bluuebunny/crossref_metadata_2025 huggingface dataset:
The Effect of Training on Length on the Performance of Kindergarten Children on Nonstandard but Related Tasks
Authors: Romberg Thomas A. , Gilbert Lynn E.
Published: August 2020

This paper reports the results of an exploratory study designed to examine whether explanation of terms via a process-by-attribute instructional approach would help children's performance on nonstandard comparison tasks involving that attribute. The study was conducted with kindergarten children in a pretest-posttest nonequivalent control group design with another treatment group not receiivng the pretest. The treatment consisted of 3 days of brief instruction concerning the definition, comparison, and representation of length. The results indicate that instruction produced significant performance gains.
Equivalence and Order Relations as Interrelated by Four- and Five-Year-Old Children
Authors: Steffe Leslie P. , Carey Russell L.
Published: August 2020

The purpose of this study was to investigate interrelationships among 4- and 5-year-old children's ability to conserve length relations not involving the asymmetric property and consequences, conserve length relations involving the asymmetric property and consequences, use the reflexive and nonreflexive properties of length relations, and use the transitive property of length relations at 2 different points in time: (1) after formal experiences only in establishing a length relation between 2 curves and (2) after selected formal experiences in (1) and in conserving length relations and the usage of properties of length relations. The conclusions of the study are: (a) an ability to conserve length relations not involving the asymmetric property and consequences precedes an ability to conserve length relations involving the asymmetric property and consequences; (b) an ability to conserve length relations involving the asymmetric property and consequences precedes an ability to use transitivity of length relations; and (c) an ability to use the reflexive and nonreflexive properties is not related to an ability to conserve length relations not involving the symmetric property and consequences, use the transitive property of length relations, or conserve length relations involving the asymmetric property and consequences.
Computer-Assisted Problem Solving in School Mathematics
Authors: Hatfield Larry L. , Kieren Thomas E.
Published: August 2020

Computer-assisted problem solving can be characterized by student-generated computer programs used to explore mathematical concepts, principles, and processes. This paper presents a brief rationale for using the computer as an inquiry tool to extend mathematical instruction. 2 investigations are reported in which seventh- and eleventh-grade mathematics students wrote computer programs in the programming language BASIC in their study of selected mathematical content. It was hypothesized that the activity of designing a computer program, studying its output, and refining or “debugging” the algorithm would positively affect mathematical performance. Data were collected on experimental and control Ss over a 2-year period, the second year representing a refinement and replication of the experiment. Comparisons involving criterion measures of learning, retention, and transfer were made using analysis of variance and covariance and item-proportions procedures. Results support this computer usage with selected content, process goals, and student abilities.
Letters to the Editor
Authors: Bright George W. , Romberg Thomas A.
Published: August 2020

I propose that the editorial board of JRME consider adding a regular department which would be modeled after the “Replications and Refinements” section of the Journal of Social Psychology. Such reports would be limited in length (e.g., 500 or 1000 words) and would refine current techniques or replicate known procedures in order to verify or refute previous findings.
A Formative Development of an Elementary School Unit on Proof
Authors: King Irvin L.
Published: August 2020

To test the feasibility of the Cambridge Conference on School Mathematics recommendation that proof be taught in the elementary school, a unit on mathematical proof was developed using an iterative procedure. The basic objective of the unit was to teach the students to prove and understand a sequence of 6 theorems in number theory. After 2 formative pilot studies were conducted, a Nonequivalent Control Group Design was used to test the revised unit with 10 capable sixth-grade students. The students displayed an understanding of the theorems and were able to learn the proofs.
Study 1-2: An Exploration of Selected Relationships among the Enactive, Iconic, and Symbolic Modes of Representation
Authors: Farris Dan C.
Published: August 2020

This study is one of three closely related studies dealing with modes of representation. The other two studies were done by Klein (1970) and Hirschbuhl (1971). Each study is based on the same theoretical framework and was designed to test the transfer of learning within a modes-of-representation matrix.
Study 1-5: An Exploration of Selected Transitivity and Conjunctive Relationships among the Enactive, Iconic, and Symbolic Modes of Representation
Authors: Hirschbuhl John J.
Published: August 2020

This study evolved from the previous modes-of-representation studies conducted by Klein (1970) and Farris (1970), and it employed the same theoretical framework.
Achievement Monitoring Via Item Sampling: a Practical Data-Gathering Procedure for Formative Evaluation
Authors: Romberg Thomas A. , Braswell James
Published: August 2020

This paper provides an illustration of the use of a periodic testing procedure--achievement monitoring--combined with an efficient testing procedure--item sampling--to assist the developers of a mathematics program in making formative decisions. The mathematics program was sixth-grade Patterns in Arithmetic. Details of item construction, periodic testing, and profile construction are described. In addition, how this information was used to modify materials is discussed.
Seeing a Colleague Encourage a Student to Make an Assumption While Proving: What Teachers Put in Play When Casting an Episode of Instruction
Authors: Nachlieli Talli , Herbst Patricio , González Gloriana
Published: August 2020

This article reports on an investigation of how teachers of geometry perceived an episode of instruction presented to them as a case of engaging students in proving. Confirming what was hypothesized, participants found it remarkable that a teacher would allow a student to make an assumption while proving. But they perceived this episode in various ways, casting the episode as one of as many as 10 different stories. Those different castings of the episode make use of intellectual resources for professional practice that practitioners could use to negotiate the norms of a situation in which they had made a tactical but problematic move. This collection of stories attests to the effectiveness of the technique used for eliciting the rationality of mathematics teaching: By confronting practitioners with episodes of teaching in which some norms have been breached, one can learn about the rationality underlying the norms of customary teaching.
Book Review: Searching for the Most Amazing Thing Over the Last 20 Years: A Review of Research on Technology and the Teaching and Learning of Mathematics, Volume 1 and Volume 2
Authors: Bowers Janet , Brandt Jeffrey , Stovall Kevin , Vargas Mailei
Published: August 2020

Back in 1988, Tom Snyder (of Tom Snyder Productions, one of the most famous early software publishing companies) and Jane Palmer wrote a prophetic book called In Search of the Most Amazing Thing: Children, Education, and Computers. Their thesis was twofold: First, they pointed out that technology, which was just beginning to be introduced in grade schools, was so compelling that educators were “… more interested in so-called computer literacy than the real thing, literacy” (p. 2). Snyder and Palmer called for stakeholders to determine what their educational priorities were, and then to figure out what technology could do to support them. Second, they emphasized the view that teachers are indispensible components in the teaching and learning process, and that no computer will ever take their place. After 20 years, we believe that Snyder and Palmer would be gratified to read Heid and Blume's newly published two-volume set that contains a thorough anthology of how educators have defined priorities for the teaching and learning of mathematics and the pivotal roles that both the teacher and the technology play within that process. In our view, the editors have attained their goal of assembling a comprehensive digest that “… will enable the creation and implementation of curricula that capitalize on technology and will help teachers orchestrate the use of technological tools in school mathematics classrooms” (vol. 2, p. viii).
Using Propensity Scores to Reduce Selection Bias in Mathematics Education Research
Authors: Graham Suzanne E.
Published: August 2020

Selection bias is a problem for mathematics education researchers interested in using observational rather than experimental data to make causal inferences about the effects of different instructional methods in mathematics on student outcomes. Propensity score methods represent 1 approach to dealing with such selection bias. This article describes general principles underlying propensity score methods and illustrates their application to mathematics education research using 2 examples investigating the impact of problem-solving emphasis in mathematics classrooms on students' subsequent mathematics achievement and course taking. Limitations of the method are discussed.
Book Review: Mathematics Educators Respond to Kaput's “Algebra Problem”: A Review of Algebra in the Early Grades
Authors: Chazan Dan , Edwards Ann R.
Published: August 2020

In the last few decades, mathematics education in the United States has seen a perfect storm with respect to the teaching and learning of algebra—one that is difficult for our colleagues in other countries to fathom. As part of recent largescale education reform in the United States, the increasingly widely perceived need for greater mathematical literacy and the desire to make access to college more equitable in the society have led to promotion of “algebra for all” and the codification of this desire in high-stakes accountability measures (e.g., as illustrated by Achieve's American Diploma Project (ADP, 2004)). Algebra in the Early Grades, an edited volume by a group of mathematics education researchers, is in important ways a response of mathematics educators to these developments.
Book Review: … A Review of Mathematical Relationships in Education: Identities and Participation
Authors: Walshaw Margaret
Published: August 2020

What might a book that is based on a seminar series titled Mathematical Relationships: Identities and Participation and held in the United Kingdom during 2006–2007 have to say to the international mathematics education community? How might the mathematical relationships of learners in a specific national setting resonate with those who seek a hold on the identities and participation of learners in other mathematics classrooms? The answer is through theory. Circumstance and setting may vary, but the theoretical notions put to use in this book have the potential to be extremely powerful in unearthing the kinds of relationships that learners, across cultures and locations, might form with mathematics. The book is a timely intervention precisely because we are only now beginning to appreciate that issues relating to learners' relationships with mathematics are among the most complex and challenging facing us today.
Editorial: The Task of Research Manuscripts—Advancing the Field of Mathematics Education
Authors: Heid M. Kathleen
Published: August 2020

Whereas it is essential that JRME manuscripts employ careful, systematic, wellargued, and appropriately documented approaches, such technical expertise is not enough to merit publication in JRME. The direction given on the JRME Web site advises reviewers to address these questions, “Does the research extend or deepen our understanding of important issues in mathematics education? Does it have the potential to lead the field in new directions?” In other words, reviewers are asked to address the question of whether the study that is reported advances the field of mathematics education. Having reviewed hundreds of articles over the past 2 years, and having received and read over 2000 reviews, I have noticed a theme that appears again and again in reviews: Successful manuscripts advance the field of mathematics education.
Editorial Comment
Authors: Weaver J. F.
Published: August 2020

Within its first four volumes (16 issues), the JOURNAL FOR RESEARCH IN MATHEMATICS EDUCATION has published more than 100 manuscripts by persons representing more than 75 educational institutions or other agencies.
The Effeuiveness of Textbook, Student-Generated, and Pictorial Versions of Presenting Mathematical Problems in Ninth-Grade Algebra
Authors: Kulm Gerald , Lewis Joan F. , Omari Issa , Cook Harold
Published: August 2020

A relatively new area within the field of complex problem solving involves the subject's mode of conceptualizing and representing a problem either verbally or visually. Frandsen and Holder (1969) suggested that when problems such as anagrams, syllogisms, and rate of travel are presented verbally, solving them requires “holding in mind” and manipulating the multiple components of the problems.
Critiques of Articles: Some General Questions about Jerman's Study of Problem Solving
Authors: Callahan Leroy G.
Published: August 2020

Experimental studies carried out in the laboratory of the public schools invariably are a compromise between the ideally controlled setting and that which is realistically attainable. Generally, when compromises are minimized, useful evidence for consumers of research is maximized. Experimental controls, however, are not the only thing that determines maximum usefulness of evidence. Clarity in formulating and reporting essential components of the research design also contributes to maximizing usefulness of a research effort. This aspect of the research process is clearly under the control of the individual researcher and fewer compromises seem necessary.
Two Scales Of Attitude Toward Mathematics
Authors: Aiken Lewis R.
Published: August 2020

Investigations concerned with the developing and influencing of attitude toward mathematics have dealt almost exclusively with enjoyment of the subject or anxiety in its presence. Although various psychometric procedures have been applied in constructing the measures of attitude employed in such investigations (see Aiken, 1972; Anttonen, 1969; Dutton, 1962; McCallon & Brown, 1971), the attitude dimension assessed by these instruments usually involves only one of the affective goals of mathematics instruction.
The Relationship between Performance on Piagetian Tasks and Impulsive Responding
Authors: Schwebel Andrew I. , Schwebel Carol R.
Published: August 2020

In a study reported in this journal, Callahan and Passi (1971) investigated the relationship in children between conceptual tempo and the ability to conserve length. These authors explained that, in contrast to reflective children, those with impulsive conceptual tempos tended to answer problems posed more quickly, often without devoting sufficient time to consider alternative responses. Agreeing with Lee, Kagan, and Rabson (1963), Callahan and Passi stated that in mathematics, a discipline with deductive structures, it is reflectiveness and not impulsiveness that has value in problem solving.
On Comparing Error Patterns and the Effect of Maturation in a Unit on Sentential Logic
Authors: Eisenberg Theodore A. , Mcginty Robert L.
Published: August 2020

The research literature dealing with critical thinking vis-à-vis formal logic implies that (a) an individual's reasoning ability seems to improve with age and (b) reasoning from negatively worded hypotheses is more difficult than reasoning from positively worded hypotheses. The purpose of this study was to investigate these two implications.

A test consisting of 30 items in sentential logic was constructed and given to elementary school children and prospective elementary school teachers. The findings indicate that only on certain forms of questions is maturation a factor in logical reasoning ability. Indeed, with certain types of items in sentential logic, maturation–and, inseparably, education–seems to be a hindrance to logical reasoning.
Measurement Concepts of First-and Second-Grade Students
Authors: Carpenter Thomas P.
Published: August 2020

The purpose of this study was to identify some of the aspects of the measurement process that young children naturally attend to and those that they ignore or are unable to make use of. Specifically the study attempted to assess the degree to which young children rely on perceptual comparisons, or at least require perceptual support, for their measurement operations. Another factor that was investigated was whether measurement comparisons involving equal quantities are of the same difficulty as those involving unequal quantities. Finally, the study attempted to identify some of the misconceptions regarding the measurement process that result from these and other factors.
Cognitive Factors and Their Interaction with Instructional Mode
Authors: Hancock Robert R.
Published: August 2020

Aptitude tests measuring cognitive factors from Guilford's Structure-of-Intellect model were given to 119 ninth-grade students who then studied 1 of 2 programmed units–one in a figural mode, the other verbal–for 3 class periods. Dependent variables were scores on a learning test administered the following day, as well as scores on a retention test four weeks later. Regression analysis revealed 17 instances of disordinal interaction of which 13 occurred on the test of retention and 11 were related to semantic factors. 8 of 9 sex-related interactions involved male students; however, as a group, female Ss scored higher on 5 of 6 criterion measures. Based on these findings, further study of memory factors, semantic factors, and sex difference is indicated.
The Effects on Preservice Elementary Teachers of Learning Mathematics and Means of Teaching Mathematics through the Active Manipulation of Materials
Authors: Fuson Karen
Published: August 2020

This study examines some effects on preservice elementary teachers of a combined mathematics and mathematics methods course that used manipulative materials as the primary means of learning. The effects investigated were changes in trainee desire to use, ability to use, and actual use of manipulative materials in teaching; changes in trainee desire or actual behavior with respect to teaching in a learner-focused manner; changes in trainee understanding of elementary mathematics; differences between learning in a concrete, physical way and learning in a symbolic, abstract way; and changes in trainee attitudes of enjoyment of and feelings of competence in teaching mathematics.
A Forum for Researchers: Replication Studies: Why So Few?
Authors: Eastman Phillip M.
Published: August 2020

The purpose of this note is to bring to the readers' attention the lack of replication studies appearing in the JRME. We are certainly all aware that one empirical study does not by itself answer a general question about the teaching or learning of mathematics. This is supported by the fact that in numerous journal articles the authors will conclude their reports by suggesting that “further research is needed” in their particular area. Hence, one would expect alJ researchers (particularly those who claim important results) to do follow-up work on their own research, and one would expect to find researchers conducting exact replication studies to lend more credence to their results.
The Effect of Teaching on Teacher Learning
Authors: Bausell R. Barker , Moody William B. , Crouse Richard
Published: August 2020

Serving as a teacher of a unit in elementary probability was found to result in superior acquisition of that topic as compared to serving as a student. However, teaching did not result in superior acquisition when preparation time was controlled by giving Ss no prior knowledge of whether they would teach or serve as students. These results were interpreted as indicating that teaching functions as a superior learning mechanism chiefly through its role as a differential study incentive.
Editorial Comment
Authors: Weaver J. F.
Published: August 2020

In the March 1975 issue of the JRME, Phillip Eastman raised questions pertaining to the need for replication studies and for the publication of findings therefrom. At the time, he did not know that the May issue of the JRME would exemplify several of the things for which he was pleading and would include some of his own efforts.
Comparison of Two Instructional Strategies for Teaching the Solution of Verbal Problems
Authors: Bassler Otto C. , Beers Morris I. , Richardson Lloyd I.
Published: August 2020

Few topics in mathematics present as much difficulty or elicit as many conflicting opinions as the teaching of problem solving. Problem solving occupies a central role in the teaching and learning or mathematics and helps to relate mathematics to other subject areas as well as to the physical world. The importance of problem solving should mean that a significant part of classroom activity is aimed at developing the student's ability to solve problems. Yet Stilwell (1967) found that only 3% of all time spent on problem-solving activity was devoted to developing a method for solving problems. Stilwell also found that only 7% of problem-solving activity was devoted to looking back at a problem or ahead to its implications.
Is Conservation of Number a Necessary Condition for Mathematical Understanding?
Authors: Mpiangu Benayame Dinzau , Gentile J. Ronald
Published: August 2020

This study investigated the importance of conservation of number as a prerequisite skill for arithmetic instruction. Piaget's theory maintains that the child's ability to conserve number constitutes a prerequisite to arithmetic understanding. 116 Ss (ages 4 to 6) were homogeneously grouped on the basis of a conservation of number pretest and randomly assigned to experimental and control groups. The experimental group was trained in arithmetic concepts, while the controls played a game under similar conditions. The 2 groups were posttested on arithmetic and number conservation tasks. The regression of arithmetic posttest scores on the conservation dimension was plotted separately for the experimental group and for the control group. The homogeneity of regression analysis showed that the 2 regression lines were separated but essentially parallel. In other words, although training had an effect, it did not have a differential (interaction) effect on nonconservers and conservers. Thus, the results failed to confirm the hypothesis that conservation of number is necessary for the understanding of arithmetic.
Research on Mathematics Education (K-12) Reported in 1974
Authors: Suydam Marilyn N. , Weaver J. F.
Published: August 2020

Research reported during the 1974 calendar year is listed, accompanied by brief annotations of findings.
An Analysis of Some of Piaget's Topological Tasks from a Mathematical Point of View
Authors: Martin J. Larry
Published: August 2020

During the 1950s and '60s, sweeping changes were made in the mathematics curriculum that were largely due to fundamental changes that had occurred in mathematics. Among these changes was a trend toward emphasizing the structural nature of mathematics. However, changes in the content of geometry represented more of a tentative groping than did changes in content dealing with the real numbers. Many approaches to geometry were proposed, such as those of transformation geometry, synthetic geometry, analytic geometry. and vector geometry. Although agreement was not reached as to approach nor indeed even as to the purpose of geometry in the curriculum, mathematics educators did agree that more geometry should be included and included much earlier than was done traditionally.
The Influence of Two Types of Advanced Organizers on an Instructional Unit about Finite Groups
Authors: Lesh Richard A.
Published: August 2020

In order to teach young children the concept “red,” it would not be sufficient to point to a single red object with the instruction, “This is red” In order to abstract redness, several red objects would have to be shown—for example, a red ball, a red hat. a red truck, a red block, and so on. However. children must not only know which objects are red, they must also know which are not red. Consequently, after showing a red ball, it might be helpful to point out some nonred objects like a yellow ball, a blue hat, or a green truck.
Factors Associated with Third– and Fourth-Grade Children's Performance in Solving Multiplication and Division Sentences
Authors: Grouws Douglas A. , Good Thomas L.
Published: August 2020

The performance of third- and fourth-grade children in solving simple multiplication and division sentences was examined in relation to certain status and mathematical factors. Significant differences in performance were associated with many of these factors, which suggests that they should be taken into account in curriculum planning and classroom instruction.
Effect of Interspersed Questions on Learning from Mathematical Text
Authors: Kuehls Ernest A.
Published: August 2020

One of the objectives of formal education is as follows: The student should become increasingly able to learn through his reading and become less and less dependent on the teacher. How should the mathematical material be written so that the reader is more actively engaged, is thinking, and hence, gains more knowledge from the reading experience? During the early 1960s many mathematics educators felt that the scheduling and control of student behavior embedded in the programmed textbooks would lead to more knowledge gained from the reading experience.
Measuring the Effectiveness of Using Slide-Tape Lessons in Teaching Basic Algebra to Mathematically Disadvantaged Students
Authors: Williams Eddie R. , Mick Harold W.
Published: August 2020

This study was designed to determine the effectiveness of slide-tape units in supporting other modes of instruction, as measured by achievement on topics in basic algebra. It was conjectured that visuals in the form of slides accompanied by synchronized narration would more nearly meet the needs of students with poor backgrounds in both reading and mathematics, as opposed to the more traditional lecture-recitation mode of instruction.
Cognitive Emphasis of Geometry Teachers' Questions
Authors: Friedman Morton
Published: August 2020

The purpose of the present study was to analyze the cognitive range of geometry teachers' classroom questions and to determine the extent to which teachers ask questions at each of four levels. In the 13 classrooms studied, 24 percent of the questions asked were at the memory level, considerably less than the percentage typically asked by teachers of other subjects. Analysis showed significantly more comprehensive questions were asked than questions on any of the other three levels. Although there was no significant difference between the frequency of memory and application questions, each was asked significantly more often than higher level questions.
Brief Reports: Use and Recall of Advance Organizers in Mathematics Instruction
Authors: Bright George W.
Published: August 2020

The two studies reported here were designed (a) to determine whether the generality and inclusiveness of advance organizers (AOs) demanded by the definition of Ausubel (1963) is the same as the mathematical generality or abstractness of concepts that might be used as AOs and (b) to measure the effects of programmed recall of AOs in enhancing the learning of a mathematics concept. In Study I, two AOs at different levels of abstraction, each in the presence of objectives, constituted the treatments given prior to common mathematics instruction. Such an approach is consistent with the defining characteristics of an AO (Ausubel, 1963, pp. 214–215) and exploits the perhaps critically important structural aspects of the mathematics content. In Study II, programmed recall of an AO during instruction was used to determine differential achievement resulting from several levels of reinforcement of the AO. This treatment was designed to exploit the fact that an AO operates because it provides stable anchorage for the concepts to be learned.
Editorial
Authors: Wilson James W.
Published: August 2020

This issue of the Journal for Research in Mathematics Education is the first for my term as editor. J. Fred Weaver served as editor for Volumes 5, 6, and 7. For the past several months we have worked on the problems of transferring editorship. Fred completed his work with the November issue. The a rticles in this issue include most of the backlog of manuscripts he had accepted for publication.
An Intraconcept Analysis of Rational Number Addition: A Validation Study
Authors: Uprichard A. Edward , Phillips E. Ray
Published: August 2020

In previous studies, researchers have attempted to generate learning hierarchies using task analysis based primarily on epistemological considerations (Gagné & Paradise, 1961; Gagné, 1962; Cox & Graham, 1966; Uprichard, 1970; Okey Gagne, & 1970; Harke, 1971; Riban, 1971; Phillips & Kane, 1973; Miller & Phillips, 1975). Studies of this type conducted in the early si xties provide substantial evidence to support the hierarchical structureofknowledge(Gagné & Paradise, 1961;Gagné & Brown, 1961:Gagné, 1962, 1963; Gagné, Mayor, Garstens, & Paradise, 1962; Gagné & Staff, 1965). An examination of results from recent studies (Niedermeyer, Brown, & SulLen, 1969; Brown, 1970; Phillips & Kane, 1973; Callahan & Robinson, 1973) suggests that optimal learning sequences can be developed by sequencing instructional materials according to validated learning hierarchies. However, both Gagné (1968) and Pyalte (1969) have pointed out that the determination of an optimal or hierarchical sequence of subtasks from simplest to most complex is not easi ly achieved.
Comparative Effectiveness of Three Sequences of Moves for Teaching Conjunctive and Relational Mathematical Concepts to College Students
Authors: Catanzano Robert , Godwin Wanda
Published: August 2020

Three sequences of moves--characterization-exemplification (CED), exemplification (E), and a modified characterization-exemplification (CEI) or (OCED) were compared on the immediate acquisition and short-term retention of conjunctive and relational mathematical concepts. Twenty-seven general mathematics students were blocked into high- and low-achievement levels and randomly assigned to three treatment groups. The E-sequence was found to be significantly (p<.05) better than the CED and the CEI on the immediate acquisition Subtest 2 at the low achievement level and the high achievement level, respectively, for the conjunctive concept only.
The Relative Effectiveness of Three Geometric Proof Construction Strategies
Authors: Carroll C. Dennis
Published: August 2020

Achievement levels of geometry classes were compared following units of instruction employing analytic, synthetic, and combination strategies. For above-average and below-average achievement groups, instruction with differing strategies was found to yield differences (p<.05) in MANOVA-identified achievement composite scores.
A Forum for Researchers
Authors: Ellsworth Randy , Isakson Richard L. , Travers Kenneth J.
Published: August 2020

Eastman's (1975) recent expression in the JRME of concern over so few replication studies is a concern that should be shared by all who have an interest in research. Replication is critical in assessing the “significance” of research results. A correlation coefficient of .20, which is statistically significant at the .01 level, will be much more “significant” if we can demonstrate by replication that the same result occurs again and again. By replicating, we help rule out the possibility that a Type I error (we rejected the null hypothesis when it was true) occurred in the original experiment. Furthermore, by independently replicating with different subjects, at different times and places, we also are helping to increase the generalizability of any “significant” results we do obtain.
The Interpretation of Statements in Standard Logical Form by Preservice Elementary Teachers
Authors: Damarin Suzanne K.
Published: August 2020

Preservice elementary teachers (N=70) were asked to judge the truth or falsity of compound statements concerning membership in pictured sets. Tetrachoric correlations computed as reliability estimates for pairs of items representing 16 conditions ranged from .66 to .97. Analysis of variance performed on item scores revealed significant effects (p<.001) for connectives, truth values of simple statements, subjects, and all interactions. The pattern of significant differences (p<.01, Tukey's HSD) between means suggested that subjects treated conjunctive, conditional, and biconditional statements equivalently.
Critique: Teaching Problem-Solving Heuristics: A Critique of Two Studies
Authors: Kulm Gerald
Published: August 2020

The mathematics curriculum innovations of the sixties generated a great deal of research comparing discovery with other teaching methods. It soon became evident that there was widespread disagreement about the definition of discovery and that results were difficult to interpret because many research reports did not make clear what the discovery treatment had been. Further, it was often impossible to learn from the studies the effects of discovery on anything other than overall achievement. Although the absence of consistent and clear research results was not the only reason, there was doubt that discovery teaching ever gained wide classroom acceptance (NACOME, 1975).
Brief Reports: Conjunctive Interpretations of Logical Connectives: Replication of Results Using a New Type of Task
Authors: Damarin Suzanne K.
Published: August 2020

In an earlier study Damarin (1977) reported on the performance of subjects who were asked to judge the truth or falsity of compound statements concerning membership of elements in pictured sets. More than 90% of these subjects—preservice elementary teachers—were found to treat both conditional and biconditional statements as conjunctions. Roughly half the population also treated the disjunction as a conjunction, whereas less than a third handled it correctly as “inclusive or”; only one subject treated the “or” exclusively.
Review
Authors: Bishop Aian J.
Published: August 2020

I predict that this book will exert a strong influence on future research in mathematics education. For those who do not know me, I should say that I do not often go around making such dogmatic statements. But the book has so much worth that I am not even going to bother to rephrase my prediction in the form of a null hypothesis! When you have read it you are bound to agree.
Editorial
Authors: Wilson James W.
Published: August 2020

In the April 1957 issue of the Arithmetic Teacher, Fred Weaver provided a bibliography on the research in the teaching of arithmetic from 1951 through 1956. This established the annual listing of research pertaining to elementary school mathematics that was to grow and continue in the Arithmetic Teacher for 14 years. In 1971, the listing was expanded to include the secondary school level and was published in the Journal for Research in Mathematics Education. The present issue of JRME contains the seventh JRME listing.
Relationships between Selected Teacher Behaviors of Prealgebra Teachers and Selected Characteristics of Their Students
Authors: Campbell N. Jo , Schoen Harold L.
Published: August 2020

Students in 73 prealgebra classes completed a questionnaire containing items about their teacher's classroom behaviors, their grades in mathematics, and their attitudes toward mathematics, school, and their mathematics teacher. Several moderate relationships were found between the student's perception of specific teaching behaviors and student attitudes. A factor analysis of the students' perceptions of teacher behaviors revealed six factors in the teaching behavior portion of the inventory. A significant relationship (p<.05p<.05) between one of the inventory factors and the students' attitudes toward their mathematics teacher was identified.
A Forum for Researchers: The Place of William A. Brownell in Mathematics Education
Authors: Kilpatrick Jeremy , Weaver J. Fred
Published: August 2020

Mathematics education has few giants. It lost one on 28 May when William A. Brownell died in Walnut Creek, California, at the age of 82. William Arthur Brownell was born on 19 May 1895 in Smethport, Pennsylvania. He went through elementary and high school in Smethport and then entered Allegheny College, where he received the A.B. in 1917. After graduation, he returned to his hometown to teach at the local high school for four years. Then he went to Illinois to begin graduate work in educational psychology at the University of Chicago.
Brief Reports: The Effects of Perceptual Transformation Experiences and Numerical Operational Experiences on Numerical Correspondence and Equivalence
Authors: Becher Rhoda McShane
Published: August 2020

Piaget's theoretical and empirical accounts of young children's development of an understanding of numerical correspondence and equivalence has stimulated extensive research and analysis. A critical examination of a wide variety of training reports indicates that in a majority of the successful investigations, subjects have possessed some aspects of the conservation response (i.e., the ability to establish one-to-one correspondence or the ability to conserve on one but not two items) prior to their inclusion in the study. In the unsuccessful studies, subjects have been generally classified as “nonconservers” without specification of developmental status. This non-specific classification suggests that children at lower stages of development (i.e., unable to establish one-to-one correspondence) were included in the sample. A second interesting observation is that although training sessions provided experiences for learning to (a) establish one-to-one correspondence, (b) recognize the eq ui valence of matched sets, and (c) maintain equi valence during perceptual transformations, assessment of the effectiveness of training has been only in terms of the maintenance of equivalence during perceptual transformations. No examination has been made of the effectiveness of training approaches in facilitating learning of the other two aspects, which are viewed as conservation subskills and necessary conditions for conservation. Nor have there been any previous studies to assess the differential effectiveness of training for preconservation children at various stages of development.
A Forum for Researchers: The Manipulative Materials Strategy: The Latest Pied Piper?
Authors: Friedman Morton
Published: August 2020

In education, unfortunately, there is a great furore about whatever is announced as the latest trend. and the schools seem to careen erratically after each Pied Piper in turn. This giddy chase keeps them almost beyond earshot of the researcher standing on his tiny, laboriously tamped patch of solid ground, crying in a pathetic voice. “Wait for me!” “Wait for me!”
The Quality of Standardized High School Mathematics Tests
Authors: Petrosko Joseph M.
Published: August 2020

An analysis was made of the educational and psychometric quality of standardized mathematics tests aimed at high school students. Trained raters judged most of such instruments available in the United States. Tests were categorized into four areas: general mathematics (N=322), applied mathematics (N=26), algebra (N=122), and geometry (N=52). Results showed many tests to be low in common types of validity and reliability. General mathematics had, as a rule, tests with higher ratings than did the other content areas. Several implications were drawn from the study. Researchers in mathematics education should carefully analyze all aspects of tests to find those congruent with a given research need. Test developers should make renewed efforts to enhance the technical quality and curricular relevance of their products.
Cognitive Style and Mathematics Learning: The Interaction of Field Independence and Instructional Treatment in Numeration Systems
Authors: McLeod Douglas B. , Carpenter Thomas P. , McCornack Robert L. , Skvarcius Romualdas
Published: August 2020

The relationship between a cognitive style variable, field-dependence-independence, and instructional treatments that differed in two dimensions of discovery learning, level of guidance and level of abstraction, was investigated. The four treatments used either minimum or maximum guidance with or without manipulative materials. The 116 subjects, all prospective elementary teachers, were pretested and then randomly assigned to treatments. Students were tested for immediate achievement at both the concrete and symbolic level, and then retested 4 weeks later. There was a significant (p<.05p<.05) aptitude-treatment interaction between field-dependence-independence (measured by the Hidden Figures Test) and level of guidance on two of the four dependent variables. As predicted, field-independent students did better with minimum guidance, whereas field-dependent students excelled with maximum guidance. Although there was one interaction between field-dependence-independence and level of abstraction, the data showed no consistent pattern for this dimension.
Intellectual Development and Reversibility of Thought in Equation Solving
Authors: Adi Helen
Published: August 2020

The study investigated how subjects of different developmental levels performed on equation solving when different reversible processes were applied. Seventy-five preservice elementary school teachers were classified into three developmental levels according to their performance on a paper-and-pencil, multiple-choice test with diagrammatic presentations. All subjects were exposed to the same instructional treatment in equation solving, and were then tested on reversal and on formal equation solving. Data were analyzed by one-way ANOVA, results were interpreted in light of Piaget's developmental theory, and teaching implications were discussed.
An Instrument for Evaluating Mental Arithmetic Skills
Authors: Sachar Jane
Published: August 2020

Although there has been extensive research in elementary mathematics education during the past 25 years, the important area of mental arithmetic has remained relatively untouched. Mental arithmetic, in contrast to traditional arithmetic, includes items presented orally with no supporting visual sti muli. Although most arithmetic students are confronted daily with problems requiring skills in mental arithmetic, schools are only beginning to recognize the importance of these skills.
On Narrowing the Performance Gap in Mathematical Thinking between Advantaged and Disadvantaged Children
Authors: Babad Elisha Y. , Bashi Joseph
Published: August 2020

A special curriculum was designed for teaching cryptarithmetic to investigate whether disadvantaged students can reach a level of competence in mathematical thinking and whether the gap between them and advantaged students can be narrowed. In this program, the students learned to apply relevant problem-solving strategies and simple mathematical rules and to test hypotheses systematically. The findings indicated that a careful application of certain learning principles to the training of disadvantaged students resulted in an appreciably narrowed gap between advantaged and disadvantaged students. The relationships between the cryptarithmetic performance and several tests of mental ability and achievement in mathematics were presented and discussed.
Size-dependent patterns of cell proliferation and migration in freely-expanding epithelia
Authors: Heinrich Matthew A , Alert Ricard , LaChance Julienne M , Zajdel Tom J , Košmrlj Andrej , Cohen Daniel J
Published: August 2020

The coordination of cell proliferation and migration in growing tissues is crucial in development and regeneration but remains poorly understood. Here, we find that, while expanding with an edge speed independent of initial conditions, millimeter-scale epithelial monolayers exhibit internal patterns of proliferation and migration that depend not on the current but on the initial tissue size, indicating memory effects. Specifically, the core of large tissues becomes very dense, almost quiescent, and ceases cell-cycle progression. In contrast, initially-smaller tissues develop a local minimum of cell density and a tissue-spanning vortex. To explain vortex formation, we propose an active polar fluid model with a feedback between cell polarization and tissue flow. Taken together, our findings suggest that expanding epithelia decouple their internal and edge regions, which enables robust expansion dynamics despite the presence of size- and history-dependent patterns in the tissue interior.
A comparison of COVID-19, SARS and MERS
Authors: Hu Tingting , Liu Ying , Zhao Mingyi , Zhuang Quan , Xu Linyong , He Qingnan
Published: August 2020

In mid-December 2019, a novel atypical pneumonia broke out in Wuhan, Hubei Province, China and was caused by a newly identified coronavirus, initially termed 2019 Novel Coronavirus and subsequently severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). As of 19 May 2020, a total of 4,731,458 individuals were reported as infected with SARS-CoV-2 among 213 countries, areas or territories with recorded cases, and the overall case-fatality rate was 6.6% (316,169 deaths among 4,731,458 recorded cases), according to the World Health Organization. Studies have shown that SARS-CoV-2 is notably similar to (severe acute respiratory syndrome coronavirus) SARS-CoV that emerged in 2002–2003 and Middle East respiratory syndrome coronavirus (MERS-CoV) that spread during 2012, and these viruses all contributed to global pandemics. The ability of SARS-CoV-2 to rapidly spread a pneumonia-like disease from Hubei Province, China, throughout the world has provoked widespread concern. The main symptoms of coronavirus disease 2019 (COVID-19) include fever, cough, myalgia, fatigue and lower respiratory signs. At present, nucleic acid tests are widely recommended as the optimal method for detecting SARS-CoV-2. However, obstacles remain, including the global shortage of testing kits and the presentation of false negatives. Experts suggest that almost everyone in China is susceptible to SARS-CoV-2 infection, and to date, there are no effective treatments. In light of the references published, this review demonstrates the biological features, spread, diagnosis and treatment of SARS-CoV-2 as a whole and aims to analyse the similarities and differences among SARS-CoV-2, SARS-CoV and MERS-CoV to provide new ideas and suggestions for prevention, diagnosis and clinical treatment.