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Productive Struggle in Mathematics: an Informative Interview with Katie Baker, E.Ed.

“I work with practicing and prospective teachers to break down the stigma—as far as there being people who can and can’t do math—and think about the power we give to kids for math to make sense.” – Dr. Katie Baker, professor at Elon University

Dr. Katie Baker is a professor of education at Elon University and focuses primarily on mathematics education and how to support teachers and their methods of engaging with students’ thought processes. She received her B.A. in Elementary Education from the University of Michigan and her M.Ed. and Ed.D. in Mathematics Education/Curriculum and Instruction from the University of North Carolina. Dr. Baker is well versed in the concept of productive struggle and set aside some time to discuss the concept with us.

Q: Productive struggle; how would you define it?

A: Productive struggle was first introduced in a chapter by Hiebert and Grouws from the 2007 Handbook of Research on Math Teaching and Learning, where they discussed the notion of struggle as useful effort towards solving a problem, not needless frustration. In regards to the term productive struggle, researchers and teachers note that kids could persist and struggle in sports, games, lego-building, and other things of interest, but when it came to math, struggling was considered problematic. Productive struggle takes math and says, “we want to frame that mathematics is just as valued and valuable as something that takes time, and we need people to work with it.”

Part of this is breaking down the stigma that math has to be formulaic, speedy, and accurate all the time. We approach so many other disciplines with the idea that it will take time, and that there is more than one way to do it—why not math?

Q: How did you end up working with the practice and theory of productive struggle?

A: Originally, I wanted to be an education major to help kids read. Personally, I had always passed along well in mathematics. I could sit with a problem for a long time and I enjoyed that. However, I realized I was doing math in a way that made sense to me, and I did not realize until college that I was doing a standard algorithm “wrong.” I wasn’t doing problems in the way teachers had taught me but because of that, the math made sense to me. And when that concept hit me, I decided I needed to learn more about teaching math—I wanted to start thinking about how we talk to kids about math, and how we teach and talk about math. After undergrad, I started teaching 5th grade and then began a math education masters program. 

Q: Why is the concept of productive struggle important?

A: We’ve been in a dire position with mathematics in this country, where we’ve traditionally learned to memorize formulas and spit them back out. Students often lack what is called productive disposition, or the ability to connect with and see the reasonability and usefulness behind mathematics. Productive struggle focuses on how we help students to see that and how to enhance professional development to get teachers to help in that process.

Q: What does working with productive struggle entail, and how do you approach or assess progress?

A: I work with practicing and prospective teachers to break down the stigma—as far as there being people who can and can’t do math—and think about the power we give to kids for math to make sense. Prospective teachers dig into the why of mathematics, why students solve mathematical problems in specific ways and trying to unpack that stigma and normalize math.

There was a term that emerged because of the push for more mathematics learning with Sputnik and the space race: the math wars. This term represents the tension between rote-only versus conceptual-based mathematics. The math wars introduced the question: what does it mean to be a better mathematician? What are we actually looking for when we say that? I believe we’re not looking for people who have memorized their multiplication tables, we’re looking for people who can think, process, and problem-solve, perhaps even in unorthodox ways. We need to make sure that everyone has access to math in these different ways, and my work now is to break that down with future teachers.

Our graduates across the country are now taking the edTPA (Teacher Performance Assessment – Education), a subject-specific performance system on planning, instruction, and assessment. They record their work and go back and reflect on their performance. If you’re doing this in elementary mathematics, that whole assessment centers around how the teacher is making their students recognize the usefulness of the subject.

Q: How does productive struggle apply for students with learning differences?

A: Reframing math in terms of productive struggle can almost feel freeing for students with learning differences. It takes time, limits, and boundaries out of the way and gives them some space and time to think things through in their own way. This is very helpful for students with dyscalculia, for example. We’re implementing what is called cognitively guided instruction, instead of saying, “today, we’re going to learn multiplication.” The term represents a research-based practice, and for me has become a mindset towards teaching all children, however, and as all students come into math differently, we’re allowed to say, “hey, however you come into math is honored here,” and that helps make them more comfortable.

Q: What tips do you have for teachers, or even parents, when it comes to working with students and mathematics?

A: Acknowledge that kids can talk first. Let the students share their strategies of thinking, knowing, and doing. We tend to go so fast-paced in classrooms, tutoring, and homework spaces, so try to focus on slowing down, especially with word problems. Questions that don’t often occur to teachers and parents are: Do they know what is happening in the story? Can they actually contextualize this to their lives? Is this an actual math issue or is it a context issue? We need to remember to optimize math problems to ensure we’re focusing on overcoming the appropriate obstacles and having a growth mindset.

Instead of focusing on things as fixed, innate abilities—as in, if we’re bad at math then that’s just the way it is—growth mindset is about falsifying that. We all have the ability to grow in these fields.

How Hill Learning Center Can Help

Learn more directly from Dr. Katie Baker and register for our Community Education Series event on January 28th, 2020. As one of the speakers at this outreach event, Dr. Baker will further discuss productive struggle for local community members and Hill Learning Center families and students. If you can’t make it for any reason, a live stream will also be available.

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