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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.
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