Using Student Work Meaningfully
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
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.
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.
Design a re-engagement task
purpose of a re-engagement
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
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, firstname.lastname@example.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.