Card Sorts Can Promote Meaningful Math Talk

A MiddleWeb Blog

Here’s the first post in MiddleWeb’s new blog about mathematics in the middle grades. Our blogger Michelle Russell will bring her experience as both a middle and high school math teacher to her articles, always with the middle level in focus.

Every teacher’s challenge is to provide meaningful activities that promote student engagement. It’s been my personal experience that this goal is much easier said than done.

In the past, it was rare for me to hear students having the kinds of mathematical conversations I wanted to hear. I wanted to hear students analyzing, comparing, and even debating about math and math processes. But simply assigning students to work with a partner to complete a worksheet or set of problems did not produce the types of exchanges that I thought they would.

Often, one student would just take over and complete the activity while the other student remained idle. I realized that simply pairing students together was not the answer. So this school year, I’ve relied heavily on card sort activities to promote math conversations among my students.

The what and why of card sorting

Card sorts are not a new activity by any means, and they can take a multitude of forms. In their simplest form, information of some kind is written on a card and students put them in groups based on some criteria.

Sounds simple, doesn’t it? However, just the act of deciding how to group the cards requires students to work at the analysis level. Every time I did a card sort in my classroom this year, I had at least one group surprise and impress me with their thinking. Often, it helped me understand where my students were having difficulties. I could listen to their conversations and see where the stumbling blocks were.

In all honesty, I had tried card sorts in the past and was a little underwhelmed with the results. However, after some reflection I realized that some of my teaching practices were sabotaging the outcomes I wanted to achieve. I had to alter a few of my own behaviors before I achieved the results I was looking for.

Making card sorts more meaningful

One of the adjustments I had to make was to quit being the go-to person when a student had a question. The card sort activity only promotes good conversation if the students are using each other as a resource.

It’s still hard for me not to answer a student’s question directly. In the back of my mind there’s always a little voice saying, “You’re the teacher, it’s your job to answer every question they ask.” I have to remind myself that the point of the card sort is for students to talk to each other.

I also had to realize that sometimes students will say the wrong thing before they say the right thing. It’s not always the best strategy to swoop in and correct a student.

The other adjustment was to only use a card sort when it was relevant and applicable. In the past, I’ve been guilty of using a card sort activity because we had just come back from a long break, or because I didn’t want one class to get ahead of another class. These were not sound reasons to bring out the cards.

To be successful, a card sort needs to be placed strategically into a lesson. I had to decide well in advance what I wanted the card sort to accomplish. Did I want to introduce a concept, reinforce or review, or even assess learning?

Card sorts should lead to a culminating activity

I have also come to see that any card sort activity needs a conclusion. Students need something to bring the activity together. It could be as simple as students sharing out how they sorted their cards and comparing their work with other students. The activity should not simply end when all the cards are matched.

Most recently I had my students complete an activity which required them to match a boxplot (box and whisker) to a frequency graph. There were 16 cards, which meant eight matches.

The only instructions were to match the cards that belong together. Students were to take turns making matches, and each student should be able to clearly explain why they thought the match was correct. I really thought the activity would be over in a matter of minutes. Wrong!

The students carefully weighed the characteristics of the graphs and discussed similarities and differences. What more could a teacher ask for? As I walked around the room, I saw numerous students holding a card and discussing the graphs’ characteristics.

The conversations that I heard would have never come about from simply assigning students problems to work. I know card sorts are not a new invention, but I find them to be highly effective in the right situation.

Have you used card sorts in middle level math? Please share ideas and questions!