by Francis (Skip) Fennell, NCTM President 2006-2008
NCTM News Bulletin, January/February 2007 (PDF) 

This month let’s think about self-concept and mathematics learning. Laurie Hart Reyes described in 1984 a positive self-concept in mathematics as the perception of or belief in one’s ability to do well in mathematics, or confidence in learning mathematics. Two challenges in the life of a mathematics teacher all too frequently affect students’ self-concept.

Teachers usually encounter the first challenge during a parent-teacher conference. A seemingly nice parent plops down in the chair to hear your analysis of his or her child’s work. You get midway through your carefully worded comments when the parent comes out with it—that oft-heard mathematics-nightmare phrase, “Well, ya know, I was never good in math, either.” Don’t you just love it! Do you ever wonder if the parents would say the same thing if you told them that their child couldn’t read?

Right now, virtually everyone is wondering why our nation’s students are not more competitive in mathematics internationally— from Tom Friedman (author of The World Is Flat and keynote speaker at NCTM’s 2007 Annual Meeting and Exposition) to the people interpreting TIMSS (the Trends in International Mathematics and Science Study). Yet, offhanded comments like this send a signal that it is quite acceptable if the next generation does not learn or care about mathematics.

Mathematics is not a “for nerds only” subject, but a “for everybody” subject! According to Adding It Up (2001), an influential report of the National Research Council, mathematical proficiency consists of conceptual understanding, procedural fluency, and the ability to formulate and solve problems, as well as a “productive disposition”— a “habitual inclination to see mathematics as sensible, useful, and worthwhile coupled with a belief in diligence and one’s own efficacy” (p. 116).

The second challenge that mathematics teachers face arises in the classroom. You make what you think is a brilliant presentation of important mathematics, only to have a student ask, “When am I ever going to use this stuff?” Such queries seem to be particularly troublesome to those who teach elementary and middle school mathematics. But why? Most topics taught at these levels have immediate application to a context, from using rational numbers in analyzing data to predicting crowd size in a stadium. (See the November 2006 focus issue of the Mathematics Teacher for more applications of the mathematics that students learn and teachers’ attempts to show how mathematics fits into students’ lives in meaningful ways.)

Students at the elementary school level eagerly display their interest— even their happiness—in learning mathematics. However, research has found that as they move through school, their belief in their ability to perform well in mathematics tends to decline. A recent report by Tom Loveless of the Brookings Institution entitled How Well Are American Students Learning? (online at www.brookings.edu/gs/brown/bc_report/2006/2006report.htm) suggests that reform efforts in mathematics tend to treat children’s happiness as if it were as important as their learning. This has been referred to as the “happiness factor” both in the introduction to the report and in related media coverage. The report points out that national indicators of student happiness are inversely related to achievement in mathematics. That is, countries with more confident students who enjoy mathematics do not do as well as countries that rank lower on indicators of confidence, enjoyment, and sense of relevance. The report further indicates that these qualities are not essential for the access to higher-level mathematics learning.

Although issues of culture and the value placed on mathematics within and across countries are important influences on achievement, the report gives us other factors to consider. For instance, it notes that American teachers rank high on making mathematics relevant to their students. Personally, I’d prefer to see students who enjoy mathematics, who are confident in their ability to do mathematics, and teachers who regularly strive to make mathematics come to life for their students. With that said, I agree with the Brookings Institution report’s recommendation that the mathematical intent of any activity should not be lost in attempts to make it real, relevant, or meaningful. Inventing real-life scenarios must not take away from the importance of the mathematics to be learned.

So, what’s really important here? Although we know that students who are regularly engaged in mathematics are likely to succeed, we also know that students need to see indications from others, including their parents, siblings, and peers, that mathematics is important. So, do we want the “happiness factor”? You bet. But we want it to extend beyond the walls of our classrooms and schools. We want students to value mathematics as an important subject. If students aren’t confident and don’t enjoy doing mathematics, will they elect to take more challenging mathematics courses? Will they major in mathematics or mathematics-related fields? Will they embrace mathematics as citizens or parents? Probably not, but self-concept is more than enjoyment and confidence.

I want all students to be curious about the mathematics they are learning. Curiosity encourages imagination and a genuine interest in mathematics learning. I also want students to persevere. From the earliest levels of learning mathematics, students need to “hang in there.” They should finish the assignment and come back to a particularly challenging problem. They should look for different ways to solve problems, find their own solutions, work to get the answer, and also understand why certain strategies work. And if our students enjoy the subject and approach it with curiosity and confidence as well as the perseverance that embraces struggle within mathematics learning— what then? Well, maybe our students will be more competitive on those international assessments. What do you think?