Shifting the Math Mindset: A Teacher's Transformation with Building Thinking Classrooms

By Michael Tauscher

In recent years, the approach to teaching mathematics has undergone significant shifts, particularly with the introduction of Peter Liljedahl's Building Thinking Classrooms in Mathematics. This revolutionary framework transforms the way children interact with mathematical concepts, encouraging a deeper understanding through active engagement. Laura Blanchet, a 4th grade teacher at University School of Milwaukee and the Preschool and Lower School Math Department chair, has been at the forefront of implementing these practices. In our discussion, she reflects on her journey with this approach and the remarkable impact it has had on her students.

A Love for Math and a Search for Innovation

Blanchet's passion for math has been evident throughout her career. "Math has always been important to me," she shares, recalling how she enjoyed math as a child and even tutored classmates in high school. Despite her early teaching years being a whirlwind of different schools and grade levels, Blanchet consistently found herself teaching math, whether in high school or middle school settings. Her journey at USM, where she has taught 4th grade for 13 years, has allowed her to delve deep into curriculum development and child-centered instruction. 

But Blanchet always felt there was more to offer. One of her goals was to help children—and even parents—shake the common misconception that some people just aren’t “good at math.” Over the years, parents would often share that they had struggled with math and accepted their child would face the same difficulties. This mindset frustrated Blanchet, and she became determined to find a way to help children build confidence and truly engage with math.

Enter Building Thinking Classrooms

Blanchet's teaching transformed when she was introduced to Peter Liljedahl's Building Thinking Classrooms in Mathematics research. Liljedahl's work, based on over 15 years of research with more than 400 teachers and thousands of children, presents 14 key practices designed to foster child engagement and thinking in math classrooms. The first three practices, which form the foundation of his approach, are creating thinking tasks, using visibly random groups, and incorporating vertical non-permanent surfaces (dry-erase boards). 

In the first 10 pages of the book, Liljedahl speaks about the different “studenting” behaviors. Blanchet realized that much of traditional math instruction involved children mimicking what the teacher showed, rather than genuinely thinking through problems and understanding the reasoning behind them. The Building Thinking Classrooms model provided a way to change that.

The Research Behind the Change

The research supporting Building Thinking Classrooms underscores its effectiveness. According to Liljedahl, the goal is to keep children thinking about math for extended periods of time, not just for immediate answers. Studies suggest that engaging children in thinking tasks leads to deeper understanding and retention.

For Blanchet, these practices have fundamentally changed her classroom dynamic. As she continues to implement and refine these methods, she remains committed to the idea that anyone can excel in math. With innovative teaching practices, a collaborative learning environment, and a focus on thinking over mimicking, children at USM are poised for success in mathematics—and beyond.

The First Three Tools

The first essential practice is creating thinking tasks—problems that have a low floor and a high ceiling, meaning children at various levels can engage with the task and still find it challenging. "You want tasks that are accessible no matter where children are in their math ability," Blanchet explains.

The second practice involves forming visibly random groups, instead of allowing children to self-select groups or be assigned to them based on perceived ability, which ensures that children enter with a sense of equal footing. As Blanchet describes, "Students often assume roles in teacher-assigned groups, but random groups eliminate those preconceived roles."

The third and perhaps most visually striking component is the use of vertical non-permanent surfaces, essentially dry-erase boards placed around the classroom. These surfaces allow children to work through problems collaboratively and comfortably erase mistakes. "It's easier to take risks when you know it’s simple to erase and start over," Blanchet points out. This sense of freedom fosters creativity and encourages children to explore solutions without the fear of making mistakes.

Hurdles and Triumphs Along the Way

One of the biggest challenges Blanchet faced was shifting children's mindsets. Building Thinking Classrooms required children to think critically from the start, which was different from what they were used to, and caused some resistance initially. "They wanted to be shown what to do first," she says, acknowledging that teaching the necessary routines and procedures took time. However, with consistent practice, the children began to take ownership of their learning.

Blanchet also had to address practical hurdles. Her classroom was not outfitted with enough vertical surfaces for all children, so she collaborated with USM’s middle school makerspace to build wooden easels for portable whiteboards. "Education is all about borrowing ideas," she says with a laugh, explaining how she used "wipebooks," disposable dry-erase boards with grids, which were affordable and easy to replace each year.

Results that Speak for Themselves

After a full year of implementing Building Thinking Classrooms, the results were clear. Blanchet observed a noticeable increase in child enthusiasm for math. "They were excited for math time," she recalls. Even more impressive was the improvement in children's stamina when solving math problems. Instead of relying on the teacher for answers, children learned to discuss, justify, and explain their reasoning—a key goal in Liljedahl’s approach.

Perhaps the most profound change was in children's self-perception. They no longer viewed math as something that was “taught” to them; they believed they were learning math independently. "They felt they were the owners of their learning," Blanchet says proudly.

A Principal’s Perspective

As the Head of the Preschool and Lower School, I had the unique opportunity to observe Blanchet's classroom over the course of the school year. This allowed me to witness not only Blanchet's journey as an educator, but also the remarkable transformation of her students. At the beginning of the year, I could see the initial uncertainty in the children as they approached this new way of learning math. By the end of the year, however, they had become genuinely excited—not just about learning math, but about sharing their understanding with others. It was especially heartening to see the pride they took in explaining their reasoning to me, and even more impressive when other teachers visited the classroom and realized this approach could work across grade levels. It wasn't just for older children; kindergartners and 1st graders could thrive with this method too.

What struck me the most was observing the mental agility Blanchet needed to plan and execute these lessons. I would enter her classroom and see six or seven different boards, each group working on variations of the same problem. Blanchet had to be prepared for the diversity of thought each group brought to the task. In traditional teaching, it might be easy to jump in with corrections, but Blanchet’s role wasn’t to simply tell children the answers. Instead, she guided them with the right questions and prompts, helping them arrive at solutions themselves. This was particularly challenging because each group was often at a different stage—some children were ahead, some were just starting, and others were deep in thought, needing only subtle nudges to advance their learning.

What I appreciated most was watching this process become a well-oiled machine as the year progressed. Blanchet seamlessly navigated the different needs of each group, offering tailored guidance while letting children take ownership of their learning. Every time I observed, I could see how much progress had been made since the last time. The children were no longer just producing answers—they were truly learning how math works. And that, in my opinion, is the ultimate goal of education: to teach children not just to find answers quickly, but to understand the underlying concepts and build a deep, lasting relationship with numbers.

A Broader Vision for Excellence in Math Education

As Blanchet continues to refine her practice, she hopes to see these methods spread across grade levels. "I want kids to be more interactive with math," she explains, envisioning a future where children collaborate and share their ideas more freely. While some teachers might find the 14 practices of Building Thinking Classrooms daunting, Blanchet believes that starting with the foundational practices—thinking tasks, random groups, and vertical non-permanent surfaces—can make a significant difference. USM's math curriculum, Reveal Math, already supports this interactive approach, giving children more opportunities to talk about their mathematical thinking. This commitment to fostering collaboration and critical thinking reflects USM's dedication to excellence in teaching, where educators are continuously evolving and adapting best practices to inspire a deep love of learning and intellectual curiosity in every child.

About Michael Tauscher

Michael Tauscher has served as the head of Preschool and Lower School at University School of Milwaukee since 2015. Born and raised on a family-owned farm in Pulaski, Wisconsin, he holds a bachelor’s degree in elementary education and a master’s degree in educational leadership. With 24 years of experience as an educator; 17 years as an administrator, Michael has worked in early childhood, elementary, and middle school settings, including teaching 3rd, 4th, and 5th grades and gaining international teaching experience in Kyoto, Japan.