Students’ math identities have a lot to do with whether they see themselves as capable of mathematics and whether they find math valuable. For the most part, math identity develops in the math classroom, through experiences of doing and learning math. This means that we have an important leverage point for shaping girls’ math identities.
What does it mean to be smart at math?
This is a question I have posed to dozens of students, teachers and parents over the past decade. The responses are generally predictable. It is someone who
- knows his or her math facts
- gets the right answer
- just "gets it"
- is fast at figuring things out.
Taken together, the answer is essentially someone who can find the right answer quickly.
Isn’t that easy to say? "Find the right answer quickly." And we see this image played out far and wide, and reinforced, through timed tests, the valuing of performances of those who can memorize formulas and execute them quickly and accurately. This is the "right-answer-quick" or the RAQ view of math. This view is narrow. It invokes competition. It provides a way for a clear hierarchy, with someone at the top. It’s very observable, quantifiable and definitive – right/wrong, fast/slow. Beyond not being an accurate reflection of mathematical competence, this view of math is outright damaging to girls and young women. First, we’ll address the accuracy.
The RAQ view of being smart in math misrepresents the field of mathematics. It overemphasizes smaller problems that can be timed and have one right answer. It misses out on large areas of skills such as taking different points of view, leveraging related solutions, communicating with others, and re-representing ideas to gain new insights. The set of skills one needs to be truly proficient with mathematics is vast, varied and powerful.
But RAQ is not just inaccurate; it is also damaging.
There is evidence to suggest that girls are less likely than boys to choose to enter into a competitive environment and/or do not enjoy environments that emphasize the individual and marginalize collaboration. They (and some boys, of course, too) are not interested in the competition and elect not to compete even when they are equally competent (Niederle & Versterlund, 2010). The vision offered in most classrooms – the RAQ view of what it means to be “smart in math”– runs counter to who girls want to be and the types of participation and engagement they value and bring with them to the classroom.
Ways to be smart in math
What does it really mean to be smart in math? Or to emphasize the point: what should it mean to be smart in a math class? We seek an answer to this question in order to more accurately represent math and to help us create classroom environments that are more productive for developing positive math identities for a wider range of students, particularly girls.
When we push a little deeper, a much richer array of qualities arise for someone that is "smart in math." It is someone who
- notices patterns and similarities across examples
- is a logical thinker and can deduce new information from what’s already known
- can clearly explain her or his thinking and ideas to others
- visualizes relationships and can represent relationships in multiple ways
- can find errors and analyze how/why they occurred
- can make sense of other’s ideas and take other perspectives
RAQ skills may help support some of these too, but this list offers a more varied and more powerful set of skills. This view of math – for which there’s no easy descriptor – is not commonly represented in classrooms or in society. We’ll call it the Analyzing, Representing and Thinking view of math, or ART. Most students do not have the opportunities to experience these as consistently valued aspects of a math classroom or of math in general.
Broadening the view of what it means to be smart at math—what it means to be competent mathematically– is crucial. When there is more to being smart in a classroom than RAQ, more students see their own talents, know they can contribute in a math classroom, feel successful and develop positive math identities. To offer an oft-cited quote of Jo Boaler: "Where there are many ways to be successful, many more students are successful" (p 630). The classroom will become a place where students see that different people have different strengths. And in such classrooms, it is less likely that a highly visible, stable hierarchy of “smartness” will emerge based on the easily measurable quantities of right and quick.
Making this kind of change to the ART view of math is not easy. Teachers – with the support of their districts and communities – will need to rethink what it means to be smart and competent in math, and then find ways to have that view reflected in their teaching and assessment practices. They will have to become skilled at recognizing different ways of being smart, and pointing these out so that the class develops a culture around these valued practices. This change also requires that the tasks given to students change. If the opportunities to do math are limited to short, algorithmic problems or tasks, there will be no opportunities to elicit and recognize ART talents. The tasks must require thinking, connecting, analyzing, representing, communicating; they must support authentic opportunities to discuss what ideas or approaches make sense and why. These are tasks at which girls – and boys – excel and which invite girls to participate in challenging mathematical work.
Such efforts are well worth the investment, and they are actionable, now. Broadening the ways that students see smartness in math, and moving from the RAQ view to the ART view, will lead to more girls having positive math identities, greater achievement in math, and more accurate views of the field of math. We are all implicated in this effort, but the classroom is a crucial space where a different, and more accurate, version of what it means to be a good at math can be created. If present throughout a school, or multiple schools in a district, and ultimately in society, we could see very different outcomes in terms of girls' and all students’ math identities and future selection to pursue and participate in STEM fields.
I would like to express my gratitude to the many amazing teachers with whom I have worked and who have allowed me in their classrooms so I could learn these important lessons. --Megan
Associate Professor of Mathematics Education
For more reading on this topic please see:
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Niederle, M., & Versterlund, L. (2010). Explaining the gender gap in math test scores: The role of competition. The Journal of Economic Perspectives, 24(2), 129-144.
Boaler, J. & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110(3), 608-645.
