Upgrade Your Card Sorts

This is the blogpost version of a talk that I gave at CMC-S 2016 and NCTM 2017 on Desmos Card Sorts. I usually post slides, but in this case I’m not sure how useful the slides are without context. Hope this post can give you a sense of the value of a card sort and ways in which a card sort can support student learning along with the benefits of using a digital card sort.

The first card sort we did in the session was Card Sort: Quadrilaterals, inspired by Lisa Bejarano. This card sort asks students to sort a set of statements about quadrilaterals according to whether they are always, sometimes, or never true.

Here’s the "Responses" view of the dashboard for the first four students in the activity (using "Anonymize").  

The green piles indicate that all of the cards in the pile have been correctly matched. Red piles tell you that one or more of the cards in the group are incorrectly matched. Gray cards haven't been grouped yet. You can also see how many cards are missing from a group. 

You can click into individual student work (above) and check the answer key to see which cards students have missed. The image above shows that Hermann only misplaced one card for the "Sometimes" true pile.

You can also use the up/down arrows on the top left to scroll through student work to get a general sense of which cards students are matching incorrectly. Better than this though, you can go back to the summary view and see right away which cards students are incorrectly matching.

From here I might pause the class and zoom in on the card that students have incorrectly matched so we can have a conversation. I might ask my students to share how they paired the card and why, and let the conversation progress from there so that I can help students build towards a correct understanding. What I love about this is the way in which it honors existing ways of thinking. Students have a chance to share what they know about rectangles, and we can use this to develop a need for a precise definition. From there, once we've agreed that a quadrilateral with four right angles is the way to define a rectangle, students can see that a square is an example of a rectangle that has perpendicular diagonals.

The second card sort we did is Card Sort: Linear Functions from the Linear Bundle, and it is an open card sort. This means that it has no answer key. After working on this card sort I showed the dashboard and we talked about different ways that the dashboard can be used to support student learning.

For an open card sort, you can see the most common groupings (above). Since there is no one right answer, the teacher can pair different groups of students together to talk about how they sorted. This is especially helpful in this open card sort where the goal is for students to deepen their understanding of the characteristics of linear functions. Instead of pairing students or groups to discuss, you might screenshot some pairings that highlight similarities and differences that you’d like the entire class to see.

Here the teacher might pose the questions “Which did you pick and why? How might the other group have decided to pair these cards together?”

This card sort had two additional screens that also provide opportunities for rich conversation and student learning. Screen 2 is below.

There are two choices a teacher can make on this screen. First, a teacher can select a set of answers that will be most beneficial for the class to hear. In many cases, sequencing these answers from less formal to more formal can help students at all levels to access the conversation and grow in their understanding of the mathematics involved. Second, a teacher can make use of a screen like this give a voice to students that don’t usually raise their hands to participate. One move I’ve seen teachers make is to let the student know ahead of time that they have an answer that will be valuable for the class to hear. 

Screen 3 (above) is similar to Screen 2 in that teachers can strategically select students to share student work. An additional benefit of a screen like this is the controversy that it can introduce. Below are some of the responses from Screen 3 from the NCTM session.

Most of us gave a response along the lines of the first three bullets. I intentionally planted three of the "Other" responses based on responses I've seen in classrooms, but there were still 5 responses from our session where participants had differing views. Being able to see these responses in the dashboard lets the teacher pair these students with other students to sort out their differences. Between this screen and the others in this open card sort, I appreciate the message that the knowledge doesn’t have to come from the teacher. I can learn from my classmates, and the can learn from me!

We ended the session with a brief tour of teacher.desmos.com, along with how to find pre-made card sorts and how to build your own. For more info on this head to learn.desmos.com/cardsort and learn.desmos.com/create. Also please feel free to chime in with your card sort successes! I’d love to hear more about how people are using card sorts to support student learning.