Observing "Bold Problem-Solving" Behaviors in High-Achieving Boys and Girls: Findings, Issues, and Reflections

• In Event: “Bold Problem Solving” and Spatial Skills: Two Important Constructs for Gender Equity in Mathematics Education

Abstract

Paper #2 describes researchers’ attempts to measure Bold Problem Solving via survey items. Paper #3 found that self-reported Bold Problem Solving approaches helped explain gender differences in problem solving performance. In this paper, we go beyond students’ self reports and examine whether “boldness” can be observed in students as they solve challenging problems. Specifically, this exploratory study examines the question, “How do the observed problem-solving approaches of high-achieving male and female students differ?”

Methods
32 high-achieving eighth graders (a subset of the sample from Papers 2 and 3) participated in think-aloud interviews while completing five multiple-choice items (see Figure 2 for example item). The timed assessment, limited to 15 minutes, consisted of challenging SAT items with previously demonstrated gender differences (Gallagher & DeLisi, 1994). Students’ voices and writing were recorded using LiveScribe pens,. Data were coded for the strategy used, the number of strategies attempted, and the productivity of their work. Strategy codes were adapted from Gallagher and DeLisi (1994).
Each problem was coded by two researchers. Students’ codes were averaged across the five problems and compared by gender using independent samples t-tests.

Results
No significant gender differences were detected in the number of strategies tried or productivity. However, boys used the “assign values to variables” strategy more than did their female peers (although not significant after adjusting for multiple comparisons). Boys and girls used other problem-solving strategies at about the same rates (Table 4).
However, two striking findings emerged that were not intended foci of the study. First, the 32 students averaged one fewer correct answer than their 44 peers assessed in a traditional testing environment (despite similar prior SSAT scores). Gender differences were similar in magnitude for both conditions (Think-aloud: M—2.40 versus F—1.45 items correct; Traditional: M—3.40, F—2.40). This suggests the behaviors observed when students are asked to think out loud may not reflect students’ typical approaches. This could explain the lack of close correlation between students’ self-reported “bold” behaviors on the survey items and coders’ observations of non-routine approaches (as will be explained more in the full paper).
Second, in our attempts to categorize students’ strategies and to consider the correctness and “boldness” of those strategies for each item (see Table 5 for example), it became clear that whether “assigning values to variables” was an unproductive, random process or a strategic, insightful process (and should therefore be coded as “logic, estimation, or insight”) depended on the problem and the values chosen. Results point to the limits of Gallagher and DeLisi’s strategy codes for studying “boldness.”

Significance
Although results from Papers 2 and 3 demonstrate that self-reported bold problem-solving behaviors vary by gender and predict mathematics performance, observing gendered patterns in students’ willingness to take mathematical risks when confronted with novel problems proved difficult. Although the small sample size and consequent lack of statistical power undoubtedly contributed to this difficulty, results suggest that future research should examine students in more natural environments and further develop “bold-related” codes specific to the mathematics problems under study.

Authors

• Martha Makowski, The University of Alabama - Tuscaloosa

• Emily Miller, West Chester University of Pennsylvania