## Reflection: Discourse and Questioning Garden Design - Section 1: Warmup

The key to facilitating discussion between students is to avoid telling them too much, but instead ask the right question and continually turn the conversation back over to them. It is really hard to get used to asking questions that will get students to think about the big math ideas. It is even harder to give them the time to wander around in their brains until they figure it out especially when they expect us to give them clues or verification.

I find that asking "why does it make sense?" questions can really get at the heart of a lot of the big mathematical ideas. For example, here I knew that the big idea was that a(b) + a(c) = a(b+c), so the question is why does it make sense. I also find that using a visual model (in this case the area model) and asking them where the math is represnted in the model can help them make sense of what's happening mathematically and help them see the structure of the math (MP7). A real world context is also helpful as long as it is comprehensible to the students. Without context there can be no mathematical modeling (MP4) which is different from concrete modeling.

Discourse in my class often takes on a back-and-forth format.

• A student shares and explains an idea (whole group)
• Small groups are asked to discuss what they think of the idea (what do you think of that idea? Why does this make sense or not? How can we decide if this is true?)
• Students respond to the idea with questions, supporting evidence, counter examples, etc. (whole group)

Sometimes I will choose a student to share or share an idea that I overhear while circulating. This process takes a lot of time, but it pays off in about 2-3 months with student led discussions.

Discourse and Questioning: Facilitating student discussion

# Garden Design

Unit 3: Equivalent Expressions
Lesson 12 of 23

## Big Idea: Students will understand the form behind the distributive property and transition from the physical model to the mathematical model.

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Subject(s):
Math, Expressions (Algebra), distributive property, area model
54 minutes

### Erica Burnison

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