Explaining Thinking: After the first weeks of school, Mia is able to create new challenges for them to explain their thinking to her and to each other. In a game called “Build it Fast” she uses the 0-99 chart to introduce the idea of patterns in place value. She elicits predictions from her students about how many numbers they are going to place on the chart, evaluating them only with “Hm!” or “Maybe!”

**CONSIDER:**

How do you expose and explore misconceptions?

These videos are discussed in the Inside Mathematics guide "Making Sense of Learning, Mia Buljan, 2nd grade," one of 10 practice-focused guides on building classroom climates for mathematical learning.

The videos document key mathematical practices observed in teacher Mia Buljan's 2nd grade classroom over the course of a school year. In the guide (available as a PDF or an iBook download), you can explore extended narratives and questions for reflection around "making sense of learning."

Day 2: Recognizing developmental trends [Understanding and Reading Problems]

Day 2: Exploring and Explaining [Finding Evidence and Justifying Strategies]

Day 2: Coming to know students as mathematicians [Understanding and Reading Problems]

Day 3: Calling learners’ attention to the structure of a problem [Understanding and Reading Problems]

Day 3: Testing and proving different ideas [Finding Evidence and Justifying Strategies]

Day 14: Exposing and exploring student misconceptions [Explaining Thinking]

Day 14: Subtracting from INSIDE the original quantity [Understanding and Reading Problems]

Day 14: Playacting problems with different quantities [Understanding and Reading Problems]

Day 14: Anticipating student misconceptions [Understanding and Reading Problems]

Day 110: Students develop different ways of showing and describing quantities [Finding Evidence and Justifying Strategies]

Day 110: Recognizing problem structure [Understanding and Reading Problems]

Day 110: Using problem structure to deepen student thinking [Understanding and Reading Problems]

Day 110: Defending answers [Explaining Thinking]

Day 110: Praising and reinforcing students’ justifications of their strategy [Explaining Thinking]

Day 158: Requiring students to identify quantities and connect them to the problem [Finding Evidence and Justifying Strategies]

Day 158: Appreciating multiple approaches [Making Sense of One’s Own Learning]

Day 158: Matching quantities to the problem and checking student thinking [The View from Day 158]