Teaching Out Of The Box

On the personality spectrum, I tend to be what people colloquially refer to as “Type A.” In my experience, the majority of teachers tend toward this personality predisposition. It can be very beneficial in teaching, but it can also be detrimental if we allow our own tendencies and preferences to become the measuring stick for student performance instead of objective criteria. Type A personalities may dominate the teaching profession, but our students are all over the spectrum, and just because they may do things differently, their strategies are not necessarily inferior.

Reminding myself to differentiate between subjective preference and objective quality has helped me value multiple student strategies in everything from keeping up with homework assignments to designing science experiments. We are individuals. One size almost never fits all. When we give students permission to get out of the box of a one-size-fits-all mentality, they can each confidently bring a different perspective to the table. Sometimes, everyone’s method is equally valuable; sometimes, one emerges as more effective or efficient. Learning to collaborate, defend ideas, and evaluate the reasoning of self and others is extremely valuable in the classroom and beyond, and we can intentionally develop these skills by restructuring our classrooms away from a culture in which the instructor hands the “correct” strategy down to the students toward a culture in which students are actively engaged in strategy design and evaluation.

Kara Suzuka, Tim Boerst, and Aileen Kennison from the University of Michigan understand this, and they have designed excellent research-based professional development for elementary school math teachers to promote this line of reasoning. I recently discovered their work when browsing the 2017 Stem For All Video Showcase sponsored by the National Science Foundation. The team highlights key differences between being able to do elementary level math and being able to teach math at the elementary level. One of these important differences is recognizing and encouraging multiple student strategies. Their work supports what I have observed while tutoring and teaching math over 15 years.

When I first started tutoring, I would basically teach students to replicate the process that I used to answer the question. In other words, I tried to put the students in my box. However, I noticed that, even when the students could use my procedure to arrive at a correct answer, they really didn’t understand what they were doing or why they were doing it. In other words, it wasn’t building number sense. Even more unfortunately, I was also inadvertently communicating to the students that there is only one correct way to do math, and that way must be affirmed by me, the instructor. When students repeatedly learn math that way, it is hard to convince them of the truth–there are multiple, valid algorithms for solving problems that students themselves should be able to create, verbalize, defend, and assess for efficiency. Now, I seek to recognize the value in each student method, allow them to present their thinking, and let them prove whether or not it will work every time. In other words, I give them permission to get out of the box. This better style of instruction satisfies every single one of the Mathematics Teaching Practices recommended by the National Council of Teachers of Mathematics:

• Establish mathematics goals to focus learning.
• Implement tasks that promote reasoning and problem solving.
• Use and connect mathematical representations.
• Facilitate meaningful mathematical discourse.
• Pose purposeful questions.
• Build procedural fluency from conceptual understanding.
• Support productive struggle in learning mathematics.
• Elicit and use evidence of student thinking.

I love knowing there are people like Kara, Tim, and Aileen who are working to shift the paradigm of mathematics instruction away from replicating processes to supporting individual student strategies. We can’t teach students every process for every problem type they will ever encounter. But we can teach students to think, create, and evaluate their own processes. Kudos to the team at the University of Michigan for recognizing the need to teach outside of the box and for offering a promising solution. I look forward to reading the final results of their research.