Mathematicians...A Follow Up

Last week I had parent teacher conferences on Tuesday and Wednesday.  On Monday I realized that I hadn't had students complete any sort of end of quarter reflection like I have in the past.  This year, after reading Tracy Zager's book Becoming the Math Teacher You Wish You'd Had, I have been helping students focus on what we do as mathematicians.  I decided to take the posters I made (blog found here) and turn them into our reflection sheet. 
Here is what I came up with:

Link to Document

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:

 Many students interpret "Ask Question" as asking when they don't understand.  I want students to tap into their natural curiosity.  Noticing, Wondering, and asking Why does that happen? are characteristics of lifelong learners.  I want this for my students.  (Insert plug for Table Talk Math Here - flyer for conferences)

 Yea! The vertical non-permanent surfaces are a success!  We often use the whiteboards to show our proofs.  That way everyone can see our work when we are explaining our reasoning and can compare strategies. 

Many students think they are bad at math because they don't get it instantly.  They want the teacher to explain it step by step so they can follow those steps.  That is not how I teach math because I don't believe that is math.  Math is what happens in the confusion.  That is where students are working to make sense of numbers and relationships and looking for patterns.  Of course we need to come out of this fog at some point but some days it is just to move to a different fog of confusion. 

 We do a lot of sense making in class.  Often times the models that parents don't understand (because we didn't learn with them) are not necessarily how we will solve the problem, but instead they show us the number relationships and deepen our understanding.  This helps engage our intuition when working so we can see if our process and answers make sense.

Some students make errors because they don't understand the concept.  The fix? Help them understand the concept.  Then there are students who make errors even though they understand the concept.  What is the fix?  Focus on precision.  A benefit to learning multiple strategies is that we can go back and solve another way to see if we get the same answer, or use a model to check our thinking and engage our intuition (see above).

Another strategy for checking over your work is to go back and tell yourself it is wrong.  It is one thing to look over work to see if there is a mistake.  We are much more analytical if we go back and look at the work as if there is a mistake. 

These two make me so happy.  Both students recognize that they need to grow in these areas, but these responses show me that understand their depth of understanding is important.  They can no longer have just surface level knowledge (memorizing rules).  We are moving to variables and more abstract math.  We need to understand these number relationships so we can apply them to problems where the numbers are not as concrete. 

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.