bluuebunny/crossref_metadata_2025 huggingface dataset:
Editorial
Authors: Kilpatrick Jeremy
Published: August 2020

In April, the President's National Commission on Excellence in Education released its report, A Nation at Risk: The Imperative for Educational Reform, which portrayed the educational foundations of American society as “being eroded by a rising tide of mediocrity that threatens our very future as a Nation and a people.” According to the commission, “we have, in effect, been committing an act of unthinking, unilateral educational disarmament.” As one of the commissioners has admitted, these apocalyptic words were intended tO grab the fickle attention of headline writers, and through them the American people, who are deemed unable to assimilate a serious message that lasts more than 30 seconds. (Although one might note that attention easily given is easily withdrawn.)
Vocabulary Instruction in Ratio and Proportion for Seventh Graders
Authors: Jackson Michael B. , Phillips E. Ray
Published: August 2020

The purpose of the study was to determine whether seventh graders' achievement in a unit on ratio and proportion was facilitated by vocabulary-oriented instruction. One hundred eleven students in three experimental classes completed some vocabulary-oriented activities daily for 4 weeks; 102 students in three control classes received similar instruction with no vocabulary-oriented activities. On an examination at the end of the unit, the mean score for students in the experimental classes was significantly higher than for students in the control classes on a set of computational items and a set of verbal items. The vocabulary-oriented activities appeared to enhance achievement by improving students' comprehension.
Dissertations in Mathematics Education at the Higher School of Education in Cracow, 1968 to 1981: An Annotated Bibliography
Authors: Turnau Stefan
Published: August 2020

The research of Krygowska's school in Poland is not well known in the English-speaking world. An annotated bibliography of 26 dissertations completed over a 14-year period suggests the nature and direction of this work.
Editorial
Authors: Kilpatrick Jeremy
Published: August 2020

Welcome to 1984! Orwell's nightmare is not yet our world, but no one who has read the appendix to 1984 can fa il to note how far we have moved toward Newspeak from the English of Orwell's time. One of his profound insights was that since thought rests on language, the range of people's thought can be narrowed by cutting their choice of words to a minimum. Newspeak had a separate vocabulary list of scientific and technical terms for each specialty, with only a few terms common across lists. Perhaps this year is an appropriate time to examine the language we use in writing research reports to see how well it reflects the range of our thought and how intelligible it is to readers outside our specialty.
Brief Reports: Measuring Agreement among Coders Who Use a Process-Sequence System
Authors: Campbell Patricia F.
Published: August 2020

Problem solving is a topic of current interest for mathematics teachers and researchers (National Council ofTeachers of Mathematics, 1980, 1981). One focus of this concern has been to study the thinking processes children use when solving mathematical problems. A common methodology is to interview children, asking them to “think aloud” as they solve a problem. The interview is tape-recorded to produce a protocol for identifying and making inferences about the child's problem-solving processes. Some researchers use the tape recording as the data source; others use a transcript of the recording.
Reviews: Mathematics in the Vernacular
Authors: Leder Gilah
Published: August 2020

In Cross-Cultural Studies in Cognition and Mathematics David Laney describes the ambitious Indigenous Mathematics Project carried out in Papua New Guinea (P.N.G.) with the full support of the P.N.G. Department of Education and set up to examine the relationship between children's cultural background and their pattern of cognitive development, particularly with respect to category formation. Whether the acquisition of school arithmetic was influenced by these factors was also investigated, though less comprehensively. The book seems a ready example of Brislin's (1983) contention that “in the last four to five years cross-cultural studies have been recognized as central to theory development by large numbers of psychologists” (p. 364).
Blacks in Mathematics: A Status Report
Authors: Johnson Martin L.
Published: August 2020

The underparticipation and underachievement of black students in precollege mathematics courses are documenred, and some possible contributing factors are discussed. A review of the literature suggests that only recently have studies been undertaken to identify and explore specific causes and to attempt interventions. A major research program is called for that would explore the problem in depth, but increased efforts to alleviate the plight of black students regarding mathematics need not await the results of research.
The Acquisition of Addition and Subtraction Concepts in Grades One through Three
Authors: Carpenter Thomas P. , Moser James M.
Published: August 2020

Children's solutions to simple addition and subtraction word problems were studied in a 3-year longitudinal study that followed 88 children from Grades 1 through 3. The children were able to solve the problems using a variety of modeling and counting strategies even before they received formal instruction in arithmetic. The invented strategies continued to be used after several years of formal instruction. Four levels of problem-solving ability were found. At the first level, children could solve problems only by externally modeling them with physical objects. Modeling strategies were gradually replaced with more sophisticated counting strategies. The results of the study are at variance with important aspects of models of children's performance proposed by Briars and Larkin and by Riley, Greeno, and Heller.
Research on Mathematics Education Reported in 1983
Authors: Suydam Marilyn N.
Published: August 2020

In this 14th annual listing of mathematics education research to appear in JRME, the references are given alphabetically by author within three categories (research summaries, articles, and dissertations). Studies focused on mathematics education are annotated, whereas studies in which mathematics education was not the primary focus are usually not annotated. Annotations generally indicate one principal finding of a study, although most studies have additional findings. The original report should be checked for other results as well as for limitations affecting the validity of the findings.
Editorial
Authors: Reyes Laurie Hart
Published: August 2020

Mathematics learning is essentially cognitive in nature, and much of the research in mathematics education has focused on cognitive aspects of teaching and learning. Few would disagree with this focus, but researchers may want to expand their view to include social aspects of mathematics learning.
Computation Routines Prescribed by Schools: Help or Hindrance?
Authors: Carraher Terezinha Nunes , Schliemann Analúcia Dias
Published: August 2020

Fifty Brazilian children between the ages of 7 and 13, all number conservers, were individually given seven addition and four subtraction exercises. The children were asked to write down and do each exercise and then explain how the answer was reached. The results showed that: (a) counting was the preferred procedure; (b) the use of school-taught algorithms was rather limited; (c) some children decomposed numbers into tens and units and then worked at both levels, combining results subsequently; and (d) children rarely referred to previously obtained results when doing related exercises. Mathematics educators could profit from a knowledge of the procedures used naturally by children and the specific difficulties related to natural and to school-prescribed routines.
Editorial
Authors: Kilpatrick jeremy
Published: August 2020

When, this month and next, researchers in mathematics education get together at the annual meetings of the American Educational Research Association and the National Council of Teachers of Mathematics, they will be exchanging their latest ideas on how students learn mathematics and how teachers teach it. To the extent that our research enterprise is a science, it thrives on the newly discovered. As Edward Wilson put it in the American Scholar last autumn, scientists are the scouts and hunters of the intellectual tribe.
Computational Estimation and Related Mathematical Skills
Authors: Rubenstein Rheta N.
Published: August 2020

Varieties of computational estimation were explored in relation to other mathematical skills and sex differences. The subjects were eighth graders (144 girls and 165 boys) from seven schools. Open-ended estimation was the most difficult, followed by estimation relative to a reference number and estimation within an order of magnitude. Verbal tasks were not more difficult than numerical tasks, but decimals were more difficult than whole numbers, and quotients were more difficult than products, which in turn were more difficult than sums and differences. Boys scored higher than girls on the total estimation test and on the order of magnitude scale. Stepwise regression analyses indicated that estimation performance was best predicted by skill in operating with tens.
Construct a Sum: A Measure of Children's Understanding of Fraction Size
Authors: Behr Merlyn J. , Wachsmuth Ipke , Post Thomas R.
Published: August 2020

This report from the Rational Number Project concerns the development of a quantitative concept of rational number in fourth and fifth graders. In a timed task, children were required to select digits to form two rational numbers whose sum was as close to 1 as possible. Two versions of the task yielded three measures of the skill. The cognitive mechanisms used by high performers in individual interviews were characterized by a flexible and spontaneous application of concepts of rational number order and fraction equivalence and by the use of a reference point. Low performers tended either not to use such cognitive mechanisms or to apply concepts in a constrained or inaccurate manner.
Critique: A Reaction to Three Early Number Papers
Authors: Cobb Paul
Published: August 2020

The three papers on early number in the May issue of this journal (Baroody, 1984; Carpenter & Moser, 1984; Fuson, 1984) focus attention on the crucial role that child-generated or invented methods play in the development of arithmetical knowledge. I will consider just two of the many issues raised in these closely related papers. The first concerns the difficulties involved in identifying developmental sequences of methods that children construct to solve specific tasks such as subtraction problems. The second issue relates to the instructional implications of recent research on early number.
Review: Minds, Machines, Mathematics, and Metaphors
Authors: Kaput James J.
Published: August 2020

During the past two decades, corresponding roughly with the span over which the ideas and data of this book were assembled, a radical enrichment has occurred in our collective conception of what constitutes scientific activity and, therefore, what constitutes mathematics education research. These changes reflect participation in an even larger historical evolution that, while only in its infancy, has admitted new entities to the universe of discou rse and has asserted new domains to be subject to systematic inquiry.
Letter to the Editor
Authors: Egan Kieran
Published: August 2020

In his review of my Education and Psychology: Plato, Piaget, and Scientific Psychology [November 1984 JRME], Ernst von Glasersfeld represents the book as a furious, incredibly confused, attack on psychology. The reviewer seems to me ro so misrepresent the book that readers of the JRME who might otherwise be interested in it will not even consider it.
The Comparative Effectiveness of Microcomputers and Flash Cards in the Drill and Practice of Basic Mathematics Facts
Authors: Fuson Karen C. , Brinko Kathleen T.
Published: August 2020

A flash card procedure was designed with some of the features of microcomputers for the drill and practice of basic facts. Second, third, and fourth graders followed the same daily routine for 6 weeks in either a flash card or a microcomputer condition, practicing basic facts in subtraction or division. Weekly tests revealed learning in the first 2 weeks, little or no learning in the third and fourth weeks, and some learning in the fifth week, when the groups changed practice conditions. The flash card and microcomputer conditions produced equivalent learning.
Rote versus Conceptual Emphases in Teaching Elementary Probability
Authors: Hansen Randall S. , McCann Joan , Myers Jerome L.
Published: August 2020

Forty-eight students with no previous exposure to probability or statistics read one of three texts that varied in the emphasis placed on rote and conceptual learning of basic concepts of elementary probability. A qualitative analysis of errors on a postinstruction test employed a model of problem solving whose stages were categorization of the problem, retrieval of the appropriate formula, and translation of values from the problem into the formula. Variations in performance on problems requiring the same formula for solution were largely attributable to surface features that affected the ease of categorization and translation. Students who read a text that emphasized conceptual learning tended to be less sensitive to surface features, which parallels results regarding novices and experts in various content domains.
Brief Report: Cognitive Functioning and Performance on Addition and Subtraction Word Problems
Authors: Romberg Thomas A. , Collis Kevin F.
Published: August 2020

The question addressed in this paper is, Do children in the third grade who differ in cognitive-processing capacity solve addition and subtraction word problems differently? Information from a more extensive study (Romberg & Collis, 1983) was used to examine this question.
Preservice Teachers' Sources of Decisions in Teaching Secondary Mathematics
Authors: Bush William S.
Published: August 2020

Five preservice teachers' perceived sources of teaching decisions were studied as the teachers proceeded through a course on methods of teaching secondary mathematics and through student reaching. They were interviewed before and after lessons they taught during the methods course and student teaching. The sources cited most often included rhe content of the methods course, school textbooks, suggestions made during teaching episodes in the methods course, past teachers' performances, and cooperating teachers' performances. Suggestions from cooperating teachers were cited more often than suggestions from rhe university supervisor. Limitations and suggestions for further research are discussed.
Review: Life in the Fast Lane
Authors: House Peggy A.
Published: August 2020

Since its official beginning on 1 September 1971, the Study of Mathematically Precocious Youth (SMPY) at Johns Hopkins University has received considerable attention as a model for the education of extremely talented young mathematics students, usually of junior high school age. Articles and books have been written about the project as it evolved and as it was replicated elsewhere in the United States. So it was appropriate that in November 1980 a symposium at Johns Hopkins was devoted to discovering what had been learned during the first decade of the SMPY. Academic Precocity, Volume 10 in the Hyman Blumberg Symposium series, reports the findings and conclusions of that symposium.
Feature Frequency and the Use of Negative Instances in a Geometric Task
Authors: Wilson Patricia S.
Published: August 2020

A geomerric task was designed to investigate the effect of the frequency of irrelevant features in learning a conjunctive concept. One hundred algebra students were assigned to one of four treatment groups formed by crossing the two independent variables of feature frequency (equal or high) and sequence type (positive instances only or mixed positive and negative instances). The frequency of irrelevant features affected the usefulness of negative instances. When six irrelevant features were equally likely, positive instances were more helpful in learning, whereas when three irrelevant features predominated, mixed positive and negative instances were more helpful. The results may explain the difference between the findings of psychological and educational research on the usefulness of negative instances.
Reviews: Why Can't Johnny Add?
Authors: Glasersfeld Ernst Von
Published: August 2020

A result of the collaboration of the Institute for Special Education and the institute for Child Psychiatry at the University of Zurich, this book will be of interest not only to those who work with disturbed or disadvantaged children but also to mathematics teachers dealing with the first six grades. The first third of the text provides an excellent introduction to a variety of methods for the diagnosis of neurological, perceptual, and emotional disturbances that may affect performance in arithmetic. The remainder describes more than 20 (mostly European) therapeutical procedures, many of which could be implemented by rhe ordinary teacher in the ordinary class setting where similar disturbances frequently crop up without reaching pathological dimensions. Thanks to the wealth of very good illustrations, even a limited ability to read German could make this large part of the book useful to teachers in North America.
The Effects of Adjusting Readability on the Difficulty of Mathematics Story Problems
Authors: Paul Douglas J. , Nibbelink William H. , Hoover Hiram D.
Published: August 2020

A 15-item story problem test was written at three different readability levels (below Grade 4, Grade 4 to Grade 6, above Grade 6) by two different methods (vocabulary control and sentence control). The six forms of the test were administered to over 1000 children in Grades 3 to 6. There was no effect of readability level on problem difficulty—not even the hint of an effect.
Brief Report: Basic Counting Principles Used by Mentally Retarded Children
Authors: Baroody Arthur J.
Published: August 2020

Evidence of basic counting principles has been found in retarded children (Gelman, 1982), including those who are moderately handicapped (Baroody & Snyder, 1983). However, Gelman found no evidence of a stable-order or a cardinality principle in mentally handicapped children with a mental age (MA) of less than 4½ years. The current study examined retarded children in the same MA category to (a) evaluate the hypothesis of a critical MA for learning basic counting principles and (b) further examine how an understanding of counting develops.
Editorial
Authors: Kilpatrick Jeremy
Published: August 2020

The mail brings a stack of envelopes. On the top is a letter from Judy Sowder with information about the NCTM's Research Agenda Project. Four conferences, each on a different topic, are scheduled for this spring to consider research issues and identify directions for further work. Each will result in a monograph, with a fifth monograph providing an overview. The project looks promising, but is it reasonable to set research agendas for mathematics education? An agenda suggests there will be someone to carry it out; do researchers follow agendas in deciding what research to conduct next? Sometimes one has the image of each researcher located on a separate island, sending messages to one another in bottles (journals) that may or may not be read. On most islands, people seem to be busier filling bottles with new messages than reading the messages they have received. What would an agenda mean to such an island community?
Characteristics of Unskilled and Skilled Mental Calculators
Authors: Hope John A. , Sherrill James M.
Published: August 2020

Fifteen skilled and 15 unskilled students were selected from 286 Grade 11 and 12 mathematics students as a result of their performances on a mental multiplication test. Introspective reports during mental multiplication tasks yielded 4 methods of solution and 12 calculative strategies. The unskilled students used strategies more suited to written than mental computation, and the skilled students used strategies based upon the number properties suggested by the factors in the task. The skilled students recalled more large products to aid in a mental calculation than the unskilled students did. Mental multiplication performance had a low positive correlation with forward and backward digit span and with multiplication fact recall.
Editorial
Authors: Kilpatrick Jeremy
Published: August 2020

Because most researchers in mathematics education have spent time in schools reaching mathematics, they rend to undertake studies that entail the improvement of instruction. They are naturally and with good reason attracted to studying not the world as it is but the world as it might be. They identify an instructional problem, find what they consider to be an effective method for dealing with that problem, and undertake research to demonstrate the effectiveness of their method.
An Analysis of Three Models of Early Number Development
Authors: Cobb Paul
Published: August 2020

Three models each posit a sequence of developmental levels that culminate with the child's construction of the part-whole concept. Two are information-processing models of arithmetical word problem-solving performance, and the third is a model of children's counting types and thinking strategies. The three research teams make several of the same basic psychological assumptions. Nevertheless, the models offer qualitatively different explanations of similar behaviors. The models are compared in terms of detail, scope, attention to individual differences, and how they deal with qualitative change and semantic processing.
Effects of Noncontent Variables on Mathematics Test Performance
Authors: Hembree Ray
Published: August 2020

Results of 120 research studies were combined by meta-analysis to determine effects on mathematics test performance of factors other than knowledge of content. Effect sizes for 18 variables were derived by the method invented by Glass and tested for consistency and significance with inferential statistics provided by Hedges and Olkin. Conditions that enhanced performance included testwiseness training, praise, word-problem pictures, and frequent testing. Conditions that depressed performance included the use of “none of these” as a multiple-choice option and the presence of extraneous information in word problems. Conditions to which performance seemed insensitive included external reward, reproof, and placement of the question in word problems.
Editorial
Authors: Kilpatrick Jeremy
Published: August 2020

The Department of Education's Office of Educational Research and Improvement is in the process of funding, for the next 3 years, a research and development center for mathematics learning and teaching. In the invitation to applicants, OERI contended that our understanding of how students learn and what they need to learn has advanced so far that now we should concentrate on identifying effective teaching strategies. For example, the first of a long list of questions the proposed center is expected to address is “What are effective instructional strategies and processes that promote the learning of mathematics subject matter and critical thinking and reasoning?” It is incredible, or more precisely unimaginable, to think that we might have the makings of an answer to such a question by 1990, but the center may at least be able to help us understand the question better.
A Case Study of a Highly Skilled Mental Calculator
Authors: Hope John A.
Published: August 2020

This case study examined the performance of a 13-year-old highly skilled mental calculator on mental multiplication tasks. She solved difficult tasks by using various ingenious calculation methods, including distributing, factoring, and recalling the product directly. She possessed an extensive memory for squares of two- and three-digit numbers. Her WISC-R digit span was much greater than average. She used her exceptional knowledge of calculation methods and verification techniques to ascertain quickly if a number was prime or composite. She claimed to be largely self-taught, and her expertise probably developed through experimentation with numbers and number patterns.
Resequencing Skills and Concepts in Applied Calculus Using the Computer as a Tool
Authors: Heid M. Kathleen
Published: August 2020

During the first 12 weeks of an applied calculus course, two classes of college students (n=39) studied calculus concepts using graphical and symbol-manipulation computer programs to perform routine manipulations. Only the last 3 weeks were spent on skill development. Class transcripts, student interviews, field notes, and test results were analyzed for patterns of understanding. Students showed better understanding of course concepts and performed almost as well on a final exam of routine skills as a class of 100 students who had practiced the skills for the entire 15 weeks.
Mathematical Problem-Solving Performance of Eighth-Grade Programmers and Nonprogrammers
Authors: Blume Glendon W. , Schoen Harold L.
Published: August 2020

The mathematical problem-solving processes used by 27 eighth graders who had studied BASIC programming for a semester were compared to those of 27 who had not. The programmers used more systematic approaches and reviewed their solutions more often than the nonprogrammers but did not make more use of equations or do more planning. Further, the groups did not differ in the number of correct answers to a set of five process problems or two written problem-solving tests.
Identifying Fractions on Number Lines
Authors: Bright George W. , Behr Merlyn J. , Post Thomas R. , Wachsmuth Ipke
Published: August 2020

This study investigated the ways students represented fractions on number lines and the effects of instruction on those representations. Two clinical teaching experiments and one large-group teaching experiment were conducted with fourth and fifth graders (N = 5, 8, and 30) The instruction primarily concerned representing fractions and ordering fractions on number lines. Tests and videotaped interviews indicated that unpartitioning, in particular, is difficult for students, although the instruction seemed to help. Associating symbols with representations also seems difficult and may depend on an understanding of the unpartitioning process.
Effect of Cognitive Entry Behavior, Mastery Level, and Information about Criterion on Third Graders' Mastery of Number Concepts
Authors: Chan Lorna K. S. , Cole Peter G. , Cahill Rosemary A.
Published: August 2020

This study examined the effects of student cognitive entry behavior (CEB), as assessed by a test on knowledge of concepts of numbers and numerals; prescribed mastery level (ML); and information about criterion (INF) on mathematics achievement in a mastery-learning program. The subjects were 36 third-grade children randomly assigned to four treatments: (a) informed of a 90% ML; (b) not informed of a 90% ML; (c) informed, 70% ML; and (d) not informed, 70% ML. Instruction involved a hierarchical sequence of three learning tasks dealing with place value, numeration, and number relations. A multiple regression analysis with a significant CEB × ML × INF interaction indicated that for the low-CEB children, information about the prescribed mastery criterion enhanced achievement in the 90% ML treatment but not in the 70% ML treatment, whereas the reverse was true for the high-CEB children.
Editorial Comment
Authors: Johnson David C.
Published: August 2020

The first issues of JRME have included experimental research manuscripts on a variety of topics. ln general these studies have attempted to satisfy most of the criteria for conducting and reporting research—listings of such criteria usually include statements about (a) the problem (clearly defined and significant), (b) the design (appropriate to the problem under consideration), (c) randomization, (d) replication (either included in the research or careful delineation of the research procedures to enable others to replicate), (d) control of va riables, (f) measurement (selection and or development of appropriate instruments), (g) mathematical treatment of the data (use of appropriate statistical techniques), (h) conclusions (confined to those justified by the data and limited to those for which the data provides an adequate basis), (i) limitations (indicating flaws in the design and providing suggestions for improvement), and (j) implications (careful and reasonable extrapolations from the results of the study). Much of the research in (mathematics) education fa ils to adequately satisfy all these criteria. Of course, many of the problems arise from the difficulties encountered in conducting research in the classroom. However, even with flaws, some of the studies are important and need to be reported. It may be necessary, however, to conduct furth er research in the area, with more refined instruments and procedures before one can draw general conclusions relevant to instructional practice.
Problem-Solving Performances of First-Grade Children
Authors: Steffe Leslie P. , Johnson David C.
Published: August 2020

A sample of 111 first-grade children was partitioned into 4 categories, where the categorization was determined by an ability to make quantitative comparisons and IQ. 6 problems of each of 8 problem types were presented to each child in a randomized sequence. Approximately one-half of the children in each category were randomly assigned to 1 of 2 levels of Problem Conditions. A multivariate analysis of variance indicated that IQ was not significant. Problem Conditions was significant (p<.01p<.01). Univariate analysis indicated a significant interaction (p<.05p<.05) due to Quantitative Comparisons and Problem Conditions for 1 problem type; significant main effects (p<.01p<.01) due to Problem Conditions for the remaining 7 problem types; and a significant (p<.05p<.05) main effect due to Quantitative Comparisons for 1 of the remaining 7 problem types.
Critiques of the International Study of Achievement in Mathematics: The Problem of Perspective
Authors: Findley Warren G.
Published: August 2020

The International Study of Achievement in Mathematics is a truly magnificent accomplishment. The task of international comparison is difficult at best. The refinements of technique applied to the task were many and were generally well done, as might have been expected of the caliber of the research staff assembled. One must be impressed with the outcomes and with the wisdom shown in interpreting them. One may also properly rejoice in the establishment and continuation of a competent team in this area of research.
Comments on The Tests for 13-Year-Olds
Authors: Sullivan John J.
Published: August 2020

In March 1967, newspapers pubJjshed advance reports of an international research project concerned with mathematics achievement. These reports were disquieting to mathematics educators for it appeared that some kind of a competition had been conducted and the U.S. team had made a poor showing. The heading of an article in the New York Times, “United States Gets Low Marks in Math,” was representative of the tenor of most of the articles.
The Complexities in the Learning of Mathematics
Authors: Lamon William E.
Published: August 2020

A few years ago, the academic community around the world focused its attention on an immense international attempt to study on the one hand the differences among the school systems of twelve countries and, on the other, their effect on ach ievement, interests. and attitudes of certain groups of school-attendi ng youngsters. Those objectives and their findings were reported through many publications, most notable in International Study of Achievement in Mathematics (Husén, 1967). These publications have motivated me to raise some serious questions.
Editorial Comment
Authors: Romberg Thomas A.
Published: August 2020

In the fall of 1967 the Research Advisory Committee submitted a proposal to the Board of Directors of the National Council of Teachers of Mathematics asking NCTM to publish a research journal for mathematics education.
Does a Terminal Mathematics Course Contribute to Changes in Attitudes toward Mathematics?
Authors: Aichele Douglas B.
Published: August 2020

An Attitude Scale was developed to assess attitudinal changes in students enrolled in a terminal mathematics course taught at the University of Missouri-Columbia. Student attitudes, or opinions, were assessed in 4 areas (a) the learning of mathematics, (b) mathematics as a process, (c) the place of mathematics in society, and (d) school and learning generally. The method of paired comparisons was used to establish the scale values for the statement of the attitude instrument. For each part of the Attitude Scale, student (N=65) responses on the initial and terminal presentations were compared and the differences were not statistically significant. However, analysis of responses to individual statements within each part of the Attitude Scale revealed several significant changes.
A Forum for Researchers: Manipulative Activity in Mathematics Learning
Authors: Kieren Thomas E.
Published: August 2020

It is obvious from reading the articles or the advertisements in any recent mathematics teachers' journal on this continent or across the Atlantic that the use of manipulative activities in the teach ing and learning of mathematics is in vogue. Much of the current practice in this regard reflects the recommendations of such individuals as E. Biggs (1965), Davis (1967), and Dienes (1960, 1964). Nonetheless it is an understatement to say that research is needed into the role and effects of manipulative activity in mathematics.
Research on MATHEMATICS EDUCATION (K–12) Reported in 1970
Authors: Suydam Marilyn N. , Weaver J. Fred
Published: August 2020

An annual annotated listing of research pertaining to elementary and secondary school mathematics.
Comparison of Teacher–Written and Empirically Derived Distractors to Multiple–Choice Test Questions
Authors: Coppedge Floyd L. , Hanna Gerald S.
Published: August 2020

A comparison was made of the discrimination power of multiple–choice geometry test question alternatives supplied by (a) students taking an experimental test in completion format, (b) experienced teachers, and (c) student teachers. Neither experienced teachers nor student teachers were successful in supplying multiple–choice item distractors that best discriminated between high–and low–scoring students on the completion test. It was concluded that the most discriminating multiple–choice item distractors are produced by administering items in completion format, item analyzing the results, and selecting the most discriminating student errors.
Cognitive Development and the Structuring of Geometric Content
Authors: McDonald Janet L.
Published: August 2020

From a pool of secondary students (n = 161), 20 students were chosen who had high (formal operations) scores and 20 who had low (concrete operations) scores on two paper-and-pencil measures of Piagetian formal reasoning (the Test of Logical Thinking and the Longeot Test). The students made similarity judgments among all possible concept pairs from 13 geometric concepts and 10 mathematical expressions from a unit on ratio, proportion, and similarity. Multidimensional scaling procedures showed that despite idiosyncrasies in individual structures, clear prototypical maps could be derived for both the formal and concrete groups. In addition, formal operational students structured subject matter content significantly more like subject matter experts than concrete operational students did.
Kindergartners' Mental Addition with Single-Digit Combinations
Authors: Baroody Arthur J.
Published: August 2020

A study involving 17 kindergartners tested association- and schema-based views of simple mental addition. Six children appeared to use mechanical rules: Two each stated one of the addends, added one to an addend, and constructed a teen answer from one of the addends. Five other children appeared to use more genuine estimation strategies. Eight weeks of computational practice affected the errors of unpracticed combinations on a retest. Moreover, 7 of 10 children mastered previously unknown combinations involving zero. This resulted from learning a relationship (adding with zero leaves a number unchanged) rather than from the practice and memorization of individual facts. The results indicate that mental-arithmetic errors, changes in error patterns, and mastering some simple facts cannot be explained entirely as a function of practice.
An Exploration of the Mathematics Self-Efficacy/Mathematics Performance Correspondence
Authors: Hackett Gail , Betz Nancy E.
Published: August 2020

This study investigated the relationship between mathematical performance and mathematics self-efficacy, attitudes toward mathematics, and the choice of mathematics-related majors by 153 college women and 109 college men. Mathematics performance was correlated moderately with mathematics self-efficacy. No support was found for Hackett and Betz's (1981) hypothesis that women's mathematics self-efficacy expectations are unrealistically low compared to men's. Both mathematics performance and mathematics self-efficacy were significantly and positively correlated with attitudes toward mathematics, masculine sex-role orientation, and a mathematics-related major. Regression analyses supported the superiority of mathematics self-efficacy over mathematics performance and achievement variables in predicting the choice of a mathematics-related major.
The Visual Syntax of Algebra
Authors: Kirshner David
Published: August 2020

A structured system of visual features can be seen to parallel the propositional hierarchy of operations usually associated with the parsing of algebraic expressions. Some students (proportionately more women than men) were found to depend on these visual cues in their syntactic decision making. Others were found to have access to sound propositional rules. Possible causes and consequences of these different syntactic representation styles are discussed.
A Forum for Researchers: Should Problem Solving Be Used as a Learning Device in Mathematics?
Authors: Owen Elizabeth , Sweller John
Published: August 2020

A theory of expertise has developed over the last few years on the basis of research into expert-novice differences. This research has shown an impressive degree of consistency in a variety of fields of knowledge and is beginning now to have direct implications for the teaching of mathematics and related disciplines. Research data, generated in part by current theories of expertise, call into question many long-held assumptions and procedures. We suggest that some views of mathematics and the way it should be taught owe more to tradition than to our current knowledge of cognitive processes. The purpose of this paper is to outline the theory, describe some of the associated experimental findings, and indicate the consequences of those findings for educational practice in mathematics.
Review: Mathematics: Are You Speaking My Language?
Authors: Cuevas Gilbert J.
Published: August 2020

What is the role of language in learning mathematics? Is mathematics a “culture free” as well as a “language free” discipline? What is the effect, if any, of proficiency in the language of instruction on the learning of mathematics? What does research have to say about these questions? These and many other issues are addressed in Linguistic and Cultural Influences on Learning Mathematics.
Review: Mathematics Meets Culture
Authors: Stigler James W.
Published: August 2020

The idea of mathematical culture is in the air, it seems, and so the title of Alan J. Bishop's Mathematical Enculturation has a nice ring to it. The tone of Bishop's essay is quite personal as he takes the reader through his own discovery process en route to understanding the nature and meaning of mathematical culture and the implications of mathematical culture for mathematics education. But as well as being personal, the book is also somewhat idiosyncratic: the sources cited, taken together, appear to represent more of a random walk through the library than a developed expertise in the field. Many contemporary writers who have done ground-breaking theoretical and empirical work in the area of mathematical culture are left uncited, while at the same time, older books that are not often read anymore, such as White's (1959) Evolution of Culture, are featured. This gives the essay a strange feel, which nevertheless is at times refreshing. In fact, the essay becomes more pleasing as one journeys through it.
Research on Mathematics Education Reported in 1988
Authors: Suydam Marilyn N.
Published: August 2020

As in previous years, this 19th annual listing of mathematics education research to appear in JRME contains research summaries, articles, and dissertations, listed alphabetically by author within each category. For each reference, the grade or age level is indicated (when the researcher has provided this information or it can be inferred). An index is included at the end to help readers locate studies on certain, generally broad, topics.
Children's Performance on Multiplicative Word Problems: Elements of a Descriptive Theory
Authors: Bell Alan , Greer Brian , Grimison Lindsay , Mangan Clare
Published: August 2020

Three hundred seventy-seven subjects in six age groups, ranging from 10 to 20 years, were asked to identify the appropriate operation for 24 multiplication and division problems involving price, speed, and measure conversion. For multiplication problems, difficulty was strongly dependent on the type of number in the preferred-multiplier role. Important differences from the general tendency were noted in those change-of-size and mixture problems in which both quantities were measured in the same units. Choice of operation also was affected by the misconception that multiplication makes bigger and division smaller. In division problems, choice was dominated by the numerical preference for dividing by an integer or the smaller of the two numbers; decimal points were sometimes ignored in determining this preference. MMBDS also operated, but not in all problems. In a second experiment with 42 fifteen-year-old students, half were asked to estimate answers and half to choose the correct operation for change-of-size and mixture problems. Estimating the outcome was easier than both choosing the operation for division, and multiplication by numbers less than 1. For multiplication by numbers substantially greater than 1, choosing the operation was easier.
Brief Report: Gender Differences in Mathematics: An International Perspective
Authors: Ethington Corinna A.
Published: August 2020

Gender-related differences on measures of quantitative performance and problem-solving abilities consistently appear in national assessments (e.g., Dossey, Mullis, Lindquist, & Chambers, 1988; Fennema & Carpenter, 1981; National Assessment of Educational Progress, 1975, 1983; Wilson, 1972). Using a variety of performance measures, investigators have examined the nature of these differences and the factors associated with them for subjects varying in age from elementary school to undergraduates in college. From these studies, it is generally concluded that no gender differences are evidenced at the elementary school level, but beginning at approximately the seventh grade, any differences that appear, such as those found in spatial problem-solving tasks and tasks requiring mathematical reasoning, favor males. (See Fennema, 1974, 1980 and Leder, 1985, for a review of this literature.)
Evoking Cognitive Conflict to Explore Preservice Teachers' Thinking about Division
Authors: Tirosh Dina , Graeber Anna O.
Published: August 2020

This study investigated conflict teaching as a means of probing the misconception held by many preservice elementary teachers that in a division problem the quotient must be less than the dividend. Individual interviews were held with 21 preservice teachers who were able to correctly compute quotients for division problems with decimal divisors less than one, but who agreed with an explicit statement that the quotient must be less than the dividend and who selected operations to solve word problems that reflected this misconception. The interviews illustrated how preservice teachers' reliance on information about the domain of whole numbers and their instrumental understanding of the division algorithm support their misconception. The authors also noted preservice teachers' lack of access to the measurement interpretation of division and their willingness to change procedural rules to preserve their misconception.
Editorial
Authors: Carpenter Thomas P.
Published: August 2020

Webster's New Collegiate Dictionary defines research as “careful, systematic, patient study and investigation in some field of knowledge undertaken to discover or establish facts or principles.” This definition is reflected in the perspective that the purpose of educational research is to provide definitive answers to important pedagogical questions.
Spatial Orientation Skill and Mathematical Problem Solving
Authors: Tartre Lindsay Anne
Published: August 2020

The purpose of this study was to explore the role of spatial orientation skill in the solution of mathematics problems. Fifty-seven tenth-grade students who scored high or low on a spatial orientation test were asked to solve mathematics problems in individual interviews. A group of specific behaviors was identified in geometric settings, which appeared to be manifestations of spatial orientation skill. Spatial orientation skill also appeared to be involved in understanding the problem and linking new problems to previous work in nongeometric settings.
Review: Constructing an International Perspective
Authors: Sowder Judith T.
Published: August 2020

The International Group for the Psychology of Mathematics Education (PME) has been active since 1976, with yearly meetings attended by researchers representing 39 countries. The proceedings of these meetings and of the meetings of the North American Chapter of PME reflect the changing concerns of the international mathematics education research community and form a rich resource of studies on the learning and teaching of mathematics. These proceedings can, however, be described as “fugitive literature” in the sense that they are not generally available through libraries. The advent of easily obtainable publications that describe the work of the PME community is overdue and welcome.
A Forum for Researchers: Issues in Place-Value and Multidigit Addition and Subtraction Learning and Teaching for Research on Mathematics Teaching
Authors: Fuson Karen C.
Published: August 2020

Research on multidigit addition and subtraction is now sufficient to question some present textbook practices and suggest alternatives. These practices revolve around the organization and placement of topics within the curriculum and around teaching/learning methods. These questions are being raised because the evidence indicates that U.S. children do not learn place-value concepts or multidigit addition and subtraction adequately and even many children who calculate correctly show little understanding of the procedures they are using (e.g., Cauley, 1988; Karnii & Joseph, 1988; Kouba et al., 1988; Labinowicz, 1985; Lindquist, 1989; Resnick, 1983; Resnick & Omanson, 1987; Ross, 1989; Stigler, Lee, & Stevenson, in press; Tougher. 1981).
A Forum for Researchers: How and When Should Place-Value Concepts and Skills Be Taught?
Authors: Baroody Arthur J.
Published: August 2020

Clearly, many children in the United States have difficulty learning place-value skills and concepts, and the teaching of these fundamental competencies needs to improve. Fuson correctly concludes that her research (Fuson, 1986, 1988; Fuson & Briars, 1990) indicates that substantial improvement over traditional textbookbased instruction is possible. However, existing research does not clearly address the issues of how place-value instruction should be changed and when it should be introduced into the curriculum (Baroody, in press).