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Shifting from teacher-centered questions to student thinking tasks:

Key principles embedded in these moves:

Every student thinks, not just volunteers

Questions become cognitive tasks with think time

Students compare, evaluate, and generate rather than recall

Peer-to-peer interaction replaces teacher-to-student

Mistakes and confusion become learning opportunities, not things to fix immediately

Students create examples rather than rely on teacher examples

Mathematical reasoning is valued as much as, or more than, answer-getting

• Instead of "Who can tell me what the next step is?" → "Take 30 seconds: Write down what you think the next step should be and why."

• Instead of "Are there any questions?" → "On your whiteboard, create an example that shows you understand this concept."

• Instead of "What do you notice about this graph?" → "List three things you notice and two things you wonder about this graph. Be ready to explain your thinking."

• Instead of "What's the answer to number 5?" → "Compare your answer to number 5 with your partner. If you got different answers, figure out where your thinking diverged."

• Instead of "Who can explain how to solve this?" → "In your notebook: Sketch or write the steps you would take. Then find someone who approached it differently and learn their method."

• Instead of "Is this answer correct?" → "Decide whether this answer is reasonable. What evidence supports your decision? What would make you doubt it?"

• Instead of "Can someone share their strategy?" → "Trade papers with a partner. What strategy did they use? How is it similar to or different from yours?"

• Instead of "Who remembers the formula?" → "Without looking at your notes, write down what you remember about this concept. Then check with a partner to see what they remember."

• Instead of "Let me show you how to do this" → "Here are three different student solutions to this problem. Study them and determine: Which approach makes the most sense to you? Which is most efficient? Which would you use?"

• Instead of "Does this make sense?" → "Explain this concept to your partner as if they were absent yesterday. Use a diagram or example."

• Instead of "What's the rule?" → "Look at these five examples. What pattern do you see? Test your pattern with two more examples. Does it still hold?"

• Instead of "Is anyone stuck?" → "Draw a line where you got stuck on this problem. Write one specific question that would help you get unstuck."

• Instead of "Who got the right answer?" → "Three people in this class got three different answers: 12, -12, and 6. Work with your group to figure out which is correct and what mistakes might have led to the other answers."

• Instead of "Let me clarify that for you" → "Turn to someone near you and explain what you understand so far. Then identify together what's still unclear."

• Instead of "Can you prove that?" → "Create an argument that would convince a skeptical classmate. What evidence would you need? What counterexamples would you address?"

• Instead of "What questions do you have?" → "Write down one thing you're confident about and one thing you're still uncertain about. Find someone who's confident about your uncertainty."

• Instead of "Here's an example" → "Generate your own example of this concept. Make one that's simple, and one that's complex. Explain what makes them different."

• Instead of "Watch how I do this" → "Before we solve this together, predict: What will be the hardest step? Where might someone make a mistake? Why?"

• Instead of "Who can come up to the board?" → "Everyone solve this on your whiteboard. In 2 minutes we'll do a gallery walk to see all the different approaches."

• Instead of "Is this a good strategy?" → "Evaluate this strategy: What are its strengths? Its limitations? When would you use it? When wouldn't you?"

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Increase rigor and assessment variety within lessons

Repurpose DOK 1-2 questions into DOK 3 level tasks (e.g. dependent questions, open-ended questions requiring evidence, reasoning, counter examples)

Leverage ELA standards (writing, reading for informational text, speaking and listening) to deepen mathematical understanding

Enhance formative assessment systems

Develop and leverage student friendly rubrics and success criteria to provide clear and measurable feedback for students

Embed error analysis, non-exemplars and exemplars throughout a lesson and not just at the end or a summative assessment

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Strategies for Building Student Mathematical Interactions (Middle School)

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Strategies for Building Student Mathematical Interactions (Carmel High School)

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Carmel Math Vertical Articulation — Session Summary

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What classroom practices and student mathematical interactions are most important to continue and strengthen as students transition from middle school to high school mathematics?

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What classroom practices and student mathematical interactions are most important to continue and strengthen as students transition from middle school to high school mathematics?

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Carmel Math Vertical Articulation Agenda

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Implementing New Curriculum at the Middle School

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Implementing New Curriculum at the Middle School

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Carmel Middle School Math Implementation Questions

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1. Share and confirm adoption decision

2. Revise ideal statements

3. Look at materials through the lens of ideal statement: creating a chart of I-ready’s “out of box strengths” and where there might be gaps to fill.

4. How to fill the gaps

5. Enhance upcoming lessons

6. Next date and schedule

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Building Thinking Classrooms is an educational approach developed by Dr. Peter Liljedahl, professor of mathematics education at Simon Fraser University in Canada. Sparked by observing dozens and dozens of teachers struggle to engage students in deep thinking and problem solving, and observing hundreds of students engaged in a lot of behavior that didn't include thinking-or learning-Peter set out to find the answer to a simple question: How can we get more students to think and to think longer?

Over the next 15 years, he set a research course to break every institutional norm possible to see what shifts could get students thinking. Out of this research grew 14 specific norm-busting teaching practices that have proven to enhance thinking-and thus learning in hundreds of thousands of classrooms around the world. And it doesn't stop there. Not only do the 14 practices enhance thinking, they enhance other competencies in students such as collaboration, perseverance, risk-taking. Further, they enhance access and equity to learning and student autonomy and ownership of learning.

First published in 2020 as the book Building Thinking Classrooms in Mathematics, the BTC model has become a global phenomenon. Educators around the world-from the United States and Canada to Norway to Japan-are finding that when implementing these 14 practices-even if in incrementally over time-their students have become more engaged and more excited to learn mathematics.

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About BTC | Building Thinking Classrooms

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Building Thinking Classrooms is an educational approach developed by Dr. Peter Liljedahl, professor of mathematics education at Simon Fraser University in Canada. Sparked by observing dozens and dozens of teachers struggle to engage students in deep thinking and problem solving, and observing hundreds of students engaged in a lot of behavior that didn't include thinking-or learning-Peter set out to find the answer to a simple question: How can we get more students to think and to think longer?

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1. Welcome

2. Recap

3. Share stories from Palm Springs and CMS

4. Building Thinking Classrooms One-pager

5. Revise ideal statements

6. Choose Individual focus

7. What would that look like in my classroom?

8. Collaborate on upcoming lesson(s)

9. Share out one thing you’re going to try

10. Next date and schedule for observations

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Building Thinking Classrooms by Peter Liljedahl

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Math Ideal Student Interaction Walkthroughs (CMS)

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Math Ideal Student Interaction Walkthroughs (CHS)

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2025 Math Adoption Reports of Findings - Instructional Materials (CA Dept of Education)

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IMR/CRE Reports of Findings for the 2025 Mathematics Instructional Materials Adoption. These advisory recommendations have not been approved by the Instructional Quality Commission or the State Board of Education.

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Carmel Math TPT Session 1_August_28_2025

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Any additional comments or suggestions for future TPT sessions?

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What would you change or improve about today's session?

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What was the most valuable part of today's session? What will you take away and apply?