Are Positive Attitudes Key to Deeper Math Learning?

Debates over math education too often focus solely on course content or—even worse—superficial questions about course titles, at the expense of the important issues of what students are learning and how they learn it. Yet, evidence abounds that, regardless of course content and titles, actual math learning is often limited and shallow. Consider these examples: 

• A 2013 Brookings Institution report called increasing enrollment in advanced math courses such as Algebra II a “hollow victory” because it “has not coincided with students learning more math.” 
• Remedial math courses, which emphasize procedural skills, do not enhance students’ performance in college-level math courses, according to a study in Washington state. 
• College Calculus students’ belief that their high school courses prepared them to succeed in the course declined from 80 percent at the start of the semester to 55 percent by the end, according to a large national study.

If prescribing higher doses of mathematics content isn’t a remedy, other aspects of learning may be at play. Could factors such as students’ interest and self-confidence play a role? Research suggests that they can, with interesting implications for math teaching (plus a funny acronym). 

Building on prior literature, Stanford researchers studied a construct called PAM—positive attitude toward math—which includes an interest in math as well as self-perceived ability (which I’ll call confidence) in the subject, in elementary school students. They found that even when controlling for cognitive and affective factors (such as IQ, working memory, and math anxiety), PAM “uniquely predicts individual differences in children’s math achievement.” Both of PAM’s components—interest and confidence in math—contributed to students’ math achievement, independently of students’ attitudes toward school in general. 

Fostering interest and confidence in mathematics, therefore, may be an important component of improving outcomes for students who struggle in math. The Stanford study didn’t address how to do so, but a recent report sheds light on some approaches that transcend math content. 

The report from the EdInsights Center looked at six innovative 12th-grade math courses developed in partnership between California schools and public universities. Some of these classes covered traditional, algebra-intensive mathematics, and others focused more on less traditional high school topics, such as statistics, data science, and discrete math. 

Analyzing teacher perceptions, the report suggests that the new courses may be contributing to PAM: “Many students in these classes changed their attitudes about math, becoming more confident as they mastered upper-level mathematical practices associated with problem solving, teamwork, and independent thinking.”

The key difference is a shift toward student-centered instruction, the report found, supporting students to “work in groups to formulate strategies and approaches to solving problems.” Teachers also observed students “begin to understand and begin to trust the process of trial and error and communication with peers as comfortable ways to approach a thorny problem and work toward a solution.” 

While ongoing longitudinal research analyzing the subsequent outcomes for students taking the innovative courses will provide a more complete picture, teacher observations suggest that such courses have the potential to lead more students to be prepared for college mathematics. 

PAM may also help explain cases where nontraditional math courses seem to boost students’ performance in traditional math courses. For example, students who take statistics courses in lieu of traditional algebra courses can outperform remedial algebra students in higher-level math classes, even classes such as calculus that build on algebra. 

I hypothesized elsewhere that such options may serve to “warm” students up for further math rather than “cool” them off. And that is why nontraditional courses needn’t be an offramp from STEM. Far more research is needed, of course, but it’s possible that the real key is the way the courses are taught, not the content itself.