Math and Metacognition: Resolving the Paradox Shanna Erickson ([email protected]) Evan Heit ([email protected]) University of California, Merced Conclusions: Predicted Postdicted Mathematics Biology Literature Mathematics Biology Literature Mathematics Postdicted Actual Predicted Predicted Postdicted Results for males 0 - All Actual - Undergraduate students are generally overconfident. Students were overconfident in mathematics, bringing into question the presence of math anxiety. Further experiments incorporating a standardized measure of math anxiety (MARS) indicate that high school and undergraduate students can be both math anxious and overconfident. Results are relevant for applications in cognitive science and education. Students are overconfident in mathematics, yet are also math phobic. These views pose two strong deterrents for students to seek practice and improvement in mathematics. If students are overconfident in their mathematical abilities and have anxiety about mathematical tasks, they have little incentive to study the subject. This reluctance likely carries over to other science, technology, and engineering subjects that require a significant amount of math background. Average Score (%) - Literature 0 Average Score (%) - General overconfidence across all domains except for biology. Highest overconfidence was in mathematics. Overconfidence higher for males. Best metacognitive calibration was females’ self-perception of mathematics performance. Lower-performing participants were worse judges of ability. Improved metacognitive judgments after taking a test. Greatest beneficial adjustment was for mathematical ability. Biology Results for females Key results: - Actual All 10 20 30 40 50 60 70 Participants were UC Merced undergraduates (n = 46). Participants took three shortened SAT II Subject Tests. Recorded self-estimates of performance before and after each test. 10 20 30 40 50 60 70 - 0 Experiment: 10 20 30 40 50 60 70 Is metacognition domain specific? Based on presence of math phobia, lower confidence in mathematics was expected in comparison to other academic domains. Results by test Average Score (%) It is common that people generally display glaring overconfidence in selfperception of their ability (1, 2). A possible exception to the general overconfidence phenomenon is the occurrence of math phobia (3). This fear of math has been linked to lower educational performance (4) and can further adversely impact student perceptions of other learning avenues that are math-based. All 0 5 10 Mathematics Test Score 15 15 5 10 male female y=x r = 0.69 r = 0.43 0 r = 0.02 r = 0.38 Calibration after math test Postdicted Mathematics Test Score 15 5 10 male female y=x 0 Predicted Mathematics Test Score Calibration before math test 0 5 10 Mathematics Test Score 15 References: 1. Dunning, D., Johnson, K., Ehrlinger, J., & Kruger, J. (2003). Why people fail to recognize their own incompetence. Current Directions in Psychological Science, 12(3), 83-87. 2. Kruger, J., & Dunning, D. (1999). Unskilled and unaware of it: how difficulties in recognizing one's own incompetence lead to inflated self-assessments. Journal of Personality and Social Psychology; Journal of Personality and Social Psychology, 77(6), 1121. 3. Furner, J. M., & Berman, B. T. (2003). Review of Research: Math Anxiety: Overcoming a Major Obstacle to the Improvement of Student Math Performance. Childhood education, 79(3), 170-174. 4. Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5),181-185.