Things Good Mathematicians Do

What make a good math student? What makes a good math teacher? 

These are questions we must ask ourselves as we begin our journey to becoming teachers. We all have horror stories of the bad math teacher who could only explain how to do a problem one way, and if you didn’t understand it, then you were in the woods alone. However, I’m sure we were also lacking the skills to open ourselves up to learning math. How were we expected to learn if we weren’t given expectations? We need to start thinking about not only how are we going to teach our students math, but how we are going to teach our students to learn math.

I started my placement at a school yesterday. It is a grade six/seven split class, and we have a lot of students at a below grade level of knowledge. However, my associate teacher had an amazing list of expectations or guidelines of math learning. This list went something like this:

“Things Good Mathematicians Do”

• Use math words when talking, sharing and recording
• Use tools to solve problems
• Share their thinking and learn from each other
• Record and use math pictures to show their thinking
• Give proof to their thinking
•  Learn from their mistakes
• Ask Why

We were working through math word problems and they were put into groups of two to solve the question and put their answer on chart paper, and we would do a gallery walk afterwards. What made this list wonderful was after we had finished the gallery walk of a math problem, she referred to this list to highlight how they excelled in their learning. She pointed out how they shared their thinking, used of math words, gave proof. Even though not all the children had the right answer, it still focused on the skills needed to excel at math. It gave a positive outlook towards problem solving. It kept things positive.

So if these expectations for students work, then why not create a list of what makes a good math teacher? An interesting article by Balland Bass discusses this very topic. Many teachers believe simply enhancing their knowledge of mathematics will make them a better teacher. The more you know, the more you can teach on the topic, right? It is important to know the subject of course. Can you imagine teaching music theory if you don’t know a rest from a note? Of course it would be rough. But knowing how to do the math is not enough. Teachers need to know how to unpack the math. We need to know how to break it down. This ability will help us guide our students though the steps the need to find the solution, especially when it’s not making sense.

At placement yesterday, while the students were figuring out their solutions to the math problem, I went around to see how they were doing. One group was struggling where to begin. They couldn’t figure out how to break down the word problem to an equation. I had to walk them through how to break down the question. Where was the information we needed to find, what information were we given? We eventually got the equation written out and they had to find the next part of their solution. It was interesting to see how they got their answer; it was a different way than I would have found the solution. Another group found the solution by themselves, but they also found it a different way. Instead of using division, they used subtraction.

When teachers know how to unpack a concept completely, they not only know how to teach students how to get to a solution, but they also know that there can be many ways to find the answer. Their students might take a different path than the “quickest” way we might do it, and that’s okay. At least they are going through the steps. This is just as important as knowing how to do the math, because not only will our students find different ways towards to solution, but it will also help us when they do not find the solution. When they show their work, if we know all the different ways they could get the answer, we can see where their thinking process is going, and intervene exactly where they might need clarification of a step.

So, this is the list I propose teachers keep in mind when teaching our students math:

“Things Good Math Teachers Do”

• Have mathematical knowledge
• Know how to unpack concepts
• Keep an open mind to unique solutions

Keeping this in mind, over the next few weeks, especially in placement, I want to focus on the mathematical process that is outlined in the Ontario curriculum:

• Problem solving
• Reasoning and proving
• Reflecting
• Selecting tools and computational strategies
• Connecting
• Representing
• Communicating

I want to particularly focus on problem solving and the reasoning behind this problem solving. Watching the children get to their answers was so interesting, and it was exciting to hear them explain and defend their reasoning behind solving it the way they did between peers. I want to keep this in mind for my teaching. I feel that sometimes my first instinct is to correct and guide them to the way I would answer the question, when I need to remember that they need the freedom to find they answer by themselves to learn.

Would you add anything to the lists? Add your suggestions in the comment section below!