Reply to the Commentaries on the Math-Fact Retrieval Hypothesis

Geary and Wigfield and Brynes (this issue) point out a number of limitations of the math-fact retrieval hypothesis that we agree with. For instance, we acknowledge that whereas the correlational evidence we offer in our article (this issue) provides suggestive evidence for a link between math-fact retrieval and gender differences in math test performance, that evidence is not compelling. We also acknowledge that even if it is the case that math-fact retrieval is one of the cognitive mechanisms responsible for the gender differences in math performance, there are still many aspects of gender differences in math performance that need to be understood. We also point out a number of areas where we disagree. Most prominently, we do not believe that the spatial cognition hypothesis or affective/motivational hypotheses account for two significant literatures—gender differences in test performance and gender differences in grade performance. We discuss the basis for our beliefs and close with a discussion of the need for intervention research that will resolve some of the issues discussed in the series of articles in this issue. At the end of the article we also present a very speculative hypothesis that would knit together all of the positions presented in the articles in this issue of CEP.     

Sex Differences in Mathematical Abilities: Commentary on the Math-Fact Retrieval Hypothesis

The hypothesis that a male advantage in speed of math-fact retrieval underlies the sex difference, favoring males, in mathematical abilities is unique and provocative. However, the hypothesis does not provide an explanation for the male advantage in mathematical domains, such as geometry, that do not require arithmetic, nor does it accommodate the sex differences in social and occupational interests that contribute to the sex difference in mathematical achievement. An alternative hypothesis focusing on the sex difference in three-dimensional spatial cognition is favored over the math-fact retrieval hypothesis.     

A Sex Difference by Item Difficulty Interaction in Multiple-Choice Mathematics Items Administered to National Probability Samples

A 1998 study by Bielinski and Davison reported a sex difference by item difficulty interaction in which easy items tended to be easier for females than males, and hard items tended to be harder for females than males. To extend their research to nationally representative samples of students, this study used math achievement data from the 1992 NAEP, the TIMSS, and the NELS:88. The data included students in grades 4, 8, 10, and 12. The interaction was assessed by correlating the item difficulty difference (b_male− b_female) with item difficulty computed on the combined male/female sample. Using only the multiple-choice mathematics items, the predicted negative correlation was found for all eight populations and was significant in five. An argument is made that this phenomenon may help explain the greater variability in math achievement among males as compared to females and the emergence of higher performance of males in late adolescence.     

More Similar Than Different: Gender Differences in Children's Basic Numerical Skills Are the Exception Not the Rule

This study investigates gender differences in basic numerical skills that are predictive of math achievement. Previous research in this area is inconsistent and has relied upon traditional hypothesis testing, which does not allow for assertive conclusions to be made regarding nonsignificant findings. This study is the first to compare male and female performance (N = 1,391; ages 6–13) on many basic numerical tasks using both Bayesian and frequentist analyses. The results provide strong evidence of gender similarities on the majority of basic numerical tasks measured, suggesting that a male advantage in foundational numerical skills is the exception rather than the rule.     

Mathematics achievement and gender: A longitudinal study of selected cognitive and affective variables [grades 6–12]

This study examined the relationship of selected cognitive and affective variables to mathematics achievement for a random sample of 60 students as they progressed through 6th, 8th,10th and 12th grades. A consistent gender difference was found for stereotyping mathematics as a male domain. No consistent significant gender difference between means was found for spatial skills, verbal skill or mathematics achievement. Confidence, verbal skill and spatial visualization were each consistently positively correlated with mathematics achievement for both males and females. No gender difference was found for these correlations. However, spatial skills alone were found to be consistent significant predictors of mathematics achievement for females each year of the study, but not for males. Verbal skill was a consistent significant predictor of mathematics achievement for males, but not for females. The results of this study could lead to a reevaluation of the hypothesis that spatial skills help boys achieve in mathematics.     

Cognitive style and gender differences in children’s mathematics achievement

Males are often found to outperform females in tests of mathematics achievement and it has been proposed that this may in part be explained by differences in cognitive style. This study investigated the relation between Wholistic-Analytic and Verbal-Imagery cognitive style, gender and mathematics achievement in a sample of 190 Australian primary school students aged between 8–11?years (M?=?9.77, SD?=?1.05). It was hypothesised that males would outperform females in mathematics achievement tests, and that gender would interact with cognitive style on mathematics performance. A significant gender/cognitive style interaction was found. Boys with an Analytic/Imagery style achieved significantly higher results than the girls with an Analytic/Imagery style, supporting the contention that certain cognitive styles affect boys and girls mathematics performance differently. Implications of results and strategies for improving mathematics achievement among girls are discussed.     

Motivational and cognitive test-taking strategies and their influence on test performance in mathematics

A structural equation model of relationships among testing-related motivation variables (test value, effort, self-efficacy, and test anxiety), test-taking strategies (test tactics and metacognitive strategies), gender, and math test performance were examined with a sample of 10th graders (N = 438; 182 males and 256 females). In general, motivation variables influenced the use of test-taking strategies and demonstrated stronger impacts on math performance than did test-taking strategies. Gender differences were found in self-efficacy and test anxiety. With a few surprising but culturally relevant results that warrant further investigation, the current study extended previous works on antecedents of academic achievement to testing situations within the self-regulated learning theory.     

Gender stereotype endorsement and achievement-related outcomes: The role of competence beliefs and task values

In most Western societies, males are stereotyped as having stronger mathematical abilities than females whereas females are stereotyped as having stronger verbal abilities than males. Exposure to negative ability stereotypes reliably undermines performance in laboratory experiments, yet the mechanisms by which such stereotypes may influence boys’ and girls’ achievement outcomes in the more naturalistic setting of primary and secondary school remain unclear. The current study evaluated a hypothesis suggested by expectancy-value theories (e.g., Eccles & Wigfield, 2002): the relationship between stereotypes and achievement outcomes is importantly mediated by a student’s perceived competence and his or her valuation of the domain in question. We tested the hypothesis by examining the career intentions and grades of 762 sixth and eighth graders. As expected, even after controlling for prior achievement, stereotype endorsement primarily predicted grades and career intentions indirectly, through students’ competence beliefs and task values. These results suggest that stereotypes predict achievement-related outcomes most clearly when students internalize them.     

Homework Goal Orientation Scale: Measurement invariance and latent mean differences across gender and grade level

The current study validated the Homework Goal Orientation Scale (HGOS) for secondary school students. Results revealed that HGOS consisted of two distinct but related subscales: mastery‐approach and performance‐approach. Given satisfactory measurement invariance, the latent mean differences were then examined across gender (males vs. females) and grade level (7th vs. 9th). Findings showed no statistically significant mean differences across gender and grade level. Finally, consistent with theoretical expectations, compared with performance‐approach, mastery‐approach was more strongly associated with homework effort, homework emotion regulation, homework completion, and math achievement.     

GENDER DIFFERENCES IN ACHIEVEMENT IN A LARGE,NATIONALLY REPRESENTATIVE SAMPLE OF CHILDREN AND ADOLESCENTS

The purpose of this study was to investigate developmental gender differences in academic achievement areas, with the primary focus on writing, using the child and adolescent portion (ages 6–21 years) of the Kaufman Test of Educational Achievement—Second Edition, Brief Form, norming sample (N = 1,574). Path analytic models with gender, parent education, age, age², and gender‐by‐age moderation as predictors of reading, writing, and math were used to test for gender differences and for the influence of development on these differences. A small but consistent advantage was identified for females in reading. No gender differences were detected in math. The most important results of the present study pertain to a gender gap in writing in favor of females that increased as a function of age. Male students are at greater risk for writing failure than are females.     

The Contribution of Memory and Anxiety to the Math Performance of College Students with Learning Disabilities

The impact of memory and anxiety on math performance was analyzed in a sample of 115 college undergraduates, all of whom had a diagnosed learning disability. The direct effects of memory and anxiety on math performance were first examined, followed by an examination of whether anxiety moderates the relationship between memory and math. Both memory and anxiety were found to directly affect math performance. Additionally, anxiety served as a moderator of the relationship between memory and math for most, but not all, measures of math achievement. The moderating effect of anxiety was stronger for long-term retrieval than for short-term memory. The relationships between memory, anxiety, and math were not significantly different for males and females. These findings suggest that, when working with individuals who have low anxiety but poor memory, enhancing memory strategies may be effective for remediating problems in math. However, for those with high levels of anxiety, it may be more efficacious to first ameliorate the anxiety, as working on memory may have a negligible effect on math performance for these individuals.     

Academic Effort and Achievement in Science: Beyond a Gendered Relationship

This study employs the 2004 School Achievement Indicators Program (SAIP) data to examine whether academic effort manifested by greater investments in school and homework does result in higher literacy scores in science for Canadian students. The study compares four gender–immigrant profiles: Canadian-born males, immigrant males, Canadian-born females, and immigrant females on their scores on teacher-assigned grades in science and on the SAIP science literacy test, and across a range of dispositions, beliefs, and behaviors suggested in the literature as predictive of achievement in science. Study findings show that Canadian-born students, particularly boys, have higher performance in the science literacy test despite their lower achievement in the science classroom and the least investments of time in doing science homework. In contrast, immigrant female students demonstrate the highest academic effort and achievement in science courses which are not matched by similar results in the science literacy test. We discuss these results in relation to different socialization experiences with science and technology that limit female and immigrant students’ abilities to transfer knowledge to new situations that have not been learned in the classroom.     

Self-Regulation and Academic Measures Across the Early Elementary School Grades: Examining Longitudinal and Bidirectional Associations

ABSTRACT

This study evaluated the association between children’s (N = 301) self-regulation and math and reading achievement in kindergarten, 1st grade, and 2nd grade. Children’s self-regulation was assessed using the Head–Toes–Knees–Shoulders (HTKS) task (involving control of gross body movements) and a computerized continuous performance task (CPT; assessing primarily inhibitory control) in kindergarten, 1st grade, and 2nd grade. Research Findings: Based on cross-lagged structural equation panel models, HTKS task performance positively predicted later math and reading achievement. Math achievement significantly and positively predicted later HTKS and CPT scores. Earlier math and reading achievement moderated the association between CPT scores and later math and reading achievement; inhibitory control–based self-regulation assessed with the CPT predicted higher math or reading achievement in subsequent grades for children with lower math or reading achievement in prior grades. Performance on the CPT moderated the paths from HTKS scores to later reading achievement; behavioral self-regulation assessed with the HTKS task predicted higher reading achievement in subsequent grades for children with low or average CPT performance in prior grades. Practice or Policy: Results from this study have the potential to inform targeted academic interventions focused on enhancing self-regulation in school contexts. The findings highlight the utility of assessing multiple measures of self-regulation.     

Career Decisional States of Australian and South African High School Students

The influence of contextualfactors on the career decision states of 429South African and 623 Australian male andfemale students in grades 8 to 12 wasinvestigated. The results for both nationalsamples on the Career Decision Scaledemonstrate that grade, gender, and theinteraction of grade and gender impact on thedevelopmental progression of career decisionbehaviour. Gender differences across nationswere more pronounced for males than females.Both South African and Australian students aremore decided in lower grades. Internationaldifferences suggest that South African studentsare less certain and evidence greaterindecision than Australian students. Theimplications for educational decision pointsand career education practices are discussed.     

Gender differences in inference generation by fourth‐grade students

The purpose of this study was to determine if there are gender differences among elementary school‐aged students in regard to the inferences they generate during reading. Fourth‐grade students (130 females; 126 males) completed think‐aloud tasks while reading one practice and one experimental narrative text. Females generated a larger number and a greater proportion of reinstatement inferences than did males (Cohen's d = .34, p = .01; Cohen's d = .26, p = .04, respectively). In contrast, there was no evidence for gender differences in other types of think‐aloud responses. These findings suggest that males and females differ in their use of cognitive processes that underlie reading comprehension, particularly with respect to the likelihood of retrieval of information from episodic memory.     

The effect of teacher–student gender matching: Evidence from OECD countries

While some educators argue that teacher–student gender matching improves student performance, there is little empirical evidence to support this hypothesis. This paper assesses the impact of teacher–student gender matching on academic achievement across fifteen OECD countries using data from the Trends in International Mathematics and Science Study (TIMSS). One attractive feature of TIMSS is that it provides information on test scores and teacher characteristics, including gender, for both math and science thereby allowing for student fixed effects estimation. The results provide little support for the conjecture that students benefit from teacher–student gender matching.     

The performance of college students on piaget-type tasks dealing with distance,time, and speed

Research was done to probe and extend Piaget's theory of the conception of speed. Specifically tested was the hypothesis that there is no hierarchical relationship in performance on the following Piaget-type tasks: conservation of distance, asymmetric series of speeds, one-to-many (circular) speeds, symmetric speeds, time, and proportional reasoning. The research also tested the gender-related performance on these six tasks. One hundred freshman and sophomore college students were shown demonstrations of equipment individually for each of the six tasks. A set of open-ended questions based on the demonstrations was administered to each subject in a 45-minute interview. Subjects were scored as “pass” on a given task if they manipulated objects in certain ways and gave specific types of explanations. A scalogram analysis of the data yielded a z-score of — 3.7 which indicated that subjects passed the task in a certain sequence. The tasks were found to form a unidimensional scale and to be increasingly difficult in the order listed above. A chi-square test for two independent samples showed a significant difference (alpha = 0.05) in performance between males and females on all speed tasks. No significant differences in performance between males and females were found for the distance and time tasks.     

Two-year study relating adolescents' self-concept and gender role perceptions to achievement and attitudes toward science

To assess the developmental relationship of perceptions of self-concept and gender role identification with adolescents' attitudes and achievement in science, a two-year longitudinal study was conducted. A battery of instruments assessing 16 dimensions of self-concept/gender role identifications was employed to predict students' achievement and attitudes toward science. Specific behaviors studied included self-concept in school and science and mathematics, attitudes toward appropriate gender roles in science activities and careers, and self-perceptions of masculine and feminine traits. One hundred and fifty-five adolescents, enrolled, respectively, in the seventh and eighth grades, participated in the study. Through Fisher z transformations of correlation coefficients, differences in relationships between these two sets of variables were studied for males and females during the two years. Results indicated that students' self-concepts/gender role perceptions were related to both achievement and attitudes toward science, but more related to attitudes than achievement. These relationships became more pronounced for students as they matured from seventh to eighth graders.     

Class size effects on mathematics achievement in Cyprus: evidence from TIMSS

Class size reduction has been viewed as one school mechanism that can improve student achievement. Nonetheless, the literature has reported mixed findings about class size effects. We used 4th- and 8th-grade data from TIMSS 2003 and 2007 to examine the association between class size and mathematics achievement in public schools in Cyprus. We employ instrumental variables methods, and take advantage of a regression discontinuity design to examine causal effects of class size on mathematics achievement. The results indicate a non-significant relationship between class size and mathematics achievement in 8th grades. However, there is evidence of positive class size effects in 4th grade. The gender gap is significant and favoured males in 4th grade and females in 8th grade. SES indexes such as parental education and items in the home are positively and significantly related to mathematics achievement. Teacher and school variables are not significantly related with mathematics achievement.