Glastonbury Public Schools Mathematics Department

Building Thinking Classrooms (BTC)

cartoon image of three stick figures actively solving a problem on a whiteboard

Think First, Formalize Later

The Building Thinking Classrooms approach is one classroom strategy we use in math classes. It shifts learning from passive listening to active problem-solving. With this learning method, math students no longer just memorize formulas. Instead, they build deep understanding, self-reliance, and genuine confidence in math.

Rethinking How Math Gets Taught

If you peeked into our classroom during a lesson on calculus, you might be surprised by what you see. You won't find students quietly sitting at desks copying notes from a whiteboard while the teacher lectures at the front.

Instead, you’ll see students standing in small groups at vertical whiteboards around the room, actively solving problems together from the very first minute of class. The teacher is circulating each small group, asking questions and facilitating learning.

This approach is called Building Thinking Classrooms (BTC). BTC is a research-backed method designed to get students actively thinking, collaborating, and problem-solving rather than passively receiving information.

Class Video Example:
Active Problem Solving

The sped-up lesson video included here shows student groups problem-solving at the board. Later, they return to their seats for consolidation in the form of more traditional teacher-led instruction.

BTC Sample Video.mp4

How a Lesson Works

[ Short Problem Setup ] ➔ [ Group Problem-Solving ] ➔ [ Whole-Class Debrief ]

Each lesson includes 4 opportunities to learn

Warm up/ Launch
Problem-solving (Working collaboratively)
Note-taking (Consolidation)
Independent student practice (Mild, Medium, Spicy)

Random, Small Groups: Students work in randomly assigned teams of three. Working on vertical whiteboards keeps everyone standing, engaged, and visibly sharing their ideas with the group and the class.

"Thin-Sliced" Tasks: Lessons are designed for students to build and apply knowledge to a new situation. The jump is small enough so students should be able to transfer learning to the new situation provided, the ultimate goal of mathematics: application and transfer.

Student-Driven Flow: Groups work through the tasks at their own pace, really individualizing learning to a small group, getting the help they need to move forward, and being able to ask the questions they need. If they get stuck, they look around the room to borrow ideas from other teams and are ready to ask the teacher questions about what they don't know.

Targeted Support: Because students are actively leading their own learning, the teacher is free to move around the room, supporting groups that need extra guidance and dropping in more challenging extension problems for groups ready to push further.

Sample 2-Day Geometry Lesson

Day 1

Teacher led warm up: review vertical angles and linear pairs (examples are drawn on the board)
Students problem-solve angle pairs at the boards
Teacher led note taking/ definitions
Independent student practice

Day 2

Teacher led warm up: review angle pairs
Students problem-solve angle pairs at the boards
Teacher-led note-taking: Angle pair theorem intro slide
Independent student practice

The Power of "Consolidation"

Think first, formalize later. Instead of always using the traditional math classroom lesson, where the teacher lectures and students mimic and repeat without thinking or knowing why, and then try to apply, students are asked to try to make connections to prior learning first, transfer previous learning to new learning, and develop a deeper understanding of the math content. After that happens, the consolidation that the teacher does is more note-driven and synthesizes the students' thinking; they can now participate in a conversation because they thought about it first, asked questions and made connections. This is better learning than ever before!

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