bluuebunny/crossref_metadata_2025 huggingface dataset:
Brief Reports: Some Aspects of Individual Differences in Mathematics Instruction
Authors: Radatz Hendrik
Published: August 2020

For some years individual differences in learners and teachers have played an important part in educational research in general and especially in research in mathematics education. There are a multitude of studies on the importance of abilities, demographic characteristics, and various cognitive, affective, and social factors to the learning of mathematics or, more precisely, to achievement in mathematics. Three developments in particular seem to have increased interest in individual differences: information-processing psychology. aptitude-treatment-interaction (ATI) research. and an increased awareness of the content- and situation-specificity of the learning process.
Brief Reports: Hand-Held Calculator Curriculum and Mathematical Achievement and Retention
Authors: Creswell John L. , Vaughn Larry R.
Published: August 2020

Mathematics teachers continue to search for more effective and efficient techniques to help children understand mathematics. Many educators feel that the small electronic hand-held calculator may serve this purpose.
A Forum for Researchers: A Reply to “Formal Thinking Strategies: A Prerequisite for Learning Basic Facts?”
Authors: Steffe Leslie P.
Published: August 2020

Two questions were posed and examined to elucidate how thinking strategies relate to basic facts instruction. The first of the two questions was “Are thinking strategies indeed necessary for learning basic facts?” The answer to this question historically depended on whether one was a drill theorist or a meaning theorist. The drill theorist would answer in the negative, and the meaning theorist would answer in the affirmative. Obviously, the question has no answer solely in empirical research because the empirical research always stands to be interpreted. A prime example is the interpretation of the Brownell and Chazal (1935) study. Brownell {1935) presented this study as being disconfirmatory of a major assumption made in the administration of drill. The assumption is that when the teacher administers flash-card drill on number combinations such as 4 + 3 = 7, “she expects all pupils to think silently or to say aloud ‘4 and 3 are 7,’ ‘8 less 6 are 2,’ and so on. It is her belief that by such repetition the children will come eventually to respond only and always ‘7,’ ‘2,’ etc. on presentation of the corresponding combination items” (p. 8).
Exemplification and Characterization Moves in the Classroom Teaching of Geometry Concepts
Authors: Charle Randall I.
Published: August 2020

The purposes of this study were to determine whether teachers can be trained to use exemplification (E) and characterization (C) moves and whether the use of these moves facilitates concept acquisition. Each of 18 preservice teachers (9 trained, 9 control) taught two 20-minute lessons on geometry concepts to small groups of second-grade students. Significant differences favoring the trained teachers were found for the number of E and C moves. Mean student posttest scores for the trained teachers were significantly greater than scores for the control teachers. The number of nonexamples used for teaching bilateral symmetry and the number of examples used for teaching rotational symmetry accounted for a significant amount of the variance in posttest scores.
Calculators and the Teaching of Ratios in Grade 7
Authors: Szetela Walter
Published: August 2020

One of the arguments supporting the use of calculators for mathematics instruction is the claim that calculators facilitate understanding and concept development and aid in problem solving (Suydam, Note 1). An analysis of studies of calculator usage in mathematics instruction reported by the Calculator Information Center in Bulletin No. 9 (Note 2) shows that of 28 findings on achievement reported in 16 studies in Grades 5-7, there were 14 findings in which the calculator group scored significantly higher, 11 findings with no significant differences, and only 3 instances in which the noncalculator groups scored higher.
A Forum for Researchers Toward Research Significance
Authors: Brown Ric
Published: August 2020

This note considers measurement of the magnitude of effect and its implications for mathematics education research. Research significance refers not only to the statistical significance of results, but also to the magnitude of effect that the independent variable(s) have on the dependent variable(s). Kerlinger (1973, p. 17) writes that problems in behavioral research are statements of relationship between two or more variables (whether categorical or interval scales). Keppel (1973, p. 548) indicates that the degree to which a researcher can account for the total variability in the dependent variable by isolating independent variable effects is of prime concern.
Children's Spatial-Perceptual Preferences: A Cross-Cultural Comparison
Authors: Shar Albert O. , Geeslin William E.
Published: August 2020

In the first stage of investigating how children perceive and conceptualize spatial figures, Geeslin and Shar (1979) developed procedures for making objective comparisons of two-dimensional figures. Piaget and lnhelder (1967, 1971) claimed that the cognitive structures of children allow them to operate on the topological properties of figures prior to being able to conceptualize Euclidean properties. However, Geeslin and Shar (1979) found no indication of spatial developmental differences on a perceptual task among American children in the nursery school through fourth-grade levels (ages 3 years and up, N = 345). Although a variety of plausible reasons for these apparently contradictory findings can be put forth, the investigation reported here pursued the possibility of cultural differences between American and Swiss children.
Differential Teacher Grading Behavior toward Female Students of Mathematics
Authors: Duval Concetta M.
Published: August 2020

This study was an attempt to determine if teachers discriminate against female learners of mathematics. More than 1000 secondary mathematics teachers, selected at random within New York State, were asked to grade four geometry proofs. Only two characteristics of the student presumed to have written the examination were conveyed to each of the teacher-graders. Student sex and ability level (above average, average, and below average) constituted the independent variables in a 2 × 3 factorial design. A seventh experimental condition, in which no biographical information was given, was included as a control. An analysis of variance of the reponses yielded no statistically significant F ratios for either of the two main effects or the interaction effect. A separate analysis of a small group of late responses similarly revealed no statistically significant differences in mean scores.
Cognitive Competence and Mathematical Development
Authors: Souviney Randall J.
Published: August 2020

Attainment relative to six cognitive operations and four number and computational skills was assessed for 90 elementary students using clinical procedures. The data were examined by correlational and stepwise multiple regression analyses. Variance associated with conservation of number, seriation, and logical classification competency accounted for a significant proportion of the variance in achievement scores. Findings indicated similar relationships between transitivity competence and multiplication/division achievement as well as conservation of area competence and understanding of fractional part-of-a-whole. The data failed to support any relationship between class inclusion competence and addition/subtraction achievement.
Brief Reports: Concept Teaching Strategy Length
Authors: Dossey John A.
Published: August 2020

This study examined the effect that the number of moves in a concept teaching venture had on student attainment of a set of 12 disjunctive mathematical concepts.
Calculator Use and Problem-Solving Performance
Authors: Wheatley Charlotte L.
Published: August 2020

The purpose of this study was to compare the problem-solving processes of elementary pupils using calculators with those of pupils not using calculators. The subjects were two groups of sixth-grade pupils of above-average ability. Both groups received 6 weeks of training in problem solving. One group (n=23) used calculators. It was found that the calculator group used a total of 152 facilitative processes, compared to 104 for the noncalculator group. The greatest differences were noted on these items: has bright ideas, estimates, uses unexpressed equations, checks conditions, and retraces steps. This suggests that calculators stimulate pupils to think about approaches to problems.
Brief Reports: Organizational Strategies and Practice Procedures for Teaching Basic Facts
Authors: Carnine Douglas W. , Stein Marcy
Published: August 2020

Elementary mathematics instruction strives for both meaningful understanding and the mastery of algorithms.
The Addition Methods of First- and Second-Grade Children
Authors: Houlihan Dorothy M. , Ginsburg Herbert P.
Published: August 2020

A clinical interview method was used to investigate the addition procedures used by first- and second-grade children on both written and orally presented problems of different magnitudes and to determine whether these children vary their strategies according to the nature and magnitude of the problem. The results showed that first graders used a variety of counting procedures to solve addition problems, while second graders used both counting and noncounting procedures. In general, second-grade children efficiently adjusted their strategies according to the magnitude of the problem's addends. Implications for education are discussed.
Initial Effect of Calculators in Elementary School Mathematics
Authors: Shumway Richard J. , Wheatley Grayson H. , Coburn Terrence G. , White Arthur L. , Revs Robert E. , Schoen Harold L.
Published: August 2020

The purpose was to determine the effect availability of calculators to students and availability of calculator-related curriculum resources, consultant resources, and in-service workshops to teachers had on elementary school children's attitudes and achievement in mathematics, Grades 2-6. Fifty classes Grades 2-6 were selected from five mid-western states and randomly assigned to Calculator and No Calculator treatments. The treatments were in effect for 67 school days over a period of 18 weeks. Results indicate no measurable detrimental effects for calculator use. Children grew significantly on basic facts and achievement regardless of use of calculators in class.
Brief Reports: Using a Computer Game to Reinforce Skills in Addition Basic Facts in Second Grade
Authors: Kraus William H.
Published: August 2020

Early work in computer-assisted instruction (CAl) involved using the computer to present drill-and-practice exercises to the student (e.g., Suppes, Jerman, & Brian, 1968; Suppes & Morningstar, 1972). Since the computer can provide immediate feedback to the student and can control the sequence in which the exercises are presented, such CAl has generally proven to be effective, although the cost-effectiveness of such systems of programmed instruction bas been questioned (Vinsonhaler & Bass, 1972).
Brief Reports: Intellectual Abilities That Discriminate Good and Poor Problem Solvers
Authors: Ann Meyer Ruth
Published: August 2020

This study investigated intellectual abilities that discriminate good and poor problem solvers. It presents further analyses of Meyer's (1978) study and is an abbreviation of Meyer (1980).
The Construction of a Logical-Empirical Structure of Knowledge for Differential Calculus Using a Theoretical Framework Based on Learning Hierarchy Theory and Order Theory
Authors: Martin Devecchi James
Published: August 2020

The principal result of this study is a logically and empirically valid structure of knowledge for differential calculus constructed using a methodology based on Learning Hierarchy Theory (LHT) and Order Theory (OT). A review of existi research into calculus learning is presented, and properties of the structure of knowledge that address deficiencies in existing knowledge are discussed. LHT is developed, and techniques for the empirical validation and generation of hierarchies are discussed. Included in this discussion is a detailed analysis of the important properties of OT.
Brief Reports: The Effects of Two Strategies for Teaching Two Mathematical Skills
Authors: Cooney Thomas J. , Davis Edward J. , Hirstein James J.
Published: August 2020

In recent years there has been a concern over the acquisition of basic mathematical skills by students. The phrase “back to basics” has been coined in reference to this concern. One of the underlying issues of the back-to-basics emphasis is the relative importance of understanding a mathematical skill versus performance of that skill.
Algebra Word Problem Solutions: Thought Processes Underlying a Common Misconception
Authors: Clement John
Published: August 2020

A large number of college students exhibit a common misconception while solving certain algebra word problems. The error appears in writing equations where a multiplying factor is placed on the wrong side of the equation: writing 6S=P instead of S=6P, for example. Protocol analysis can allow us to investigate the cognitive processes producing the error as well as those leading to the correct solution. The findings have also led us to view the nature of the processes underlying the correct use of algebraic symbolization in a new way. The description of these basic processes should make it easier to design more effective strategies for teaching algebraic symbolization skills.
Reviews
Authors: Cooney Thomas J.
Published: August 2020

I found the book Selected Issues in Mathematics Education, jointly published with the National Society for the Study of Education, to be a worthy candidate for one's library. It provides interesting perspectives on a wide range of centrally important topics without getting bogged down in “disease of the week” issues that are parochial in nature. The book is not issue oriented in the sense of presenting various positions for the reader to consider and judge. Many of the chapters convey the authors' views of the state of the art in a particular research area. In some sense, the book could be a companion volume to NCTM's professional reference, Research in Mathematics Education. Still, if one is willing to look beyond what the title suggests, Selected Issues generally makes for good reading, as several authors are willing to share their insights into some rather knotty problems that are likely to be with our profession for some time.
Fourth Graders' Heuristic Problem-Solving Behavior
Authors: Lee Kil S.
Published: August 2020

Two questions were explored, (a) can fourth graders use specific heuristics appropriately and effectively when attempting to solve challenging word problems, and (b) are there differences in the use of heuristics by students at the two substages of the concrete operational stage described by Piaget? Clinical methodology was used in collecting and analyzing the data. After instruction, the students were able to use heuristics appropriately and, in many cases, effectively in solving challenging word problems. There were differences in the use of heuristics by students at the two substages of the concrete operational stage.
Careless Errors Made by Sixth-Grade Children on Written Mathematical Tasks
Authors: Clements M. A.
Published: August 2020

An investigation into mathematical errors made by 50 sixth-grade children attending an international primary school in Lae, Papua New Guinea, is described. The children were given a battery of tests, with one of the tests, the Monash Assessment of Mathematical Performance (MAMP), being administered twice. Errors made by the children on either, or both, occasions they did the MAMP test were analyzed by means of the Newman interview technique. Attention was focused on errors made on one occasion but not on the other: An error of this type was deemed to have been ”careless” if a child confidently demonstrated, to the interviewer, that he or she knew how to obtain the correct answer to the question and if neither the child nor the interviewer could identify why the original error had been made. Of all the errors made by the children on MAMP questions, 21% were in this category. Analysis revealed that the proportion of careless errors correlated significantly and positively with measures of arithmetical competence, mathematical language, and mathematical confidence but negatively with a measure of misplaced confidence.
Brief Reports: Effective Mathematics Instruction for Low-Income Students: Results of Longitudinal Field Research in 12 School Districts
Authors: Carnine Douglas , Gersten Russell
Published: August 2020

The present brief report attempts to first integrate and then briefly discuss some of the empirical findings from field research on educational programs for low-income students. Though quasi-experiments cannot possibly offer the same precision in either the delineation of the independent variables or in the control for potential threats to internal validity as tightly controlled classical experiments can, they do have certain advantages—information is gathered in natural, representative settings (Snow, 1974), and effects over long periods of time can be assessed (Gallagher, Ramey, Haskins, & Finkelstein, 1975; Bronfenbrenner, 1975). Though important for any type of research, replications with different groups of children and in a range of settings is essential for validating results of quasi-experiments (Cook & Campbell, 1979). The longitudinal evaluation of the Follow Through project offers an opportunity to examine the effects of 10 clearly articulated educational models (cf. Stallings, 1975) on lowincome primary grade students in different settings and across several years.
Story Problem Solving in Elementary School Mathematics: What Differences Do Calculators Make?
Authors: Szetela Walter
Published: August 2020

For 8 to 12 weeks, 180 students in Grades 3, 5, 7, and 8 used calculators (C) or no calculators (N) for problem solving. A parallel study in which all 116 students, Grades 5, 6, and 7, used calculators for problem solving was conducted simultaneously. Posttesting with and without calculators produced few differences on the number of problems attempted and the number with correct operations. When using calculators on posttests, C groups obtained significantly more correct answers to problems than N groups in 7 out of 12 comparisons. On paper-and-pencil tests of computation and problem solving, C groups performed at least as well as N groups.
Critiques: Cognitive Development and Children's Solutions to Verbal Arithmetic Problems: A Critique
Authors: Steffe Leslie P. , Cobb Paul
Published: August 2020

One primary reason for writing this critique of the report by Hiebert, Carpenter, and Moser (1982) is to emphasize the intricate relationship between theory and data. First, we question the classical empiricist assumption that observation is free from the prejudices of theory. We then consider the role that explanatory theoretical constructs played in the study. Finally, we discuss briefly a claim that number conservation is not a readiness variable for acquiring counting strategies.
Children's Use of Mathematical Structure
Authors: Baroody Arthur J. , Ginsburg Herbert P. , Waxman Barbara
Published: August 2020

This study examined the use of the commutativity, addition-subtraction complement, and N+1 progression principles in a numerical task by capable first, second, and third graders. Fifty-four children were interviewed individually. A series of number combinations was given as a game in which one had to compute in solving some items but could avoid computation in others by using one of the principles. Commutativity was used extensively by children at each grade. Use of the addition-subtraction complement principle to solve subtraction items varied across grades and depended on how efficiently the preceding addition counterpart had been solved. The N+1 pattern was seldom used at any grade.
Brief Report: A Multisensory Approach to Thinking Strategies for Remedial Instruction in Basic Addition Facts
Authors: Thornton Carol A. , Jones Graham A. , Toohey Margaret A.
Published: August 2020

An earlier study by Thornton (1978) emphasized the use of thinking strategies over the traditional “sums to” approach for helping pupils learn the basic facts. The present study extended this research by using thinking strategies with pupils requiring special help because of severe learning deficiencies in mathematics and by using an approach with characteristics not tested in the previous study.
Review: Symbolism from A to W
Authors: Howson Geoffrey
Published: August 2020

My pleasure at being sent for review this collection of papers on symbolism in mathematics was somewhat diminished when I saw that the first article was by Josette Adda and the last by Derek Woodrow. This was not due to any lack of respect for these two authors; rather, it indicated that readers were being offered not a structured survey of the problems of symbolism within mathematics education but an ad hoc collection of articles arranged alphabetically by author. In fact, although the nine articles vary considerably in quality, the overall standard is quite high, and any mathematics educator will find two or three of interest. Nevertheless, I very much felt the absence of a framework that would help the reader to identify more clearly the sa lient problems and to recognize fruitful avenues for research. In particular, the actual role of symbols within mathematics and within mathematical activity would seem to me to be given insufficient attention, although, almost of necessity, most authors touch on it.
Increasing the Participation of Native Americans in Mathematics
Authors: Cheek Helen Neely
Published: August 2020

Needed research inro the problem of increasing Native Americans' underparticipation and underachievement in mathematics can be directed at (a) raismg expectations for performance, (b) devising culturally based programs, and (c) improving pedagogy. To raise expectations, possible modifications of intervention programs using videotapes, conferences, and workshops arc proposed. Culturally based curricula need to consider intertribe differences that raise important research questions. Pedagogical reform suggests investigating an applications-oriented approach and the use of computer-assisted instruction. Community input is needed in all research and development activity.
The Mathematics Education of Asian Americans
Authors: Tsang Sau-Lim
Published: August 2020

A review of the research literature on the mathematics education of Asian-American students indicates that although their achievement in mathematics has been relatively high, the effects of the recent wave of immigration from Asia have not been studied. Problems faced by immigrant students in taking mathematics tests have been identified, and research has begun into cognitive differences between them and students educated entirely in the United States. Researchers and educators alike need a greater sensitivity to differences within the Asian-American population.
Reviews: America Counts
Authors: Jones Phillip S.
Published: August 2020

This book supplies an interesting set of answers to the question, “Why the sudden popularity of numbers and statistics in Jacksonian [1829–1837] America?” This question also supplies a partial definition of numeracy as used in the subtitle. The introduction defines it more formally as “ability with or knowledge of numbers” and suggests the use of innumerate as parallel in meaning to illiterate.
Predicting Eighth-Grade Algebra Achievement
Authors: Flexer Barbara K.
Published: August 2020

The relative importance of a group of cognitive variables in explaining the algebra achievement of high-ability eighth graders was investigated. Stepwise multiple regression analyses identified algebra prognosis test scores and performance in seventh-grade mathematics as the most influential predictors of algebra grades, whereas mathematics problem solving, the prognosis test, and IQ were shown to best predict achievement on a standardized algebra test. A discriminant analysis demonstrated the importance of the prognosis test in discriminating between students who successfully completed first-year algebra and those who dropped out of or failed the course. Although the study showed no sex difference in algebra achievement test scores, girls in the sample attained higher percentage grades for the course.
Brief Report: Sex Differences in Rote-Counting Ability on Entry to First Grade: Some Observations
Authors: Callahan Leroy G. , Clements Douglas H.
Published: August 2020

Currently, the issue of sex differences in mathematical abilities is of great concern. This article focuses on one early number skill: rote counting. Almost a century of research has produced equivocal results. These discrepancies might be accounted for by differences in methodology and data analysis. This report presents data on sex differences in rote-counting ability and illustrates how different data-gathering methods and different statistical treatments of the data can yield different results.
Order and Equivalence of Rational Numbers: A Cognitive Analysis
Authors: Post Thomas R. , Wachsmuth Ipke , Lesh Richard , Behr Merlyn J.
Published: August 2020

Fourth-grade students' understanding of the order and equivalence of rational numbers was investigated in an 18-week teaching experiment. Data from observations of, and interviews with, two children were employed to identify patterns over time in the strategies used in performing tasks. Three related characteristics of thinking are hypothesized to be related to the successful performance of tasks on order and equivalence: (a) thought flexibility in coordinating between-mode translations, (b) thought flexibility for within-mode transformations, and (c) reasoning that becomes increasingly independent of specific concrete embodiments.
Brief Reports: The Problem of Inflated Significance When Testing Individual Correlations From a Correlation Matrix
Authors: Collis Betty A. , Rosenblood Lorne K.
Published: August 2020

Testing the relationship between variables is an important part of educational research. The rest is commonly done by using the Pearson productmoment correlation coefficient. The basic question in determining the significance of an observed correlation is the likel ihood of the observed relationship occurring by chance, given that there is nor a true correlation. When only two variables are involved, the significance is determined by using the standard t or z statistics or by consulting a table (see, for example, Ferguson, 1981, Table D). The significance level obtained can be referred to as the comparison-wise error rate. What this expresses, of course, is the probability that the single observed correlation is being declared significant when in fact there is no significant correlation.
Critiques: Behavioral Objections: A Response to Wollman
Authors: Kaput James J. , Sims-Knight Judith E. , Clement John
Published: August 2020

That behaviorist horse, although badly flogged, continues to stalk among us. The well-executed Wollman (1983) study provides a clear example of how psychological and educational behaviorism remains at work influencing both research objectives and methods—even among researchers who are patently not behaviorists. Now, however, one must look beneath the patina to find its effects.
Metacognition, Cognitive Monitoring, and Mathematical Performance
Authors: Garofalo Joe , Lester Frank K.
Published: August 2020

Recent research on cognitive development, memory, and reading indicates that much attention is being given to metacognition. There is also growing support for the view that purely cognitive analyses of mathematical performance are inadequate because they overlook metacognitive actions. This paper is intended as an introduction to metacognition and the role it plays in mathematical performance.
Letters to the Editor
Authors: Osborne Alan , Hedges Larry V.
Published: August 2020

In your editorial in the january issue, you discuss the usefulness of the JRME to the profession at this point in the history of mathematics education. I think the issue you raise needs more than an offhand dismissal.
Logical Reasoning Hierarchies in Mathematics
Authors: Jansson Lars C.
Published: August 2020

Ordering theory was used ro empirically determine hierarchies of developmental precedence for Piager's 16 logical combinations. In two studies carried out in the Netherlands, subjects were tested in individual interviews. In Study 1, 94 subjects responded to statements about odd and even numbers; in Study 2, 30 subjects responded to statements about line segments. For each study, a hierarchy of operations was produced from the responses. The two hierarchies were similar to each other and to a hierarchy from a previous study in which a nonmathematical task was used. Different linguistic forms for the same logical operation appeared to yield greater differences in performance than differences in tasks.
Brief Report: The Keller Plan, Final Examinations, and Long-Term Retention
Authors: Watson Jane M.
Published: August 2020

The Keller Plan for a personalized system of instruction as applied to college-level courses is usually characterized by (a) individual pacing, (b) a mastery orientation, (c) the presence of student tutors, (d) the use of printed study guides, and (e) the inclusion of a few lectures for enrichment (Kulik, Kulik, & Carmichael, 1974). In mathematics courses the plan has led to positive reactions from students, lower dropout rates, and higher final examination scores (Anderson & Pritchett, 1977; Peluso & Baranchik, 1977; Rogers & Young, 1977; Struik & Flexer, 1977; Waits & Riner, 1975; Weir, 1977). The issue of the long-term retention of concepts in personalized mathematics courses, however, appears not to have been addressed.
A Technique for Assessing Mathematical Problem-Solving Ability
Authors: Collis Kevin F. , Romberg Thomas A. , Jurdak Murad E.
Published: August 2020

This report sets out the procedures followed in developing, administering, and scoring a set of mathematical problem-solving superitems and examining their construct validity through a recently developed technique of evaluation associated with a taxonomy of the structure of learned outcomes. Each superitem includes a mathematical situation and a structured set of questions about that situation. To judge whether the response patterns of students to the superitems were interpretable, two questions were raised about the response patterns. For each question, the data strongly support the validity of the underlying theoretical constructs.
Where are the Data?—A Reply to Confrey
Authors: Brophy Jere
Published: August 2020

I find Confrey's (1986) contribution to be engaging as a work of fiction and provocative as an allegorical statement of a point of view, but I believe that it leaves much to be desired as a response to my own contribution (Brophy, 1986). I have three basic complaints: (a) unbalanced content coverage, (b) distortions in the treatment of the content that is covered, and (c) the lack of evidence of readiness to come to grips with the realities of classroom teaching.
An Empirical Classification Model for Errors in High School Mathematics
Authors: Movshovitz-Hadar Nitsa , Zaslavsky Orit , Inbar Shlomo
Published: August 2020

A content-oriented analysis of written solutions to test items in Israeli high school graduation examinations in mathematics yielded a system of six error categories: misused data, misinterpreted language, logically invalid inference, distorted theorem or definition, unverifed solution, and technical error. This system enabled most of the documented errors to be classified. A reliability test showed that the categories are inclusive and mutually exclusive.
Sex Differences in the Association between Secondary School Students' Attitudes toward Mathematics and toward Computers
Authors: Collis Betty
Published: August 2020

Sex differences in the positive association between attitudes toward mathematics and attitudes toward computers were examined in 1 018 Grade 8 students and 800 Grade 12 students. The female students were more likely than the male students to associate negative attitudes toward mathematics with negative attitudes toward computers. Participation in an eighth-grade mathematics course with a computer component was associated with positive attitudes toward computers for males but not for females. The integration of computer experiences with mathematics instruction may require some caution to yield more positive attitudes toward mathematics and computers from secondary school females.
Review: A Conceptual Collage
Authors: Kieren Thomas E.
Published: August 2020

Representation, particularly “multiple representations” of mathematical notions, is a hot topic in the field of mathematics education today in both research and curriculum development. The image-generating capabilities of microcomputers contribute to the popularity of the topic. Thus, this collection of articles, related to a 1984 symposium at ClRADE (Centre lnterdisciplinaire de Recherche sur I' Apprentissage et le Développement en Education) in Montreal, is timely. The book attempts to develop a comprehensive theoretical framework for representation in mathematics.
Letter to the Editor
Authors: Anderson Oliver D.
Published: August 2020

I have only recendy seen the interesting letter by Philinda Denson in the November 1986 issue. Her suggestions a re sensible, even insptrarional, but regrettably seem doomed to failure.
Editorial
Authors: Kilpatrick Jeremy
Published: August 2020

The theme of the first joint conference of the Australian Educational Research Association and the New Zealand Educational Research Association, held in Christchurch in December, was “ Educational Research: Scientific or Political?” The final two adjectives in the question are often taken as antithetical when they are better seen as describing complementary facets of our research.
Development and Validation of the Underprepared Mathematics Teacher Assessment
Authors: Cangelosi James S.
Published: August 2020

Formative validation methods were used with over 90 mathematics teachers in Utah to design an assessment of the mathematical and mathematics teaching cognitive competencies of underprepared middle and secondary school mathematics teachers. The resulting written-response test produces a score for each of 12 subtests: mathematics teaching methods, number theory, algebra, geometry, analysis, trigonometry, statistics, sets, knowledge of algorithms, comprehension of communications, conceptualization, and application. A summative validation study using 47 subjects indicated that the test is valid and reliable. The test has been adopted by the Utah State Office of Education for use in making recommendations for granting mathematics teaching endorsements and for planning in-service programs.
Editorial
Authors: Kilpatrick Jeremy
Published: August 2020

The scientific ideal is that knowledge claims ought to be tested, both by gathering more data and by exposing one's work to the analyses and criticisms of others. That is not to say that science need be strictly objective (indeed we are constantly reminded that intellectual fads and personal vendettas permeate science just as they do other human affairs) but only that it should strive to be falsifiable and public.
Effect of Assignment Projects on Students' Mathematical Activity
Authors: Zehavi Nurit , Bruckheimer Maxim , Ben-Zvi Ruth
Published: August 2020

The object of the work described in this paper was to explore and enhance student mathematical activity in open problem-solving situations. Assignment projects for high-achieving ninth graders were developed within a framework of cognitive and affective goals. A comparative evaluation study of the effectiveness of the projects in enhancing student mathematical activity in a pretest-posttest design (N = 385) indicated that they were effective. During this study it became clear that teachers needed more practical support. Therefore, a diagnostic study (N = 30) was undertaken, which led to the establishment of a link between a categorization of student difficulties and a hierarchy of guidance. A subsequent study in six classes (N = 167) examined the applicability of the diagnostic guidance.
The Philosophical Basis for the Study
Authors: Webb Dean
Published: August 2020

Professors have traditionally been cast in the role of open, critical, and independent arbiters of the wisdom or morality of human endeavor. Some professors are exchanging this traditional role for one in which they exercise their technical skills without examining the nature and meaning of their work.
A Rejoinder from Iea
Authors: Peaker Gilbert F.
Published: August 2020

It would be out of place to attempt to reply in detail to all the points made in the eleven commentaries. The writers have made many constructive criticisms, for which the members of IEA are indebted to them, and from which they hope to profit in their present enterprise. There are, however, some salient topics, running through several commentaries, on which something might usefully be said.
A Reply to Romberg, Montgomery, and Peaker
Authors: Fletcher Harold J.
Published: August 2020

Romberg and Montgomery make the obvious point that “only items a student has had an opportunity to learn should be scored [p. 236]” in order to derive a more accurate index of efficiency. They admit, however, that without access to the original raw data I could not have computed such a score. Moreover they reason that my efficiency score and their proposed score should be highly correlated because the number of correctly answered items for which the student did not have an opportunity to learn (i.e., correct guesses) should be small and randomly distributed across subjects. Clearly, these were the simplifying assumptions underlying my efficiency score.
Learning Hierarchies—Numerical Considerations
Authors: Eisenberg Theodore A. , Walbesser Henry H.
Published: August 2020

A behavioral objective learning hierarchy viewpoint is a recent facet in curriculum construction theory. But numerical procedures needed to test researchable hypotheses in this area are lacking. The purpose of this article is to present numerical procedures for the validation and comparison of hierarchically organized curricula.
Editorial
Authors: Carpenter Thomas P.
Published: August 2020

This issue marks the beginning of the twentieth year of publication of the Journal for Research in Mathematics Education. As a parent of two teenagers, I fully appreciate the significance of this milestone. Over the first two decades the journal has undergone a number of transformations. Departments have been added, and a variety of cosmetic changes have been instituted. What has remained constant throughout the period bas been the commitment to publish high quality research articles in mathematics education.
Assessing and Improving the Psychosocial Environment of Mathematics Classrooms
Authors: Fraser Barry J. , Malone John A. , Neale Jillian M.
Published: August 2020

Despite international interest in research on classroom environment, very little attention has been given to exploring how mathematics teachers might apply ideas from that research in guiding practical improvements in mathematics classrooms. To facilitate the use of classroom climate assessments, an economical, hand-scorable short form (25 items) of the My Class Inventory was developed. Data supported each scale's internal consistency, discriminant validity, and ability to differentiate between the perceptions of students in different classrooms. Some methods for improving classrooms are illustrated in a case study of a successful change attempt in a sixth-grade mathematics class. When assessments of actual and preferred environment were used in an attempt to improve the climate of the class, a significant improvement occurred only on the dimension on which change had been attempted.
Secondary School Students' Representations of Solids
Authors: Cooper Martin , Sweller John
Published: August 2020

The study examined secondary school students' ability to interpret various representations of simple three-dimensional objects. Verbal descriptions, descriptions based on coordinates, graphical representations, and actual prototypes were employed. The two-dimensional graphical representations were plans, elevations, and perspective drawings. Grade 7, Grade 9, and Grade 11 students were given four identical wooden cubes and asked to construct the objects represented by a particular description, graphical representation, or prototype. For all ages studied, verbal descriptions, perspective drawings, and prototypes were more easily interpreted than plans, elevations, and descriptions based on coordinates. Perspective drawings and prototypes were more easily interpreted than verbal descriptions, but students did not find copying a prototype easier than using a perspective drawing. Grade 9 and Grade 11 students were more successful than Grade 7 students in interpreting plans, elevations, and descriptions based on coordinates; no difference was found between Grade 9 and Grade 11 students.
Review: A Double-Edged Sword
Authors: Cobb Paul
Published: August 2020

The notion of intuition frequently crops up in accounts of mathematical experiences (e.g., Davis & Hersh, 1981), and we have an intuitive idea of what is meant. As Fischbein notes, “intuition is generally seen as a primary phenomenon which may be described but which is not reducible to more elementary components” (p. ix). To rectify this situation, Fischbein presents a theory of mathematical and scientific intuition. In doing so, he synthesizes empirical research on problem solving, images and models, beliefs, and developmental stages of intelligence, drawing on examples from the history of science and mathematics. The book is marked by a masterly display of scholarship and makes a fundamental contribution to the analysis of mathematical cognition.
Analyzing and Modeling Arithmetic Errors
Authors: Blando John A. , Kelly Anthony E. , Schneider Beth R. , Sleeman D.
Published: August 2020

Thirty-nine seventh-grade students completed an arithmetic test designed to uncover errors involving misunderstandings of (a) operations with whole numbers, (b) grouping symbols, and (c) rules of precedence (order of operations). Both the students' final answers and the intermediate steps for each test item were analyzed, and models to represent students' behaviors were developed. Certain types of errors were common across students. Errors were found to be closely tied to the format of the test item. Variations in the formats of test items that left the underlying computations unchanged exposed some students' superficial understandings of mathematical concepts.
Letters to the Editor
Authors: Isaacs Ian , Sweller John , Owen Elizabeth
Published: August 2020

Elizabeth Owen and John Sweller (JRME 20 (3), 322–328) made the observation that novice problem solvers are so preoccupied with using means-end strategies when solving “transfonnation” types of problems that they cannot spare any thought for an overview of the total problem. This leads them to suggest that it might be counterproductive to teach this problem-solving strategy. This tunnel-vision behaviour is quite common for most beginners learning a complex task, whether it is a psychomotor skill (like learning to drive a car), an algorithmic task (such as learning the traditional long division algorithm), or a novel problem-solving task (for example, verifying a trigonometric identity). In all three learning situations the novice needs to practise the required skills in various contexts to be able to transfer them eventually to other contexts. For transfer to take place effectively, the novice has to apply these skjlls in the new context under the guidru1ce of a skilled tutor, who makes the Ieamer aware of the similarities and differences between the new context and that in which the ski ll was initially acquired and the resulting modifications required to carry out the present task effectively.
Children's Symbolic Representation of Addition and Subtraction Word Problems
Authors: Bebout Harriett C.
Published: August 2020

Forty-five first graders were categorized into three levels according to their informal strategies for solving addition and subtraction word problems. They were taught to write canonical and noncanonical open number sentences to symbolically represent the structure of eight types of Change and Combine word problems. Their performances on the posttest indicated that children at each level were successful in learning to symbolically represent and solve the instructed problem types.
Brief Reports: Affect and Mathematics Achievement of Nontraditional College Students
Authors: Elliott John C.
Published: August 2020

In the past 20 years, there has been a significant increase in the number of older returning students in the undergraduate population. From 1974 to 1980, the total representation of students at least 25 years old increased from one-fourth to onethird of the undergraduate enrollment (Kasworm, 1980). In this article, these students are referred to as nontraditional students.
Brief Reports: Measuring a van Hiele Geometry Sequence: A Reanalysis
Authors: Wilson Mark
Published: August 2020

This report summarizes a reanalysis of the data from an investigation (Usiskin, 1982) of a test designed to measure a learning sequence in geometry based on the work of van Hiele (1986). It extends the analyses that were originally conducted through the use of a probabilistic model. This model describes how performance on an item is related to the underlying ability that is the subject of the learning sequence.
Critique: On the Limited Evidence for the Effectiveness of Teaching General Problem-Solving Strategies
Authors: Sweller John
Published: August 2020

Lawson (1990) summarizes well views that have had considerable currency in the recent past. As he indicates, the opinions he espouses have been held sufficiently widely to have resulted in revisions in some mathematics curricula. Owen and Sweller's (1989) purpose was to suggest that there may be alternative conceptualizations that have both greater theoretical coherence and, more importantly in the present context, vastly more empirical support.
Using Data Tables to Represent and Solve Multiplicative Story Problems
Authors: Sellke Donald H. , Behr Merlyn J. , Voelker Alan M.
Published: August 2020

This study tested the effectiveness of an experimental instructional strategy for writing arithmetic sentences for simple multiplication and division story problems involving nonintegral factors. The experimental strategy consisted of building an intermediate problem representation to display the problem quantities in the form of a data table and using multiplicative reasoning. This strategy was compared with a traditional strategy of solving an analogous problem with simpler numbers. Five intact seventh-grade classes participated in the study. Significant effects in favor of the experimental group were found on an intermediate test and a posttest.