“In all 34 countries studied, overconfident students were less likely to have above average math scores, and under-confident students were more likely to have above average math scores,” says UB professor of learning and instruction Ming Ming Chiu, the lead author of an international study that examined this connection and offers recommendations for parents and teachers.
According to the study, students who can accurately gauge their strengths and weaknesses are more likely to recognize how much more work and help they need to achieve their goals. On the other hand, “students who overestimate their mathematics skills often do too little homework, do not ask for help and ultimately perform poorly on both school tests,” Chiu says.
The study, “Relations of mathematics self-concept and its calibration with mathematics achievement: Cultural differences among fifteen-year-olds in 34 countries,” was the first large-scale international study of almost 90,000 students’ overconfidence and math levels (including nearly 4,000 U.S. students). It was co-written by Robert Klassen, associate professor at the University of Alberta’s Department of Educational Psychology, and is published in the winter edition of the professional educators’ journal Learning and Instruction.
The researchers used data from the Organization for Economic Cooperation and Development’s Program for International Student Assessment.
In the study, Chiu and Klassen found large differences in confidence levels and mathematics levels across countries. Brazilian students showed the most overconfidence (88 percent) and the lowest math score (333). In contrast, only 16 percent of South Korean students were overconfident, and they had the third highest math score (548). In comparison, 57 percent of U.S. students were overconfident, and they scored somewhat below average (493; average is 500).
The study is particularly important because mathematics is a “gateway to many professions (for example, business and engineering) and critical to daily financial decisions, according to Chiu. “Understanding numbers is an absolute must for many high-paying jobs and making smart money decisions,” he says.
The two researchers recommend that parents and teachers help their children and students become appropriately confident and learn vital mathematics ideas and skills by doing the following:
• Check Math Answers. Unlike other subjects, mathematics allows students to put their answer back into the original problem to see if a result makes sense. If a question asks, “How much money do Jack and Jill have if they each owe ten dollars?” and a student’s computation yields 100, clearly the answer is wrong and can easily be checked. These checks help students test the validity of their answers and to develop an appropriate level of self-confidence, Chiu says.
• Apply Math to the Real World. Ask students to apply the ideas they’ve learned that day to the world around them. For example, “If I know the length of the shadow of my house and its angle with the sun, I can figure out how tall it is.” These applications help students recognize how well they understand the math, Chiu says.
• Compare With Peers. Students should use classmates as a ruler to measure their own strengths and weaknesses, Chiu says. (“Do I understand and solve mathematics problems as well as my classmates?”)
• Review Past Homework and Tests. Examining homework and tests, especially wrong answers, helps anchor student confidence to a suitable level and prevents overconfidence.
“Boys and richer students are more likely than other students to overestimate their mathematics abilities,” says Chiu. “Thus, they should be especially encouraged to follow the above tips.”
The University at Buffalo is a premier research-intensive public university, a flagship institution in the State University of New York system and its largest and most comprehensive campus. UB’s more than 28,000 students pursue their academic interests through more than 300 undergraduate, graduate and professional degree programs. Founded in 1846, the University at Buffalo is a member of the Association of American Universities.