Here is what I came up with:
I had students mark which areas they felt were strengths and which ones had room for growth. There are many bullet points for each characteristic and many students wanted to just put marks down the middle for all. I made them choose and offered room for them to explain their thinking. I only gave them 20 minutes so many students were not able to explain all of them. They were really being thoughtful about their choices and I appreciated that. To be honest, all of my students have strengths and room to grow in each of these areas. I was more concerned about their perception.
I absolutely loved reading the students' responses. What I loved more was sharing these reflections with parents. My conferences had a different feel and the conversations were more meaningful. Here are some examples of responses and conversations that surrounded them:
Most students marked that they needed to improve their ability to prove and reason. At conferences I often get a peek into the past. "Last year they had to show their work in a specific way and would lose points if they didn't have it exactly as they should." "He always was marked down in his ability to explain." I do think that different teachers have different expectations in terms of work and what constitutes as an explanation and that is a vertical discussion that districts should have. Here is what I tried to focus on at conferences:
- Showing work is part of what mathematicians do to prove their answer. They need to show their thought process. It also help us understand mistakes. It is hard to reflect on an error if we cannot see where it happened.
- Explanations cannot just have the steps taken: first I multiplied then I added. The explanation is a proof. It must explain why those are the steps that make sense for this problem.
- How do I help students to improve their explanations?
- Models: Some students need models to figure out the answer. Because models show the number relationships they can show what operations make sense for the problem.
- Vocabulary: A good explanation is not determined by its length. We focus on vocabulary so we can be concise and clear in our explanations. Many students understand the relationships in their head but struggle to put it into words because they don't have the words.
- Skeptic: Your explanation is persuasive writing. It has to convince someone who does not agree with you. You aren't just explaining to your friend. You said you multiply and you are convincing someone who thinks you should divide. In class we share our reasoning and help each other find holes in our reasoning.
I did pull out some samples of student work at the conferences. After going through the reflection sheet, we were now looking at these characteristics of mathematicians in their work. It was a different conversation. I was in my nerdy math zone but still able to explain things to parents in ways that they were able to connect with and understand.
As always please feel free to continue the conversation in the comment section below.
If you are interested in my other Becoming the Math Teacher You Wish You'd Had blog posts you can find a complete list here.