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“Should I be concerned about my students’ attitudes toward mathematics?”
This is one of the questions researchers sought to answer when they set out to analyze the 2012 Programme for International Student Assessment (PISA) results. That year, 510,000 high schoolaged students (specifically 15 and 16yearolds) in 65 countries and economies, including the United States, participated in the assessment.^{1}
The question is especially important when we consider how few students say they study mathematics because they enjoy it—only 38% of students in the 34 Organisation for Economic Cooperation and Development (OECD) countries said they did. Moreover, 43% of students believed they were not good at math and 59% often worried that math class would be difficult for them.^{2}
So what is the answer? Do students’ attitudes about math matter?
The PISA researchers concluded that, yes, we should be concerned about students’ feelings toward math—and they’re not the only experts who say so.
How does math motivation relate to math achievement?
High school
A separate PISA analysis reviewed the association between math motivation and math achievement in high schoolaged students. This study looked at two different types of motivation—intrinsic, which described if students enjoyed and were interested in math, and instrumental, which described if students valued math for its role in their education or career goals—and found both correlated to math achievement.^{3}
On average, students in the bottom quarter of the intrinsic math motivation index scored 472, well below the international average of 494, while students in the top quarter scored 521—well above the average. For instrumental math motivation, students in the bottom quarter had an average score of 477 and students in the top quarter had an average score of 519.
On average, across all student groups, an increase in one “unit” of intrinsic math motivation was associated with an increase of 19.4 points on the math assessment. Similarly, an increase in one “unit” of instrumental math motivation was associated with math scores rising by 17.6 points. (To put this data in perspective, there was a difference of about 2.5 “units” of motivation between the bottom and top quarters for both intrinsic and instrumental motivation.)
Middle school
The relationship between math motivation and math achievement is not unique to high school; it can be seen among middle school students as well. A study of roughly 3,000 eighthgrade students across the United States found students’ attitudes toward and interest in math had a “substantial direct effect” on their math achievement.^{4}
While general motivation toward school (as measured by attendance and punctuality) also had a direct effect on math achievement, it was smaller than that of math attitude. Motivation toward classwork, as measured by whether students showed up prepared for class, had no significant direct effect on math achievement. However, both affected math attitude—the authors suggested attendance and participation in classes exposed students to math instruction and mathrelated experiences that influenced math attitude—and thus indirectly affected math achievement.
Math attitude didn’t just affect math achievement. It also appeared to play a role in the effort students put into mathematics. Students with a more positive attitude toward math were more likely to spend more time on their math homework—which, in turn, had a direct effect on their math achievement. (Classwork motivation also had an effect on time spent on homework and influenced math achievement via this route as well.) Overall, the researchers’ fourvariable model explained a “significant amount of variance” (46%) in mathematics achievement.
Elementary school
What about elementary school, when students are just beginning their math journeys? Once again, it seems students’ feelings toward math may play a role in achievement. One study of second and third graders found that students who felt nervous when answering math questions had lower performance than students who had little or no math anxiety. The authors concluded that “math anxiety was significantly and negatively correlated with math proficiency.”^{5}
(Note that math anxiety is not quite the same as a negative attitude toward math; anxiety is more emotional whereas attitude is more related to students’ motivations and thoughts. However, the two tend to correlate quite closely with each other.^{6})
What are students’ attitudes toward math?
Among the OECD countries that participated in the 2012 PISA, the United States performed below average in mathematics, ranked 27 out of 34.^{7} When we examine American students’ attitudes toward math, we also see low levels of math motivation.^{3}
In terms of intrinsic motivation, only 34% said they enjoyed reading about math and 37% said they did math because they enjoyed it. A higher number, 46%, said they looked forward to their math lessons—but the same number also said their teacher had not explained math concepts well that week. While half the students said they were interested in the things they learned in math class (50%), nearly as many said their teacher did not get students interested in the material (47%).
For instrumental motivation, American students generally recognized the importance of math for college and career success. Four out of five believed that learning math would help them get a job and the same number felt math would improve their career prospects in general. A large majority, 81%, also said math was important because it would help them in the future. However, despite recognizing the key connections between math and future success, only 48% of students felt math was one of their best subjects, 46% said they weren’t good at solving math problems, and 32% admitted to making bad guesses on math quizzes. Perhaps more worryingly, 23% felt helpless when doing math problems and 57% often worried that they would have a difficult time in math class.
There is good news, too: Almost all American students (95%) believed they can succeed in math if they put in enough effort! Most also felt they were in control of their test scores: Only 28% felt they would do poorly on a math test even if they studied for it and 62% even said they would study harder than required for math classes.
Students aren’t wrong to believe in the power of effort. An analysis of nearly 7,000 American high school students found that effort had a “significant, positive effect on math gains.” In fact, across all four tracks studied—honors/advanced, academic, general (reference), and vocational/other—effort had significant, positive effects on achievement in every track. The results further indicated that the effects of effort on learning are the same for all students, regardless of their track.^{8}
Another important finding of this study was that, while prior effort did have an effect on current achievement—learning is cumulative, after all—the effect was much smaller than that of current effort. The authors concluded that students who try harder learn more, regardless of how much effort they exerted in previous years. In other words, it’s never too late for students to see the benefits of trying harder, even if they didn’t do so in the past.
It seems that our students have great potential, if only we can harness it.
How can we motivate students to boost math achievement?
Students are as varied as the math problems they’re asked to solve, which means there is no single approach that’s guaranteed to work for all of them. Still, researchers have detected patterns and approaches that seem to help the majority of students develop positive attitudes toward math, reduce math anxiety, and increase math achievement. Here are some researchbased recommendations from notable math experts.
The PISA researchers mentioned at the beginning of this post have several suggestions for educators,^{2} such as:

Tell students what they have to learn, what is expected of them, and how they are progressing.

Provide students with ongoing, informal feedback on their progress (using a formative assessment process).

Encourage students to work in small groups to build confidence.

Use computers in mathematics lessons to increase motivation.

Explore innovative teaching tools for math, including dynamic graphical, numerical, and visual technology applications.

Make math lessons personally relevant to learners.
Dr. Carol S. Dweck, one of the world’s leading researchers in the field of motivation and the Lewis and Virginia Eaton Professor of Psychology at Stanford University, suggests that improving students’ math mindsets can also improve their math achievement.^{9} Her recommendations include:

Encourage a growth mindset and teach students that the brain is like a muscle that gets stronger and works better the more it is exercised.

Present “math geniuses” and famous mathematicians as people who loved and were dedicated to their craft.

Recognize and admire students who seek out challenges, work hard, and learn from their mistakes.

Compliment effort, especially when students work hard but don’t do well—and express confidence that students can and will reach their goals if they keep working on them.
Two cognitive scientists—Daniel T. Willingham from the University of Virginia and Sian Beilock from the University of Chicago—examined how math anxiety develops to provide educators with recommendations for preventing or reducing its impact on students’ math performance.10 They offered these suggestions:

Ensure students master fundamental skills, as proficiency with basic numerical and spatial processing may prevent math anxiety from developing in young students.

Focus on how to teach math concepts rather than on the math concepts themselves, because strong teaching strategies can lessen educator anxiety—and lessanxious teachers have lessanxious students.

Give students the time and space to work through their answers, since time pressure can increase students’ math anxiety.

Provide students with the opportunity to write freely about their emotions about math exams prior to taking them.

Suggest concrete strategies for approaching a particular problem differently, especially when students struggle.
Another expert with great advice for teaching math and improving achievement is Margaret (Peg) Smith, emeritus faculty at the University of Pittsburgh, author/coauthor of more than 75 books and articles, and allaround living legend in math education. Last year, we were lucky enough to have Dr. Smith join us and share her expert insights in an enormously popular webinar, Mathematical Discourse: What It Takes & How to Do It. Be sure to watch the recording for stepbystep strategies you can start using today!
Although a positive attitude toward math cannot replace time spent learning and practicing math skills, it can certainly provide the fuel students need to keep going when they encounter new or challenging math concepts. Imagine what your students might accomplish if they approached math with the power of a positive attitude!
References
^{1} Organisation for Economic Cooperation and Development (OECD). (2014). PISA 2012 results in focus: What 15yearolds know and what they can do with what they know. Retrieved from http://www.oecd.org/pisa/keyfindings/pisa2012resultsoverview.pdf
^{2} Organisation for Economic Cooperation and Development (OECD). (2016). Ten questions for mathematics teachers … and how PISA can help answer them. Paris, France: OECD Publishing.
^{3} Organisation for Economic Cooperation and Development (OECD). (2013). PISA 2012 results: Ready to learn: Students’ engagement, drive and selfbeliefs (Volume III). Retrieved from http://www.oecdilibrary.org/education/pisa2012resultsreadytolearnvolumeiii_9789264201170en
^{4} Singh, K., Granville, M., & Dika, S. (2002). Mathematics and science achievement: Effects of motivation, interest, and academic engagement. The Journal of Educational Research, 2(6), 323332.
^{5} Wu, S. S., Barth, M., Amin, H., Malcarne, V., & Menon, V. (2012). Math anxiety in second and third graders and its relation to mathematics achievement. Frontiers in Psychology, 3, 162, 111.
^{6} Dowker, A., Sarkar, A., & Looi, C. Y. (2016). Mathematics anxiety: What have we learned in 60 years? Frontiers in Psychology, 7, 508, 116. Retrieved from http://doi.org/10.3389/fpsyg.2016.00508
^{7} Organisation for Economic Cooperation and Development (OECD). (n.d.). Programme for International Student Assessment (PISA) results from PISA 2012: United States country note. Retrieved from http://www.oecd.org/unitedstates/PISA2012resultsUS.pdf
^{8} Carbonaro, W. (2005). Tracking, students’ effort, and academic achievement. Sociology of Education, 78(1), 2749.
^{9} Dweck, C. (2008). Mindsets and math/science achievement. New York, NY: The Opportunity Equation.
^{10} Beilock, S. L., & Willingham, D. T. (2014). Ask the cognitive scientist: Math anxiety: Can teachers help students reduce it? American Educator. Retrieved from http://www.aft.org/pdfs/americaneducator/summer2014/Beilock.pdf