Article: Learning to See Students’ Mathematical Strengths

Skinner, A., Louie, N., & Baldinger, E. M. (2019). Learning to See Students’ Mathematical Strengths. Teaching Children Mathematics, 25(6), 338–345. https://doi.org/10.5951/teacchilmath.25.6.0338

Learning to See Students’ Mathematical Strengths
Author(s): Abbe Skinner, Nicole Louie and Evra M. Baldinger
Source: Teaching Children Mathematics , Vol. 25, No. 6 (April 2019), pp. 338-345
Published by: National Council of Teachers of Mathematics
Stable URL: https://www.jstor.org/stable/10.5951/teacchilmath.25.6.0338

339

Children who do not believe in themselves are unlikely to share their ideas, persevere through challenges, or take risks that lead to new insights.

340

Strategies to look for and try

If we want to be able to see students’ smartness, we have to give them opportunities to show it. This requires

1. (1) providing them with tasks that are rich enough to invite diverse ways of exercising creativity and strategy (see the sections on “group worthy tasks” in Featherstone et al. 2011) and

1. (2) grouping students in ways that do not carry assumptions about what students will be good at or what they will need (e.g., randomly drawing their names from a hat) (Cohen and Lotan 2014).

[Note: Student E has pointed out that they are not in the best maths group, that they are dumb because of this, and like all students can easily recognise who the ‘smart’ kids are in any topic, meaning that if they are not with the children perceived to be ‘smart’ in a topic they are by default, dumb]

Power and privilege make it easy to see some students as smarter than others.

Actively working to notice and disrupt societal views of what it looks like to be “good at math” is essential or seeing all students’ mathematical strengths and for nurturing positive mathematics identities for all students.

Strategies in action

Pg 340

• Explain how you are thinking.
• Listen to new ideas.
• Visualize in lots of ways.
• Represent (show) your thinking.
• Make connections.
• Try ideas.

341 …Baldinger noticed that Luna—a girl with an IEP and Latinx heritage—was very ready to interpret her mathematics as invalid (strategy 4). Many teachers might interpret her work that way, too; we are trained to look for students’ weaknesses so that we can help fix them.

Here are five strategies for seeing students’ mathematical strengths. As you read about the lesson, consider what it could look like for you to try out these strategies. Which ones seem easy? Which ones seem hard? How could they help you see mathematical smartness in each of your students?

1. Trust students with open-ended, multidimensional, challenging tasks.
2. Randomly assign students to partners or groups (and check your assumptions about who is successful).
3. Have explicit, inclusive conversations with students, parents, and colleagues that broaden what it means to be smart in math.
4. Work to notice power and privilege as they play out in classroom interactions.
5. Seek out critical friends to challenge and support you.

Later she called on Luna to present to the class, reiterating that she and David had done impressive thinking. A look of disbelief crossed Luna’s face, followed quickly by pride. The shift in her body language and her facial expression as she stood to make her presentation opened a new possibility for me: Luna could believe in herself as a mathematical thinker with important ideas.

342 Working with others has helped me notice things that I was not seeing on my own. Having the opportunity to observe my students while Baldinger took responsibility for instruction was powerful. I realized afterward that I had been treating Nasira and Luna differently than I treated James, and that those differences were not just a matter of individual idiosyncrasies but were related to our positions within systems of privilege and oppression. As a middleclass White person who was successful in
school, my unconscious tendency had been to view James as a model of how children should operate and achieve in math. Other ways of participating and succeeding were invisible to me. This limited perspective affected my teaching in concrete ways. For example, without really thinking about it, I provided Nasira and Luna with feedback that was less open-ended and more directive than the feedback I typically gave James. In doing so, I gave them less room to explore, to create, and to shine.

pg 343

I am noticing them feeling success in exploring rich tasks, asking questions, listening to others’ ideas, and inventing and testing new strategies.

Learning to see students’ mathematical strengths

Reflective teaching is a process of self-observation and self-evaluation. It means looking at your classroom practice, thinking about what you do and why you do it, and then evaluating whether it works. By collecting information about what goes on in our classrooms and then analyzing and evaluating this information, we identify and explore our own practices and underlying beliefs.

Prompts for noticing and disrupting power and privilege in classroom interactions (strategy 4)

• Name aspects of students’ backgrounds (and your own)—race, ethnicity, socio-economic status, personality quirks, disability status, and so on. Think about particular students and ask yourself, How is their background similar to/different from mine? How could our backgrounds shape how we interact in the classroom? How could they shape how I interpret their actions?
• Seek evidence and alternative interpretations. Why do I think a student did something? What evidence do I have for reaching that conclusion? What other reasons or intentions might they have had that I could consider?
• Notice what students are doing instead of what they have not done yet. What smart things do I see happening that I can explicitly name?
• Reflect on your own feelings and how they shape your interactions with every individual student. Why might I be feeling frustrated, indifferent, or excited about this student? How am I communicating with this student? What am I saying, how I am saying it, and how often am I saying it?
• Consume media from diverse authors/creators. Which students and families do I feel the least similar or least connected to? How can I access authentic voices from their community to broaden my awareness as well as connecting with them personally?
• What does being “good at math” look like and sound like to you? How could you expand your definition to include more of the diverse strengths that support mathematics learning—and to include more students?
• When you think about assigning your students to random groups, what possibilities worry you? What unintended consequences might our efforts to carefully control student groups have?
• Look at a math task you plan to use in your classroom. How could you adapt it to make more space for students to create their own strategies and representations, as Luna, David, and Nasira did here?
• Who could you recruit as critical friends? Who shares your commitments and is likely to offer you perspectives different from your own? How can you nurture your relationships and make changes if they are not support your learning?

Privileged or not

Regardless of anyone’s beliefs or intentions, power and privilege are constantly at work in our classrooms.

…the dynamics in all our classrooms are shaped by the privilege that different students are afforded—or not—both inside and outside schools, which are structured by race, gender, class, disability status, and other social categories (evident in, for instance, James’ readiness to claim mathematical authority and competence versus Luna’s readiness to view her work as “wrong”). When we ignore these differences, we are much more likely to miss their effects, unknowingly centering some students while pushing others to the margins, denying some students chances to shine, and limiting all students’ opportunities to learn with and from one another.

Learning to see differently than we have been taught is demanding and potentially uncomfortable.

Giving students a task that we have not shown them how to solve and then watching them struggle without stepping in to share our way of doing it is risky.

However, the learning that such risks can spark and the relationships they can foster are crucial for creating environments that celebrate and nurture all students, especially those whom our society typically positions as inferior.

Ultimately, the point is not the strategies. The goal is to support all of our students to experience mathematics as a humanizing and empowering activity, in which their brilliance is celebrated.