
Science-Technology Coupling: The Case of Mathematical Logic and Computer Science.

ERIC Educational Resources Information Center

Wagner-Dobler, Roland

1997-01-01

In the history of science, there have often been periods of sudden rapprochements between pure science and technology-oriented branches of science. Mathematical logic as pure science and computer science as technology-oriented science have experienced such a rapprochement, which is studied in this article in a bibliometric manner. (Author)
Brain Activity Associated with Logical Inferences in Geometry: Focusing on Students with Different Levels of Ability

ERIC Educational Resources Information Center

Waisman, Ilana; Leikin, Mark; Leikin, Roza

2016-01-01

Mathematical processing associated with solving short geometry problems requiring logical inference was examined among students who differ in their levels of general giftedness (G) and excellence in mathematics (EM) using ERP research methodology. Sixty-seven male adolescents formed four major research groups designed according to various…
Some Implications of a Behavioral Analysis of Verbal Behavior for Logic and Mathematics

PubMed Central

2013-01-01

The evident power and utility of the formal models of logic and mathematics pose a puzzle: Although such models are instances of verbal behavior, they are also essentialistic. But behavioral terms, and indeed all products of selection contingencies, are intrinsically variable and in this respect appear to be incommensurate with essentialism. A distinctive feature of verbal contingencies resolves this puzzle: The control of behavior by the nonverbal environment is often mediated by the verbal behavior of others, and behavior under control of verbal stimuli is blind to the intrinsic variability of the stimulating environment. Thus, words and sentences serve as filters of variability and thereby facilitate essentialistic model building and the formal structures of logic, mathematics, and science. Autoclitic frames, verbal chains interrupted by interchangeable variable terms, are ubiquitous in verbal behavior. Variable terms can be substituted in such frames almost without limit, a feature fundamental to formal models. Consequently, our fluency with autoclitic frames fosters generalization to formal models, which in turn permit deduction and other kinds of logical and mathematical inference. PMID:28018038
The Influence of Theoretical Mathematical Foundations on Teaching and Learning: A Case Study of Whole Numbers in Elementary School

ERIC Educational Resources Information Center

Chambris, Christine

2018-01-01

This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform--which was eventually itself replaced in the longer term--provides some keys to understanding the influence of mathematical theories on…
The Effect of Peer-Assessment on the Attitudes of Pre-Service Elementary and Middle School Teachers about Writing and Assessing Mathematics

ERIC Educational Resources Information Center

Beaver, Cheryl; Beaver, Scott

2011-01-01

Through a study conducted in a core Foundations of Mathematics course at Western Oregon University, the authors investigate the thesis that peer-grading helps future elementary and middle school teachers improve their own attitudes about writing and assessing mathematics. Study participants were asked to provide scale responses to a series of…
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…

Love It, Like It, or Leave It--Elementary Preservice Teachers' Field-Based Perspectives toward the Integration of Literature in Mathematics

ERIC Educational Resources Information Center

Nesmith, Suzanne M.; Purdum-Cassidy, Barbara; Cooper, Sandi; Rogers, Rachelle D.

2017-01-01

Integrating literature in mathematics is a powerful strategy used by many teachers to meet the reformative goals outlined by the National Council of Teachers of Mathematics. This article reports a teacher education study in which 15 elementary preservice teachers engaged in a task that challenged them to link the pedagogical strategy of…
Advanced Mathematical Study and the Development of Conditional Reasoning Skills

PubMed Central

Attridge, Nina; Inglis, Matthew

2013-01-01

Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general ‘thinking skills’. Today, this argument, known as the ‘Theory of Formal Discipline’ is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by tracking the development of conditional reasoning behavior in students studying post-compulsory mathematics compared to post-compulsory English literature. In line with the Theory of Formal Discipline, the mathematics students did develop their conditional reasoning to a greater extent than the literature students, despite them having received no explicit tuition in conditional logic. However, this development appeared to be towards the so-called defective conditional understanding, rather than the logically normative material conditional understanding. We conclude by arguing that Plato may have been correct to claim that studying advanced mathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought. PMID:23869241
Elementary Students' Mathematical Explanations and Attention to Audience with Screencasts

ERIC Educational Resources Information Center

Soto, Melissa

2015-01-01

Reasoning and constructing mathematical explanations for an audience have become increasingly important activities in elementary classrooms with the implementation of reform-oriented curriculum and standards. Mobile learning tools and applications, such as screencasts, allow students to generate multimedia presentations of their solution…
The Evaluation of Project SEED, 1990-91.

ERIC Educational Resources Information Center

Webster, William J.; Chadbourn, Russell A.

Project Special Elementary Education for the Disadvantaged (SEED) is a national program in which professional mathematicians and scientists from universities and industry teach abstract, conceptually oriented mathematics to full-sized classes of elementary school children as a supplement to their regular mathematics instruction. In the Dallas…
Project Logic Handbook: Computer Literacy through BASIC.

ERIC Educational Resources Information Center

Huber, Leonard; And Others

This handbook for teachers offers guidance on introducing computer literacy into elementary and secondary classrooms. It includes a list of computer concepts exemplified by each step in learning to write programs in BASIC Programming Language and the objectives for the elementary and secondary activities; suggestions for using computers in…
Elementary ELA/Social Studies Integration: Challenges and Limitations

ERIC Educational Resources Information Center

Heafner, Tina L.

2018-01-01

Adding instructional time and holding teachers accountable for teaching social studies are touted as practical, logical steps toward reforming the age-old tradition of marginalization. This qualitative case study of an urban elementary school, examines how nine teachers and one administrator enacted district reforms that added 45 minutes to the…
Mathematical Logic in the Human Brain: Semantics

PubMed Central

Friedrich, Roland M.; Friederici, Angela D.

2013-01-01

As a higher cognitive function in humans, mathematics is supported by parietal and prefrontal brain regions. Here, we give an integrative account of the role of the different brain systems in processing the semantics of mathematical logic from the perspective of macroscopic polysynaptic networks. By comparing algebraic and arithmetic expressions of identical underlying structure, we show how the different subparts of a fronto-parietal network are modulated by the semantic domain, over which the mathematical formulae are interpreted. Within this network, the prefrontal cortex represents a system that hosts three major components, namely, control, arithmetic-logic, and short-term memory. This prefrontal system operates on data fed to it by two other systems: a premotor-parietal top-down system that updates and transforms (external) data into an internal format, and a hippocampal bottom-up system that either detects novel information or serves as an access device to memory for previously acquired knowledge. PMID:23301101
Mathematical logic in the human brain: semantics.

PubMed

Friedrich, Roland M; Friederici, Angela D

2013-01-01

As a higher cognitive function in humans, mathematics is supported by parietal and prefrontal brain regions. Here, we give an integrative account of the role of the different brain systems in processing the semantics of mathematical logic from the perspective of macroscopic polysynaptic networks. By comparing algebraic and arithmetic expressions of identical underlying structure, we show how the different subparts of a fronto-parietal network are modulated by the semantic domain, over which the mathematical formulae are interpreted. Within this network, the prefrontal cortex represents a system that hosts three major components, namely, control, arithmetic-logic, and short-term memory. This prefrontal system operates on data fed to it by two other systems: a premotor-parietal top-down system that updates and transforms (external) data into an internal format, and a hippocampal bottom-up system that either detects novel information or serves as an access device to memory for previously acquired knowledge.
A Mathematics Software Database Update.

ERIC Educational Resources Information Center

Cunningham, R. S.; Smith, David A.

1987-01-01

Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)
Music Activities as a Meaningful Context for Teaching Elementary Students Mathematics: A Quasi-Experiment Time Series Design with Random Assigned Control Group

ERIC Educational Resources Information Center

An, Song A.; Tillman, Daniel A.

2015-01-01

The purpose of the current research was to examine the effects of a sequence of classroom activities that integrated mathematics content with music elements aimed at providing teachers an alternative approach for teaching mathematics. Two classes of third grade students (n = 56) from an elementary school in the west coast of the United States…
Dynamic Assessment, Potential Giftedness and Mathematics Achievement in Elementary School

ERIC Educational Resources Information Center

Popa, Nicoleta Laura; Pauc, Ramona Loredana

2015-01-01

Dynamic assessment is currently discussed in educational literature as one of the most promising practices in stimulating learning among various groups of students, including gifted and potentially gifted students. The present study investigates effects of dynamic assessment on mathematics achievement among elementary school students, with…
Orchestrating Mathematical Discourse: Affordances and Hindrances for Novice Elementary Teachers

ERIC Educational Resources Information Center

Lee, Carrie Wilkerson

2016-01-01

The purpose of this study was to examine the mathematical discourse within novice elementary teachers' classrooms. More specifically, this study employed a sequential, explanatory mixed methods design to first quantitatively analyze the relationship between teachers' discourse practices and teacher attributes and school context. Next, a…
Indigenous Languages and Mathematics in Elementary Schools

ERIC Educational Resources Information Center

Edmonds-Wathen, Cris; Owens, Kay; Sakopa, Priscilla; Bino, Vagi

2014-01-01

Indigenous languages are used for instruction in elementary schools in Papua New Guinea, but teachers have generally received their own education in English. The challenges of identifying terminology to use in mathematics include many-to-one correspondences between English and the vernacular languages, and different grammatical structures.…
Striking the Right Balance: Students' Motivation and Affect in Elementary Mathematics

ERIC Educational Resources Information Center

Schweinle, Amy; Meyer, Debra K.; Turner, Julianne C.

2006-01-01

The authors explored the relationship between motivation and affect in upper elementary mathematics classes from the perspective of flow theory. They also investigated the relationship between students' motivation and teachers' instructional practices. Students' reported classroom experiences formed 4 factors--Social Affect, Personal Affect,…
Mathematical intelligence developed in math learning with classical backsound music of the classical era

NASA Astrophysics Data System (ADS)

Karlimah

2018-05-01

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

ERIC Educational Resources Information Center

Ahl, David H.

This combination teacher's guide and student workbook serves as a companion volume to 101 BASIC Computer Games (EM 011 681). It presents ideas, exercises and supplemental projects which will aid the teaching and learning of a wide variety of academic subjects in grades 7 through 12, although the emphasis is upon mathematics and logic. In addition,…
Possibility of Identifying the Logical-Mathematical Giftedness with Students of Lower Primary School Grades through Evaluations

ERIC Educational Resources Information Center

Milic, Sanja; Simeunovic, Vlado

2017-01-01

The objective of this work is examination of co-ordinance amongst assessments of logical-mathematical giftedness with young primary school students, made by four groups of evaluators: teachers, parents, coevals and self-evaluators. Teachers of 11 primary schools selected at the area of Republic Srpska were assigned to follow Instructions for…
Identification of Prospective Science Teachers' Mathematical-Logical Structures in Reference to Magnetism

ERIC Educational Resources Information Center

Yilmaz, Ismail

2014-01-01

This paper is a qualitative case study designed to identify prospective science teachers' mathematical-logical structures on the basis of their knowledge and achievement levels in magnetism. The study also made an attempt to reveal the effects of knowledge-level variables and procedural variables, which were considered to be potential…
An Analysis of Mathematics Teacher Candidates' Critical Thinking Dispositions and Their Logical Thinking Skills

ERIC Educational Resources Information Center

Incikabi, Lutfi; Tuna, Abdulkadir; Biber, Abdullah Cagri

2013-01-01

This study aimed to investigate the existence of the relationship between mathematics teacher candidates' critical thinking skills and their logical thinking dispositions in terms of the variables of grade level in college, high school type, and gender. The current study utilized relational survey model and included a total of 99 mathematics…
Logical Aspects of Question-Answering by Computer.

ERIC Educational Resources Information Center

Kuhns, J. L.

The problem of computerized question-answering is discussed in this paper from the point of view of certain technical, although elementary, notions of logic. Although the work reported herein has general application to the design of information systems, it is specifically motivated by the RAND Relational Data File. This system, for which a…

Dilemma in Teaching Mathematics

ERIC Educational Resources Information Center

Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain

2012-01-01

The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…
Careers in STEM Begin with Elementary Student Interest in Mathematics

ERIC Educational Resources Information Center

Brimmer, Linda Ertrachter

2017-01-01

I investigated why math capable students are not entering science, technology, engineering, and math (STEM) careers. To research the problem, I explored how highly effective elementary math teachers (HEMT) create student interest in mathematics using the self- efficacy (SE) theory and information and communication technology (ICT). The purpose of…
Teacher Perceptions of an Online Tutoring Program for Elementary Mathematics

ERIC Educational Resources Information Center

Whetstone, Patti; Clark, Amy; Flake, Mari Wheeler

2014-01-01

This study explores elementary teacher perceptions related to the implementation of an online tutoring program. Teachers were surveyed regarding factors that affected use of the online tutoring program as a supplement to mathematics instruction. Results indicated that teachers overwhelmingly reported positive views of the training and support…
"Project NEO": A Video Game to Promote STEM Competency for Preservice Elementary Teachers

ERIC Educational Resources Information Center

Van Eck, Richard N.; Guy, Mark; Young, Timothy; Winger, Austin T.; Brewster, Scott

2015-01-01

The need for science, technology, engineering, and mathematics majors for our future workforce is growing, yet fewer students are choosing to major in science, technology, engineering, and mathematics areas, and many are underprepared, in part because elementary school preservice teachers are also underprepared. This National Science…
Practicing Elementary Teachers' Perspectives of "Investigations" Curriculum.

ERIC Educational Resources Information Center

Ogolla, Penina A.

This in-depth case study explored the successes and struggles of elementary teachers as they implemented "Investigations in Number, Data, and Space," a K-5 research-based mathematics curriculum that offered students connected and meaningful mathematical problems and in-depth thinking. Data collection and analysis were based on the Zone…
Elementary School Mathematics Priorities

ERIC Educational Resources Information Center

Wilson, W. Stephen

2009-01-01

This article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five…
Autonomy, Beliefs and the Learning of Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Warfield, J.; Wood, T.; Lehman, J.D.

2005-01-01

Seven elementary teachers participated in a project designed to help them learn to teach mathematics according to reform recommendations. Teachers were provided opportunities to learn through both private reflection and public inquiry about their teaching and children's learning. The teachers' instruction, reflection, and beliefs were studied. All…
Prospective Elementary and Secondary School Mathematics Teachers' Statistical Reasoning

ERIC Educational Resources Information Center

Karatoprak, Rabia; Karagöz Akar, Gülseren; Börkan, Bengü

2015-01-01

This study investigated prospective elementary (PEMTs) and secondary (PSMTs) school mathematics teachers' statistical reasoning. The study began with the adaptation of the Statistical Reasoning Assessment (Garfield, 2003) test. Then, the test was administered to 82 PEMTs and 91 PSMTs in a metropolitan city of Turkey. Results showed that both…
The Computational Estimation and Instructional Perspectives of Elementary School Teachers

ERIC Educational Resources Information Center

Tsao, Yea-Ling; Pan, Ting-Rung

2013-01-01

The purpose of this study is to investigate teachers' understanding and knowledge of computational estimation, and teaching practice toward to computational estimation. There are six fifth-grade elementary teachers who participated in this study; three teachers with mathematics/ science major and three teachers with non-mathematics/science major.…
Teachers' Perceptions of Examining Students' Thinking: Changing Mathematics Instructional Practice

ERIC Educational Resources Information Center

Anderson-Pence, Katie L.

2015-01-01

This paper seeks to illuminate teachers' perceptions of the challenges and benefits of systematically examining students' thinking as part of a professional development program in elementary mathematics education. Using a framework of models of conceptual change and principles of discomfort, three elementary teachers' perceptions of their…
Changing Mathematics Teaching Practices and Improving Student Outcomes through Collaborative Evaluation

ERIC Educational Resources Information Center

Thomas, Kelli

2013-01-01

This longitudinal study examines the effects of a collaborative evaluation process on mathematics instruction and student outcomes in an elementary school serving a low-resource community. Thirty-two elementary teachers participated in a 3-year collaborative evaluation professional development process that contributed to improved mathematics…
Changes in Pre-Service Teachers' Algebraic Misconceptions by Using Computer-Assisted Instruction

ERIC Educational Resources Information Center

Lin, ByCheng-Yao; Ko, Yi-Yin; Kuo, Yu-Chun

2014-01-01

In order to carry out current reforms regarding algebra and technology in elementary school mathematics successfully, pre-service elementary mathematics teachers must be equipped with adequate understandings of algebraic concepts and self-confidence in using computers for their future teaching. This paper examines the differences in preservice…
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…
Conflicts in Developing an Elementary STEM Magnet School

ERIC Educational Resources Information Center

Sikma, Lynn; Osborne, Margery

2014-01-01

Elementary schools in the United States have been the terrain of a highly politicized push for improved reading and mathematics attainment, as well as calls for increased importance to be given to science, technology, engineering, and mathematics (STEM). With priorities placed on basic skills, however, instructional time in subjects such as…
Entelek Programmed Instruction Guide. Volume l: Elementary/High School. 3rd Edition.

ERIC Educational Resources Information Center

Entelek, Inc., Newburyport, MA.

Individualized instruction has become an important objective in schools. This programmed instruction guide provides information about the ENTELEK system for elementary and high schools. The data bank covers a variety of subject areas and is catalogued according to the Dewey Decimal System: library; psychology; logic; political science; economics;…
System for corrosion monitoring in pipeline applying fuzzy logic mathematics

NASA Astrophysics Data System (ADS)

Kuzyakov, O. N.; Kolosova, A. L.; Andreeva, M. A.

2018-05-01

A list of factors influencing corrosion rate on the external side of underground pipeline is determined. Principles of constructing a corrosion monitoring system are described; the system performance algorithm and program are elaborated. A comparative analysis of methods for calculating corrosion rate is undertaken. Fuzzy logic mathematics is applied to reduce calculations while considering a wider range of corrosion factors.
The Role of Logic in the Validation of Mathematical Proofs. Technical Report. No. 1999-1

ERIC Educational Resources Information Center

Selden, Annie; Selden, John

1999-01-01

Mathematics departments rarely require students to study very much logic before working with proofs. Normally, the most they will offer is contained in a small portion of a "bridge" course designed to help students move from more procedurally-based lower-division courses (e.g., abstract algebra and real analysis). What accounts for this seeming…
A Classification of Designated Logic Systems

DTIC Science & Technology

1988-02-01

Introduction to Logic. New York: Macmillan Publishing, 1972. Grimaldi , Ralph P . Discrete and Combinatorial Mathematics. Reading: Addison-Wesley...sound basis for understanding non-classical logic systems. I would like to thank the Air Force Institute of Technology for funding this research. vi p ...6 p ILLUSTRATIONS Figure Page 1. Two Classifications of Designated Logic Systems 13 2. Two Partitions of Two-valued Logic Systems 14 3. Two
Fuzzy Logic and Education: Teaching the Basics of Fuzzy Logic through an Example (By Way of Cycling)

ERIC Educational Resources Information Center

Sobrino, Alejandro

2013-01-01

Fuzzy logic dates back to 1965 and it is related not only to current areas of knowledge, such as Control Theory and Computer Science, but also to traditional ones, such as Philosophy and Linguistics. Like any logic, fuzzy logic is concerned with argumentation, but unlike other modalities, which focus on the crisp reasoning of Mathematics, it deals…
Edmodo social learning network for elementary school mathematics learning

NASA Astrophysics Data System (ADS)

Ariani, Y.; Helsa, Y.; Ahmad, S.; Prahmana, RCI

2017-12-01

A developed instructional media can be as printed media, visual media, audio media, and multimedia. The development of instructional media can also take advantage of technological development by utilizing Edmodo social network. This research aims to develop a digital classroom learning model using Edmodo social learning network for elementary school mathematics learning which is practical, valid and effective in order to improve the quality of learning activities. The result of this research showed that the prototype of mathematics learning device for elementary school students using Edmodo was in good category. There were 72% of students passed the assessment as a result of Edmodo learning. Edmodo has become a promising way to engage students in a collaborative learning process.

A Safety Conundrum Illustrated: Logic, Mathematics, and Science Are Not Enough

NASA Technical Reports Server (NTRS)

Holloway, C. M.; Johnson, C. W.; Collins, Kristine R.

2010-01-01

In an ideal world, conversations about whether a particular system is safe, or whether a particular method or tool enhances safety, would be emotion-free discussions concentrating on the level of safety required, available evidence, and coherent logical, mathematical, or scientific arguments based on that evidence. In the real world, discussions about safety are often not emotion-free. Political and economic arguments may play a bigger role than logical, mathematical, and scientific arguments, and psychological factors may be as important, or even more important, than purely technical factors. This paper illustrates the conundrum that can result from this clash of the ideal and the real by means of an imagined conversation among a collection of fictional characters representing various types of people who may be participating in a safety discussion.
Enhancing Core Mathematics Courses

ERIC Educational Resources Information Center

Billings, Esther; Schlicker, Steven; Novotny, Karen; Tefera, Akalu

2004-01-01

The Departments of Mathematics and Statistics at Grand Valley State University are engaged in a project to address the mathematical preparation of all its majors, including prospective elementary and secondary mathematics teachers. In this article, we describe how the mathematics and mathematics education faculty in our mathematics department…
Microcomputer Referents in Elementary Mathematics: A Sample Approach.

ERIC Educational Resources Information Center

Connell, Michael L.

The mathematical experiences of elementary students often focus on memorizing facts and rules as opposed to making sense of the subject and developing problem solving skills. Students spend large amounts of time processing, memorizing and sorting collections of data which are tasks well performed by computer technology. To correct this situation,…
The Effects of Technology-Mediated Dialogic Learning in Elementary Mathematics Instruction

ERIC Educational Resources Information Center

Working, Christopher

2018-01-01

The use of technology in elementary mathematics instruction tends to be low-level, despite its affordance of supporting the development of students' high-level reasoning ability. This study builds upon a sociocultural view of learning and was designed to determine what effect a technology-mediated dialogic learning intervention has on third-grade…
Developing Mathematical Processes (DMP). Field Test Evaluation, 1972-1973.

ERIC Educational Resources Information Center

Schall, William E.; And Others

The field test of the Developing Mathematical Processes (DMP) program was conducted jointly by the Falconer Central School, St. Mary's Elementary School in Dunkirk, New York, and the Teacher Education Research Center at the State University College in Fredonia, New York. DMP is a research-based, innovative, process-oriented elementary mathematics…
Kendall Demonstration Elementary School: Mathematics Curriculum Guide. Second Edition.

ERIC Educational Resources Information Center

Mason, Virgyl

This mathematics curriculum guide is one of a series developed by the Kendall Demonstration Elementary School (KDES), which serves hearing-impaired students in grades 1-8, to provide a clear representation of the school's programs in various subject areas. Essential classroom practices in the areas of planning, instruction, and evaluation are…
Use of Creative Drama in Science and Mathematics by Preservice Elementary Teachers

ERIC Educational Resources Information Center

Ozdemir, Pinar; Akkus Cikla, Oylum

2005-01-01

The purpose of this study is to analyse science and mathematics lesson plans prepared in the light of drama based instruction by preservice elementary teachers. For this purpose, 12 female participants were chosen volunteerly. They gained basic knowledge and experience about creative drama by involving sample creative drama activities and lesson…
Pre-Service Elementary Mathematics Teachers' Metaphors on Scientific Research and Foundations of Their Perceptions

ERIC Educational Resources Information Center

Bas, Fatih

2016-01-01

In this study, it is aimed to investigate pre-service elementary mathematics teachers' perceptions about scientific research with metaphor analysis and determine the foundations of these perceptions. This phenomenological study was conducted with 182 participants. The data were collected with two open-ended survey forms formed for investigating…
Measuring Practices of Teaching for Social Justice in Elementary Mathematics Classrooms

ERIC Educational Resources Information Center

Reagan, Emilie Mitescu; Pedulla, Joseph J.; Jong, Cindy; Cannady, Mac; Cochran-Smith, Marilyn

2011-01-01

This study used the Teaching for Social Justice Observation Scale (TSJOS) of the Reformed Teaching Observation Protocol-Plus (RTOP+) to examine the extent to which twenty-two novice elementary teachers implemented practices related to teaching for social justice in their mathematics instruction. In addition, this study sought to examine the extent…
A Living Metaphor of Differentiation: A Meta-Ethnography of Cognitively Guided Instruction in the Elementary Classroom

ERIC Educational Resources Information Center

Baker, Katherine; Harter, Meghan Evelynne

2015-01-01

This meta-ethnography explores qualitative studies around the Cognitively Guided Instruction (CGI) framework of mathematics and illustrates how CGI epitomizes differentiation. The meta-ethnographic process is used to synthesize CGI as differentiation, specifically within the elementary mathematics classroom. Thomas P. Carpenter is credited as one…
Elementary Teachers' Perceptions of Mathematics Instruction in Montessori and Traditional Classrooms

ERIC Educational Resources Information Center

Kofa, Linda

2017-01-01

Students in grades 3 and 4 attending a traditional public elementary school in a northeastern state did not meet proficiency levels in mathematics as measured by the state's assessment system. Published reports indicated that students attending the Montessori programs were more proficient in solving math problems compared to students in…
Course and Curriculum Improvement Materials: Mathematics, Science, Social Sciences - Elementary, Intermediate, Secondary.

ERIC Educational Resources Information Center

National Science Foundation, Washington, DC.

This is a list of curriculum improvement materials produced by major course and curriculum projects supported by the National Science Foundation's Division of Pre-College Education in Science. The materials are grouped by educational level (elementary, intermediate, and secondary) and within each level by broad discipline groupings (mathematics,…
Traffic Flow - USMES Teacher Resource Book. Fourth Edition. Trial Edition.

ERIC Educational Resources Information Center

Keskulla, Jean

This Unified Sciences and Mathematics for Elementary Schools (USMES) unit challenges students to improve traffic flow at a problem location. The challenge is general enough to apply to many problem-solving situations in mathematics, science, social science, and language arts at any elementary school level (grades 1-8). The Teacher Resource Book…
Pedestrian Crossings - USMES Teacher Resource Book. Fifth Edition. Trial Edition.

ERIC Educational Resources Information Center

Keskulla, Jean

This Unified Sciences and Mathematics for Elementary Schools (USMES) unit challenges students to improve the safety and convenience of a pedestrian crossing near a school. The challenge is general enough to apply to many problem-solving situations in mathematics, science, social science, and language arts at any elementary school level (grades…
Motivational and Affective Determinants of Self-Regulatory Strategy Use in Elementary School Mathematics

ERIC Educational Resources Information Center

Chatzistamatiou, Mariza; Dermitzaki, Irini; Efklides, Anastasia; Leondari, Angeliki

2015-01-01

The aim of the study was to investigate the relationships between elementary students' reported use of self-regulatory strategies in mathematics and their motivational and affective determinants. Participants of the study were 344 fifth- and sixth-grade Greek students. Students were asked to complete self-reported measures regarding the strategies…
Investigating Classroom Teaching Competencies of Pre Service Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Gokalp, Murat

2016-01-01

The study has sought answers to two major questions: What is the current situation in Elementary Mathematics Education programs at Faculty of Education in terms of classroom teaching competencies? To what extent do pre service teachers acquire these competencies? The research was conducted on 202 senior pre service teachers studying at the…
The Effects of Elementary Departmentalization on Mathematics Proficiency

ERIC Educational Resources Information Center

Taylor-Buckner, Nicole C.

2014-01-01

Mathematics education in the elementary schools has experienced many changes in recent decades. With the curriculum becoming more complex as a result of each modification, immense pressure has been put on schools to increase student proficiency. The Common Core State Standards is the latest example of this. These revisions to the mathematics…
Elementary Teachers' Learning to Construct High-Quality Mathematics Lesson Plans: A Use of the IES Recommendations

ERIC Educational Resources Information Center

Ding, Meixia; Carlson, Mary Alice

2013-01-01

This study explored a group of elementary teachers' ("n" = 35) learning to construct high-quality lesson plans that foster student understanding of fundamental mathematical ideas. The conceptual framework for this study was gleaned from the recently released Institute of Education Sciences (IES) recommendations, including (a)…
Protecting Property - USMES Teacher Resource Book. First Edition. Trial Edition.

ERIC Educational Resources Information Center

Bussey, Margery Koo

This Unified Sciences and Mathematics for Elementary Schools (USMES) unit challenges students to find good ways to protect property (property in desks or lockers; animals; bicycles; tools). The challenge is general enough to apply to many problem-solving situations in mathematics, science, social science, and language arts at any elementary school…
The Notion of Proof in the Context of Elementary School Mathematics

ERIC Educational Resources Information Center

Stylianides, Andreas J.

2007-01-01

Despite increased appreciation of the role of "proof" in students' mathematical experiences across "all" grades, little research has focused on the issue of understanding and characterizing the notion of proof at the elementary school level. This paper takes a step toward addressing this limitation, by examining the characteristics of four major…

Adding It Up: Is Computer Use Associated with Higher Achievement in Public Elementary Mathematics Classrooms?

ERIC Educational Resources Information Center

Kao, Linda Lee

2009-01-01

Despite support for technology in schools, there is little evidence indicating whether using computers in public elementary mathematics classrooms is associated with improved outcomes for students. This exploratory study examined data from the Early Childhood Longitudinal Study, investigating whether students' frequency of computer use was related…
Developing Prospective Elementary Teachers' Abilities to Identify Evidence of Student Mathematical Achievement

ERIC Educational Resources Information Center

Spitzer, Sandy M.; Phelps, Christine M.; Beyers, James E. R.; Johnson, Delayne Y.; Sieminski, Elizabeth M.

2011-01-01

This study investigated the effects of a classroom intervention on prospective elementary teachers' ability to evaluate evidence of student achievement of mathematical learning goals. The intervention was informed by a framework for teacher education which aims to provide prospective teachers (PTs) with the skills needed to systematically learn…
Proceedings: Summer Conference for College Teachers on Applied Mathematics, University of Missouri-Rolla, 1971.

ERIC Educational Resources Information Center

Committee on the Undergraduate Program in Mathematics, Berkeley, CA.

Proceedings from four sessions of the Summer Conference for College Teachers on Applied Mathematics are presented. The four sessions were: (1) Applications of Elementary Calculus, (2) Applications of Linear Algebra, (3) Applications of Elementary Differential Equations, and (4) Applications of Probability and Statistics. Nine lectures were given…
Manufacturing - USMES Teacher Resource Book. Second Edition. Trial Edition.

ERIC Educational Resources Information Center

Agro, Sally

This Unified Sciences and Mathematics for Elementary Schools (USMES) unit challenges students to find the best way to produce an item in quantities needed. The challenge is general enough to apply to many problem-solving situations in mathematics, science, social science, and language arts at any elementary school level (grades 1-8). The Teacher…
Elementary Modeling: Connecting Counting with Sharing

ERIC Educational Resources Information Center

Wickstrom, Megan H.; Aytes, Tracy

2018-01-01

Mathematical modeling is an important and accessible process for elementary school students because it allows them to use mathematics to engage with the world and consider if and when to use it to help them reason about a situation. It fosters productive struggle and twenty-first-century skills that will aid them throughout their lifetime.
Jane and Johnny Love Math: Recognizing and Encouraging Mathematical Talent in Elementary Students; A Guidebook for Educators and Parents.

ERIC Educational Resources Information Center

Lupkowski, Ann E.; Assouline, Susan G.

This book is a guide for parents and teachers of mathematically talented elementary school students. Chapters and sections include: (1) "Overview"; (2) "Historical and Current Perspectives"; (3) "Making Informed Educational Decisions"; (4) "Diagnostic Testing Followed by Prescriptive Instruction: SMPY's DT to PI…
Initial Ada components evaluation

NASA Technical Reports Server (NTRS)

Moebes, Travis

1989-01-01

The SAIC has the responsibility for independent test and validation of the SSE. They have been using a mathematical functions library package implemented in Ada to test the SSE IV and V process. The library package consists of elementary mathematical functions and is both machine and accuracy independent. The SSE Ada components evaluation includes code complexity metrics based on Halstead's software science metrics and McCabe's measure of cyclomatic complexity. Halstead's metrics are based on the number of operators and operands on a logical unit of code and are compiled from the number of distinct operators, distinct operands, and total number of occurrences of operators and operands. These metrics give an indication of the physical size of a program in terms of operators and operands and are used diagnostically to point to potential problems. McCabe's Cyclomatic Complexity Metrics (CCM) are compiled from flow charts transformed to equivalent directed graphs. The CCM is a measure of the total number of linearly independent paths through the code's control structure. These metrics were computed for the Ada mathematical functions library using Software Automated Verification and Validation (SAVVAS), the SSE IV and V tool. A table with selected results was shown, indicating that most of these routines are of good quality. Thresholds for the Halstead measures indicate poor quality if the length metric exceeds 260 or difficulty is greater than 190. The McCabe CCM indicated a high quality of software products.
On the notion of free will in the Free Will Theorem

NASA Astrophysics Data System (ADS)

Landsman, Klaas

2017-02-01

The (Strong) Free Will Theorem (FWT) of Conway and Kochen (2009) on the one hand follows from uncontroversial parts of modern physics and elementary mathematical and logical reasoning, but on the other hand seems predicated on an undefined notion of free will (allowing physicists to "freely choose" the settings of their experiments). This makes the theorem philosophically vulnerable, especially if it is construed as a proof of indeterminism or even of libertarian free will (as Conway & Kochen suggest). However, Cator and Landsman (Foundations of Physics 44, 781-791, 2014) previously gave a reformulation of the FWT that does not presuppose indeterminism, but rather assumes a mathematically specific form of such "free choices" even in a deterministic world (based on a non-probabilistic independence assumption). In the present paper, which is a philosophical sequel to the one just mentioned, I argue that the concept of free will used in the latter version of the FWT is essentially the one proposed by Lewis (1981), also known as 'local miracle compatibilism' (of which I give a mathematical interpretation that might be of some independent interest also beyond its application to the FWT). As such, the (reformulated) FWT in my view challenges compatibilist free will à la Lewis (albeit in a contrived way via bipartite EPR-type experiments), falling short of supporting libertarian free will.
Hydraulic logic gates: building a digital water computer

NASA Astrophysics Data System (ADS)

Taberlet, Nicolas; Marsal, Quentin; Ferrand, Jérémy; Plihon, Nicolas

2018-03-01

In this article, we propose an easy-to-build hydraulic machine which serves as a digital binary computer. We first explain how an elementary adder can be built from test tubes and pipes (a cup filled with water representing a 1, and empty cup a 0). Using a siphon and a slow drain, the proposed setup combines AND and XOR logical gates in a single device which can add two binary digits. We then show how these elementary units can be combined to construct a full 4-bit adder. The sequencing of the computation is discussed and a water clock can be incorporated so that the machine can run without any exterior intervention.
On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2016-03-01

Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.
A pedagogical example of second-order arithmetic sequences applied to the construction of computer passwords by upper elementary grade students

NASA Astrophysics Data System (ADS)

Coggins, Porter E.

2015-04-01

The purpose of this paper is (1) to present how general education elementary school age students constructed computer passwords using digital root sums and second-order arithmetic sequences, (2) argue that computer password construction can be used as an engaging introduction to generate interest in elementary school students to study mathematics related to computer science, and (3) share additional mathematical ideas accessible to elementary school students that can be used to create computer passwords. This paper serves to fill a current gap in the literature regarding the integration of mathematical content accessible to upper elementary school students and aspects of computer science in general, and computer password construction in particular. In addition, the protocols presented here can serve as a hook to generate further interest in mathematics and computer science. Students learned to create a random-looking computer password by using biometric measurements of their shoe size, height, and age in months and to create a second-order arithmetic sequence, then converted the resulting numbers into characters that become their computer passwords. This password protocol can be used to introduce students to good computer password habits that can serve a foundation for a life-long awareness of data security. A refinement of the password protocol is also presented.
Cooperative Learning Model toward a Reading Comprehensions on the Elementary School

ERIC Educational Resources Information Center

Murtono

2015-01-01

The purposes of this research are: (1) description of reading skill the students who join in CIRC learning model, Jigsaw learning model, and STAD learning model; (2) finding out the effective of learning model cooperative toward a reading comprehensions between the students who have high language logic and low language logic; and (3) finding out…
Logic integer programming models for signaling networks.

PubMed

Haus, Utz-Uwe; Niermann, Kathrin; Truemper, Klaus; Weismantel, Robert

2009-05-01

We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this, we use the two different mathematical tools of Propositional Logic and Integer Programming. The power of discrete mathematics for handling qualitative as well as quantitative data has so far not been exploited in molecular biology, which is mostly driven by experimental research, relying on first-order or statistical models. The arising logic statements and integer programs are analyzed and can be solved with standard software. For a restricted class of problems the logic models reduce to a polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic model enables enumeration of possible time resolutions in poly-logarithmic time. Computational experiments are included.
The knowledge instinct, cognitive algorithms, modeling of language and cultural evolution

NASA Astrophysics Data System (ADS)

Perlovsky, Leonid I.

2008-04-01

The talk discusses mechanisms of the mind and their engineering applications. The past attempts at designing "intelligent systems" encountered mathematical difficulties related to algorithmic complexity. The culprit turned out to be logic, which in one way or another was used not only in logic rule systems, but also in statistical, neural, and fuzzy systems. Algorithmic complexity is related to Godel's theory, a most fundamental mathematical result. These difficulties were overcome by replacing logic with a dynamic process "from vague to crisp," dynamic logic. It leads to algorithms overcoming combinatorial complexity, and resulting in orders of magnitude improvement in classical problems of detection, tracking, fusion, and prediction in noise. I present engineering applications to pattern recognition, detection, tracking, fusion, financial predictions, and Internet search engines. Mathematical and engineering efficiency of dynamic logic can also be understood as cognitive algorithm, which describes fundamental property of the mind, the knowledge instinct responsible for all our higher cognitive functions: concepts, perception, cognition, instincts, imaginations, intuitions, emotions, including emotions of the beautiful. I present our latest results in modeling evolution of languages and cultures, their interactions in these processes, and role of music in cultural evolution. Experimental data is presented that support the theory. Future directions are outlined.
Elementary Content Specialization: Models, Affordances, and Constraints

ERIC Educational Resources Information Center

Markworth, Kimberly A.; Brobst, Joseph; Ohana, Chris; Parker, Ruth

2016-01-01

Background: This study investigates the models of elementary content specialization (ECS) in elementary mathematics and science and the affordances and constraints related to ECS--both generally and in relation to specific models. Elementary content specialists are defined as full-time classroom teachers who are responsible for content instruction…
Preservice Elementary Teachers and the Fundamentals of Probability

ERIC Educational Resources Information Center

Dollard, Clark

2011-01-01

This study examined how preservice elementary teachers think about situations involving probability. Twenty-four preservice elementary teachers who had not yet studied probability as part of their preservice elementary mathematics coursework were interviewed using a task-based interview. The participants' responses showed a wide variety of…
Circuit Sense for Elementary Teachers and Students: Understanding and Building Simple Logic Circuits.

ERIC Educational Resources Information Center

Houghton, Janaye Matteson; Houghton, Robert S.

Today and in the future, critical toolmaking advances will need to be made in the area of circuit design, construction, and implementation. Traditional school curriculum has sidestepped the area of tool design, especially at the elementary level. This publication addresses a calling for a new curriculum direction, based not only on the study of…
Distributed neural representations of logical arguments in school-age children

PubMed Central

Mathieu, Romain; Booth, James R.; Prado, Jérôme

2016-01-01

Children’s understanding of linear-order (e.g., Dan is taller than Lisa, Lisa is taller than Jess) and set-inclusion (i.e., All tulips are flowers, All flowers are plants) relationships is critical for the acquisition of deductive reasoning, i.e., the ability to reach logically valid conclusions from given premises. Behavioral and neuroimaging studies in adults suggest processing differences between these relations: While arguments that involve linear-orders may be preferentially associated with spatial processing, arguments that involve set-inclusions may be preferentially associated with verbal processing. In the present study, we used functional magnetic resonance imaging (fMRI) to investigate whether these processing differences appear during the period of elementary school in development. Consistent with previous studies in adults, we found that arguments that involve linear-order and set-inclusion relationships preferentially involve spatial and verbal brain mechanisms (respectively) in school-age children (9 to 14 year olds). Because this neural sensitivity was not related to age, it likely emerges before the period of elementary education. However, the period of elementary education might play an important role in shaping the neural processing of logical reasoning, as indicated by developmental changes in frontal and parietal regions that were dependent upon the type of relation. PMID:25355487
Tyramine Hydrochloride Based Label-Free System for Operating Various DNA Logic Gates and a DNA Caliper for Base Number Measurements.

PubMed

Fan, Daoqing; Zhu, Xiaoqing; Dong, Shaojun; Wang, Erkang

2017-07-05

DNA is believed to be a promising candidate for molecular logic computation, and the fluorogenic/colorimetric substrates of G-quadruplex DNAzyme (G4zyme) are broadly used as label-free output reporters of DNA logic circuits. Herein, for the first time, tyramine-HCl (a fluorogenic substrate of G4zyme) is applied to DNA logic computation and a series of label-free DNA-input logic gates, including elementary AND, OR, and INHIBIT logic gates, as well as a two to one encoder, are constructed. Furthermore, a DNA caliper that can measure the base number of target DNA as low as three bases is also fabricated. This DNA caliper can also perform concatenated AND-AND logic computation to fulfil the requirements of sophisticated logic computing. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
A Descriptive Study Examining the Impact of Digital Writing Environments on Communication and Mathematical Reasoning for Students with Learning Disabilities

ERIC Educational Resources Information Center

Huscroft-D'Angelo, Jacqueline; Higgins, Kristina N.; Crawford, Lindy L.

2014-01-01

Proficiency in mathematics, including mathematical reasoning skills, requires students to communicate their mathematical thinking. Mathematical reasoning involves making sense of mathematical concepts in a logical way to form conclusions or judgments, and is often underdeveloped in students with learning disabilities. Technology-based environments…

Probing when Japanese junior high school students begin to feel difficulty in learning mathematics

NASA Astrophysics Data System (ADS)

Nishikawa, Tomoko; Izuta, Giido

2017-05-01

It is thought that the increasing number of Japanese students avoiding mathematics has become a serious problem in the last decades. Japanese junior high school students are learning the basic understanding and skills of mathematics during the years of mandatory education. To our knowledge, there are few reports about the time when Japanese junior high school students begin to feel difficulty in mathematics learning. The aim of this work is to examine this case. To accomplish this purpose, a typical public junior high school in a country city with 616 students (182 first-year, 212 second-year, 222 third-year) in all was chosen to be the field of investigation. Likert scale type questionnaires to assess their feelings were conducted, and the respondents who answered `difficulty' and `a little difficulty' were extracted. The number of respondents were 89 first-year (26 males, 63 females), 76 second-year (27 males, 49 females), and 112 third-year (45 males, 67 females) students. The beginning time was divided into school years when it was in elementary school, and semesters when it was in junior high school. Ordinary statistical processings for each grade and gender were performed to analyze them. It was found that the time when they began to have difficulty learning mathematics was different in gender. Male students tended to start from higher-grade of elementary school whereas female students from middle-grade of elementary school. In other words, these results showed differences in gender and time. Finally, these examinations suggest that teachers need to provide appropriate support for students at a suitable time in the elementary school. Also these results are useful in mathematics education of elementary school.
Learning styles and approaches to learning mathematics of students majoring in elementary education: a three-year study.

PubMed

Alkhateeb, Haitham M; Mji, Andile

2009-10-01

The goal of this 3-yr. study was to explore the learning styles and approaches to learning mathematics of elementary education majors. Two questionnaires, the Learning Style Inventory and the Approaches to Learning Mathematics Questionnaire, were administered to 149 women and 32 men (M = 20.1 yr., SD. = 2.1; range = 18-31). All were in their first or second years of college and enrolled in Mathematics for Elementary School Teachers at a Midwestern U.S. university. Results on the Learning Style Inventory indicated that a majority scored as either Accommodators, i.e., they primarily followed learning modes involving Active Experimentation and Concrete Experience, or as Divergers, i.e., approaching learning by focusing on Concrete Experience and Reflective Observation. A weak but statistically significant association was observed on the Approaches questionnaire between the Surface Approach and Reflective Observation.
Promoting Preservice Teachers' Mathematics Identity Exploration

ERIC Educational Resources Information Center

Heffernan, Kayla

2016-01-01

Despite the effort of teacher education programs, early childhood, and elementary preservice teachers often fear mathematics, have high mathematics anxiety, hold negative self-perceptions in relation to mathematics, find mathematics irrelevant, and have low mathematics achievement. The aim of this study was to implement and investigate the…
Science and Mathematics Books for Elementary and Secondary Schools, A Bibliography from the Educational Materials Center.

ERIC Educational Resources Information Center

Watt, Lois B.; And Others

This is an annotated bibliography of science and mathematics textbooks and juvenile trade books received in the Educational Materials Center between January, 1969 and February, 1970. The contents are divided into two major sections: Juvenile Literature, and Textbooks for Elementary and Secondary Schools. The first section includes only those books…
eWorkbooks for Mathematics: Mapping the Independent Learning Experiences of Elementary Students with Learning Disabilities

ERIC Educational Resources Information Center

Kaczorowski, Tara; Raimondi, Sharon

2014-01-01

In this paper, we describe a small case study exploring how four elementary students with mathematics learning disabilities utilized mobile technology (the eWorkbook) during core math instruction in a general education setting. The lead author designed the eWorkbook intervention to provide a flexible learning experience optimized for diverse…
Measurement Approach to Teaching Fractions: A Design Experiment in a Pre-Service Course for Elementary Teachers

ERIC Educational Resources Information Center

Bobos, Georgeana; Sierpinska, Anna

2017-01-01

In this paper, we present a design experiment in a "Teaching Mathematics" course for prospective elementary teachers where we sought to develop a "measurement approach" to fractions. We focus on the conceptualization of the mathematical content of the approach. We attribute our progress in the conceptualization to our efforts…
What Form of Mathematics Are Assessments Assessing? The Case of Multiplication and Division in Fourth Grade NAEP Items

ERIC Educational Resources Information Center

Kosko Karl W.; Singh, Rashmi

2018-01-01

Multiplicative reasoning is a key concept in elementary school mathematics. Item statistics reported by the National Assessment of Educational Progress (NAEP) assessment provide the best current indicator for how well elementary students across the U.S. understand this, and other concepts. However, beyond expert reviews and statistical analysis,…
Differentiated Instruction: Understanding the Personal Factors and Organizational Conditions that Facilitate Differentiated Instruction in Elementary Mathematics Classrooms

ERIC Educational Resources Information Center

Abbati, Diana Guglielmo

2012-01-01

Differentiated instruction is a widely held practice used by teachers to provide diverse learners with complex learning opportunities in the area of mathematics. Research on differentiated instruction shows a multitude of factors that support high quality instruction in mixed-ability elementary classrooms. These factors include small-class size,…
Examining Elementary School Teachers' Integration of Technology and Enactment of TPACK in Mathematics

ERIC Educational Resources Information Center

Urbina, Angela; Polly, Drew

2017-01-01

Purpose: The purpose of this paper is to examine how elementary school teachers integrated technology into their mathematics teaching in classroom settings that were one-to-one computer environments for most of the day. Following a series of classroom observations and interviews, inductive qualitative analyses of data indicated that teachers felt…
Improving the Mathematics Preparation of Elementary Teachers, One Lesson at a Time

ERIC Educational Resources Information Center

Berk, Dawn; Hiebert, James

2009-01-01

In this paper, we describe a model for systematically improving the mathematics preparation of elementary teachers, one lesson at a time. We begin by identifying a serious obstacle for teacher educators: the absence of mechanisms for developing a shareable knowledge base for teacher preparation. We propose our model as a way to address this…
The Diagnosis and Remediation of Mathematical Skills for Prospective Elementary School Teachers. Final Report.

ERIC Educational Resources Information Center

Schwartz, Lita L.; And Others

Investigated was the development of a diagnostic and individualized remedial program for prospective elementary teachers in the area of mathematical skills. Subjects were 120 students in the pre-methods course on number systems during the Winter and Spring 1971 terms at the Ogontz Campus, Pennsylvania State University. All subjects were given a…
Five Affordances of Computational Thinking to Support Elementary Mathematics Education

ERIC Educational Resources Information Center

Gadanidis, George

2017-01-01

With the increased focus on computational thinking (CT) in education, it is important to investigate the affordances that CT may offer to support teaching and learning. This paper outlines five affordances of CT that may support elementary mathematics education, whose conceptualization was refined in a year-long study involving eight Grades 3-4…
Professional Development School Triads Inquiring about Student Work in Elementary Mathematics

ERIC Educational Resources Information Center

Coon-Kitt, Mary Jayne; Nolan, James F.; Lloyd, Gwendolyn M.; Romig, Gail

2015-01-01

This article reports on a case of cross-role triads (mentor, intern, and supervisor) in a professional development school (PDS) setting engaged in the process of looking at student work in elementary mathematics over time. The study represents a significant effort to understand what inquiry-oriented behavior looks like in this context. By…
Study of Fractions in Elementary Mathematics Textbooks from Finland and Taiwan

ERIC Educational Resources Information Center

Yang, Der-Ching

2018-01-01

This study examines the different ways in which fractions are dealt with in two elementary mathematics textbook series: Kang Hsuan (KH) in Taiwan and Laskutaito in Finland. The results showed that the total number of fraction questions in Laskutaito is higher than that in KH and that Laskutaito highlights the basic definition of fractions to help…
School Leaders' Guide to Elementary Mathematics

ERIC Educational Resources Information Center

Curtis-Bey, Linda

2013-01-01

High achievement in mathematics is a critical part of the portfolios of students seeking admission to the best high schools and colleges; it is essential to a school's success at district, state, and national levels and to America's future as a global competitor. Elementary school leaders need to provide their students with a balanced,…
Designing for Human Proportions - USMES Teacher Resource Book. Fourth Edition. Trial Edition.

ERIC Educational Resources Information Center

Bussey, Margery Koo

Designing or making changes in things students use or wear is the challenge of this Unified Sciences and Mathematics for Elementary Schools (USMES) unit. The challenge is general enough to apply to many problem-solving situations in mathematics, science, social science, and language arts at any elementary school level (grades 1-8). The Teacher…
Designing and Testing a Mathematics Card Game for Teaching and Learning Elementary Group Theory

ERIC Educational Resources Information Center

Galarza, Patrick

2017-01-01

This paper explores the viability and development of the first edition of the researcher's mathematical card game, Groups, as a learning tool for elementary group theory, a topic in abstract algebra. "Groups" was play-tested by six undergraduate students in late 2016 who provided feedback on "Groups" from both utility-centric…
Integration of Technology in Elementary Pre-Service Teacher Education: An Examination of Mathematics Methods Courses

ERIC Educational Resources Information Center

Mitchell, Rebecca; Laski, Elida

2013-01-01

Instructors (N = 204) of elementary mathematics methods courses completed a survey assessing the extent to which they stay informed about research related to effective uses of educational technology and the kinds and numbers of educational technologies they include in their courses. Findings indicate that, while they view educational technology…
Interactive Whiteboards Produce Small Gains in Elementary Students' Self-Reported Motivation in Mathematics

ERIC Educational Resources Information Center

Torff, Bruce; Tirotta, Rose

2010-01-01

A treatment/control study (N = 773) was conducted to determine the extent to which use of interactive whiteboard technology (IWB) was associated with upper elementary students' self-reported level of motivation in mathematics. Students in the treatment group reported higher levels of motivation relative to control students, but the effect was…
Gender Differences in Attitudes toward Mathematics between Low-Achieving and High-Achieving Fifth Grade Elementary Students.

ERIC Educational Resources Information Center

Rathbone, A. Sue

Possible gender differences in attitudes toward mathematics were studied between low-achieving and high-achieving fifth-grade students in selected elementary schools within a large, metropolitan area. The attitudes of pre-adolescent children at an intermediate grade level were assessed to determine the effects of rapidly emerging gender-related…

New York State Elementary School Teacher Certification and Examinations in Mathematics in the Nineteenth Century

ERIC Educational Resources Information Center

Kyriakou, Raeann

2014-01-01

This dissertation is devoted to a history of the New York State elementary school teacher certification requirements, specifically in mathematics, during the nineteenth century. In the last half of nineteenth century, teacher education and uniform certification procedures were beginning to become the norm in the educational systems throughout the…
The Presentation of Technology for Teaching and Learning Mathematics in Textbooks: Content Courses for Elementary Teachers

ERIC Educational Resources Information Center

Jones, Dustin; Hollas, Victoria; Klespis, Mark

2017-01-01

This article presents an overview of the ways technology is presented in textbooks written for mathematics content courses for prospective elementary teachers. Six popular textbooks comprising a total of more than 5,000 pages were examined, and 1,055 distinct references to technology were identified. These references are coded according to…
Identity Development of Preservice Elementary Teachers of Mathematics from Teacher Education Program to Student Teaching

ERIC Educational Resources Information Center

Kang, Hyun Jung

2012-01-01

Drawing on Lave and Wenger (1991) this study explores how preservice elementary teachers develop themselves as teachers of mathematics, in particular, from the time of their teacher education courses to their field experiences. This study also researches the critical experiences that contributed to the construction of their identities and their…
Young Women Majoring in Mathematics and Elementary Education: A Perspective on Enacting Liberatory Pedagogy

ERIC Educational Resources Information Center

Bray, Paige M.

2004-01-01

In this research I examined the enactment of liberatory pedagogy, a teaching practice that promotes equity for all learners, from the uniquely informative perspective of young women majoring in mathematics and elementary education. It is grounded theory that seeks to understand the role of personal identity and social location in learning and…
A Study of Pre-Service Elementary Teachers' Mathematical Sophistication in a Reform-Oriented Calculus Course

ERIC Educational Resources Information Center

Ritter, Carrie Lineberry

2015-01-01

Calls for better preparation of STEM teachers have been prominent in educational communities and among the public for the past several years (e.g. American Association of Colleges for Teacher Education, 2007). Some research suggests one way to improve mathematics instruction is to increase elementary pre-service teachers' "mathematical…
Leveraging Cognitive Technology Tools to Expand Opportunities for Critical Thinking in Elementary Mathematics

ERIC Educational Resources Information Center

Suh, Jennifer

2010-01-01

The following study describes design research in an elementary school near the metropolitan D.C. area with a diverse student population. The goal of the project was to design tasks that leveraged technology and enhance the access to critical thinking in specific mathematical concepts: data analysis and probability. It highlights the opportunities…
Preservice Elementary and Middle School Teachers' Conceptions of Algebra Revealed through the Use of Exemplary Curriculum Materials.

ERIC Educational Resources Information Center

Stump, Sheryl; Bishop, Joyce

One of the greatest challenges for mathematics teacher educators committed to reforming and improving mathematics education is to help preservice elementary and middle school teachers develop an appreciation for algebraic reasoning. Preservice teachers' views of algebra are typically derived from their experiences in middle school and high school…
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)
Photochromic molecular implementations of universal computation.

PubMed

Chaplin, Jack C; Krasnogor, Natalio; Russell, Noah A

2014-12-01

Unconventional computing is an area of research in which novel materials and paradigms are utilised to implement computation. Previously we have demonstrated how registers, logic gates and logic circuits can be implemented, unconventionally, with a biocompatible molecular switch, NitroBIPS, embedded in a polymer matrix. NitroBIPS and related molecules have been shown elsewhere to be capable of modifying many biological processes in a manner that is dependent on its molecular form. Thus, one possible application of this type of unconventional computing is to embed computational processes into biological systems. Here we expand on our earlier proof-of-principle work and demonstrate that universal computation can be implemented using NitroBIPS. We have previously shown that spatially localised computational elements, including registers and logic gates, can be produced. We explain how parallel registers can be implemented, then demonstrate an application of parallel registers in the form of Turing machine tapes, and demonstrate both parallel registers and logic circuits in the form of elementary cellular automata. The Turing machines and elementary cellular automata utilise the same samples and same hardware to implement their registers, logic gates and logic circuits; and both represent examples of universal computing paradigms. This shows that homogenous photochromic computational devices can be dynamically repurposed without invasive reconfiguration. The result represents an important, necessary step towards demonstrating the general feasibility of interfacial computation embedded in biological systems or other unconventional materials and environments. Copyright © 2014 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.
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.
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.
The Effect of Scratch- and Lego Mindstorms Ev3-Based Programming Activities on Academic Achievement, Problem-Solving Skills and Logical-Mathematical Thinking Skills of Students

ERIC Educational Resources Information Center

Korkmaz, Özgen

2016-01-01

The aim of this study was to investigate the effect of the Scratch and Lego Mindstorms Ev3 programming activities on academic achievement with respect to computer programming, and on the problem-solving and logical-mathematical thinking skills of students. This study was a semi-experimental, pretest-posttest study with two experimental groups and…
From Searle's Chinese Room to the Mathematics Classroom: Technical and Cognitive Mathematics

ERIC Educational Resources Information Center

Gavalas, Dimitris

2007-01-01

Employing Searle's views, I begin by arguing that students of Mathematics behave similarly to machines that manage symbols using a set of rules. I then consider two types of Mathematics, which I call "Cognitive Mathematics" and "Technical Mathematics" respectively. The former type relates to concepts and meanings, logic and sense, whilst the…
Pre-Service Primary School Teachers' Logical Reasoning Skills

ERIC Educational Resources Information Center

Marchis, Iuliana

2013-01-01

Logical reasoning skills are important for a successful mathematical learning and in students' future career. These skills are essential for a primary school teacher, because they need to explain solving methods and solutions to their pupils. In this research we studied pre-service primary school teachers' logical reasoning skills. The results…
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…
Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication

ERIC Educational Resources Information Center

Kaya, Defne; Aydin, Hasan

2016-01-01

Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…
Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

ERIC Educational Resources Information Center

Yilmaz, Suha; Tekin-Dede, Ayse

2016-01-01

Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…
Mathematical logic as a mean of solving the problems of power supply for buildings and constructions

NASA Astrophysics Data System (ADS)

Pryadko, Igor; Nozdrina, Ekaterina; Boltaevsky, Andrey

2017-10-01

The article analyzes the questions of application of mathematical logic in engineering design associated with machinery and construction. The aim of the work is to study the logical working-out of Russian electrical engineer V.I. Shestakov. These elaborations are considered in connection with the problem of analysis and synthesis of relay contact circuits of the degenerate (A) class which the scientist solved. The article proposes to use Shestakov’s elaborations for optimization of buildings and constructions of modern high-tech. In the second part of the article the events are actualized in association with the development of problems of application of mathematical logic in the analysis and synthesis of electric circuits, relay and bridging. The arguments in favor of the priority of the authorship of the elaborations of Russian electrical engineer V. I. Shestakov, K. Shannon - one of the founders of computer science, and Japanese engineer A. Nakashima are discussed. The issue of contradiction between V. I. Shestakov and representatives of the school of M. A. Gavrilov is touched on.
Mathematics and Science Teaching for English Learners (MAST-EL) Partnership: A Relationship among Elementary School Teachers, Preservice Teachers, Principals, Coaches, and College Faculty

ERIC Educational Resources Information Center

Harding-DeKam, Jenni L.; Reinsvold, Lori; Olmos, Antonio; Song, Youngjin; Franklin, Elizabeth; Enríquez, Mariana; Higgins, Teresa

2014-01-01

The MAST-EL University and School Partnership supports a strategic infrastructure for preparing preservice and in-service teachers ensuring high quality mathematics and science instruction for English learners (ELs). The partnership in its second year consists of thirty-two in-service elementary teachers, three instructional coaches, thirty…
Perspectives of Prospective Elementary School Teachers on Feedback in the Mathematics Instruction I and II Courses

ERIC Educational Resources Information Center

Kögce, Davut

2015-01-01

The purpose of this study was to examine prospective elementary teachers' views on the feedback provided by the instructor and their peers during the courses, Mathematics Instruction I and II, and its contribution to their learning. Forty participants were regularly given feedback by the instructor and their peers while they were taking…

The Educational Approaches of Turkish Pre-Service Elementary Mathematics Teachers in Their First Teaching Practices: Traditional or Constructivist?

ERIC Educational Resources Information Center

Doruk, Bekir Kürsat

2014-01-01

This research aimed to identify the educational approaches that pre-service elementary mathematics teachers adopt for their first teaching practice (TP) and the reasons for their choices. It was carried out with thirteen pre-service teachers (PTs). These PTs were observed during their first TP in a real school setting, and interviews were…
Mathematical Teachers' Perception: Mobile Learning and Constructing 21st Century Collaborative Cloud-Computing Environments in Elementary Public Schools in the State of Kuwait

ERIC Educational Resources Information Center

Alqallaf, Nadeyah

2016-01-01

The purpose of this study was to examine Kuwaiti mathematical elementary teachers' perceptions about their ability to integrate M-learning (mobile learning) into their current teaching practices and the major barriers hindering teachers' ability to create an M-learning environment. Furthermore, this study sought to understand teachers' perceptions…
Goals for Mathematical Education of Elementary School Teachers: A Report of the Cambridge Conference on Teacher Training.

ERIC Educational Resources Information Center

Education Development Center, Inc., Newton, MA.

This report is intended to provide attention to issues that the Cambridge Conference feels are related to the mathematical training of elementary school teachers. The document is divided into three parts. Part I, titled "The Problems and Proposals Towards the Solution," contains the following chapters: (1) Introduction to the Report; (2)…
Applying NAEP to Improve Mathematics Content and Methods Courses for Preservice Elementary and Middle School Teachers

ERIC Educational Resources Information Center

Goodson-Espy, Tracy; Cifarelli, Victor V.; Pugalee, David; Lynch-Davis, Kathleen; Morge, Shelby; Salinas, Tracie

2014-01-01

This study explored how mathematics content and methods courses for preservice elementary and middle school teachers could be improved through the integration of a set of instructional materials based on the National Assessment of Educational Progress (NAEP). A set of eight instructional modules was developed and tested. The study involved 7…
Working toward a Third Space in the Teaching of Elementary Mathematics

ERIC Educational Resources Information Center

Flessner, Ryan

2009-01-01

Building on work in the area of third space theory, this study documents one teacher's efforts to create third spaces in an elementary mathematics classroom. In an attempt to link the worlds of theory and practice, I examine how the work of other theorists and researchers--inside and outside the field of education--can create new lenses for…
A Comparative Study of Geometry in Elementary School Mathematics Textbooks from Five Countries

ERIC Educational Resources Information Center

Wang, Tzu-Ling; Yang, Der-Ching

2016-01-01

The purposes of this study were to compare the differences in the use of geometry in elementary school mathematics textbooks among Finland, Mainland China, Singapore, Taiwan, and the USA and to investigate the relationships between the design of the textbooks and students' performance on large-scale tests such as TIMSS-4 geometry, TIMSS-8…
The Reality of Professional Development of Mathematics and Science Teachers at Elementary Schools in Najran, Saudi Arabia

ERIC Educational Resources Information Center

Aseeri, Mohammed Mofreh Yahya

2015-01-01

This study aimed to identify the practice extent of mathematics and science teachers of professional development activities, its sources and obstacles at elementary schools in Najran, and its relationship with specialty, gender, number of training courses. To achieve the study aims, the research questionnaire was prepared and consisted of (70)…
The Status of Mathematics Achievement in Two Elementary Schools in Palau: 1984-1990. A Report to the Ministry of Education.

ERIC Educational Resources Information Center

King, Irvin L.; Emesiochl, Masa-Aki

When the Trust Territory of the Pacific Islands gradually dissolved in the 1980s, the Republic of Palau assumed a greater responsibility for its own education system. In order to monitor the mathematical achievement of elementary school students during the transition from external to local control of educational procedures, basic skills…
The Effects of Single-Sex Classrooms on Student Outcomes on Mathematics and Reading in an Elementary School

ERIC Educational Resources Information Center

Pilson, Sylvia Yvonne Reddick

2013-01-01

The curriculum for elementary students has undergone a significant change in the past decade. This led to an increased expectation for higher academic performance for fifth grade students in the areas of reading and mathematics. Teachers seek innovative ways to provide instructional practices within their classrooms that will aid success for all…
The Adaptation of the Mathematics Anxiety Rating Scale-Elementary Form into Turkish, Language Validity, and Preliminary Psychometric Investigation

ERIC Educational Resources Information Center

Baloglu, Mustafa; Balgalmis, Esra

2010-01-01

The purpose of the present study was to adapt the Mathematics Anxiety Rating Scale- Elementary Form (MARS-E, Suinn, 1988) into Turkish by first doing the translation of its items and then the preliminary psychometric investigation of the Turkish form. The study included four different samples: 30 bilingual language experts, 50 Turkish language…
How Do Elementary Textbooks Address Fractions? A Review of Mathematics Textbooks in the USA, Japan, and Kuwait

ERIC Educational Resources Information Center

Alajmi, Amal Hussain

2012-01-01

Textbooks play an important part in the design of instruction. This study analyzed the presentation of fractions in textbooks designed for the elementary grades in Kuwait, Japan, and the USA. The analysis focused on the physical characteristics of the books, the structure of the lessons, and the nature of the mathematical problems presented.…
A Comparison of Mathematics Achievement Outcomes among Three Instruction Programs for Pacific Island Elementary Students

ERIC Educational Resources Information Center

Bernardo, Jonathan Christian Amor

2013-01-01

The purpose of this study was to compare the mathematics achievement outcomes of 3rd grade students from some Pacific Island elementary schools that use 1 of 3 different modes of instruction: Direct Instruction (DI), Success for All (SFA), and noncomprehensive school reform (non-CSR). The need for this research stems from the large proportion of…
Elementary Teachers' Perceptions of Practices and Professional Development for Differentiating Mathematics Instruction

ERIC Educational Resources Information Center

Varajic, Sandra

2017-01-01

Teachers and administrators in a Title I elementary school in a southeastern state are concerned that there has been a trend over the past 3 years of declining standardized assessment scores in mathematics for students in Grades 3, 4, and 5. The purpose of this qualitative case study was to explore teachers' perceptions of practices, and…
Analyzing the Psychological Symptoms of Students in Undergraduate Program in Elementary Mathematics Teaching

ERIC Educational Resources Information Center

Masal, Ercan; Koc, Mustafa; Colak, Tugba Seda; Takunyaci, Mithat

2013-01-01

The main purpose of this research is to analyse whether there is a difference or not in levels of having psychological symptoms of the students of undergraduate program in elementary mathematics teaching. Another aim of the research is to determine whether the levels of having psychological symptoms of the students differ or not regarding various…
Pre-Service and In-Service Education in Mathematics of Colorado Elementary School Teachers - A Status Report.

ERIC Educational Resources Information Center

Fisher, John J.; And Others

Described are two studies related to the teaching of mathematics. A sample of 729 teachers who had received teaching certificates in 1965 and an endorsement to teach at the elementary level in Colorado schools were analyzed to determine their college preparation. The college transcripts of these teachers were examined to ascertain how many quarter…
Performance-based classrooms: A case study of two elementary teachers of mathematics and science

NASA Astrophysics Data System (ADS)

Jones, Kenneth W.

This case study depicts how two elementary teachers develop classrooms devoted to performance-based instruction in mathematics and science. The purpose is to develop empirical evidence of classroom practices that leads to a conceptual framework about the nature of performance-based instruction. Performance-based assessment and instruction are defined from the literature to entail involving students in tasks that are complex and engaging, requiring them to apply knowledge and skills in authentic contexts. In elementary mathematics and science, such an approach emphasizes problem solving, exploration, inquiry, and reasoning. The body of the work examines teacher beliefs, curricular orientations, instructional strategies, assessment approaches, management and organizational skills, and interpersonal relationships. The focus throughout is on those aspects that foster student performance in elementary mathematics and science. The resulting framework describes five characteristics that contribute to performance-based classrooms: a caring classroom community, a connectionist learning theory, a thinking and doing curriculum, diverse opportunities for learning, and ongoing assessment, feedback, and adjustment. The conclusion analyzes factors external to the classroom that support or constrain the development of performance-based classrooms and discusses the implications for educational policy and further research.
The link between logic, mathematics and imagination: evidence from children with developmental dyscalculia and mathematically gifted children.

PubMed

Morsanyi, Kinga; Devine, Amy; Nobes, Alison; Szűcs, Dénes

2013-07-01

This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized that the development of mathematical skills is closely related to the development of logical abilities, a domain-general skill. In particular, we expected a close link between mathematical skills and the ability to reason independently of one's beliefs. Our results showed that this was indeed the case, with children with DD performing more poorly than controls, and high maths ability children showing outstanding skills in logical reasoning about belief-laden problems. Nevertheless, all groups performed poorly on structurally equivalent problems with belief-neutral content. This is in line with suggestions that abstract reasoning skills (i.e. the ability to reason about content without real-life referents) develops later than the ability to reason about belief-inconsistent fantasy content.A video abstract of this article can be viewed at http://www.youtube.com/watch?v=90DWY3O4xx8. © 2013 Blackwell Publishing Ltd.
Transcoding abilities in typical and atypical mathematics achievers: the role of working memory and procedural and lexical competencies.

PubMed

Moura, Ricardo; Wood, Guilherme; Pinheiro-Chagas, Pedro; Lonnemann, Jan; Krinzinger, Helga; Willmes, Klaus; Haase, Vitor Geraldi

2013-11-01

Transcoding between numerical systems is one of the most basic abilities acquired by children during their early school years. One important topic that requires further exploration is how mathematics proficiency can affect number transcoding. The aim of the current study was to investigate transcoding abilities (i.e., reading Arabic numerals and writing dictation) in Brazilian children with and without mathematics difficulties, focusing on different school grades. We observed that children with learning difficulties in mathematics demonstrated lower achievement in number transcoding in both early and middle elementary school. In early elementary school, difficulties were observed in both the basic numerical lexicon and the management of numerical syntax. In middle elementary school, difficulties appeared mainly in the transcoding of more complex numbers. An error analysis revealed that the children with mathematics difficulties struggled mainly with the acquisition of transcoding rules. Although we confirmed the previous evidence on the impact of working memory capacity on number transcoding, we found that it did not fully account for the observed group differences. The results are discussed in the context of a maturational lag in number transcoding ability in children with mathematics difficulties. Copyright © 2013 Elsevier Inc. All rights reserved.
The mysterious connection between mathematics and physics.

PubMed

Kauffman, Louis H; Ul-Haq, Rukhsan

2015-12-01

The essay is in the form of a dialogue between the two authors. We take John Wheeler's idea of "It from Bit" as an essential clue and we rework the structure of the bit not to the qubit, but to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We emphasize that mathematics is a combination of calculation and concept. At the conceptual level, mathematics is structured to be independent of time and multiplicity. Mathematics in this way occurs before number and counting. From this timeless domain, mathematics and mathematicians can explore worlds of multiplicity and infinity beyond the apparent limitations of the physical world and see that among these possible worlds there are coincidences with what is observed. Copyright © 2015. Published by Elsevier Ltd.
Teaching Mathematics: Challenging the Sacred Cow of Mathematical Certainty.

ERIC Educational Resources Information Center

Borba, Marcelo C.

1992-01-01

Challenges the concept of mathematical certainty and questions whether it is a useful concept for elementary and secondary mathematics curriculum. Encourages teachers to bring this issue into the classroom and ask students to think about it critically. (HB)

Negative Difference Resistance and Its Application to Construct Boolean Logic Circuits

NASA Astrophysics Data System (ADS)

Nikodem, Maciej; Bawiec, Marek A.; Surmacz, Tomasz R.

Electronic circuits based on nanodevices and quantum effect are the future of logic circuits design. Today's technology allows constructing resonant tunneling diodes, quantum cellular automata and nanowires/nanoribbons that are the elementary components of threshold gates. However, synthesizing a threshold circuit for an arbitrary logic function is still a challenging task where no efficient algorithms exist. This paper focuses on Generalised Threshold Gates (GTG), giving the overview of threshold circuit synthesis methods and presenting an algorithm that considerably simplifies the task in case of GTG circuits.
Predicting Scientific Understanding of Prospective Elementary Teachers: Role of Gender, Education Level, Courses in Science, and Attitudes Toward Science and Mathematics

NASA Astrophysics Data System (ADS)

Kumar, David D.; Morris, John D.

2005-12-01

A multiple regression analysis of the relationship between prospective teachers' scientific understanding and Gender, Education Level (High School, College), Courses in Science (Biology, Chemistry, Physics, Earth Science, Astronomy, and Agriculture), Attitude Towards Science, and Attitude Towards Mathematics is reported. Undergraduate elementary science students ( N = 176) in an urban doctoral-level university in the United States participated in this study. The results of this study showed Gender, completion of courses in High School Chemistry and Physics, College Chemistry and Physics, and Attitudes Toward Mathematics and Science significantly correlated with scientific understanding. Based on a regression model, Gender, and College Chemistry and Physics experiences added significant predictive accuracy to scientific understanding among prospective elementary teachers compared to the other variables.
Computing and Engineering in Elementary School: The Effect of Year-Long Training on Elementary Teacher Self-Efficacy and Beliefs about Teaching Computing and Engineering

ERIC Educational Resources Information Center

Rich, Peter Jacob; Jones, Brian; Belikov, Olga; Yoshikawa, Emily; Perkins, McKay

2017-01-01

STEM, the integration of Science, Technology, Engineering, and Mathematics is increasingly being promoted in elementary education. However, elementary educators are largely untrained in the 21st century skills of computing (a subset of technology) and engineering. The purpose of this study was to better understand elementary teachers'…
Teaching Math More Effectively, Through the Design of Calculational Proofs.

DTIC Science & Technology

1994-03-01

typically taught in a first discrete math course -e.g. set theory, mathematical induction, a theory of integers, finc- tions and relations, combinatorics...by all who want to teach mathematics effectively. 4 4 The authors’ 500-pape text A Logical Approach to Discrete Math (Springer Verlag NY, 1993) uses...the appr,.., h described in this article in teaching the usual topics in discrete math -logic, set theory, & theory of integers, induct,., functions
Launching a Discourse-Rich Mathematics Lesson

ERIC Educational Resources Information Center

Trocki, Aaron; Taylor, Christine; Starling, Tina; Sztajn, Paola; Heck, Daniel

2014-01-01

The idea of elementary school students working together on mathematical tasks is not new, but recent attention to creating purposeful discourse in mathematics classrooms prompts teachers to revisit discourse-promoting strategies for mathematics lessons. The Common Core's Standards for Mathematical Practice (CCSSI 2010) encourage teachers to…
Correlates of Mathematics Anxiety.

ERIC Educational Resources Information Center

McCoy, Leah, P.

1992-01-01

Presents a survey of 78 pre- and in-service elementary teachers in a midwestern region to examine the relationship between mathematics anxiety, perceptual preference, and previous mathematics instructional experiences with workbooks and manipulatives. Results indicate that the variables significant in predicting mathematics anxiety were…
Learning To Teach: Constructing Meaningful Understanding of Mathematical Content. Craft Paper 89-3.

ERIC Educational Resources Information Center

Lappan, Glenda; Even, Ruhama

This paper discusses the development of the mathematical experiences which make up the three-term sequence of mathematics courses taken by participants in the Elementary Mathematics Project (EMP), a longitudinal study of change in preservice teachers' perceptions and beliefs about mathematics. For the mathematics courses, both content and teaching…
Investigating Pre-Service Teachers' Mathematics Anxiety Using the Revised Mathematics Anxiety Scale (RMARS)

ERIC Educational Resources Information Center

Wilson, Sue

2012-01-01

Pre-service primary (elementary) teachers' mathematics anxiety affects their engagement with and future teaching of mathematics. The study measured the range of mathematics anxiety in 219 pre-service teachers starting a teacher education course in an Australian university. They responded to the Revised Mathematics Anxiety Scale (RMARS) and a set…
A Logic Programming Testbed for Inductive Thought and Specification.

ERIC Educational Resources Information Center

Neff, Norman D.

This paper describes applications of logic programming technology to the teaching of the inductive method in computer science and mathematics. It discusses the nature of inductive thought and its place in those fields of inquiry, arguing that a complete logic programming system for supporting inductive inference is not only feasible but necessary.…
Which Kind of Mathematics for Quantum Mechanics? the Relevance of H. Weyl's Program of Research

NASA Astrophysics Data System (ADS)

Drago, Antonino

In 1918 Weyl's book Das Kontinuum planned to found anew mathematics upon more conservative bases than both rigorous mathematics and set theory. It gave birth to the so-called Weyl's elementary mathematics, i.e. an intermediate mathematics between the mathematics rejecting at all actual infinity and the classical one including it almost freely. The present paper scrutinises the subsequent Weyl's book Gruppentheorie und Quantenmechanik (1928) as a program for founding anew theoretical physics - through quantum theory - and at the same time developing his mathematics through an improvement of group theory; which, according to Weyl, is a mathematical theory effacing the old distinction between discrete and continuous mathematics. Evidence from Weyl's writings is collected for supporting this interpretation. Then Weyl's program is evaluated as unsuccessful, owing to some crucial difficulties of both physical and mathematical nature. The present clear-cut knowledge of Weyl's elementary mathematics allows us to re-evaluate Weyl's program in order to look for more adequate formulations of quantum mechanics in any weaker kind of mathematics than the classical one.
New Trends in Mathematics Teaching, Volume III.

ERIC Educational Resources Information Center

United Nations Educational, Scientific, and Cultural Organization, Paris (France).

Each of the ten chapters in this volume is intended to present an objective analysis of the trends of some important subtopic in mathematics education and each includes a bibliography for fuller study. The chapters cover primary school mathematics, algebra, geometry, probability and statistics, analysis, logic, applications of mathematics, methods…
Mathematical Teaching Strategies: Pathways to Critical Thinking and Metacognition

ERIC Educational Resources Information Center

Su, Hui Fang Huang; Ricci, Frederick A.; Mnatsakanian, Mamikon

2016-01-01

A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible…
The Challenges in Developing a Mathematics Curriculum for Training Elementary Teachers in Papua New Guinea

ERIC Educational Resources Information Center

Vagi, Oneau; Green, Rosemary

2004-01-01

As Papua New Guinea undergoes a period of major education reform that includes the establishment of an elementary education programme, the development of an elementary teacher education curriculum is proving to be a challenging task. As a background this paper provides contextual information about the elementary education programme and highlights…
Dispositional logic

NASA Technical Reports Server (NTRS)

Le Balleur, J. C.

1988-01-01

The applicability of conventional mathematical analysis (based on the combination of two-valued logic and probability theory) to problems in which human judgment, perception, or emotions play significant roles is considered theoretically. It is shown that dispositional logic, a branch of fuzzy logic, has particular relevance to the common-sense reasoning typical of human decision-making. The concepts of dispositionality and usuality are defined analytically, and a dispositional conjunctive rule and dispositional modus ponens are derived.
The Relationship between Comprehension and Conceptual Mathematics of Third Grade Students at a Selected Elementary School

ERIC Educational Resources Information Center

Kariuki, Patrick N.; Morris, Dustin A.

2013-01-01

The purpose of this study was to determine the relationship between reading comprehension scores and conceptual mathematics scores of third grade students at a selected elementary school. The sample consisted of 27 students of which 15 were females and 12 were males. Data were collected using a teacher made conceptual math exam and the scores from…
Contribution of Mathematics In-Service Training Course to the Professional Development of Elementary School Teachers in Israel

ERIC Educational Resources Information Center

Mishal, Adina; Patkin, Dorit

2016-01-01

The present study aimed to explore the contribution of a mathematics in-service training course to elementary school teachers (1st-6th grades) in Israel. The study was conducted among 449 educators. They were required to respond to background questions. Moreover, they were asked to indicate their expectations from the in-service training course…
Impact of the Developing Mathematical Ideas Professional Development Program on Grade 4 Students' and Teachers' Understanding of Fractions. REL 2017-256

ERIC Educational Resources Information Center

Jayanthi, Madhavi; Gersten, Russell; Taylor, Mary Jo; Smolkowski, Keith; Dimino, Joseph

2017-01-01

Contemporary state math standards emphasize that students must demonstrate an understanding of the mathematical ideas underlying the computations that have typically been the core of the elementary school math curriculum. The standards have put an increased emphasis on the study of fractions in upper elementary grades, which are the years during…
The Relationship between Elementary Teachers' Background in Mathematics, Teaching Self-Efficacy, and Teaching Outcome Expectancy When Implementing the Common Core State Standards

ERIC Educational Resources Information Center

Stuart, Jennifer Lynn

2017-01-01

The purpose of this correlation study was to identify a possible relationship between elementary teacher background in mathematics as measured by completed college math credit hours, district-provided professional development hours of training in Common Core math standards, and years of teaching experience, and teacher efficacy in math as measured…
The Language Factor in Elementary Mathematics Assessments: Computational Skills and Applied Problem Solving in a Multidimensional IRT Framework

ERIC Educational Resources Information Center

Hickendorff, Marian

2013-01-01

The results of an exploratory study into measurement of elementary mathematics ability are presented. The focus is on the abilities involved in solving standard computation problems on the one hand and problems presented in a realistic context on the other. The objectives were to assess to what extent these abilities are shared or distinct, and…
Effects of a Mathematics Intervention Program on the Computational Skills and Attitudes of Preservice Elementary and Secondary Teachers.

ERIC Educational Resources Information Center

Amodeo, Luiza B.; Emslie, Julia Rosa

Mathematics anxiety and competence of 57 Anglo and Hispanic pre-service teachers were measured before and after a 30-hour workshop using the training program EQUALS. Students were divided into three groups: elementary, secondary, and library media. Students in the library media class served as the control group; the other two groups were the…

Problem Posing and Solving with Mathematical Modeling

ERIC Educational Resources Information Center

English, Lyn D.; Fox, Jillian L.; Watters, James J.

2005-01-01

Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.
What Is the Long-Run Impact of Learning Mathematics during Preschool?

ERIC Educational Resources Information Center

Watts, Tyler W.; Duncan, Greg J.; Clements, Douglas H.; Sarama, Julie

2018-01-01

The current study estimated the causal links between preschool mathematics learning and late elementary school mathematics achievement using variation in treatment assignment to an early mathematics intervention as an instrument for preschool mathematics change. Estimates indicate (n = 410) that a standard deviation of intervention-produced change…
Studies in Mathematics, Volume X. Applied Mathematics in the High School.

ERIC Educational Resources Information Center

Schiffer, Max M.

This publication contains a sequence of lectures given to high school mathematics teachers by the author. Applications of mathematics emphasized are elementary algebra, geometry, and matrix algebra. Included are: (1) an introduction concerning teaching applications of mathematics; (2) Chapter 1: Mechanics for the High School Student; (3) Chapter…
Asynchronous Discourse in a Web-Assisted Mathematics Education Course

ERIC Educational Resources Information Center

Li, Zhongxiao

2009-01-01

Fall term of 2006, a web-assisted undergraduate mathematics course was taught at the University of Idaho: Math 235 Mathematics for Elementary Teachers I. The course goals were: To foster a deep understanding of critical mathematical content; and to promote the development of mathematical communication and collaboration concepts, skills, and…
Mathematics in Tribal Philippines and Other Societies in the South Pacific.

ERIC Educational Resources Information Center

Lee-Chua, Queena N.

2001-01-01

Investigates mathematics in the societies of Southeast Asia and the South Pacific with special focus on the Philippines. Presents mathematical practices such as counting and measurement, time, geometry, and logic, in ancient and present day times. (KHR)
The Impact of Competition on Raising Mathematics Competency at Camelot Elementary School in Chesapeake, Virginia

NASA Astrophysics Data System (ADS)

Hayden, L. B.; Johnson, D.

2012-12-01

In 1995, the Virginia Department of Education approved a federal mandate for No Child Left Behind 2001 Education Act implementing the Standards of Learning (SOL) in four content areas: Mathematics, Science, English, and History and Social Sciences. These new guidelines set forth learning and achievement expectations for content areas for grades K-12 in Virginia's Public Schools. Given the SOL mandates, Virginia's elementary teachers and school leaders utilized research for specific teaching methods intended to encourage score improvements on end of year mathematics tests. In 2001, the concept of the Math Sprint Competition was introduced to Camelot Elementary School in Chesapeake Virginia, by researchers at Elizabeth City State University of Elizabeth City, North Carolina. Camelot Elementary, a K-5 school, is a Title I school nestled in a lower middle class neighborhood and houses a high number of minority students. On average, these students achieve lower test score gains than students in higher socioeconomic status district schools. Defined as a test-review based in relay format that utilizes released SOL test items, Math Sprint promotes mathematical skills outlined in Virginia SOL's and encourages competition among students that motivated them to quickly pick up on new material and retain the old material in order to out-do the others. Research identified was based on specific relationships between student competition and statewide testing results in mathematics for grades three, four, and five at Camelot Elementary. Data was compiled from results of the Math Sprint Competition and research focused on methods for motivating students encouraged by the use of a math sprint competition. Individual Pearson Product Moment Correlations were conducted to determine which variables possess strong and statistically significant relationships. Significantly, positive results came from 2005 to 2010 math sprints data from which students participated.
The Study on the Effect of Educational Games for the Development of Students’ Logic-Mathematics of Multiple Intelligence

NASA Astrophysics Data System (ADS)

Li, Jing; Ma, Sujuan; Ma, Linqing

Firstly, in this article, we expound the theory of the educational games and multiple intelligence and analyze the relationship between them. Then, further, we elaborate educational games' effect on the development of students' multiple intelligence, taking logic-mathematics intelligence for example. Also, we discuss the strategies of using educational games to improve students' intelligence. In a word, we can use the computer games to develop the students' multi-intelligence.
Effects of Cooperative Learning STAD on Mathematical Communication Ability of Elementary School Student

NASA Astrophysics Data System (ADS)

Maelasari, E.; Wahyudin

2017-09-01

The aim of this study is to describe the increasing of mathematical communications capability, and difference between students who get STAD cooperative learning and students who receive Direct Instruction. This study is a quasi-experimental study with pretest posttest study design. Subjects in this study in one of the fifth grade elementary school located in Cibeureum District, Kuningan. The research instrument used was a written test mathematical communication skills. The results showed that the improvement of mathematical communication capabilities Direct Instruction students who scored significantly better than students who learned with STAD cooperative learning. By grouping according to the ability of students will show a positive impact on student achievement in the classroom.
Is There a Relationship between Pre-Service Teachers' Mathematical Values and Their Teaching Anxiety in Mathematics?

ERIC Educational Resources Information Center

Yazici, Ersen; Peker, Murat; Ertekin, Erhan; Dilmac, Bulent

2011-01-01

Introduction: The aim of this study is to investigate the relation between the pre-service teachers' mathematical values and teaching anxieties in mathematics. Method: The research was carried out on 359 teacher candidates attending the elementary school mathematics, secondary school mathematics and primary school teaching programs. To this end,…
Mathematical Games

ERIC Educational Resources Information Center

Gardner, Martin

1978-01-01

Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)
SELECTED ANNOTATED BIBLIOGRAPHY ON SYSTEMS OF THEORETICAL DEVICES,

DTIC Science & Technology

BIONICS, BIBLIOGRAPHIES), (*BIBLIOGRAPHIES, BIONICS), (*CYBERNETICS, BIBLIOGRAPHIES), MATHEMATICS, COMPUTER LOGIC, NETWORKS, NERVOUS SYSTEM , THEORY , SEQUENCE SWITCHES, SWITCHING CIRCUITS, REDUNDANT COMPONENTS, LEARNING, MATHEMATICAL MODELS, BEHAVIOR, NERVES, SIMULATION, NERVE CELLS
Dispositional logic

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

Zadeh, L.A.

1988-01-01

The applicability of conventional mathematical analysis (based on the combination of two-valued logic and probability theory) to problems in which human judgment, perception, or emotions play significant roles is considered theoretically. It is shown that dispositional logic, a branch of fuzzy logic, has particular relevance to the common-sense reasoning typical of human decision-making. The concepts of dispositionality and usuality are defined analytically, and a dispositional conjunctive rule and dispositional modus ponens are derived. 7 references.
STEM Is Elementary: Challenges Faced by Elementary Teachers in the Era of the Next Generation Science Standards

ERIC Educational Resources Information Center

Isabelle, Aaron D.

2017-01-01

For students to achieve the goals of the Next Generation Science Standards (NGSS) by Grade 12, thinking and acting like scientists and engineers must begin in the elementary grades. However, elementary teachers may find this challenging -because language arts and mathematics still dominate many classrooms--often at the expense of science. This…
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…
How Syntactic Reasoners Can Develop Understanding, Evaluate Conjectures, and Generate Counterexamples in Advanced Mathematics

ERIC Educational Resources Information Center

Weber, Keith

2009-01-01

This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…
Triple Play: From De Morgan to Stirling to Euler to Maclaurin to Stirling

ERIC Educational Resources Information Center

Kolpas, Sid

2011-01-01

Augustus De Morgan (1806-1871) was a significant Victorian Mathematician who made contributions to mathematics history, mathematical recreations, mathematical logic, calculus, and probability and statistics. He was an inspiring mathematics professor who influenced many of his students to join the profession. One of De Morgan's significant books…
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.
Math is Functional! A Math Fair for Kids.

ERIC Educational Resources Information Center

Reys, Barbara J.; Wasman, Deanna G.

1998-01-01

Describes a mathematics fair prepared by the University of Missouri Mathematics Teachers Organization (UM2TO) which includes games involving numbers and computation, logic puzzles, geometry and spatial-visualization exploration, and probability and statistics activities. Presents tips for developing a mathematics fair. (ASK)
Improving the Reasoning Ability of Elementary School Student through the Indonesian Realistic Mathematics Education

ERIC Educational Resources Information Center

Saleh, Muhamad; Prahmana, Rully Charitas Indra; Isa, Muhammad; Murni

2018-01-01

By taking the role as a mentor and a facilitator, a teacher in the 4th grade of elementary school needs to look at the condition of the students in the concrete thinking stage. Learning process needs to be adjusted such that the abstract objects in mathematics can be represented through concrete objects as a bridge to enter the knowledge that the…
Are Graphic Novels Always "Cool"? Parent and Student Perspectives on Elementary Mathematics and Science Graphic Novels: The Need for Action Research by School Leaders

ERIC Educational Resources Information Center

Nesmith, Suzanne; Cooper, Sandi; Schwarz, Gretchen; Walker, Amanda

2016-01-01

Often the stakeholders most affected by curriculum change are uninvolved in the change process, leading to curriculum reforms that fail. Thus, a group of university researchers conducted a small-scale study to explore the thoughts and opinions of parents and elementary students on the use of mathematics and science graphic novels to support the…

Photonic ququart logic assisted by the cavity-QED system.

PubMed

Luo, Ming-Xing; Deng, Yun; Li, Hui-Ran; Ma, Song-Ya

2015-08-14

Universal quantum logic gates are important elements for a quantum computer. In contrast to previous constructions of qubit systems, we investigate the possibility of ququart systems (four-dimensional states) dependent on two DOFs of photon systems. We propose some useful one-parameter four-dimensional quantum transformations for the construction of universal ququart logic gates. The interface between the spin of a photon and an electron spin confined in a quantum dot embedded in a microcavity is applied to build universal ququart logic gates on the photon system with two freedoms. Our elementary controlled-ququart gates cost no more than 8 CNOT gates in a qubit system, which is far less than the 104 CNOT gates required for a general four-qubit logic gate. The ququart logic is also used to generate useful hyperentanglements and hyperentanglement-assisted quantum error-correcting code, which may be available in modern physical technology.
Photonic ququart logic assisted by the cavity-QED system

PubMed Central

Luo, Ming-Xing; Deng, Yun; Li, Hui-Ran; Ma, Song-Ya

2015-01-01

Universal quantum logic gates are important elements for a quantum computer. In contrast to previous constructions of qubit systems, we investigate the possibility of ququart systems (four-dimensional states) dependent on two DOFs of photon systems. We propose some useful one-parameter four-dimensional quantum transformations for the construction of universal ququart logic gates. The interface between the spin of a photon and an electron spin confined in a quantum dot embedded in a microcavity is applied to build universal ququart logic gates on the photon system with two freedoms. Our elementary controlled-ququart gates cost no more than 8 CNOT gates in a qubit system, which is far less than the 104 CNOT gates required for a general four-qubit logic gate. The ququart logic is also used to generate useful hyperentanglements and hyperentanglement-assisted quantum error-correcting code, which may be available in modern physical technology. PMID:26272869
The Influence of Mathematics Vocabulary Instruction Embedded within Addition Tutoring for First-Grade Students with Mathematics Difficulty

ERIC Educational Resources Information Center

Powell, Sarah R.; Driver, Melissa K.

2015-01-01

Researchers and practitioners indicate students require explicit instruction on mathematics vocabulary terms, yet no study has examined the effects of an embedded vocabulary component within mathematics tutoring for early elementary students. First-grade students with mathematics difficulty (MD; n = 98) were randomly assigned to addition tutoring…
Preparing Mathematics Teachers for Elementary High-Poverty Schools: Perceptions and Suggestions from Preservice Teachers

ERIC Educational Resources Information Center

McKinney, Sueanne E.; Berry, Robert Q., III; Jackson, Joan M.

2007-01-01

The National Council of Teachers of Mathematics articulates an ambitious vision of a high-quality mathematics program. Achieving this vision requires competent and knowledgeable teachers who can support all students in learning mathematics concepts with understanding. Effective mathematics teachers are especially needed for high-poverty schools…
Moving toward Positive Mathematics Beliefs and Developing Socio-Mathematical Authority: Urban Preservice Teachers in Mathematics Methods Courses

ERIC Educational Resources Information Center

Saran, Rupam; Gujarati, Joan

2013-01-01

This article explores how preservice elementary teachers change their negative beliefs toward mathematics into positive ones after taking a mathematics methods course that follows the Concrete-Pictorial-Abstract (CPA) instructional method. Also explored is the relationship between those beliefs and sociomathematical authority. By administering…
Symbolic Drawings Reveal Changes in Preservice Teacher Mathematics Attitudes after a Mathematics Methods Course

ERIC Educational Resources Information Center

Rule, Audrey C.; Harrell, Mary H.

2006-01-01

A new method of analyzing mathematics attitudes through symbolic drawings, situated within the field of Jungian-oriented analytical psychology, was applied to 52 preservice elementary teachers before and after a mathematics methods course. In this triangulation mixed methods design study, pretest images related to past mathematics experiences…
Game Multimedia in Numeracy Learning for Elementary School Students

NASA Astrophysics Data System (ADS)

Rohendi, D.; Sumarna, N.; Sutarno, H.

2017-03-01

Numeracy is one of the basic skills for elementary students to understand further concepts of mathematics. However teaching numeracy is still using recitation that can overload student’s memory and make them reluctant to learn mathematics, so an innovative way by using multimedia to attract student interest in numeracy is needed. Therefore, the purpose of this study are: 1) to develop numeracy learning multimedia for elementary school students; and 2) to find out whether the implementation of numeracy learning multimedia can improve the students numeracy skills, and how is the response of elementary school students by using multimedia in learning numeracy? The results showed that multimedia can improve students’ numeracy skill which is quit medium and the student response by using multimedia in numeracy learning are good.
Robust Fuzzy Logic Stabilization with Disturbance Elimination

PubMed Central

Danapalasingam, Kumeresan A.

2014-01-01

A robust fuzzy logic controller is proposed for stabilization and disturbance rejection in nonlinear control systems of a particular type. The dynamic feedback controller is designed as a combination of a control law that compensates for nonlinear terms in a control system and a dynamic fuzzy logic controller that addresses unknown model uncertainties and an unmeasured disturbance. Since it is challenging to derive a highly accurate mathematical model, the proposed controller requires only nominal functions of a control system. In this paper, a mathematical derivation is carried out to prove that the controller is able to achieve asymptotic stability by processing state measurements. Robustness here refers to the ability of the controller to asymptotically steer the state vector towards the origin in the presence of model uncertainties and a disturbance input. Simulation results of the robust fuzzy logic controller application in a magnetic levitation system demonstrate the feasibility of the control design. PMID:25177713
Synchronous Online Collaborative Professional Development for Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Francis, Krista; Jacobsen, Michele

2013-01-01

Math is often taught poorly emphasizing rote, procedural methods rather than creativity and problem solving. Alberta Education developed a new mathematics curriculum to transform mathematics teaching to inquiry driven methods. This revised curriculum provides a new vision for mathematics and creates opportunities and requirements for professional…
Social Risk Takers: Understanding Bilingualism in Mathematical Discussions

ERIC Educational Resources Information Center

Dominguez, Higinio

2017-01-01

The teaching and research communities in mathematics education agree that mathematical discussions pose challenges in elementary classrooms. These challenges continue to motivate research on mathematical discussions, with a focus on how students use talk in discussions. This study addresses the question, "What can teachers and researchers…
Didactical Design Material Units of Distance and Speed to Developed Mathematical Connection in Elementary School

NASA Astrophysics Data System (ADS)

Jannah, R. R.; Apriliya, S.; Karlimah

2017-03-01

This study aims to develop alternative instructional design based of barriers learning which identified by developing mathematical connection capabilities to the material unit of distance and speed. The research was conducted in the fifth grade elementary school Instructional design is complemented with a hypothetical learning trajectory in the form of a pedagogical didactic anticipation. The method used is descriptive method with qualitative approach. Techniques data collection used were observation, interviews, and documentation. The instrument used the researchers themselves are equipped with an instrument written test. The data were analyzed qualitatively to determine the student learning obstacles, then arrange hypothetical learning trajectory and pedagogical didactic anticipation. Learning obstacle are identified, it is learning obstacle related the connections between mathematical topics, learning obstacle related with other disciplines, and learning obstacle related with everyday life. The results of this research are improvement and development of didactic design in mathematics which has activities mathematical connection to the material unit of distance and speed in elementary school. The learning activities are carried out is using varied methods include method lectures, demonstrations, practice and exercise, as well as using the modified instructional media.
An adaptive maneuvering logic computer program for the simulation of one-to-one air-to-air combat. Volume 2: Program description

NASA Technical Reports Server (NTRS)

Burgin, G. H.; Owens, A. J.

1975-01-01

A detailed description is presented of the computer programs in order to provide an understanding of the mathematical and geometrical relationships as implemented in the programs. The individual sbbroutines and their underlying mathematical relationships are described, and the required input data and the output provided by the program are explained. The relationship of the adaptive maneuvering logic program with the program to drive the differential maneuvering simulator is discussed.
Assessing Elementary Prospective Teachers' Mathematical Explanations after Engagement in Online Mentoring Modules

ERIC Educational Resources Information Center

Wall, Jennifer; Selmer, Sarah; Bingham Brown, Amy

2016-01-01

Prospective elementary teachers at three universities engaged in online modules called the Virtual Field Experience, created by the Math Forum. The prospective teachers learned about problem solving and mentoring elementary students in composing solutions and explanations to nonroutine challenge problems. Finally, through an asynchronous online…
A Collaborative Approach for Elementary Science

ERIC Educational Resources Information Center

Nelson, George D.; Landel, Carolyn C.

2007-01-01

The authors question whether elementary students will have access to effective science and mathematics instruction within the current structure of elementary schools, in which each classroom teachers is expected to possess the expertise to teach all subjects well. They review research showing that good teachers are the key to student achievement…
Prospective Elementary Teachers' Development of Fraction Number Sense

ERIC Educational Resources Information Center

Utley, Juliana; Reeder, Stacy

2012-01-01

Can prospective elementary teachers "unlearn" harmful algorithms used with fractions as they are invited to develop fraction number sense? This study examined the development of prospective elementary teachers' fraction number sense during an intermediate (grades 5-8) mathematics methods course. During this course, participants' were involved in a…
Secondary School Mathematics Curriculum Improvement Study Information Bulletin 7.

ERIC Educational Resources Information Center

Secondary School Mathematics Curriculum Improvement Study, New York, NY.

The background, objectives, and design of Secondary School Mathematics Curriculum Improvement Study (SSMCIS) are summarized. Details are given of the content of the text series, "Unified Modern Mathematics," in the areas of algebra, geometry, linear algebra, probability and statistics, analysis (calculus), logic, and computer…
Unpacking the Logic of Mathematical Statements.

ERIC Educational Resources Information Center

Selden, John; Selden, Annie

1995-01-01

Investigated (n=61) undergraduates' ability to unpack informally written mathematical statements into the language of predicate calculus in an introduction to proofs and mathematical reasoning. Found that students were unable to construct proofs or validate them. Appendices are "A Sample Validation" and "Building a Statement Image." (MKR)
To Know and to Teach: Mathematical Pedagogy from a Historical Context.

ERIC Educational Resources Information Center

Swetz, Frank

1995-01-01

Investigated historical works for pedagogical techniques. Found the use of instructional discourse, logical sequencing of mathematical problems and exercises, and employment of visual aids. Concludes that much of present day mathematical pedagogy evolved from distant historical antecedents. (30 references) (Author/MKR)
Humanize Your Classroom with the History of Mathematics.

ERIC Educational Resources Information Center

Bidwell, James K.

1993-01-01

History humanizes mathematics and explains the "whys" by showing its logical development. Communicating, connecting, and valuing of mathematics can be effected by interjecting historical moments, reading biographies, creating displays for the classroom, and tracing historically accurate developments of topics in class. (Contains 26…
A "True" Story about Mathematical Reasoning Made Easy

ERIC Educational Resources Information Center

Bragg, Leicha A.; Herbert, Sandra

2017-01-01

Mathematical reasoning is one of the four proficiencies in the Australian Curriculum: Mathematics (AC:M) where it is described as: "[the] capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising" (Australian Curriculum, Assessment and Reporting Authority [ACARA],…

Olympiads for Elementary Schools.

ERIC Educational Resources Information Center

Lenchner, George

1985-01-01

The goals and history of the Mathematical Olympiads for Elementary Schools are described. Teams, levels, and gender are discussed, as well as teacher training, administration, scoring, and awards. Sample problems are included. (MNS)
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.
Elementary school students visual spatial comprehension based on van Hiele Theory: the case in Madiun, East Java, Indonesia

NASA Astrophysics Data System (ADS)

Andini, S.; Fitriana, L.; Budiyono

2018-03-01

This study presents partial result from the project “Geometry in Flipbook Multimedia: A Technology Role in Improving Mathematical Learning Quality in Madiun”, which was undertaken to explore the skill of geometry and passing rate of van Hiele’s geometric thinking level, especially for the first three level. The material focus of the study is a two-dimensional figure and reviewed from basic skill aspect of geometry (visual, verbal, drawing, logic, and application). The participants were 30 students in the 6 grade of elementary school in Madiun, East Java. The data collecting technique for this study there are a test instrument of van Hiele geometry (VHG) and an interview’s instrument about characteristics geometry basic skill. After the test, twelve students from participants were randomly selected interviewed to determine their geometry basic skill. This study found that (1) most of the students of 6 grade can only reach the first level is about 69%, the passing rate at the second level test is about 49%, and at the third level, the average of students' achievement is 35%, (2) if viewed from five basic skills of geometry, most of the students have a low mastery, and (3) the achievement of grade six students are inclined high in first level and low in third level based on van Hiele’s Geometric Thinking Level.
ABCs of Early Mathematics Experiences

ERIC Educational Resources Information Center

Hensen, Laurie E.

2005-01-01

Children begin to develop mathematical thinking before they enter school. Art, baking, playing with blocks, counting numbers, games, puzzles, singing, playing with pretend money, water play all these early mathematical experiences help the children to learn in the elementary school years.
Logic. Geometry Module for Use in a Mathematics Laboratory Setting.

ERIC Educational Resources Information Center

Brotherton, Sheila; And Others

Within this single module there are two approaches to this brief survey of logic. Since most geometry textbooks fail to give an adequate discussion of logic, a "textbook" treatment of the subject has been included. This is found as explanations interspersed in the exercises and these can be used as a textbook approach. However, also included is an…
Group Solutions, Too! More Cooperative Logic Activities for Grades K-4. Teacher's Guide. LHS GEMS.

ERIC Educational Resources Information Center

Goodman, Jan M.; Kopp, Jaine

There is evidence that structured cooperative logic is an effective way to introduce or reinforce mathematics concepts, explore thinking processes basic to both math and science, and develop the important social skills of cooperative problem-solving. This book contains a number of cooperative logic activities for grades K-4 in order to improve…
Using the Title I Control Group Model for Evaluation Research and Development of a Supplemental Mathematics Project for Third and Fifth Grade Students.

ERIC Educational Resources Information Center

Slaughter, Helen B.

Mathematics achievement of Elementary Secondary Education Act Title I students was evaluated, using RMC Model B, the control group model. The third-grade students in 8 of 17 Title I elementary schools and the fifth-grade students in the remaining 9 schools were chosen for the pilot project. The remaining third-and fifth-grade students served as…
Competency Based Teacher Education Component. Curriculum Methods and Materials, Elementary Mathematics and Social Studies.

ERIC Educational Resources Information Center

Woodworth, William D.

Four mathematical/social studies module clusters are presented in an effort to develop proficiency in instruction and in inductive and deductive teaching procedures. Modules within the first cluster concern systems of numeration, set operations, numbers, measurement, geometry, mathematics, and reasoning. The second mathematical cluster presents…
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…
The Effectiveness of Technology Integration in a Metropolitan Elementary Mathematics Program: Mad Dog Math

ERIC Educational Resources Information Center

Cohen, Miriam

2012-01-01

The outcome of American students' performances during international comparisons consistently scoring inadequately in mathematics exposes the crisis of deficient mathematics achievement thus causing deep concerns. Learners who acquire a strong theoretical foundation in mathematics at the primary level thrived later in more advanced level…
Forces and Issues Related to Curriculum and Instruction, K-6

ERIC Educational Resources Information Center

DeVault, M. Vere; Weaver, J. Fred

1970-01-01

Traces the development of elementary mathematics curriculum and instruction from colonial times to the present. Each section emphasizes four major issues: Why teach mathematics? What mathematics should be taught? How should the mathematics we teach be organized? How should we organize and implement instruction? Also included are several items…
Expanding Mathematics Preparation of Elementary and Middle School Teachers

ERIC Educational Resources Information Center

Buck, Robert E.

2004-01-01

One of the major problems facing education today is the inadequate mathematics' preparation of pre-college students and their teachers. Most colleges and universities have well established programs for students planning to teach mathematics at the secondary schools; however, in many institutions pre-secondary mathematics has been addressed only…
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…
Investigations in Mathematics Education, Vol. 10, No. 1.

ERIC Educational Resources Information Center

Osborne, Alan R., Ed.

Eighteen research reports related to mathematics education are abstracted and analyzed. Studies include elementary, secondary, and college mathematics education areas. A majority of the studies relate to instruction and learning. Research related to mathematics education which was reported in RESOURCES IN EDUCATION and CURRENT INDEX TO JOURNALS IN…
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
What Is the Long-Run Impact of Learning Mathematics During Preschool?

PubMed

Watts, Tyler W; Duncan, Greg J; Clements, Douglas H; Sarama, Julie

2018-03-01

The current study estimated the causal links between preschool mathematics learning and late elementary school mathematics achievement using variation in treatment assignment to an early mathematics intervention as an instrument for preschool mathematics change. Estimates indicate (n = 410) that a standard deviation of intervention-produced change at age 4 is associated with a 0.24-SD gain in achievement in late elementary school. This impact is approximately half the size of the association produced by correlational models relating later achievement to preschool math change, and is approximately 35% smaller than the effect reported by highly controlled ordinary least squares (OLS) regression models (Claessens et al., 2009; Watts et al., ) using national data sets. Implications for developmental theory and practice are discussed. © 2017 The Authors. Child Development © 2017 Society for Research in Child Development, Inc.
A logic-based dynamic modeling approach to explicate the evolution of the central dogma of molecular biology.

PubMed

Jafari, Mohieddin; Ansari-Pour, Naser; Azimzadeh, Sadegh; Mirzaie, Mehdi

It is nearly half a century past the age of the introduction of the Central Dogma (CD) of molecular biology. This biological axiom has been developed and currently appears to be all the more complex. In this study, we modified CD by adding further species to the CD information flow and mathematically expressed CD within a dynamic framework by using Boolean network based on its present-day and 1965 editions. We show that the enhancement of the Dogma not only now entails a higher level of complexity, but it also shows a higher level of robustness, thus far more consistent with the nature of biological systems. Using this mathematical modeling approach, we put forward a logic-based expression of our conceptual view of molecular biology. Finally, we show that such biological concepts can be converted into dynamic mathematical models using a logic-based approach and thus may be useful as a framework for improving static conceptual models in biology.
A logic-based dynamic modeling approach to explicate the evolution of the central dogma of molecular biology

PubMed Central

Jafari, Mohieddin; Ansari-Pour, Naser; Azimzadeh, Sadegh; Mirzaie, Mehdi

2017-01-01

It is nearly half a century past the age of the introduction of the Central Dogma (CD) of molecular biology. This biological axiom has been developed and currently appears to be all the more complex. In this study, we modified CD by adding further species to the CD information flow and mathematically expressed CD within a dynamic framework by using Boolean network based on its present-day and 1965 editions. We show that the enhancement of the Dogma not only now entails a higher level of complexity, but it also shows a higher level of robustness, thus far more consistent with the nature of biological systems. Using this mathematical modeling approach, we put forward a logic-based expression of our conceptual view of molecular biology. Finally, we show that such biological concepts can be converted into dynamic mathematical models using a logic-based approach and thus may be useful as a framework for improving static conceptual models in biology. PMID:29267315
Effects of a Mathematics Fluency Program on Mathematics Performance of Students with Challenging Behaviors

ERIC Educational Resources Information Center

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

2016-01-01

In the present study, we examined the effects of a fluency-building mathematics program called Great Leaps Math on fluency of basic addition mathematics facts zero to nine and word problem solving using a multiple probe design across participants. Three elementary students with challenging behaviors and mathematics difficulty participated in the…
The Effect of Cognitive- and Metacognitive-Based Instruction on Problem Solving by Elementary Students with Mathematical Learning Difficulties

ERIC Educational Resources Information Center

Grizzle-Martin, Tamieka

2014-01-01

Children who struggle in mathematics may also lack cognitive awareness in mathematical problem solving. The cognitively-driven program IMPROVE, a multidimensional method for teaching mathematics, has been shown to be helpful for students with mathematical learning difficulties (MLD). Guided by cognitive theory, the purpose of this…

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…
Elementary School Teachers' Interpretation and Promotion of Creativity in the Learning of Mathematics: A Grounded Theory Study

ERIC Educational Resources Information Center

Shen, Yinjing

2014-01-01

Creativity is important for young children learning mathematics. Comparing the investment theory of creativity and national standards and principles for early mathematics shows that doing mathematics is more than applying rules and procedures; rather, learning mathematics takes a lot of creativity. However, much literature claimed that creativity…
Mathematics Teacher Identity in the Context of Mathematics Reform: Elementary Teacher Experiences

ERIC Educational Resources Information Center

Sun, Jennifer

2017-01-01

Reform efforts and changes in mathematics education have brought on a shift towards a new vision of mathematics teaching in the United States. In light of recent accountability standards, the focus on teacher learning within the context of mathematics professional development is even more pressing. Prior research on teacher learning in the context…
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…
Simulation and Verification of Synchronous Set Relations in Rewriting Logic

NASA Technical Reports Server (NTRS)

Rocha, Camilo; Munoz, Cesar A.

2011-01-01

This paper presents a mathematical foundation and a rewriting logic infrastructure for the execution and property veri cation of synchronous set relations. The mathematical foundation is given in the language of abstract set relations. The infrastructure consists of an ordersorted rewrite theory in Maude, a rewriting logic system, that enables the synchronous execution of a set relation provided by the user. By using the infrastructure, existing algorithm veri cation techniques already available in Maude for traditional asynchronous rewriting, such as reachability analysis and model checking, are automatically available to synchronous set rewriting. The use of the infrastructure is illustrated with an executable operational semantics of a simple synchronous language and the veri cation of temporal properties of a synchronous system.
Execution of Educational Mechanical Production Programs for School Children

NASA Astrophysics Data System (ADS)

Itoh, Nobuhide; Itoh, Goroh; Shibata, Takayuki

The authors are conducting experience-based engineering educational programs for elementary and junior high school students with the aim to provide a chance for them to experience mechanical production. As part of this endeavor, we planned and conducted a program called “Fabrication of Original Magnet Plates by Casting” for elementary school students. This program included a course for leading nature laws and logical thinking method. Prior to the program, a preliminary program was applied to school teachers to get comments and to modify for the program accordingly. The children responded excellently to the production process which realizes their ideas, but it was found that the course on natural laws and logical methods need to be improved to draw their interest and attention. We will continue to plan more effective programs, deepening ties with the local community.
Urban Elementary Single-Sex Math Classrooms: Mitigating Stereotype Threat for African American Girls

ERIC Educational Resources Information Center

Bowe, Anica G.; Desjardins, Christopher D.; Covington Clarkson, Lesa M.; Lawrenz, Frances

2017-01-01

This study utilized a mixed-methods approach to holistically examine single-sex and coeducational urban elementary mathematics classes through situated cognitive theory. Participants came from two urban low-income Midwestern elementary schools with a high representation of minority students (n = 77 sixth graders, n = 4 teachers, n = 2 principals).…
The Association between Elementary School Start Time and Students' Academic Achievement in Wayzata Public Schools

ERIC Educational Resources Information Center

Dupuis, Danielle N.

2015-01-01

The Center for Applied Research and Educational Improvement (CAREI) conducted two analyses with the purpose of examining the association between elementary school start time and students' academic achievement in mathematics and reading in Wayzata Public Schools. The first analysis examined the association between elementary school start time and…
Teacher Perspectives on Specialisation in the Elementary Classroom: Implications for Science Instruction

ERIC Educational Resources Information Center

Poland, Susan; Colburn, Amanda; Long, David E.

2017-01-01

In the current educational climate of testing and accountability, many elementary teachers find they lack adequate time and confidence to enact reform-based science teaching due to pressure to perform in reading and mathematics. With this tension in mind, we explore the phenomenon of elementary teacher specialisation in comparison to the…
The Effects of a STEM Intervention on Elementary Students' Science Knowledge and Skills

ERIC Educational Resources Information Center

Cotabish, Alicia; Dailey, Debbie; Robinson, Ann; Hughes, Gail

2013-01-01

The purpose of the study was to assess elementary students' science process skills, content knowledge, and concept knowledge after one year of participation in an elementary Science, Technology, Engineering, and Mathematics (STEM) program. This study documented the effects of the combination of intensive professional development and the use of…
Conceptualizing Routines of Practice That Support Algebraic Reasoning in Elementary Schools: A Constructivist Grounded Theory

ERIC Educational Resources Information Center

Store, Jessie Chitsanzo

2012-01-01

There is ample literature documenting that, for many decades, high school students view algebra as difficult and do not demonstrate understanding of algebraic concepts. Algebraic reasoning in elementary school aims at meaningfully introducing algebra to elementary school students in preparation for higher-level mathematics. While there is research…
Using Citizen Science to Engage Preservice Elementary Educators in Scientific Fieldwork

ERIC Educational Resources Information Center

Scott, Catherine M.

2016-01-01

Preservice elementary teachers' lack of confidence in teaching science is an ongoing concern. Only 29% of elementary teachers in the field felt "very well prepared to teach life science," according to the National Survey of Science and Mathematics Education. Research has suggested that bridging informal and formal science education can…
Prospective Elementary School Teachers' Professional Noticing of Children's Early Numeracy

ERIC Educational Resources Information Center

Schack, Edna O.; Fisher, Molly H.; Thomas, Jonathan N.; Eisenhardt, Sara; Tassell, Janet; Yoder, Margaret

2013-01-01

The goal of this study is to develop the professional noticing abilities of prospective elementary school teachers in the context of the Stages of Early Arithmetic Learning. In their mathematics methods course, ninety-four prospective elementary school teachers from three institutions participated in a researcher-developed five-session module that…
Pre-Service Elementary Teachers' Understanding of Pattern and Function

ERIC Educational Resources Information Center

Sharon, Valerie Vinyard

2010-01-01

Scope and method of study: The purpose of this study was to unpack the understandings pre-service elementary teachers have pertaining to the ideas of pattern and function. The intent was to bring insight into how mathematics teacher educators can use patterning activities to prepare pre-service elementary teachers to support the development of…
Assessing Elementary Algebra with STACK

ERIC Educational Resources Information Center

Sangwin, Christopher J.

2007-01-01

This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…
Preservice Elementary School Teachers' Conceptual Understanding of Place Value within a Constructivist Framework

ERIC Educational Resources Information Center

Murawska, Jaclyn Marie

2013-01-01

This research study examined the development of 43 preservice elementary school teachers' conceptual understanding of place value after participating in a research-based constructivist unit of instruction in place value. The preservice teachers were enrolled in one of three terms of an elementary mathematics methods course in a private midwestern…
Prospective Elementary Teachers Making Sense of Multidigit Multiplication: Leveraging Resources

ERIC Educational Resources Information Center

Whitacre, Ian; Nickerson, Susan D.

2016-01-01

This study examines how collective activity related to multiplication evolved over several class sessions in an elementary mathematics content course that was designed to foster prospective elementary teachers' number-sense development. We document how the class drew on as-if-shared ideas to make sense of multidigit multiplication in terms of…
Elementary Particle Spectroscopy in Regular Solid Rewrite

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

Trell, Erik

The Nilpotent Universal Computer Rewrite System (NUCRS) has operationalized the radical ontological dilemma of Nothing at All versus Anything at All down to the ground recursive syntax and principal mathematical realisation of this categorical dichotomy as such and so governing all its sui generis modalities, leading to fulfilment of their individual terms and compass when the respective choice sequence operations are brought to closure. Focussing on the general grammar, NUCRS by pure logic and its algebraic notations hence bootstraps Quantum Mechanics, aware that it ''is the likely keystone of a fundamental computational foundation'' also for e.g. physics, molecular biology andmore » neuroscience. The present work deals with classical geometry where morphology is the modality, and ventures that the ancient regular solids are its specific rewrite system, in effect extensively anticipating the detailed elementary particle spectroscopy, and further on to essential structures at large both over the inorganic and organic realms. The geodetic antipode to Nothing is extension, with natural eigenvector the endless straight line which when deployed according to the NUCRS as well as Plotelemeian topographic prescriptions forms a real three-dimensional eigenspace with cubical eigenelements where observed quark-skewed quantum-chromodynamical particle events self-generate as an Aristotelean phase transition between the straight and round extremes of absolute endlessness under the symmetry- and gauge-preserving, canonical coset decomposition SO(3)xO(5) of Lie algebra SU(3). The cubical eigen-space and eigen-elements are the parental state and frame, and the other solids are a range of transition matrix elements and portions adapting to the spherical root vector symmetries and so reproducibly reproducing the elementary particle spectroscopy, including a modular, truncated octahedron nano-composition of the Electron which piecemeal enter into molecular structures or compressed to each other fuse into atomic honeycombs of periodic table signature.« less
Investigating Student Use of Electronic Support Tools and Mathematical Reasoning

ERIC Educational Resources Information Center

Higgins, Kristina N.; Crawford, Lindy; Huscroft-D'Angelo, Jacqueline; Horney, Mark

2016-01-01

Mathematical reasoning involves comprehending mathematical information and concepts in a logical way and forming conclusions and generalizations based on this comprehension. Computer-based learning has been incorporated into classrooms across the country, and specific aspects of technology need to be studied to determine how programs are…
A Mathematics Educator's Introduction to Rural Policy Issues

ERIC Educational Resources Information Center

Waters, Michael S., Ed.

2005-01-01

Most of the scholarship and commentary on mathematics education deals with issues of curriculum and instruction; this is understandable in a field logically belonging to the domain of curriculum and instruction. Moreover, issues of teaching and learning are compelling to people who love to learn and teach mathematics. Policy receives shorter…

Mathematical Modeling and Computational Thinking

ERIC Educational Resources Information Center

Sanford, John F.; Naidu, Jaideep T.

2017-01-01

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…
Matematicas Para La Escuela Primaria, Grado 4 (Parte 1), Comentario. Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for the Elementary School, Grade 4, Part 1, Teacher's Commentary. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Beatty, Leslie; And Others

This is Part 1 of the teacher's commentary for the grade 4 mathematics program. Part 1 includes the commentary for chapters 1 through 5. Topics covered include congruence, numbers and number bases, subtraction of numbers, division of numbers, and elementary geometry. References to the student text are cited. (RH)
Young Children's Reasoning in Games of Nonsocial and Social Logic: "Tic Tac Toe" and a "Guessing Game."

ERIC Educational Resources Information Center

Fernie, David E.; DeVries, Rheta

1990-01-01

A total of 87 children, 3- to 7-years old, were examined in a study of children's play and reasoning in games of mathematical logic and social logic. Children's sophistication in reasoning was positively related for two games, suggesting a common three-level progression from mastery of procedures to a competitive attitude to advanced strategy. (SH)
Use of CAS in Secondary School: A Factor Influencing the Transition to University-Level Mathematics?

ERIC Educational Resources Information Center

Varsavsky, Cristina

2012-01-01

Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one…
An Investigation into Pre-Service Special Education Teachers' Mathematical Skills, Self-Efficacy, and Teaching Methodology

ERIC Educational Resources Information Center

Hinton, Vanessa; Flores, Margaret; Burton, Megan; Curtis, Rebecca

2015-01-01

The purpose of this mixed method study was to investigate future special education teachers' preparation for effectively teaching mathematics. During the last semester of their program, pre-service special education teachers completed elementary level mathematics computation and problem solving assessments, a mathematics efficacy beliefs survey,…
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…
Elementary Students' Spontaneous Metacognitive Functions in Different Types of Mathematical Problems

ERIC Educational Resources Information Center

Mokos, Evagelos; Kafoussi, Sonia

2013-01-01

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

ERIC Educational Resources Information Center

Katz, Sara

2015-01-01

Mathematics is a key to all scientific subjects. Learning mathematics requires cognitive and meta-cognitive effort. Many students suffer from mathematics anxiety that very often leads to physiological symptoms. Self-efficacy is defined as people's beliefs about their capabilities to produce designated levels of performance that affect their lives.…
Experiences of Mathematics Student Teachers in a Series of Science Experiments

ERIC Educational Resources Information Center

Aydin, Emin; Delice, Ali

2007-01-01

There is an increased interest in finding connections with mathematics and areas outside mathematics such as hard and soft sciences. This increased interest reflected in many of curriculum reforms that took place during the past few decades including the one in Turkish elementary and secondary mathematics education. Hence we believe that Turkish…
"Real Teaching" in the Mathematics Classroom: A Comparison of the Instructional Practices of Elementary Teachers in Urban High-Poverty Schools

ERIC Educational Resources Information Center

McKinney, Sueanne E.; Robinson, Jack; Berube, Clair T.

2013-01-01

The National Council of Teachers of Mathematics' "Principles and Standards for School Mathematics" outlines fundamental elements that are crucial for creating a problem-solving and inquiry-driven classroom learning environment that highlights conceptual understandings of mathematics ideas. Even though this document outlines…
Visuospatial training improves elementary students' mathematics performance.

PubMed

Lowrie, Tom; Logan, Tracy; Ramful, Ajay

2017-06-01

Although spatial ability and mathematics performance are highly correlated, there is scant research on the extent to which spatial ability training can improve mathematics performance. This study evaluated the efficacy of a visuospatial intervention programme within classrooms to determine the effect on students' (1) spatial reasoning and (2) mathematics performance as a result of the intervention. The study involved grade six students (ages 10-12) in eight classes. There were five intervention classes (n = 120) and three non-intervention control classes (n = 66). A specifically designed 10-week spatial reasoning programme was developed collaboratively with the participating teachers, with the intervention replacing the standard mathematics curriculum. The five classroom teachers in the intervention programme presented 20 hr of activities aimed at enhancing students' spatial visualization, mental rotation, and spatial orientation skills. The spatial reasoning programme led to improvements in both spatial ability and mathematics performance relative to the control group who received standard mathematics instruction. Our study is the first to show that a classroom-based spatial reasoning intervention improves elementary school students' mathematics performance. © 2017 The British Psychological Society.
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…
Communication and Academic Vocabulary in Mathematics: A Content Analysis of Prompts Eliciting Written Responses in Two Elementary Mathematics Textbooks

ERIC Educational Resources Information Center

Joseph, Christine M.

2012-01-01

The purpose of this study was to investigate how writing in mathematics is treated in one 4th grade National Science Foundation (NSF)-funded mathematics textbook titled "Everyday Mathematics" and one publisher-generated textbook titled "enVision MATH." The developed framework provided categories to support each of the research…
Beyond the Scores: Mathematics Identities of African American and Hispanic Fifth Graders in an Urban Elementary Community School

ERIC Educational Resources Information Center

Fleshman, Paula Jenniver

2012-01-01

As mathematics identity affects students' learning and doing of mathematics, it is critical to understand the mathematics identities of African American and Hispanic students as the mathematical performance and pursuits of far too many continue to lag behind. Further, as community schools have been shown to positively impact students in urban…
Mathematical Graphic Organizers

ERIC Educational Resources Information Center

Zollman, Alan

2009-01-01

As part of a math-science partnership, a university mathematics educator and ten elementary school teachers developed a novel approach to mathematical problem solving derived from research on reading and writing pedagogy. Specifically, research indicates that students who use graphic organizers to arrange their ideas improve their comprehension…
Numerical Capacities as Domain-Specific Predictors beyond Early Mathematics Learning: A Longitudinal Study

PubMed Central

Reigosa-Crespo, Vivian; González-Alemañy, Eduardo; León, Teresa; Torres, Rosario; Mosquera, Raysil; Valdés-Sosa, Mitchell

2013-01-01

The first aim of the present study was to investigate whether numerical effects (Numerical Distance Effect, Counting Effect and Subitizing Effect) are domain-specific predictors of mathematics development at the end of elementary school by exploring whether they explain additional variance of later mathematics fluency after controlling for the effects of general cognitive skills, focused on nonnumerical aspects. The second aim was to address the same issues but applied to achievement in mathematics curriculum that requires solutions to fluency in calculation. These analyses assess whether the relationship found for fluency are generalized to mathematics content beyond fluency in calculation. As a third aim, the domain specificity of the numerical effects was examined by analyzing whether they contribute to the development of reading skills, such as decoding fluency and reading comprehension, after controlling for general cognitive skills and phonological processing. Basic numerical capacities were evaluated in children of 3rd and 4th grades (n=49). Mathematics and reading achievements were assessed in these children one year later. Results showed that the size of the Subitizing Effect was a significant domain-specific predictor of fluency in calculation and also in curricular mathematics achievement, but not in reading skills, assessed at the end of elementary school. Furthermore, the size of the Counting Effect also predicted fluency in calculation, although this association only approached significance. These findings contrast with proposals that the core numerical competencies measured by enumeration will bear little relationship to mathematics achievement. We conclude that basic numerical capacities constitute domain-specific predictors and that they are not exclusively “start-up” tools for the acquisition of Mathematics; but they continue modulating this learning at the end of elementary school. PMID:24255710
Numerical capacities as domain-specific predictors beyond early mathematics learning: a longitudinal study.

PubMed

Reigosa-Crespo, Vivian; González-Alemañy, Eduardo; León, Teresa; Torres, Rosario; Mosquera, Raysil; Valdés-Sosa, Mitchell

2013-01-01

The first aim of the present study was to investigate whether numerical effects (Numerical Distance Effect, Counting Effect and Subitizing Effect) are domain-specific predictors of mathematics development at the end of elementary school by exploring whether they explain additional variance of later mathematics fluency after controlling for the effects of general cognitive skills, focused on nonnumerical aspects. The second aim was to address the same issues but applied to achievement in mathematics curriculum that requires solutions to fluency in calculation. These analyses assess whether the relationship found for fluency are generalized to mathematics content beyond fluency in calculation. As a third aim, the domain specificity of the numerical effects was examined by analyzing whether they contribute to the development of reading skills, such as decoding fluency and reading comprehension, after controlling for general cognitive skills and phonological processing. Basic numerical capacities were evaluated in children of 3(rd) and 4(th) grades (n=49). Mathematics and reading achievements were assessed in these children one year later. Results showed that the size of the Subitizing Effect was a significant domain-specific predictor of fluency in calculation and also in curricular mathematics achievement, but not in reading skills, assessed at the end of elementary school. Furthermore, the size of the Counting Effect also predicted fluency in calculation, although this association only approached significance. These findings contrast with proposals that the core numerical competencies measured by enumeration will bear little relationship to mathematics achievement. We conclude that basic numerical capacities constitute domain-specific predictors and that they are not exclusively "start-up" tools for the acquisition of Mathematics; but they continue modulating this learning at the end of elementary school.
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; classroom management; and application of standards-based instruction. Prolonged, extensive classroom involvement provided familiarity with the ability levels of elementary students. Gains in positive attitudes and confidence in teaching mathematics and science were identified as direct results of this experience. This may be attributed to the immersion in the school-based setting (hands-on) and the standards-based approach (minds-on) methods course. The results are written in case study form using thick description with an emphasis on preservice teachers.
Elementary Teacher Self-Efficacy in Engineering and Student Achievement in Math and Science

ERIC Educational Resources Information Center

Gorena, Jacquelyn L.

2015-01-01

STEM education is a national priority, and more schools are implementing STEM K-12. Elementary teachers are prepared to teach science, mathematics, and technology, but teachers may not feel as prepared to teach engineering. Engineering is a new genre for elementary schools, and it is not typically a content area included in teacher preparation…
Preservice Elementary Teachers Use Drawings and Make Sets of Materials to Explain Multiplication and Division by Fractions

ERIC Educational Resources Information Center

Rule, Audrey C., Ed.; Hallagan, Jean E., Ed.

2006-01-01

Background: Multiplication and division by fractions are among the most troublesome concepts in the elementary mathematics curriculum. Recent studies have shown that preservice elementary teachers in the United States do not have deep understandings of these concepts. Effective ways to improve preservice teachers' conceptual understanding of these…

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