By David Wees, posted June 22, 2015 –

If you read my first and second post, you learned about a strategy that allows you to sort student work into categories of responses. Now what can you actually do with this work? The goal of this post is to describe a few ways that you can use the categorized student work meaningfully.

1. Group students homogeneously by strategy

In the diagram below, the colors represent the strategy the student used, and the shading of the color represents the degree of sophistication with which each student used that strategy.

One way to use the categorized student work meaningfully is to group students so that they can talk through their approaches, perhaps homogeneously grouped by strategy but not separated by success with their strategy. In other words, you might want to place students who used numerical calculations to solve a problem in one group and those who used an algebraic approach to solve a problem, regardless of their individual success with that strategy, in another group.

One caveat of this approach is that you should ensure that the way you have designed the categories does not lead to all the highly successful students being placed in one group and all the unsuccessful students being placed in another. The groups should have homogeneity around strategy but variety around overall success.

The primary advantages to this approach are that you can offer different feedback to each group based on their choice of strategy. This will push all those students to consider a strategy. You can structure their work together so that students also get feedback on how well they used that strategy.

An obvious issue with this approach to using the categorized student work is that it leads to a potentially much larger variety of groups than you or your students may be accustomed to, but there is some recent evidence that this is actually a good thing. Asking students to sit in different locations and work with different people means that they are less likely to attach those ideas to where they were sitting and with whom they were working.

2. Group students heterogeneously by strategy

You can also form groups of students who thought about the mathematical task in different ways, and create heterogeneous groups based on strategy and based on each individual’s success with the strategy. In this case, the purpose would be to offer students a chance to share their different strategies and still have the potential to get feedback on their individual approaches to the task. This has to be carefully described to students as an opportunity to learn about different approaches and to explore those different approaches, rather than to abandon one approach in favor of someone else’s approach.

3. Design a re-engagement task

The purpose of a re-engagement task is to use specific examples of students’ work to have all students rethink how to approach a task differently. Here is an example of a re-engagement task for students based on looking at how a pair of students (incorrectly) factored a quartic expression.

To be able to plan this activity, you not only need access to the student work but also need to be strategic about which student work will help all your students deepen their understanding of the mathematics. It is helpful, therefore, to look over your student work and analyze it for what it might mean and what approaches might be helpful for everyone to see. The categorization of student work may help you find the approaches students have used that align to a mathematical goal you have for them.

4. Plan your unit or lessons based on the mathematics students are using

The diagram above is an abstraction and visualization of a potential learning progression.

The last strategy I will share is simply stated but hard to do. If you look at these learning progression documents produced by the authors of the Common Core, you may notice that they describe arcs of mathematical understanding for your students. If you categorize what students are able to do and then compare it with the learning progressions, it may help you make decisions about how to move each of these groups of students forward in their learning by helping you focus on the mathematical ideas that may be next in their learning progression.

Choosing this response to the categorization exercise will require you to dig into the learning progression documents. You will, also, need to examine the topics and the level of understanding your students have about mathematics that they were exposed to in earlier grades. Student understandings then become stepping-stones to developing future mathematical understandings.

In my final post, I will outline how this work connects to developing your practice as an educator using the framework outlined by Deborah Ball, Mark Thames, and Geoffrey Phelps about the mathematics that educators need to know to be successful with their students.

David Wees, dwees@newvisions.org, is a Formative Assessment Specialist for New Visions for Public Schools in New York. He tweets at @davidwees and blogs at http://davidwees.com.