bluuebunny/crossref_metadata_2025 huggingface dataset:
Alan: A Case Study of Knowledge of Units and Performance with Fractions
Authors: Hunting Robert P.
Published: August 2020

Nine-year-old Alan's conception of fractions, including equivalence of fractions, is considered in the light of his knowledge of types of units. He possessed effective schemes for solving partition problems with definite numbers of discrete objects as units and partition problems containing indefinite numbers of objects. Alan did not consistently use a scheme involving units of different sizes in interpreting fractions. His solutions to equivalence problems, produced using inappropriate figure-based algorithms, were unsupported by any coherent method of verification. The mental processes known to be available to Alan for dealing with unit systems are contrasted with the extent to which the processes were reflected in his solutions to fraction problems.
Critiques: Seeking Meaning in Mathematics Instruction: A Response to Gagné
Authors: Steffe Leslie P. , Blake Rick N.
Published: August 2020

Mathematics educators have for some time been interested in psychological bases for the teaching of mathematics in the schools (Buswell, 1951). They have naturally turned to cognitive theorists in their quest to understand such terms as knowledge, meaning, concepts, mental operations, problem solving, and insight. Gagné's (1983) paper is bur one example of this historical collaboration. His purpose is to “relate what is known about learning, … from the kind of theory [he has] described, to the problem of improving mathematics learning” (p. 10).
Research on Mathematics Education Reported in 1982
Authors: Suydam Marilyn N.
Published: August 2020

ln this 13th 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). Some studies in which mathematics education was not the primary focus are included. Such studies are usually not annotated, as are studies focused on mathematics education. 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.
Sex Differences in Mathematical Errors: An Analysis of Distracter Choices
Authors: Marshall Sandra P.
Published: August 2020

Distracter analysis was introduced as a means of investigating sex differences in mathematical performance. The data were responses to an assessment test given each year from 1976 to 1979 to all sixth-grade children enrolled in California public schools. Loglinear models were used to evaluate the consistency of response by each sex over 4 years. A significant interaction between sex and choice of distracter occurred for a large majority of the items. Hypotheses of sex differences based on Radatz's (1979) information-processing classification of errors were evaluated.
An Evaluation of a Process-Oriented Instructional Program in Mathematical Problem Solving in Grades 5 and 7
Authors: Charles Randall I. , Lester Frank K.
Published: August 2020

This paper provides an overview of a process-oriented instructional program and reports the results of an evaluation of that program. Twelve fifth-grade and 10 seventh-grade teachers implemented the Mathematical Problem Solving program for 23 weeks. Eleven fifth-grade and 13 seventh-grade teachers taught control classes. The experimental classes scored significantly higher than the control classes on measures of ability to understand problems, plan solution st rategies, and get correct results. Trend analyses showed different student growth patterns for the three measures of problem-solving performance. Data from interviews with teachers supported the results of the quantitative analysis and suggested that both students and teachers had changed positively with respect to attitudes toward problem solving. In addition, teachers gained confidence in their ability to teach problem solving.
Mathematics Anxiety, Instructional Method, and Achievement in a Survey Course in College Mathematics
Authors: Clute Pamela S.
Published: August 2020

Two in structional strategies were used in different sections of a survey course in college mathematics at each of two colleges. One strategy consisted of a series of lectures structured to assist students in mastering an organized body of knowledge; the other was based on questioning sequences that guided students in discovering mathematical principles. Achievement was measured by an examination covering course content. Students wtth a high level of mathematics anxiety had significantly lower achievement (p < .01) than students with a low level of anxiety. A significant interaction between method of instruction and level of anxiety (p < .01) suggested that students with high anxiety benefited more from the expository approach, whereas students with low anxiety benefited more from the discovery approach.
Reviews: Words to Solve by
Authors: Harvey John G.
Published: August 2020

Unlike most books reviewed in the journal for Research in Mathematics Education, Problem Solving in the Mathematics Curriculum (PSMC) does not report research. Instead, it seems designed to (a) recommend that problem solving be consistently included in collegiate mathematics instruction, (b) describe some considerations in and ways of teaching problem solving, (c) present an extensive bibliography chosen to help those initiating or teaching problem-solving courses or problem-solving sequences within courses, and (d) give the results of a survey conducted by the Committee on the Teaching of Mathematics of the Mathematical Association of America; the survey provided the impetus for PSMC. Accordingly, the book is divided into four parts. The short first part describes the evolution of PSMC and the recommendations of the Committee on the Teaching of Mathematics. The second part, a more-or-less personal essay by Alan Schoenfeld, gives suggestions for teaching problem solving. The third and most extensive part is an annotated bibliography of journals, books, and articles that might be used to develop in struction in problem solving or to find appropriate problems for such instruction. The last part presents both the survey instrument and the results of the survey.
Influences on the Learning and Participation of Minorities in Mathematics
Authors: Matthews Westina
Published: August 2020

Minorities and mathematics have not been the central focus of much published research, but a sizable relevant literature does exist. A review of 24 studies since 1975 is organized according to three types of variables—parent, student, and school—that influence the learning and participation of minority students in school mathematics. Few of the parental variables likely to influence performance or participation have been studied directly. A variety of studenr characteristics have been identified and their influence examined. Several school characteristics that appear tO be influential have not been quantified. The review suggests some directions for future research.
Issues in Mathematics Education for Native Americans and Directions for Research
Authors: Bradley Claudette
Published: August 2020

Native Americans need an improved education in mathematics if they are ro have equal economic opportunity. The enrollment, preparation, and achievement of Indian scudents in mathematics courses fall below the norms for their non-Indian counterparts. Identified as contributing factors are cultural differences, insufficient preparation of teachers, and unsatisfactory instructional materials. Various solutions are suggested to the problem of improving the mathematics education of Native Americans. Whatever the instructional activities used, more appropriate curricula and better evaluation procedures should be developed. A teacher center is proposed, and some directions for research are indicated.
Monitoring the Mathematics Achievement of Black Students
Authors: Jones Lyle V. , Burton Nancy W. , Davenport Ernest C.
Published: August 2020

Findings from the National Assessment of Educational Progress for 1973 and 1978 are reviewed. They show improvement in levels of mathematics achievement for black students at ages 9 and 13, compared with a decline for white students at those ages. rn a special National Assessment of mathematics in 1975–76 for ages l3 and 17, substantial differences are found between average mathematics achievement scores of white and black youth. Based on a multiple regression analysis at age 17, more than half of the total variance in mathematics achievement scores is accounted for by regression, with school-to-school differences in background variables and individual background differences within school about equally influential. About half of the white-black mean difference is accounted for by regression and, in this accounting, school differences in background variables play a more prominent role than individual differences within school. A particularly influential predictor of mathematics achievement is the number of high school algebra and geometry courses taken. Marked differences are found between predominantly black and predominantly white high schools in the average numbers of such courses taken. The adoption of policies that reduce those differences would be expected to result in relatively higher levels of mathematics achievement for black students.
Reviews: Complementary Perspectives
Authors: Hiebert James
Published: August 2020

As suggested by the titles, the chapters in all three books deal with children's mathematical thinking and learning. The authors are leading psychologists and mathematics educators in this broad field of research, and the volumes present some of the most comprehensive, systematic, and careful research recently conducted on problems of current interest in the field. There is no question that these books will serve as major reference works for those interested in research on the learning of mathematics. With some exceptions, the volume edited by Lesh and Landau presents work of mathematics educators, and the volumes edited by Brainerd and by Ginsburg contain work of cognitive psychologists. The three volumes were selected for a single review because they represent significant approaches to studying a common problem—children's mathematical thinking and learning.
Reviews: By the Numbers
Authors: McLeod Douglas B.
Published: August 2020

This book reports a decade of research by the Missouri Mathematics Project. The project, funded by the National Institute of Education, has conducted probably the best example of process-product research on mathematics teaching that has been done so far. The project has many strengths. For example, the authors represent an interdisciplinary team from educational psychology, mathematics education, and school administration. The studies are designed with care and are responsive to the concerns of the various disciplines that are interested in research on teaching mathematics. The work of the project is reported thoroughly, and the conclusions are based on a reasonable interpretation of the data.
Sex Differences in a Causal Model of Mathematics Achievement
Authors: Ethington Corinna A. , Wolfle Lee M.
Published: August 2020

Using data from the “High School and Beyond” study, this paper reexamines the reason men and women differ in mathematics achievement by means of a covariance-structures causal model of mathematics achievement, which permits the estimation of effects while accounting for known measurement error in the predictor variables. Our results indicate that sex continues to have a significant effect on mathematics achievement even after controlling for sex differences in spatial abilities, background in mathematics, and interest in mathematics. Separate analyses by sex, however, indicate that the process of mathematics achievement differs between men and women. In particular, women tend to have less spatial visualization ability than men, but the effects of this variable on mathematics achievement are greater for women.
Review: Un Esprit Simpliste
Authors: Stanic George M.A.
Published: August 2020

Research and discussions about American education during the twentieth century have been characterized by an esprit simpliste—by an urge to make simple what is fundamentally complex in nature. The five reports that are the subject of this essay review fir nicely and unfortunately into that tradition.
Review: To Hell with Psychology
Authors: Glasersfel Ernst Von
Published: August 2020

Advertised as “a direct attack on one of the accepted bases of current study and research in education,” this text fulfills the promise. It attacks and attacks. Indeed, the author's dogged persistence leads him stumbling far into areas of philosophy in which, as he himself admits, he should not be considered an expert.
Editorial
Authors: Kilpatrick jeremy
Published: August 2020

The Fifth International Congress on Mathematical Education, held in Adelaide, Australia, last August, attracted 1984 mathematics educators of every ilk from 68 countries. Among the participants were people whose primary professional interest is research in mathematics education, as well as people who are currently teaching mathematics in schools. The confluence of the congress with the biennial meeting of the Australian Association of Mathematics Teachers guaranteed that a large share of the participants would be practicing teachers.
The Role of Implicit Models in Solving Verbal Problems in Multiplication and Division
Authors: Fischbein Efraim , Deri Maria , Nello Maria Sainat , Marino Maria Sciolis
Published: August 2020

Arithmetical operations were assumed to remain attached to primitive behavioral models that influence tacitly the choice of an operation even after the learner has had solid formal-algorithmic training. The model for multiplication was conjectured to be repeated addition, and two primitive models (partitive and quotative) were seen as linked to division. A total of 623 pupils enrolled in 13 Italian schools (Grades 5, 7, and 9) were asked to choose the operation needed to solve 26 multiplication and division word problems. Violations by the numerical data of the constraints imposed by the assumed tacit models (for instance, when the operator was a decimal number) constituted particular sources of difficulty at all three grade levels. The findings seemed to confirm the impact of the repeated addition model on multiplication and of the partitive model on division. The quotative division model influenced the pupils' choices only at the ninth-grade level.
Brief Reports: Using Microcomputers with Fourth-Grade Students to Reinforce Arithmetic Skills
Authors: Carrier Carol , Post Thomas R. , Heck William
Published: August 2020

Microcomputers in elementary school classrooms will soon be as common as handheld calculators and reading stations. Luehrmann (1981) states that within 3 years the average school will have 16 microcomputers. The acceptance and availability of reasonably priced computer technology for the classroom and the home suggests that elementary teachers will be encouraged to incorporate computer-based activities into many areas of the curriculum. Although some of the most intriguing applications of computers in instruction at the elementary level can be seen in tutorials, si mulations, or interactive systems such as Logo, many teachers will continue to use the computer primarily to give children skill-building experiences in ma thematics and other school subjects.
Review: Toward a Theory of Construction
Authors: Carpenter Thomas P.
Published: August 2020

Children's Counting Types takes a different approach to the study of counting than most other analyses (d. Fuson & Hall, 1983; Gelman & Gallistel, 1978). It is not concerned with the learning of number word sequences or how children acquire the ability to count sets of objects. In fact, it picks up where most other research on counting leaves off. Steffe and his colleagues define counting as the correspondence of number words with the things to be counted, which they call “unit items” or “units.” Their primary concern is the development of the ability co count increasingly abstract unit items.
Letter to the Editor
Authors: Becker Betsy Jane
Published: August 2020

In your editorial in the July 1984 issue ofrhe JRME you discussed rwo symposia that took place at rhe American Educational Research Association meetings. One concerned the quality of educational research, the other meta-analysis.
Mastery of Basic Number Combinations: Internalization of Relationships or Facts?
Authors: Baroody Arthur J.
Published: August 2020

The thesis is advanced that children do not learn and store basic number combinations as so many separate entities or bonds (as hundreds of specific numerical associations) but as a system of rules, procedures, and principles as well as arbitrary associations. In this view, “mastering the basic facts” largely involves discovering, labeling, and internalizing relationships--processes encouraged by teaching thinking strategies. Moreover, internalized rules, procedures, and principles may become routinized and may help to account for the efficient production of number combinations in adults. Given an infinitely large arithmetic system, the use of such automatic reconstructive processes would make sense--would be cognitively economical. Accessibility, which has been advanced to account for anomalous retrieval time results, could be affected by input from semantic and procedural knowledge.
The Use of Spatial Visualization in Mathematics by Girls and Boys
Authors: Fennema Elizabeth , Tartre Lindsay A.
Published: August 2020

This longitudinal study investigated how girls and boys who were discrepant in their spatial and verbal performance used spatial visualization skills in solving word problems and fraction problems. The subjects, 36 girls and 33 boys, were interviewed annually in Grades 6, 7, and 8. Each student was asked to read a problem, draw a picture to help solve it, solve it, and then explain how the picture was used in the solution. Students who differed in spatial visualization skill did not differ in their ability to find correct problem solutions, but students with a higher level of spatial visualization skill tended to use spatial skills in problem solving more often than students with a lower level of skill. Girls tended to use pictures more during problem solving than boys did, but this did not enable them to get as many correct solutions. Low spatial visualization skill may be more debilitating to girls' mathematical problem solving than to boys'.
Critique: Pitfalls in Equating Informal Arithmetic Procedures with Specific Mathematical Conceptions
Authors: Baroody Arthur J.
Published: August 2020

This article is an elaboration on the theoretical point made by Paul Cobb (1985) in “A Reaction to Three Early Number Papers” that appeared in the March issue of this journal. Cobb notes a discrepancy between a model of subtraction that posits a developmental progression from counting down to a choice between counting down and counting up (Baroody, 1984b) and longitudinal data (Carpenter & Moser, 1984) that indicate that counting up develops at least as early as counting down. He presents longitudinal data from four case studies that corroborate the model (and, I should add, the earlier cross-sectional data and position of Woods, Resnick, & Groen, 1975). To reconcile these results with those of Carpenter and Moser, Cobb argues that a child's use of an informal arithmetic procedure may not be an accurate reflection of his or her conceptual sophistication.
Editorial
Authors: Kilpatrick Jeremy
Published: August 2020

Word has come of the death of George Polya in September at the age of 97-a long time on the planet perhaps but not nearly long enough for those who knew him. In recent years, as his eyesight and memory began to fail, he drew on seemingly inexhaustible reserves of joie de vivre and spirit. One got the feeling that if his body had been able, he might simply have gone on forever.
Review: Many Voices, Many Views
Authors: Kulm Gerald
Published: August 2020

This book is the latest published account of what is becoming a concerted effort on the part of a group of mathematics educators and cognitive scientists to share research results, methodologies, and directions. As has been the case in previous similar books (e.g., Carpenter, Moser, & Romberg, 1982; Lester & Garofalo, 1982), this volume contains a set of papers delivered at a conference arranged by the editor. The present effort was more ambitious than some previous work in two significant ways. First, the breadth of cognitive science was extended to include artificial intelligence and metacognition; second, the mathematical problem-solving research was opened to embrace concerns related to teaching and affective factors. In this sense, the volume certainly lives up to its subtitle.
Editorial
Authors: Kilpatrick Jeremy
Published: August 2020

At the joint AMS-MAA Mathematics Meetings in Laramie last summer, Saunders Mac Lane gave a splendid address on developments in geometry and topology during the 20th century. He stressed the value of an axiomatic approach in improving our understanding of mathematical phenomena, arguing that we understand such phenomena better when we approach them geometrically and set up the right axioms. He also invited his audience to consider whether the developments he cited constituted a revolution or were no more than a natural outgrowth of developments in the 19th century and earlier.
Characterizing the Van Hiele Levels of Development in Geometry
Authors: Burger William F. , Shaughnessy J. Michael
Published: August 2020

This study provides a description of the van Hiele levels of reasoning in geometry according to responses to clinical interview tasks concerning triangles and quadrilaterals. The subjects were 13 students from Grades 1 through 12 plus a university mathematics major. The tasks included drawing shapes, identifying and defining shapes, sorting shapes, determining a mystery shape, establishing properties of parallelograms, and comparing components of a mathematical system. The students' behavior on the tasks was consistent with the van Hieles' original general description of the levels, although the discreteness of levels, particularly of analysis and abstraction, was not confirmed. The use of formal deduction among students who were taking or had taken secondary school geometry was nearly absent, consistent with earlier observations by Usiskin (1982).
Editorial
Authors: Reyes Laurie Hart
Published: August 2020

It is the time of year when mathematics educators gather at the annual conventions of the National Council of Teachers of Mathematics and the American Educational Research Association. These meetings are important to the profession for a number of reasons. Valuable communication about ongoing and completed work takes place among researchers. At both meetings there are formal presentations of research results. Equally important, the meetings provide an opportunity to create informal networks of researchers studying the same topic.
Learning Numbers: A Linguistic Perspective
Authors: Nesher Pearla , Katriel Tamar
Published: August 2020

The difference in the status of numbers—as predicates in natural language and as objects in the formal language of mathematics—is argued to have consequences for children's learning of numbers and for the construction of arithmetic texts in the primary grades. This distinction is exemplified by the findings of an empirical study that utilized particular morphological properties of Hebrew relating to gender inflections for number words. The findings indicate that there is a crossing of the two language systems in children's oral reading of a mixed arithmetic text (words and numerals).
An Analysis of the Relationships among Computation-Related Skills Using a Hierarchical-Clustering Technique
Authors: Close John S. , Murtagh Fionn
Published: August 2020

A hierarchical-clustering technique was applied to data on the mastery of mathematical skills for the purpose of examining relationships among the skills. The data were obtained from two administrations of criterion-referenced tests to 715 pupils in Grades 1 to 4 in two Irish elememary schools toward the end of their school year. A clear hierarchical ordering of skills was obtained at each grade. An examination of groups of computation-related skills showing a high degree of consistency in their orderings across the two administrations suggested that factors considered in the formulation of the skills could account for some of the orderings obtained. The results highlight the value of cluster analysis as a tool for the preliminary analysis of relationships among mathematical skills.
Brief Reports: A Comparison of Advanced Placement and College Students on a Calculus Achievement Test
Authors: Dickey Edwin M.
Published: August 2020

The articulation of secondary school and college mathematics is a critical problem facing educators today (National Council of Teachers of Mathematics, 1980; Staff, 1984). The placement in college mathematics courses of students who have taken calculus in secondary school is an especially critical and difficult task. Calculus can be taught at various levels, and its subject matter components can receive varying degrees of emphasis. The Advanced Placement (AP) program attempts to provide a uniform and high-quality calculus course for secondary school students by publishing a detailed course syllabus, encouraging special training for AP instructors, and administering an examination that validates a student's AP Calculus experience (College Entrance Examination Board, 1984). Nonetheless, some evidence suggests that AP Calculus students have difficulty earning advanced placement and credit for the calculus they learned in secondary school (Lefkowitz, 1971; Neatrour & Mullenex, 1973; Pocock, 1974; Rash, 1977; Sklar, 1980; Sorge & Wheatley, 1977). One reason for this difficulty may be that AP Calculus students are not achieving at the same level as college students.
Reviews: But is it Different in the South?
Authors: Ponte João
Published: August 2020

This book contains a selection of papers on the analysis of educational issues and the assessment of instructional innovations in Latin America. The papers report studies undertaken for thesis requirements in a master's degree program in science and mathematics education at the University of Campinas between 1975 and 1984. An explanation of the context and goals of the program is provided by D'Ambrósio, who supervised several of the candidates. In this review I focus on the papers that deal with the learning and teaching of mathematics and with the training of mathematics teachers.
Teaching Children to Subtract by Counting up
Authors: Fuson Karen C.
Published: August 2020

Symbolic subtraction problems such as 14 − 8 =? were interpreted to children as story problems with dot pictures that supported count-up solutions. Children in first-grade mathematics classes were taught with considerable success to solve such symbolic subtraction problems by counting up from the smaller number to the larger (“8, 9, 10, 11, 12, 13, 14; 6 more make 14”) while keeping track of the number counted up by using one-handed finger panerns. The children improved quire considerably on a rimed test of the more difficult subtraction combinations, and this improvement held up over a month. Interviews indicated that almost all children could count up to solve subtraction combinations they did not know. Many used counting up to solve subtraction story problems with different semantic structures: performance on compare, separate (take-away), and equalize (how many more to make the same?) story problems was similar and good.
The Growing Crisis in Mathematics Education in the Early Twentieth Century
Authors: Stanic George M. A.
Published: August 2020

The place of mathematics in the American school curriculum was challenged during the early years of the twentieth century. Specifically questioned was the requirement that all high school students take mathematics. By the 1930s, mathematics educators were speaking of the situation as a crisis. The crisis had grown in the context of major social changes arising from intense urbanization, industrialization, and immigration around the turn of the century; America's involvement in World War I; and the Grear Depression. Along with significant growth in the school population had come a perceived decrease in the quality of that population. It was within this historical context that mathematics educators responded to suggested changes in the curriculum. Some of their responses may have exacerbated the crisis about which they were so concerned.
Brief-Report: Sex Differences in the Mathematics Achievement of Eighth Graders in Ontario
Authors: Hanna Gila
Published: August 2020

In the past two decades researchers have shown considerable interest in the relationship between the sex and the mathematics achievement of children in the upper grades of elementary school. Some researchers have examined sex differences by comparing total test scores (Backman, 1972; Benbow & Stanley, 1980, 1983; Maccoby & Jacklin, 1974), whereas others have focused on the proportion of students who answered a particular item correctly (Armstrong, 1980; Fennema, 1978; Raphael, Wahlstrom, & Mclean, 1984). In a recent study by Marshall (1983) the analysis is based on a comparison of the kinds of errors made by male and female students.
Editorial
Authors: Kilpatrick Jeremy
Published: August 2020

As anyone who has ever done copy editing will tell you, it is possible to edit anywhere on a continuum from light to heavy. Light editing simply provides the minimum needed for the printer to use in setting type—correcting typos, marking out hyphens at the end of lines, and the like. Heavy editing involves all of that plus reconstructing faulty sentences—and sometimes whole paragraphs—so that the thoughts trapped therein are freed from the murk of jargon, cliché, and stilted language. Heavy editing ventures away from the rule-bound precincts of punctuation and spelling into the wilds of grammar, syntax, and idiom.
Editorial
Authors: Kilpatrick Jeremy
Published: August 2020

Testing is on people's minds these days. In Georgia, students face standardized tests or other state-mandated tests every year but one (fifth grade) between kindergarten and 12th grade. Reports have surfaced of large numbers of Georgia kindergarteners who cried because they could nor do the California Achievement Test, which, as of 1988, they must “pass” to be promoted to first grade. Other reports claim that many high school students have become complacent about taking standardized tests because they cannot see what relevance the tests have. Meanwhile, chambers of commerce offer monetary rewards to those teachers whose students' year-end test scores reach arbitrary targets, and real estate agents add thousands of dollar to rhe prices of houses in suburban school districts where Scholastic Aptitude Test score averages exceed those of neighboring districts. School personnel respond to these developments in various ways—instituting test-preparation units or courses, setting aside class periods for intensive review, discouraging ill-prepared students from taking the tests, and “realigning” curricula to fit test content.
Teaching and Learning Mathematics: Where Research Should Be Going
Authors: Brophy Jere
Published: August 2020

Several lines of research on reaching that have not been conducted with a specific interest in mathematics instruction have relevance to mathematics education. Topics discussed include process-outcome research linking teacher behavior ro student achievement, structuring the content for clarity and ease of comprehension, teaching cognitive skills and problem-solving strategies, recitation and board work activities, seatwork and homework assignments, conceptual change teaching, classroom organization and grouping, cooperative learning methods, sex equity issues, and motivating students to learn mathematics. Each topic is reviewed with an emphasis on its relevance to mathematics educators and on methodological refinements or extensions inro new topic areas that are needed ro move these lines of research forward.
Editorial
Authors: Kilpatrick Jeremy
Published: August 2020

Many—probably most—researchers in mathematics education have spent considerable time as teacher educators, working with people who soon will be or currently are reaching mathematics. Perhaps surprisingly, then, these researchers have not viewed teacher education as a potential research site. Immersed in the activities of teacher education, they have not stepped outside the arena of their daily work to view it with the researcher's eye. They resemble the fish in the saying, who, if they were scientists, would be a long time discovering water.
Sex-Related Differences in Expectations of Success in Undergraduate Mathematics
Authors: Mura Roberta
Published: August 2020

Students (n=1270) from five Canadian universities were asked to predict their final grades in undergraduate mathematics courses. The percentages of women who overestimated, estimated correctly, and underestimated their grades were 51, 26, and 23; the corresponding percentages for the men were 61, 26, and 13. No sex-related difference was found in the level of confidence expressed by students in their ability to complete their bachelor's program, whereas women expressed less confidence than men in their ability to obtain a PhD. Proportionally fewer women than men expressed an intention to engage in doctoral studies. Although that intention was related to a student's confidence level, a discrepancy between women and men was found even within groups at the same confidence level.
Sex and Ethnic Group Differences in Mathematics Achievement: Results from the National Longitudinal Study
Authors: Moore Elsie G. J. , Smith A. Wade
Published: August 2020

The mathematics test achievement of 11 914 young men and women, aged 15 to 22, who participated in the National Longitudinal Study of Youth Labor Force Behavior in 1980 was analyzed to assess sex, education, and ethnic group effects. The mathematics knowledge and arithmetic reasoning subtests of the Armed Services Vocational Aptitude Battery were the measures of achievement. A multivariate analysis of variance revealed significant main effects for sex, education, and ethnic group membership. Generally, the mathematics achievement of all groups increased the longer they were in school. White males showed the greatest benefit of continued education, and blacks as a group showed the smallest. However, significant two-way interaction effects confounded these general trends.
Reviews: A Window and a Frame
Authors: Edward A. Silver
Published: August 2020

During the past decade, problem solving has emerged as one of the foremost topics of interest in the mathematics education community.
Written and Oral Mathematics
Authors: Carraher Terezinha Nunes , Carraher David William , Schliemann Analúcia Dias
Published: August 2020

Previous studies have demonstrated that children use oral calculation procedures not taught in school. The present study provided evidence for situational variables that strongly influence the tendency to use such procedures. It also provided a qualitative analysis of the oral mathematics used by Brazilian third graders. Concrete problem situations were powerful elicitors of oral computation procedures, whereas computation exercises tended to elicit school-learned computation algorithms. Oral computation procedures involved the use of two reliably identifiable routines, decomposition and repeated grouping, that revealed the children's solid understanding of the decimal system. In general, the children were far more successful in using oral mathematics than written mathematics. An understanding of children's oral procedures may be useful in developing more successful programs for elementary mathematics instruction.
Spatial Training for Calculus Students: Sex Differences in Achievement and in Visualization Ability
Authors: Ferrini-Mundy Joan
Published: August 2020

This study investigated the effects of spatial training upon calculus achievement, spatial visualization ability, and the use of visualization in solving problems on solids of revolution. After pretesting, 250 college students participated in one of two spatial-training treatments or in a control treatment. Multivariate analyses of covariance revealed no treatment effect on calculus achievement or spatial visualization ability, but there were significant sex differences favoring women in calculus achievement and favoring men in spatial visualization ability. There were interaction effects for calculus achievement and the use of visualization in solving solid-of-revolution problems and a significant treatment effect for visualization of solids of revolution. Spatial training may benefit performance in certain areas of calculus for women more than for men.
The Development of Counting Strategies for Single-Digit Addition
Authors: Baroody Arthur J.
Published: August 2020

Over 9 months, structured clinical interviews with 17 kindergartners were used to study (a) the learning of a concrete counting strategy for addition, (b) the transition from concrete to mental counting strategies, and (c) the role of the commutativity principle in developing more economical counting strategies. Kindergartners appear to differ in their readiness to use a concrete strategy. Many children persisted in counting all with objects. The most common sequence of mental counting strategies was counting all starting with the first addend, counting all starting with the larger addend, and then counting on from the larger addend. A knowledge of commutativity does not appear to be necessary to invent counting strategies that disregard addend order.
Review: Missing Links
Authors: Sowder Larry
Published: August 2020

The purpose of this book is to move toward describing the relationship between conceptual knowledge and procedural knowledge.
Research on Mathematics Education Reported in 1986
Authors: Suydam Marilyn N.
Published: August 2020

This 17th annual listing of mathematics education research to appear in the JRME presents, as usual, references listed alphabetically by author within three categories: research summaries, articles, and dissertations. Grade or age is indi cated for each reference, and an index is included to help readers locate studies of par ticular interest. This index does not include all studies, nor is it detailed. Rather, it lists studies within broad topics. To provide a more detailed index would consume too much space.
Children's Learning of Geometrical Concepts through Logo
Authors: Noss Richard
Published: August 2020

This exploratory study aimed to investigate some elements of geometrical concepts that children learn through Logo programming. A test designed to probe children's conceptions of three components of length and angle was administered to 84 children who had learned Logo for one year and 92 who had not. The components of the concept of length were (a) length conservation, (b) length combination, and (c) length measurement. The components of angle were (a) right angle conservation, (b) angle conservation, and (c) angle measurement. Analysis of data using a linear modeling technique indicated a consistent trend toward a sex-treatment interaction.
The Effect of Semantic Structure on First Graders' Strategies for Solving Addition and Subtraction Word Problems
Authors: Corte Erik De , Verschaffel Lieven
Published: August 2020

In a longitudinal investigation, data were collected on the problem representations and solution strategies of 30 first graders who were given a series of simple addition and subtraction word problems (Verschaffel, 1984). The children were interviewed three times during the school year, and data obtained on their solution strategies and on the influence of problem structure on the strategies. The results complement those of recent related research, especially the work of Carpenter and Moser (1982, 1984). More precisely, the influence of problem structure on children's solution strategies appears even more extensive and decisive than that described by previous researchers.
Comprehension of Mathematical Relationships Expressed in Graphs
Authors: Curcio Frances R.
Published: August 2020

In this study, the schema-theoretic perspective of understanding general discourse was extended to include graph comprehension. Fourth graders (n=204) and seventh graders (n=185) were given a prior-knowledge inventory, a graph test, and the SRA Reading and Mathematics Achievement Tests during four testing sessions. The unique predictors of graph comprehension for Grade 4 included reading achievement, mathematics achievement, and prior knowledge of the topic, mathematical content, and form of the graph. The unique predictors for Grade 7 were the same except that prior knowledge of topic and graphical form were not included. The results suggest that children should be involved in graphing activities to build and expand relevant schemata needed for comprehension.
Strategies Used by Secondary Mathematics Teachers to Solve Proportion Problems
Authors: Fisher Linda C.
Published: August 2020

Twenty secondary mathematics teachers described their thinking as they solved four proportion problems (Task 1), explained how they would teach two of the problems (Task 2), and solved four similar problems after being asked to use proportion strategies (Task 3). Their solution strategies were classified using a nine-category scheme. Overall, the teachers were more successful with direct proportion than with inverse proportion. On Task 1 proportion strategies were used on only half the problems. On Task 3 three fourths of the responses depended upon proportion strategies. On Task 2 most teachers said they would use the same strategies in teaching the problems that they used in solving them.
Brief Reports: Fraction Knowledge in Preschool Children
Authors: Hunting Robert P. , Sharpley Christopher F.
Published: August 2020

Much school mathematics is devoted to teaching concepts and procedures based on those units that form the core of whole number arithmetic (ones, tens, hundreds, etc.). But other topics such as fractions and decimals demand a new and extended understanding of units and their relationships. Behr, Wachsmuth, Post, and Lesh (1984) and Streefland (1984) have noted how children's whole number ideas interfere with their efforts to learn fractions. Hunting (1986) suggested that a reason children seem to have difficulty learning stable and appropriate meanings for fractions is that instruction on fractions, if delayed too long, allows whole number knowledge to become the predominant scheme to which fraction language and symbolism is then related.
Brief Report: Grade Placement of Addition and Subtraction Topics in Japan, Mainland China, the Soviet Union, Taiwan, and the United States
Authors: Fuson Karen C. , Stigler James W. , Bartsch Karen
Published: August 2020

There has been considerable recent concern about the mathematics achievement of children in the United States compared to that of children in the Soviet Union and in countries of the Far East (Benderson, 1984; Fiske, 1987; Husen, 1967; Stevenson, Lee, & Stigler, 1986; Stigler, Lee, Lucker, & Stevenson, 1982; Wirszup, 1986). One possible source of the superior achievement in these other countries is the placement of topics within the mathematics curriculum. If topics are presented earlier in these countries, children would be given an opportunity to cover more topics and thus might be able to learn more mathematics by comparable grade levels. The present study examined the grade placement of topics in basic addition and subtraction computation with whole numbers across five countries: Japan, mainland China, the Soviet Union, Taiwan, and the United States.
The First Nine Years—A Study of The Advanced Placement Program in Mathematics
Authors: Lefkowitz Ruth S.
Published: August 2020

A follow-up study was made of the students in the mathematics Advanced Placement classes at a large New York City high school from 1956-57 to 1964-65, inclusive. Of the 182 students who responded to the questionnaire 52% were offered placement and 32% were offered credit. Beginning with 1964, all students with a score of at least 3 on the Advanced Placement Examination received an offer of placement and/or credit. The students attended 45 different colleges. Almost 90% of the students indicated that the program was a good experience for them. Their chief criticism of the Advanced Placement course, however, was its lack of emphasis on theory.
The Relationship Between The Ability to Conserve Length and Conceptual Tempo
Authors: Callahan Leroy G. , Passi Sneh Lata
Published: August 2020

This study explored the relationship between conservation of length and impulsive-reflectivity. 72 kindergarten and first-grade children were administered 2 conservation-of-length tasks and an impulsive-reflective scale. A chi-square analysis of the data indicated no statistically significant relationship between the two characteristics. However, the trend was in the direction of more reflective children conserving on the Piagetian tasks. Post hoc point-biserial correlations were carried out. Relations investigated were: errors on impulsive-reflective scale with ability to conserve length, and latency on impulsive-reflective scale with ability to conserve length. Results tended to confirm the chi-square analysis of the study.
Editorial Comment
Authors: Wilson James W.
Published: August 2020

One of the early decisions of the JRME Editorial Board (December 1968) was to occasionally devote a special issue of the journal to a review and analysis of a major research project. The first project chosen for discussion in a special issue was the International Study of Achievement in Mathematics.
On The Value of Status Studies in Education
Authors: Scandura Joseph M.
Published: August 2020

A number of questions arose when one of my doctoral students reported on “The International Study of Achievement in Mathematics” in our research seminar. In light of the concerns expressed there and in thinking about the study, I feel that a few remarks might be helpful in pu tting this type of research in to better perspective.
The Relevance of the Study to Teacher-Education Programs
Authors: Cooney Thomas J.
Published: August 2020

The purpose of this article is to examine the relevance of the International Study of Achievement in Mathematics to those mathematics educators in volved in the preparation of teachers. While the explicit purpose of the Study is not to provide directions for teacher-education programs, the Study nevertheless examines questions which indirectly involve the training of mathematics teachers. While all of the hypotheses in the Study deal with some aspect of education as they relate to mathematics, some hypotheses, namely Hypotheses 12–26, arc involved with probl ems more directly related to the mathematics education community. In particular, Hypotheses 12, 13, 14, 15, 18, 19, and 20. in the opinion of the writer, take on added significance when considering the preparation of mathematics teachers.
Publicity and Educational Research: A Case Study
Authors: Romberg Thomas A.
Published: August 2020

On March 12, 1967 the following headune appeared in the New York Times: “United States Gets Low Marks in Math.” A 250-word article followed summarizing the failure of American schools to win the international mathematics race. Emotional reaction to this account was instantaneous. Parents, teachers, educators, and even Congressmen, taking the article at face value began demanding ex planations. as if the lid had been lifted from a teeming educational scandal. Even today the vestiges of this account linger to haunt the image of mathematics education.