Print    Close This Window
Heights High Students Engage in Active Thinking to Learn Math
Sept. 18, 2023 -- Teaching upper-level math is hard. Experts and educators are frequently testing out new instructional methods, from spiraling content to incorporating manipulatives. But what if there was research that showed that students learned math better when … standing up?

Well, that research exists. Sixteen Heights High math teachers and instructional specialists spent the summer reading and discussing Peter Liljedahl’s Building Thinking Classrooms in Mathematics, which uses years of research to lay out fourteen practices that enhance math education. With the ultimate goal of engaging students in active thinking instead of passive learning, Heights’ Math Department is incorporating the practices into their classrooms this year.

One of the biggest differences students have no doubt noticed is that they are rarely seated in their math classes this year. Liljedahl’s research shows that standing at vertical dry erase boards in groups of three completing daily tasks is the most conducive to student thinking. Each detail matters: Using a non-permanent dry erase surface promotes risk-taking as it’s easy to wipe away unsuccessful attempts. A vertical board is better than a horizontal one because it forces the group to engage together without allowing anyone to stand off to the side disengaged; they have to be clustered close together. Sharing one writing utensil encourages the sharing of ideas and collaborating instead of students attempting to solve the problem on their own. And groups of three are small enough to make it almost impossible for any one student to disengage.

Teaching strategies have also shifted, away from a teacher-centered approach where students rely on adults to provide the correct answer or tell them what to do to one where students are allowed, encouraged, even required to make mistakes, disagree, discuss, and generally persevere when things get hard.

That’s one of the biggest goals for the head of the Math Department, Karen Kastor, who also teaches Geometry. “We found that many of our students didn’t have the skills to stick with the hard problems. This is really teaching them how to engage.”

Another of Liljedahl’s practices is using randomly formed groups so students aren’t always working with their friends or only relying on the one “smart kid” figure out the answer. When they walk into their room each day, they draw from a deck of cards and then meet at the board labeled with the number card they drew. Over time, students recognize and expect that everyone will be an active contributor. According to the Building Thinking Classrooms website, “the use of frequent and visibly random groupings was shown to break down social barriers within the room, increase knowledge mobility, reduce stress, and increase enthusiasm for mathematics.”

Ms. Kastor reports that students are also encouraged to “steal ideas” from other groups. “When I notice that one group is stuck, I might praise another group’s thought process, pointing out the steps they took so that the stuck group can try those.” Students are free to walk around the room, look at how other groups are approaching the problem, and ask questions of each other.  

It's an innovative and perhaps surprising shift away from explicit instruction, but the principles are very intuitive. “When you look at these practices, they’re ingenious,” said Ms. Kastor.

While classes are incorporating the ideas to varying degrees, the goal is to increase from using five or six of the practices to ultimately using all of them. The district’s middle school math teachers are also reading the book over the course of this year, so students may soon simply expect to be standing up in math. And actively thinking and engaging.

hhs building thinking classrooms
hhs math building thinking classrooms