Here’s a math problem for you: Using four 4s and any operations (addition, subtraction, square roots, etc.), create an expression that equals all values from 0-10. An example is: 4 + 4 – (4/4) = 7.* 

All done? How about up to 20? 50? 100?

This is one example of the problem-solving tasks that Senior School students at Trinity College School may have faced in the opening math classes of the 2023-2024 school year. The mathematics department has piloted the research-based “Thinking Classroom” framework in our classrooms for the past three years, including a day-long session with a Building Thinking Classrooms facilitator. 

The Thinking Classroom framework is an innovative approach to math education that challenges the traditional model of rote memorization and passive learning. We believe this new methodology will empower our students to excel in mathematics and cultivate essential critical-thinking and problem-solving skills that will serve them well throughout their lives.

In a traditional mathematics lesson, the teacher stands at the front of the classroom and delivers the content for the day. This often follows the “I do, we do, you do” approach, where the teacher works through an example, gets input from the class to complete another example, and then sets the class loose to work through a set of problems. Students are encouraged to mimic the steps outlined by their teacher without doing much critical thinking about what is occurring. 

So, what sets the Thinking Classroom apart from the traditional approach? Let’s explore some key differences:

1. Collaborative Learning: In the Thinking Classroom, students work in small groups of two or three, often at a whiteboard. They are encouraged to work together to tackle math problems. This collaborative environment fosters communication, teamwork and the exchange of different problem-solving strategies. 
    
2. Teacher as Facilitator: Unlike the traditional model where the teacher stands at the front of the class and delivers content, the teacher takes on the role of a facilitator in the Thinking Classroom. Initially, teachers may refrain from providing direct answers to questions, promoting independent thinking and exploration among students. 
    
3. Standing in Class: Students in the Thinking Classroom might find themselves standing more often than sitting. This dynamic approach keeps students engaged and encourages movement, creating a more active and interactive learning experience. 
    
4. Challenging Questions: Expect your children to come home with tales of challenging math questions. At first, they might find these questions difficult, but that is the point. These thought-provoking queries are designed to stimulate critical thinking, creativity and problem-solving skills, which are essential for mathematical proficiency. 
    
5. Check Your Understanding: Instead of completing homework, students in the Thinking Classroom engage in “Check Your Understanding” questions during the lesson and outside of class time. These questions help consolidate their learning and enable them to transfer knowledge from collaborative groups to individual comprehension. As the name suggests, the sole purpose of these questions is for the students to check their understanding. Solutions are provided, and the completion of the questions is not checked by the teacher. Students’ understanding of the content is, of course, assessed through various quizzes, tests and assignments. 

In summary, the Thinking Classroom represents a paradigm shift in math education. We are moving away from passive learning and memorization, focusing instead on active problem-solving, collaboration and cultivating independent thinkers. While this approach may seem different to students, we believe it is a step in the right direction toward fostering a deeper understanding of mathematical concepts and processes.

We encourage you to ask about your child’s math experience and encourage them to embrace the challenges that may arise. Together, we can help our students become confident, critical and creative mathematicians.

- By Matt Murray, head of mathematics

* Source: Building Thinking Classrooms in Mathematics, Peter Liljedahl