• The Spark

How to Advance Mathematical Thinking with Student-Focused Learning, a Growth Mindset, an End to Tracking, and Personalized Standards

Author:  Dr. Cathy Seeley, Math Solutions author and former president of the National Council of Teachers of Mathematics  | 06/22/2017

How to Advance Mathematical Thinking

In Part 2 of our Q & A with Dr. Cathy Seeley (read Part 1) on transforming math instruction, she offers valuable advice on ways to create a risk-free, student-focused learning environment to spark mathematical thinking.

Q: We previously discussed upside-down learning and how teachers can help students learn to think mathematically. Looking at this topic from the student perspective, how do you advise teachers to guide this shift in the classroom…to help students reach their potential and discover untapped abilities?

CS: It doesn’t happen in isolation of the overall teaching experience. If we shift our focus to the kind of teaching we’re talking about—where students are engaged and thinking—for that to succeed we really need a classroom environment where students are taught to listen to each other and respect what others think and where all students are expected to engage in the activity. And if you do small-group activities, it’s important that students in the group are responsible for making sure that everybody else in the group is getting what’s going on. When we teach in ways that engage students in thinking about challenging problems and sharing their thinking with others, we actually discover far more students being successful and being interested in math than we have found when students are expected to sit and listen to a teacher telling them stuff. That’s the problem with this traditional and still very widespread model—what some call an I-we-you model, where “I’m going to show you something, we’ll do some guided practice, and then you’ll be given one or more problems where you apply what you just learned.

I advocate shifting to a you-we-I model, meaning “you’re going to mess around with a problem, we’re going to talk about it, and then I’m going to make sure you understand the mathematics of the lesson.” Making that kind of shift, you discover new stars. It happens over and over again. Any teacher who has made that shift will tell you that more students, including different students, become the successful students. It may surprise everybody—even the students themselves—because it’s a different sort of engagement, and it invites more students to express themselves. If you can create that kind of risk-free environment, students become comfortable with the idea that “even if I say something that isn’t right, we’ll have a discussion, and it’s OK. I’m not going to be embarrassed.”

Now, by the way, that can be kind of threatening to students who have traditionally been successful. The students who have always played by the book may find that other students are now also successful, and it can be a challenge for everyone in the system to adjust to this different kind of culture—a culture of success for all, or nearly all students.

Q: Do you find that kids who were previously successful and “playing by the book” are struggling with this classroom model? Can they change their way of learning?

CS: Students who’ve been engaged in this kind of discourse-focused classroom around thinking and problem solving tend to be more open to ideas from other students, more willing to share ideas, and better at understanding that they may approach a problem in a different way from their peers.

Those who have figured out the system, who have always been good at listening and doing their homework—they may actually run into difficulties when they get to more challenging problems or problems that look different from the way they’ve learned them. The kind of teaching we’re talking about here sets up every student for success, including those who have succeeded by listening, practicing, and memorizing, as well as those who have been frustrated with a traditional teaching approach.

All of this relates to what we’re now learning about growth mindset and intelligence.
Dr. Cathy Seeley

If a student believes you’re only as smart as when you were born, it’s important to help them understand the nature of intelligence and that working on challenging problems can make you smarter… that intelligence has as much to do with effort as with the genes you’re born with. The notion of a growth mindset is absolutely at the core of a lot of this. Students’ willingness to make mistakes, to share their thinking out loud, to listen to other students—all of that depends on their mindset about intelligence and how they see themselves as math learners.

Q: In terms of leveling the playing field for different types of learners, do you have examples of how schools have successfully raised the floor and also raised the ceiling?

CS: The key to raising the floor—giving more students access to challenging mathematics—and also raising the ceiling is to take an honest look at tracking practices. We have so many schools that continue to track kids in some way or other. If we have five levels of algebra, we’re tracking. If we pull out kids for special programs, we’re tracking. And the verdict is in—tracking kills equity. Research has shown for decades that tracking practices do not work to help students learn better. Yes, it may be helpful for our very gifted students to have opportunities to work together for some period of time. But for day-to-day learning, students are better off without being tracked by so-called ‘ability’—something we really don’t have a good way to measure anyway. Every student can become more intelligent than he or she is today and every student can benefit from teacher expectations that all students will do well.

I would argue that we even deny our most advanced or accelerated students—those in pre-calculus and calculus classes—the opportunity to think deeply about things. In many classrooms we haven’t given them the proper challenge to deal with problems or situations they haven’t already been taught. It’s important to help students and their parents understand that tackling problems they haven’t already been taught how to solve is a good thing.

It doesn’t mean the teacher is shirking responsibility—it means the teacher is helping the student develop responsibility and deepen the level of thinking.
Dr. Cathy Seeley

Q: How does this all fit in with current standards and education policy?

CS: The tendency we have in education is what I call ‘yo-yo decision making’: we ask teachers to invest their time and energy, and ask the system to invest money, in new programs. And it takes time for any new program to take root—whether it’s an instructional program, a testing system, or a new set of standards—it takes time and a lot of sustained effort from teachers and students and support from communities and administrators. And what I see happening too often is, when a program is starting to have the potential to do some good, a new person in a key leadership role comes in and says, “wait a minute, I’ve heard that some people don’t like this,” and they throw it out and try to bring in some new program. I would like to encourage leaders and policy makers to think very carefully before rejecting an initiative if it hasn’t immediately shown results or if people think it’s hard to do. Change is a process and it takes some time to achieve intended goals, especially if the change involves a major shift in philosophy or teaching approach. Instead of throwing out a whole program and replacing it with yet another whole program, let’s see what needs to be fixed. I think that’s one of the ways in which we really hurt progress in this country—by yanking the rug out from under teachers and students every couple of years and saying, “oh, never mind that, we’re going to do this instead,” and never allowing ourselves to get the momentum of building each year on what was done before. Instead, we can get feedback from teachers (or even students and their families) on what’s working and what’s not, identifying whatever improvements might be needed, instead of throwing things out and starting over.

One place we may be making some progress is in terms of states updating and revising their standards. While it may appear that some states keep starting over as they ‘reject’ their current standards, in reality we seem to be moving toward consensus across the country. Some states have chosen to keep key ideas and progressions from their current standards, even as they make minor adjustments elsewhere. I see this as a far better approach than trying to create brand new standards just for the sake of not doing something that may be a target for criticism. As a result, we’re moving more or less in a direction that is still largely common, with people keeping certain things that were working for them, rather than starting from scratch and throwing teachers into a chaotic and unstable situation of ‘yet another new program.’ It’s an improvement that we now have things being taught at the same grade level across states.

Simply put, my advice is let’s tweak, let’s not throw things out.
Dr. Cathy Seeley

# # #

Two upcoming opportunities to hear Cathy Seeley speak!

  • Add your comment

    Your name will not be published to our website. Please enter comment name. We’re sorry—there are some invalid characters.

     

    Your nickname will appear with your comment. Please enter comment nickname. We’re sorry—there are some invalid characters.

     

    Please enter comment email.

     

    Please enter comment. We’re sorry—there are some invalid characters.