DOCSLIB.ORG

Report on Studies Related to Lgebra (3), Arithmetic (2) and the Use of Desk Calculators (1)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Report on Studies Related to Lgebra (3), Arithmetic (2) and the Use of Desk Calculators (1) DOCUMENT RESUME 30'113 152. SE 019 635 AUTHOR Suydam, Marilyn N. Ed.; Osborne, Alan R., Ed. _TITLE . Algorithmic- Learning. INSTITUTION ERIC Information Analysis Center fOr Science, Mathematics, and Environmental Education, Columbus, Ohio.; Ohio State Univ., Columbus. Center for Science and Mathematics Education. SPONS AGENCY National Inst. of Education (DREW), Washington, D.C. Career Education Program. PUB DATE [75] NOTE 194p. AVAILABLE FROMOhio State University, Center for Science and Mathematics Education, 244;Arps Hall, Columbus, Ohio 43210 ($3.75) \ EDRS PRICE MF-$0.76 HC-$9.51 Plus Postage DESCRIPTORS *Algorithms; Cognitive Processes; Elementary Secondary Education; Instruction; *Learning; Learning Theories; *Literature Reviews; *Mathematics Education; Memory; *Research; Teaching Methods IDENTIFIERS *Algorithmic Learning ABSTRACT Thi volume contains a series of papers on algorithmic learning. Included are six reviews of research pertaining to various aspects of algorithmic learning, six reports of pilot experiments in this area, a theoretical discussion of "The Conditions for'Algol:ithmic Imagivation," and an annotated bibliography. All the papers assume a common definition of algorithmic learning as "the process,of developing and/or applying methods or procedures, i.e., algorithms, with the goal of learning-how-to-learn." 2 common definition of algorithm is also used. Topics covered by literature reviews include algorithmic processes for r,'gnition, algorithms and hierarchies, conceptual bases for the learning of algorithms, interference with the learning of algorithms, algorithmic problem solving, and algorithms and mental computations. Research papers report on studies related to lgebra (3), arithmetic (2) and the use of desk calculators (1). The authors conclude that there are many open researchable questions in tharea of algorithmic learning. (SD) *********************************************************************** Documents acquired by ERIC include many informal unpublished * materials not available from other sources. ERIC makes every, effort * * to obtain the best copy available. Nevertheless, items of marginal * * reproducibility are often encountered arid this' affects the quality * * of the microfiche and hardcopy reprodudtions ERIC makes available * * via the ERIC Document Reproduction Service (EDRS). EDRS is not * responsible foi the quality of the original document. Reproiuctions * * supplied by EMS are the be t that can be made from the original. *********************************************************************** U.S. DEPARTMENT OF HEALTH, EDUCATION & WELFARE NATIONAL INSTITUTE OF EDUCATION THIS DOCUMENT HAS SEEN 'REPRO OUCED EXACTLY, AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGIN ATtNG IT POINTS OF VIEW OR OPINIONS STATED 00 NOT NECESSARILY RE PRE SENT OFFICIAL NATIONAL INSTITUTE OF EOUCATION POSITION OR POLICY ATICS ION TION THE ERIC SCIENCE, MATHEMATICS AND ENVIRONMENTAL EDUCATION CLEARINGHOUSE in cooperation with Center for Science and Mathematics Education The Ohio State University Algorithmic Learning edited by Marilyn. N. Suydam and Alan R. Osborne Mathematics Education Reports Mathematics Education Reports are being deyeloped to disseminate information concerning mathematics.educationdocumehts analyzed at the ERIC Information Analysis Center for Science, Mathematics and Environ- Mental Education. These reports fall into three broad categories. Research reviews summarize and analyze recent research in specific areas of mathematics education. Resource guides identify and analyze materials and references for use by mathematics teachers at all levels. Special bibliographies announce the availability of documents and review the literature in selected interest areas of mathematics education. Reports in each of these categories may also be targeted for specific sub-populations of the mathematics education community. Priorities for the development of furture Mathematics Education Reports are estab- lished by the advisory board of the Center, in\cooperation with the National Council of Teachers of Mathematics, the Special Interest Group for Research in Mathematics Education, the Conference Board of the Mathematical Sciences, and other professional groups in mathematics education. Individual comments on past Reports and suggestions for future Reports are always welcomed. This publication was prepared pursuant to a contract with the National Institute of Education, U.S. Department of Health, Educa- tion and Welfare. Contractors undertaking such projects under Government sponsorship are encouraged to express freely their judgment in professional and technical matters. Points of view or opinions do not, therefore, necessarily represent official National Institute of Education position or policy ii CONTENTS Algorithmic Learning Section Page I Algorithmic Learning: Introduction 3 II Conditions for Algorithmic Imagination, by Alan R. Osborne 13 III Reviews of Previous,Research on Specific Aspects A. Algorithmic Processes for Cognition, by Jesse D. Parete 25 r B. Algorithmic Learning and Hierarchies, by Paul H. Wozniak C. Investigations of Conceptual Bases Under- lying the Learning of Algorithms, by .1, Diane Thomas ti 56 D. Algorithms: Interference, Facilitation, and Comparisons, by Brady Shafer 73 E. Algorithmic Problem Solving, by-Richard W. Corner 85 F. Algorithms and Mental Computation, by Raymond Zepp 9r( IV Report's of Some Exploratory Research A. Algorithmic Processes in Arithmetic and ,Logic, by Jesse D. Parete 107 B. A Comparison of Different Conceptual Bases for Teaching Subtraction of Integers, by Diane Thomas 119 C. Solving Quadratic Inequalities:,More Than One Algorithm? by Brady Shafer 137 D. A Comparison of Two Strategies for Teaching Algorithms for Finding Linear Equations, by 147 . Richard W. Corner E. Some Computational Strategies of Students Using Desk Calculators, by Raymond Zepp... 154 iii CONTENTS (continued) Section Page V Annotated List of Selected Research References Related to Computational Algorithms, by Marilyn N. Suydam 165 VI Summary 197A iv- \ I. Algorithmic Learning: Introduction 1 Algorithmic Learning: Introduction Marilyn N. Suydam To many people, "algorithmic.,learning" means "the learning of algorithms". They think of algorithms for addition, subtraction, multiplication, and division with whole numbers,such as: / 13 6, 54 86 183W +37 4 x7 18 11 27 774 74 80 602 54 91 6794 They think of algorithms for operationswith fractions and dedimals, of a square root algorithm,of procedures in the content of algebra and calculus and other mathematical areas. But algorithmic learning involves morethan just the learning of specific algorithms. It connotes having learners generalize from specific skills to broader process applications. It is related to learning-how-to-learn. As Simon (1975) pointed out, teaching the algo- rithm and teaching the characteristics of analgorithmic solution are / two different things. The importance of algorithmiclearning is being increasingly recognized, across other content areas aswell as within mathematics. In the past few years, it has beendeveloped as the approach in at least one textbook. The research interest in artificial intelligence is built on a foundation of algorithmiclearning. Several Russian psychologists, among others, have been Very muchconcerned with the implications of algorithmic learning(Gerlach and Brecke, 1974; Landa, 1974). The focus of much current writing isstill on algorithms, but the need to provide for algorithmiclearning is becoming increasingly more evident. The use of hand-held calculators atall levels from the ele- mentary years through life has raised newquestions about algorithms-- 3 and emphasizes the need to explore ways in which algorithmic learning can be .promoted, as calculators decrease the need to focus'so much of our attention on the algorithms for calculation. Explanation This document is not intended to be all-inclusive (although we had dreams of being comprehensive at one early point:).It is basically the reiport of a year of emphasis on algorithms and algorithmic learning in a seminar for mathematics education doctoral students at The Ohio State University. It dogsn't include all that the seminar encompassed. But it does present some results, both in the form ofresearch reviews and mini- research studies. It is hoped that it will serve to have others do more thinking.about what is known about algorithmic learning, and, even more important, to think about what still needs to be explored and learned, In proposing the seminar, it was noted that there is a tradition of concern for algorithms in the computational orientation of elementary school mathematics, but new information-processing models of learning seem to be stimulating a new body of research problems and studies. A more general interest is suggested, in broadly conceived algorithmic learning non-specific to the computational needs of young children. The relation of algorithmic learning to problem solving, logical ability, creativity, and the like have not been explored. And they should be. Our focus was indicated by this flow diagram for our initial discussions: What in an algorithm? Definitions from texts 4 Computational algorithms (examples, research, selected studies) Other elementary Secondary school algorithms Computers t Broad meaning/purpose of algorithms Learning hOw to learn ALGORITHMIC LEARNING: the evolving focus )4. Thus, this document attempts to: (1) review the status of some aspects of research related to algorithmic learning
Load more

Recommended publications
  • Representing Exact Number Visually Using Mental Abacus
    Journal of Experimental Psychology: General © 2011 American Psychological Association 2011, Vol. ●●, No. ●, 000–000 0096-3445/11/$12.00 DOI: 10.1037/a0024427 Representing Exact Number Visually Using Mental Abacus Michael C. Frank David Barner Stanford University University of California, San Diego Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation. Keywords: abacus, mental arithmetic, number, visual cognition Human adults, unlike other animals, have the capacity to per- Previous work, reviewed below, has described the MA phenom- form exact numerical computations. Although other creatures are enon and has provided suggestive evidence that MA is represented sensitive to precise differences between small quantities and can nonlinguistically, in a visual format. However, this proposal re- represent the approximate magnitude of large sets, no nonhuman mains tentative for two reasons.
    [Show full text]
  • A Review of Research on Addition and Subtraction. Working Paper No
    DOCADIENIIRESUME ED 223 447 SE 039, 613 AUTHOR' Carpenter, Thomas P.; And Others TITLE A Review of Re'search on Addition andSubtraction. Working Paper No. 330.-Report from the Program on Student Diversity and Classroom Processes. -INSTITUTION Wisconsin Center for Education Research, Madison. SPONS AGENCY National Inst. of Education (ED), Washington, DC. PUB DATE Sep 82 GRANT NIE-G-81-0009 NOTE 186p. PUB TYPE Information Analyses (070) EDRS PRICE MF01/PC08 Plus Postage. DESCRIPTORS *Addition; *Basic Skills; Cognitive Processes; Computation; Educational Research; Elementary Education; *Elementary School Mathematics; *Learning Theories; Literature Reviews; Mathematical Concepts; Mathematics Instructioh; Problem Solving; *SubtraCtion IDENTIFIERS *Mathematics Education Research; Word PrOblems ABSTRACT This material is designed to examine the research on how children acquire basic addition and subtractionconcepts and skills. Two major lines of theories of the development ofbasic number concepts, called logical concept and quantificationskill approaches, are identified. Mjcir recurring issues in thedevelopment of early number concepts are also discussed.This is followed by examination of studies specifically related to addition and subtraction: It is noted that by kindergarten mostchildren understand the rudiments of these operations, but a complete understanding develops over a protracted span of years.The direction 4of initial and ongoing ,research is discussed,and word problem studies and investigations on children's Solutions ofsymbolic
    [Show full text]
  • Roles of Semantic Structure of Arithmetic Word Problems on Pupils’ Ability to Identify the Correct Operation
    ROLES OF SEMANTIC STRUCTURE OF ARITHMETIC WORD PROBLEMS ON PUPILS’ ABILITY TO IDENTIFY THE CORRECT OPERATION J ustin D. V ale nt in and Dr Lim Chap Sam (University of Science Malaysia) December,Dec em ber , 20042 004 Abstract This paper draws on findings from a study conducted in seven primary schools in Seychelles about pupils’ proficiency in one-step arithmetic word problems to discuss the roles of semantic structures of the problems on the pupils’ ability to identify the operation required to solve them. A sample of 530 pupils drawn from Primary 4, 5 and 6 responded to a 52 multiple choice item test in which they were to read a problem and select the operation that is required to solve it. The results showed some consistencies with other international studies in which pupil related better to additive than to multiplicative problems. Moreover, they could solve better those problems that do not involve relational statements. The general picture indicated that there is an overall increase in performance with an increase in grade level yet, when individual schools are considered this increase in performance in significant in only one school. In the other results there were many cases of homogenous pairs of means. Analysis of distractors conducted on the pupils’ responses to the seventeen most difficult items reveal that in most cases when an item required the operation indicating an additive or multiplicative structure, the most popular wrong answer would be one of the same semantic structure. Otherwise there is a strong tendency for the pupils to select the operation of addition when they could not identify the correct operation for a particular problem.
    [Show full text]
  • Strategy Use and Basic Arithmetic Cognition in Adults
    STRATEGY USE AND BASIC ARITHMETIC COGNITION IN ADULTS A Thesis Submitted to the College of Graduate Studies and Research in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Department of Psychology University of Saskatchewan Saskatoon By Arron W. S. Metcalfe ©Copyright Arron W. Metcalfe, October 2010. All Rights Reserved. PERMISSION TO USE In presenting this dissertation in partial fulfillment of the requirements for a Postgraduate degree from the University of Saskatchewan, I agree that the Libraries of this University may make it freely available for inspection. I further agree that permission for copying of this dissertation in any manner, in whole or in part, for scholarly purposes may be granted by the professor or professors who supervised my dissertation work or, in their absence, by the Head of the Department or the Dean of the College in which my thesis work was done. It is understood that any copying or publication or use of this dissertation or parts thereof for financial gain shall not be allowed without my written permission. It is also understood that due recognition shall be given to me and to the University of Saskatchewan in any scholarly use which may be made of any material in my thesis/dissertation. Requests for permission to copy or to make other uses of materials in this dissertation in whole or part should be addressed to: Head of the Department of Psychology University of Saskatchewan Saskatoon, Saskatchewan S7N 5A5 Canada i ABSTRACT Arithmetic cognition research was at one time concerned mostly with the representation and retrieval of arithmetic facts in memory.
    [Show full text]
  • Human-Computer Interaction in 3D Object Manipulation in Virtual Environments: a Cognitive Ergonomics Contribution Sarwan Abbasi
    Human-computer interaction in 3D object manipulation in virtual environments: A cognitive ergonomics contribution Sarwan Abbasi To cite this version: Sarwan Abbasi. Human-computer interaction in 3D object manipulation in virtual environments: A cognitive ergonomics contribution. Computer Science [cs]. Université Paris Sud - Paris XI, 2010. English. tel-00603331 HAL Id: tel-00603331 https://tel.archives-ouvertes.fr/tel-00603331 Submitted on 24 Jun 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Human‐computer interaction in 3D object manipulation in virtual environments: A cognitive ergonomics contribution Doctoral Thesis submitted to the Université de Paris‐Sud 11, Orsay Ecole Doctorale d'Informatique Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI‐CNRS) 26 November 2010 By Sarwan Abbasi Jury Michel Denis (Directeur de thèse) Jean‐Marie Burkhardt (Co‐directeur) Françoise Détienne (Rapporteur) Stéphane Donikian (Rapporteur) Philippe Tarroux (Examinateur) Indira Thouvenin (Examinatrice) Object Manipulation in Virtual Environments Thesis Report by Sarwan ABBASI Acknowledgements One of my former professors, M. Ali YUSUF had once told me that if I learnt a new language in a culture different than mine, it would enable me to look at the world in an entirely new way and in fact would open up for me a whole new world for me.
    [Show full text]
  • The Posing of Division Problems by Preservice Elementary School Teachers: Conceptual Knowledge and Contextual Connections
    DOCUMENT RESUME ED 381 348 SE 056 020 AUTHOR Silver, Edward A.; Burkett, Mary Lee TITLE The Posing of Divis;nn Problems by Preservice Elementary School Teachers: Conceptual Knowledge and Contextual Connections. SPONS AGENCY National Science Foundation, Washington, D.C. PUB DATE May 94 CONTRACT NSF-MDR-8850580 NOTE 32p.; Paper presented at the Annual Meeting of the American Educational Research Association (New Orleans, LA, April 1994). PUB TYPE Reports Research/Technical (143) Speeches /Conference Papers (150) EDRS PRICE MF01/PCO2 Plus Postage. DESCRIPTORS Arithmetic; *Division; Elementary Education; *Elementary School Teachers; Higher Education; 'Mathematics Instruction; Preservice Teacher Education; *Questioning Techniques IDENTIFIERS Mathematics Education Research; *Preservice Teachers; Problem Posing; Situated Lep.rning; *Subject Content Knowledge ABSTRACT Previous research has suggested that many elementary school teachers have a firmer understanding of addition and subtraction concepts than they have of more complex topics in elementary mathematics, such as division. In this study, (n=24) prospective elementary teachers' understanding of aspects of division involving remainders was explored by examining the problems they posed. The tea-:hers' responses revealed a clear preference for posing problems associated with real world contexts, suggesting that the term "story problem" had that particular meaning for this group. Although the vast majority of problems were situated in contexts, the problems and solutions frequently did not represent a solid connection between the mathematical and situational aspects of the problem. About two-thirds of the subjects spontaneously posed problems and proposed solutions that reflected their understanding of the relationship between the given computation and at least one member of its family of associated computations.
    [Show full text]
  • Arithmetical Development: Commentary on Chapters 9 Through 15 and Future Directions
    ARITHMETICAL DEVELOPMENT: COMMENTARY ON CHAPTERS 9 THROUGH 15 AND FUTURE DIRECTIONS David C. Geary University of Missouri at Columbia The second half of this book focuses on the important issues of arithmetical instruction and arithmetical learning in special populations. The former repre- sents an area of considerable debate in the United States, and the outcome of this debate could affect the mathematics education of millions of American children (Hirsch, 1996; Loveless, 2001). At one of the end points of this debate are those who advocate an educational approach based on a constructivist philosophy, whereby teachers provide materials and problems to solve but allow students leeway to discover for themselves the associated concepts and problem-solving procedures. At the other end are those who advocate direct instruction, whereby teachers provide explicit instruction on basic skills and concepts and children are required to practice these basic skills. In the first section of my commentary, I briefly address this debate, as it relates to chapters 9, 10, and 11 (by Dowker; Fuson and Burghardt; and Ambrose; Baek, and Carpenter respectively). Chapters 12 to 15 (by Donlan; Jordan, Hanich, and Uberti; and Delazer; and Heavey respectively) focus on the important issue of arithmetical learning in special populations, a topic that has been largely neglected, at least in relation to research on reading competencies in special populations. I discuss these chapters and related issues in the second section of my commentary. In the third, I briefly consider future directions. Instructional Research (Chapters 9 to 11) Constructivism is an instructional approach based on the developmental theories of Piaget and Vygotsky (e.g., Cobb, Yackel, & Wood, 1992).
    [Show full text]
  • Developing a Pedagogical Domain Theory of Early Algebra Problem Solving Kenneth R
    Developing a Pedagogical Domain Theory of Early Algebra Problem Solving Kenneth R. Koedinger Benjamin A. MacLaren March 2002 CMU-CS-02-119 CMU-HCII-02-100 School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 Abstract We describe a theory of quantitative representations and processes that makes novel predictions about student problem-solving and learning during the transition from arithmetic to algebraic competence or "early algebra". Our Early Algebra Problem Solving (EAPS) theory comes in the form of a cognitive model within the ACT-R cognitive architecture. As a "pedagogical domain theory", our EAPS theory can be used to make sense of the pattern of difficulties and successes students experience in early algebra problem solving and learning. In particular, the theory provides an explanation for the surprising result that algebra students perform better on certain word problems than on equivalent equations (Koedinger & Nathan, 2000; Nathan & Koedinger, 2000). It also makes explicit the knowledge and knowledge selection processes behind student strategies and errors and provides a theoretical tool for psychologists and mathematics educators to both productively generate and accurately evaluate hypotheses about early algebra learning and instruction. We have abstracted our development process into six model-building constraints that may be appropriate for creating cognitive models of problem solving in other domains. This research was supported by a grant from the James S. McDonnell Foundation program in Cognitive Studies for Educational Practice, grant #95-11. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the McDonnell Foundation.
    [Show full text]
  • Problem Formatting, Domain Specificity, and Arithmetic Processing: the Promise of a Factor Analytic Framework
    Georgia State University ScholarWorks @ Georgia State University Psychology Dissertations Department of Psychology 8-11-2015 Problem Formatting, Domain Specificity, and Arithmetic Processing: The Promise of a Factor Analytic Framework Katherine Rhodes Follow this and additional works at: https://scholarworks.gsu.edu/psych_diss Recommended Citation Rhodes, Katherine, "Problem Formatting, Domain Specificity, and Arithmetic Processing: The Promise of a Factor Analytic Framework." Dissertation, Georgia State University, 2015. https://scholarworks.gsu.edu/psych_diss/138 This Dissertation is brought to you for free and open access by the Department of Psychology at ScholarWorks @ Georgia State University. It has been accepted for inclusion in Psychology Dissertations by an authorized administrator of ScholarWorks @ Georgia State University. For more information, please contact [email protected]. PROBLEM FORMATTING, DOMAIN SPECIFICITY, AND ARITHMETIC PROCESSING: THE PROMISE OF A FACTOR ANALYTIC FRAMEWORK by KATHERINE T. RHODES Under the direction of Julie A. Washington, Ph.D. and Lee Branum-Martin, Ph.D. ABSTRACT Leading theories of arithmetic cognition take a variety of positions regarding item formatting and its possible effects on encoding, retrieval, and calculation. The extent to which formats might require processing from domains other than mathematics (e.g., a language domain and/or an executive functioning domain) is unclear and an area in need of additional research. The purpose of the current study is to evaluate several leading theories of arithmetic cognition with attention to possible systematic measurement error associated with instrument formatting (method effects) and possible contributions of cognitive domains other than a quantitative domain that is specialized for numeric processing (trait effects). In order to simultaneously examine measurement methods and cognitive abilities, this research is approached from a multi- trait, multi-method factor analytic framework.
    [Show full text]
  • AUTHOR Problem Solving
    DOCUMENT RESUME ED 068 340 SE 014 918 AUTHOR Aiken, Lewis R., Jr. TITLE Language Factors in Learning Mathematics. INSTITUTION ERIC Information Analysis Center for Science, Mathematics, and Environmental Education, Columbus, Ohio. PUB DATE Oct 72 NOTE 47p. EDRS PRICE MF-$0.65 HC-$3.29 DESCRIPTORS Achievement; Learning; *Mathematical Linguistics; Mathematical Vocabulary; *Mathematics Education; Problem Solving; *Readability; *Research Reviews (Publications); *Verbal Ability ABSTRACT This paper focuses on the relationship of verbal factors to mathematics achievement and reviews research from 1930 to the present. The effects of verbalization in the mathematics learning process are considered; mathematics functioning as a unique language in its own right is analyzed. Research on the readability of mathematics materials and research relating problem-solving abilities to verbal abilities are reviewed. An extensive bibliography is included. (Editor/DT) 440 'clt 44. e CZ) '4 4447'Ws'7`. 4t,.? S Of PAN TN't NT OF41 At T14 IDUCATION h WI IF AFil Of FICI OF IDUCATION SMEAC/SCIENCE, MATHEMATICS, AND ENVIRONMENTAL EDUCATION INFORMATION ANALYSIS CENTER . an information center to organize and disseminate information and materials on science, mathematics, Cep and environmental education to teachers, administrators, supervisors. researchers, and the public. A joint project of The Ohio State University and the Educational Resources Information Center of USOE. FILMED FROM BEST AVAILABLE COPY 4-3 C) MATHEMATICS EDUCATION REPORTS LANGUAGE FACTORS IN LEARNING MATHEMATICS by Lewis R. Aiken, Jr. ERIC Information Analysis Center for Science, Mathematics, and Environmental Education 1460 West Lane Avenue Columbus, Ohio43216 October, 1972 Mathematics Education Reports Mathematics Education Reports are being developedto disseminate information concerning mathematics education documentsanalysed at the ERIC Information Analysis Center for Science,Mathematics, and Environmental Education.
    [Show full text]
  • Word Problem Solving of Students with Autistic Spectrum Disorders
    Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development Young Seh Bae Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy under the Executive Committee of the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2013 © 2013 Young Seh Bae All rights reserved ABSTRACT Mathematical Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development Young Seh Bae This study investigated mathematical word problem solving and the factors associated with the solution paths adopted by two groups of participants (N=40), students with autism spectrum disorders (ASDs) and typically developing students in fourth and fifth grade, who were comparable on age and IQ ( >80). The factors examined in the study were: word problem solving accuracy; word reading/decoding; sentence comprehension; math vocabulary; arithmetic computation; everyday math knowledge; attitude toward math; identification of problem type schemas; and visual representation. Results indicated that the students with typical development significantly outperformed the students with ASDs on word problem solving and everyday math knowledge. Correlation analysis showed that word problem solving performance of the students with ASDs was significantly associated with sentence comprehension, math vocabulary, computation and everyday math knowledge, but that these relationships were strongest and most consistent in the students with ASDs. No significant associations were found between word problem solving and attitude toward math, identification of schema knowledge, or visual representation for either diagnostic group. Additional analyses suggested that everyday math knowledge may account for the differences in word problem solving performance between the two diagnostic groups.
    [Show full text]
  • “Count on Me!” Mathematical Development, Developmental Dyscalculia and Computer-Based Intervention
    “Count on me!” Mathematical development, developmental dyscalculia and computer-based intervention Linda Olsson Linköping Studies in Arts and Science No 728 Linköping Studies in Behavioural Science No 204 Linköping 2018 Linköping Studies in Arts and Science No 728 Linköping Studies in Behavioural Science No 204 At the Faculty of Arts and Sciences at Linköping University, research and doctoral studies are carried out within broad problem areas. Research is organized in interdisciplinary research environments and doctoral studies mainly in graduate schools. Jointly, they publish the series Linköping Studies in arts and Science. This thesis comes from the Division of psychology at the Department of Behavioral Sciences and Learning. Distributed by: Department of Behavioral Sciences and Learning Linköping University 581 83 Linköping, Sweden Linda Olsson “Count on me!” Mathematical development, developmental dyscalculia and computer-based intervention Edition 1:1 ISBN 978-91-7685-409-9 ISSN 0282-9800 ISSN 1654-2029 ©Linda Olsson Department of Behavioral Sciences and Learning, 2018 Cover illustration: Linda Olsson Printed by: LiU-Tryck, Linköping, 2017 Abstract A “sense” of number can be found across species, yet only humans supplement it with exact and symbolic number, such as number words and digits. However, what abilities leads to successful or unsuccessful arithmetic proficiency is still debated. Furthermore, as the predictability between early understanding of math and later achievement is stronger than for other subjects, early deficits can cause significant later deficits. The purpose of the current thesis was to contribute to the description of what aspects of non-symbolic and symbolic processing leads to later successful or unsuccessful arithmetic proficiency, and to study the effects of different designs of computer-programs on pre-school class aged children.
    [Show full text]