An Analysis of Gender and the Mathematical Reasoning Ability Sub-Skill of Analysis-Synthesis

Article excerpt

The difference between the achievement of girls and boys in mathematics has been an issue in the educational arena for more than a century. This difference has prompted researchers to focus their studies on different variables believed to be associated with mathematical achievement such as spatial ability (Casey, Nuttall, Pezaris, and Benbow, 1995), attitude toward mathematics (Vanayan, White, Yuen, & Teper, 1997), risk-taking behavior (Ramos & Lambating, 1996), personality (Weiner & Robinson, 1986), problem solving (Duffy, Gunther & Walters, 1997), parental gender stereotyping and teacher beliefs (Raymond & Benbow, 1986; Tiedemann, 2000), and genetics (Benbow, 1987; Zohar, 1998). Rather than grappling with the nature-nurture dichotomy, this study approaches the issue by exploring the variables that are associated with mathematical achievement.

One variable associated with mathematical achievement is mathematical reasoning ability. When this variable was analyzed, boys consistently outscored the girls (Benbow 1988; Mills, Abalard, & Stumpf, 1993). The research by Mills, et al (1993) found that mathematical reasoning ability could be divided into sub-skills based on the tasked required (i.e., identify if enough information is present). These sub-skills appeared to vary in their degree of gender sensitivity. "Examining differences across sub-skills, however, may ultimately prove to be more useful than considering overall scores for understanding cognitive development of males and females" (Mills, et al, 1993. p. 344). The authors point out that more research is needed to discover a delineation of basic cognitive processes that make up mathematical reasoning ability. However, a review of available literature shows no such studies have been reported.

Throughout research on gender differences in mathematical achievement, a common thread of concern emerges: boys outperform girls in the area of mathematics. Results from selected studies agree that mathematical reasoning ability consistently demonstrates this difference and that mathematical reasoning ability can be delineated into sub-skills that are individually gender sensitive. However, the delineation of these sub-skills is incomplete, as is their gender sensitivity and the age at which differences appear. Further research is warranted.

Methodology

Subjects

The subjects were elementary aged students, grades 1-5, from a moderate-sized, rural community in South Dakota. The students had been referred to the district's Gifted and Talented (TAG) program for evaluation for possible placement in the program. Selection for testing was based upon teacher recommendation and/or high score(s) on the Stanford Achievement Test. All elementary level students tested were included in the analysis regardless of placement or non-placement in the TAG program.

Instrumentation

Data for the study was gathered from the files of all students tested for the TAG program regardless of whether they qualified for placement in the program. The ability measure collected was the Woodcock-Johnson Tests of Cognitive Ability (WJTCA).

The WJTCA was developed by Woodcock, Johnson, Mather, McGrew, and Weder in 1977. It was designed to measure cognitive abilities, scholastic aptitude, and achievement. There are seven standard battery test scores plus one cluster score including: memory of names, memory for sentences, visual matching, incomplete words, visual closure, picture vocabulary, and analysis-synthesis, plus broad cognitive ability.

According to Woodcock and Johnson (1990), the analysis-synthesis subtest "is designed to measure the ability to analyze the presented components of an incomplete logic puzzle and to determine the missing components. The task primarily measures reasoning. The task involves learning a miniature system of mathematics--though this is not pointed out to the subject." (p. 21). …