Differences In Mathematical Ability Research Articles

Sex, handedness, mathematical ability, and biological causation.

An important part of Benbow's (1988) assertion that sex differences in mathematical ability are primarily due to biological factors is the link between a trait that is assumed to reflect differences in brain organization (left-handedness) and mathematical giftedness. It is shown that the link between mathematical giftedness and an increased prevalence of left-handedness is not convincing. However, Benbow's (1986) data do show a convincing link between strong right-handedness and the lack of mathematical giftedness, in agreement with Annett and Manning's (1990a, 1990b) recent work.

The Effects of Using Calculators to Reduce the Computational Burden on a Standardized Test of Mathematics Problem Solving

Problem solving is a key skill in mathematics education. Thus, it is important to be able to assess students' proficiencies as problem solvers. The Quantitative Thinking Subtest (Test Q) of the Iowa Tests of Educational Development is a test of problem solving ability. However, if this test is to be considered a pure measure of problem solving ability, it must be demonstrated that this test does not measure other factors such as computational ability. To this end, a study was designed in which two groups of students took Test Q; one group using calculators to eliminate the need for computation, and the other just using paper and pencil to solve the problems. It was found that after controlling for differences in mathematical ability, the two groups did not differ in their scores on Test Q. This result seemed to support the validity of Test Q as a test of problem solving.

The formal setting as context for cognitive activities. An empirical study of arithmetic operations under conflicting premisses for communication

The general concern of the present article is to contribute to an understanding of the contextual determination of cognitive activities. More specifically, the focus of the empirical research reported has been to study how pupils define and deal with cognitive tasks in situations that are recognised as pedagogical in character. Within the context of their everyday mathematics teaching, 206 twelve year old primary school pupils were given work sheets containing elementary arithmetic problems. The experimental treatment consisted of introducing (through headings and instructions) pedagogical definitions of problems that were in conflict with the nature of the problems themselves. The results indicate that the predefinitions of cognitive activities typical of educational contexts have a strong impact on the way problems are dealt with. Clear differences could be discerned between groups at different achievement levels in the extent to which the cues present in pedagogical contexts were used in defining the problem. A crucial aspect of what are conventionally conceived as differences in mathematical ability seems, judging from the present results, to have more to do with the capacity to decipher ambiguous communicative situations than with the mastery of a mathematical algorithm per se.

Sex Differences in the Mathematics Achievement of Eighth Graders in Ontario

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. Some of the studies done to date purport to have established that by age 13 there is a significant difference in mathematical ability between the sexes and that it is especially pronounced among high-scoring exceptionally gifted students, with boys outnumbering girls 13 to 1 (Benbow & Stanley, 1983), whereas others have argued the opposite: that very little difference exists, if any, and that when a difference is detected it favors boys only slightly (Fennema & Carpenter, 1981). According to Schildkamp-Kiindiger (1982), reporting on research carried out in nine countries, sex-related differences in achievement have been found to vary considerably both within and among countries.

Male/Female Differences in Mathematical Ability: A Function of Biological Sex or Perceived Gender Role?

The effects of sex referents in test items and subjects' perceived gender roles were assessed in an attempt to explain sex differences in mathematics performance. The arithmetic subtest of the Wechsler Adult Intelligence Scale (WAIS) was administered to 50 male and 145 female college students. Test items were experimentally manipulated so that their orientation was either masculine, feminine, or neutral. Participants were randomly assigned to each group. No significant differences in performance were found. The Bern Sex-role Inventory was used to classify subjects as either masculine, androgynous, or undifferentiated. Irrespective of biological sex, masculine-oriented subjects performed significantly better on the WAIS arithmetic subtest than feminine oriented subjects. No other significant differences were noted. It was concluded that, for adults, personality variables appear to be a more salient factor than biological sex in explaining differences in basic mathematical skill performance.

Sex Differences in Rote-Counting Ability on Entry to First Grade: Some Observations

Currently, the issue of sex differences in mathematical abilities is of great concern. This article focuses on one early number skill: rote counting. Almost a century of research has produced equivocal results. These discrepancies might be accounted for by differences in methodology and data analysis. This report presents data on sex differences in rote-counting ability and illustrates how different data-gathering methods and different statistical treatments of the data can yield different results. Almost a century ago G. Stanley Hall (1891) included specific number skills in his survey of the content of children's minds on entering school and concluded: girls excel in space concepts and boys in numbers (p. 143). Illustrative of the findings on which this observation was based are the data on 660 boys and 652 girls entering schools in Annaberg, Germany, between 1881 and 1884. There, 69% of the boys and 62% of the girls could count by rote to 10 on entry to first grade. These were hardly grounds for an unequivocal generalization about boys being superior to girls in number abilities, but a slight trend appeared discernible. Nearly 50 years later, Buckingham and MacLatchy (1930) surveyed the number abilities of children entering Grade 1. They concluded that the 6-year-old girls consistently surpassed the 6-year-old boys in counting abilities. However, a higher percentage of boys than girls counted to 100. Recent research on similarities and differences between boys and girls on early counting has been inconclusive and inconsistent in its findings. No differences during the preschool or early school years have been reported in a number of reports and reviews (e.g., Brace & Nelson, 1965; Fuson, Richards, & Briars, 1982; Maccoby, 1966; Maccoby & Jacklin, 1974; Mitchell, 1981; Tavris & Offir, 1977). Performance differences favoring girls have been reported by Aiken (1971) and Rea and Reys (1970). The Gesell Institute's position remains that differences between boys and girls do exist during early school years and that girls' performance tends to be more advanced (Ames, Gillespie, Haines, & Ilg, 1976). Although data on similarities and differences between boys and girls on

Ratios exaggerate gender differences in mathematical ability.

Ratios exaggerate gender differences in mathematical ability.

Women and Mathematics: Does Research Matter?

On Monday, March 23, I was in a somewhat unusual and comfortable situation for a university professor. (Perhaps one should really substitute the w6rd lazy for comfortable.) I had written a chapter for the 1982 NCTM Yearbook on the middle school, and it could serve as my NCTM speech at St. Louis. True, I had not said anything very new, innovative, or controversial; but after all, this was the third year in a row that I had talked about sex-related differences at NCTM, so no one could expect me to have much new information or insight. Then, as I was reading the newspaper and having a leisurely cup of tea before going to school, I read the following: Due to evolutionary factors, males are also better at doing math problems . (Wisconsin State Journal, March 23, 1981). Almost immediately, my feeling of comfort fled, and I was made aware once again of how research, used well or misused effectively, can affect the lives of many. This quote is a direct result of research and its reporting, which I believe will have a deleterious effect on the learning of mathematics by girls. It is a result of an article published in Science in December 1980, entitled Sex Differences in Mathematical Ability: Fact of Artifact? (Benbow & Stanley, 1980).' In this article, data were presented from the Study of Mathematically Precocious Youth that show sex-related differences on the Scholastic Aptitude Test-Mathematics (SAT-M) in several large samples of highly gifted seventhand eighth-grade students. In each of six testings done from March 1972 to January 1979, boys had higher scores than girls, and a larger percentage of boys than girls scored above 600, This is not a new finding. What is new in the Benbow and Stanley article is how they attributed causation of the differences they found. According to Benbow and Stanley, since boys and girls have received the same mathematical education, the environmental factors are equivalent. Therefore, Benbow and Stanley conclude inherent factors must be responsible for the differences.

Spatial visualization and sex differences in quantitative ability

The hypothesis that sex differences in spatial visualization ability might account for sex differences in mathematical ability was supported for a group of 183 male and 81 female college students. With spatial visualization statistically controlled, no significant sex differences in Quantitative Scholastic Aptitude Test (QSAT) scores was found; including sex as a predictor variable increased the variance explained by less than 1%. Although the slope of the regression of mathematics on spatial visualization did not differ as a function of sex, males were somewhat more predictable than females. As the OSAT of both males and females high on spatial visualization was more predictable than the QSAT of those scoring less well, it appears that the sex difference in predictability is due to males having higher spatial ability than females.

Evidence of a detrimental effect of extrinsic incentives on breaking a mental set

College students were either rewarded ($1.50) or not for solving a series of 10 water-jar problems. The first 9 of these were designed to establish a set for a relatively complicated, three-jar solution (B − A − 2C). The 10th problem was a set breaker which required that subjects discover a simple (A-C) solution. The mental activities needed to produce a solution to the two types of problems (Problems 1 to 9 and Problem 10) were, therefore, different and one interest was in seeing whether reward would be detrimental for performance on both types of problems. It was not. Poorer reward group performance was obtained only on Problem 10. This result was not due to between-group differences in mathematical ability, and explanations in terms of differences in time taken to check answers or concern over quality of performance were considered and discounted. Measures of intrinsic interest (subject evaluations of the task and a measure of willingness to volunteer for future research) failed to support the belief that interest differences account for performance differences.