ALTERNATIVE LOGICS AND APPLIED MATHEMATICS

Many advocates of non‐classical logic for reasons external to mathematics claim that their proposed revisions are consistent with the use of classical logic within pure mathematics. Doubts are raised about such claims, concerning the applicability of pure mathematics to natural and social science.     

MATHEMATICS,MODELS AND ZENO'S PARADOXES

A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in discussing motion, only intervals, rather than instants, of time are meaningful. The approach presented here reconciles resolutions of the paradoxes based on considering a finite number of acts with those based on analysis of the full infinite set Zeno seems to require. The paper concludes with a brief discussion of the classical and quantum mechanics of performing an infinite number of acts in a finite time.     

GENDER COMPARISONS OF MATHEMATICS ATTITUDES AND AFFECT

This article reports the complex results of meta-analyses of gender differences in attitudes and affect specific to mathematics. Overall, effect sizes were small and were similar in size to gender differences in mathematics performance. When differences exist, the pattern is for females to hold more negative attitudes. Gender differences in self-confidence and general mathematics attitudes are larger among high school and college students than among younger students. Effect sizes for mathematics anxiety differ depending upon the sample (highly selected or general). One exception to the general pattern is in stereotyping mathematics as a male domain, where males hold much more stereotyped attitudes ( d = -.90). While affect and attitudes toward mathematics are not the only influences on the development of gender differences in mathematics performance, they are important, and both male and female affect and attitudes should be considered in conjunction with other social and political influences as explanations.     

数学成绩与代数应用题分类结果的相关研究

以初中代数应用题为材料,探讨了不同年级学生对代数应用题的分类结果与数学成绩的关系。结果表明：不同年级学生对代数应用题分类结果差异显著;数学成绩优生与数学成绩差生对代数应用题分类结果差异显著。     

MATHEMATICS AND SELF-ESTEEM: IMPLICATIONS FOR WOMEN'S CAREER CHOICE

The relationship of math participation and success to self-esteem and career goals is examined in a sample of 64 women and 52 men college students at the end of their sophomore year. No gender differences were found in math anxiety or perceptions of the usefulness of mathematics, but women were less likely to select a math-related career goal. Among the men students, math participation and self-assessments of math ability were positively related to more general self-estimates of competence; among women, these variables were not related significantly. Women's choices for math-related careers were more closely associated with scholastic ability and math background than were men's career choices. These results are discussed in the context of societal pressures and supports for men and women in regard to math participation.     

MATHEMATICS ANXIETY AND SCIENCE CAREERS AMONG ABLE COLLEGE WOMEN

Abstract —Does mathematics anxiety deflect able students from pursuing scientific careers? We obtained the Scholastic Aptitude Test (SAT) scores of 1,366 students entering Barnard College and also questioned them about their career interests and their feelings about mathematics learning At every level of mathematical skill, math anxiety correlated negatively with interest in scientific careers Contrariwise, quantitative SAT score was unrelated lo career interests, within relatively homogeneous categories of math anxiety or confidence Students were also asked directly whether the desire to avoid math affected their career choices The responses suggested a mediating role for math anxiety or confidence in career choice.     

CAUSAL ATTRIBUTIONS BY JAPANESE AND AMERICAN MOTHERS AND CHILDREN ABOUT PERFORMANCE IN MATHEMATICS*

In this study we examined the possibility that causal inferences about performance may help explain the relatively superior achievement of Japanese students in mathematics. Data from mothers and children in Japan and the U.S. were examined for (a) attributions about causes of performance in math; (b) intra-family transmission of beliefs; and (c) effect of sex of child on attributions. Results showed that Japanese mothers and children emphasized effort, particularly for low performance, while American mothers and children emphasized ability. Beliefs of mothers and children were similar within country but not within family, suggesting that transmission is diffuse. Differences in attributions about performance of boys and girls did not appear in Japan and in the U.S. appeared for mothers only. The emphasis placed on attributions to effort seems to offer a highly motivating context for Japanese students.     

PREDICTORS OF SAT MATHEMATICS SCORES OF GIFTED MALE AND GIFTED FEMALE ADOLESCENTS

A regression analysis was conducted to determine the relative importance of a series of variables in the prediction of SAT-Mathematics (SAT-M) scores of gifted males and females. Among the variables considered were visual-spatial ability, cognitive reasoning ability, learning style, and SAT-Verbal (SAT-V) scores. Scores on the visual-spatial task were analyzed for speed of response as well as ability. For both sexes, reasoning skills were the predominant factor in the prediction formulas. Differences in the two formulas seemed to reflect males' greater facility with process skills necessary for the SAT-M. Implications are discussed regarding how to interpret the differential performance of gifted males and females on the SAT-M.     

EFFECTS OF HIGH-PREFERENCE SINGLE-DIGIT MATHEMATICS PROBLEM COMPLETION ON MULTIPLE-DIGIT MATHEMATICS PROBLEM PERFORMANCE

The purpose of this study was to examine the effects of a sequence of three single-digit (1 digit × 1 digit) multiplication problems on the latency to initiate multiple-digit (3 digit × 3 digit) multiplication problems for 2 students in an alternative education school. Data showed that (a) during the preference assessment, both students selected the single-digit problems in a majority of the sessions, and (b) intervention resulted in a decrease in latency between problems for both students. Results are discussed in relation to using high-preference sequences to promote behavioral momentum in academic content areas.     

学前数学教法和儿童智能发展的追踪研究

本研究从儿童心理发展的特点和数学学习之间的内在规律出发,综合考查了各类教学法在学前施教的利弊;同时,在活动教法、指导操作法、演示法和讲授法之间做了对比实验,并设计了一整套以指导操作法为主的学前数学教法,以演示为主的数学教法之间进行了长期、深人的跟踪对比实验。结果表明,在其他变量基本被控制的条件下,指导操作法优于其他的教法;实验班儿童的智能发展,特别是数学能力的发展,明显好于对照班的儿童。这个优势一直持续到小学毕业。     

ON NATURALIZING THE EPISTEMOLOGY OF MATHEMATICS

In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered.     

USING NUMBER LINE PROCEDURES AND PEER TUTORING TO IMPROVE THE MATHEMATICS COMPUTATION OF LOW-PERFORMING FIRST GRADERS

Recommendations for mathematics instruction frequently include the use of manipulatives as a critical component. There are few experimental analyses of teaching strategies involving the use of manipulatives (e.g., the number line). This investigation used a multiple baseline design across three groups of students to examine the effectiveness of an experimental procedure for improving low-performing children's skills in solving missing addend arithmetic problems using the number line. To address concerns about inadequate time for instruction and insufficient practice in most mathematics instruction, trained peer tutors implemented the procedure. The results suggest that student performance improved when trained tutors taught the students number line procedures and gave them feedback on accuracy. Further, social validation data indicate that the students, their tutors, and their classroom teachers liked the procedures.