Simple Steps for SELECTING and SEQUENCING Student Work
Post 4 of 5 in the Series ‘Orchestrating Math Discussions’
This blog series is inspired by the book 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret S. Smith and Mary Kay Stein as well as our own classroom experiences.
In our previous post, we discussed monitoring student work to learn how students are engaging with a task. This takes us to our next two practices in orchestrating productive mathematics discussions – selecting and sequencing. While monitoring, we intentionally select and sequence student work to be shared during the class discussion. Selecting and sequencing prepares us to intentionally navigate the discussion toward our learning goals. Here are four simple steps for selecting and sequencing student work.
Steps We Can Take When Selecting and Sequencing:
- Seek a variety of approaches. While monitoring exploration of a task, look for student work that represents a range of approaches and levels of understanding. Choose work samples that highlight different problem-solving strategies, have varying amounts of detail, approach the math in unique ways, and support classmates in moving toward the learning goal.
- Consider addressing common mistakes and misconceptions. When appropriate, select a student to share a mistake or misconception related to the underlying math. This provides a valuable teaching moment to address misunderstandings, clarify concepts, and highlight the benefits of learning from mistakes. During task exploration, prepare this student by posing questions to uncover their mistake or misconception. This allows the student to change paths, adjust their work, and not be caught off-guard during the class discussion. Once the mistake or misconception is brought to the surface, ask the student to share this experience with the class so others may learn from it.
- Prepare students to share their work. Consider telling those students who will be sharing their work, and suggest they rehearse explaining their thinking to a classmate. This allows students to think through their strategy a second time, practice using precise language, and refine their ideas if needed. It can also be helpful to take pictures of the work to be shared and display these pictures during the class discussion. Taking pictures ‘freezes’ student work in the moment and allows students to easily share work involving concrete objects.
- Intentionally sequence the tasks to be shared. Finally, consider how to order the selected work samples in a deliberate sequence that builds to the lesson goal. This sequence can be thought of as a storyline. Just as there are many ways to tell a story, there is no one correct way to sequence student responses (Smith and Stein 2011). Often, teachers start with the most accessible strategies and move toward more complex or abstract ones. However, there are many ways to sequence student work:
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- Most accessible strategy to more complex or abstract strategy
- Most common to most unique approaches
- Concrete to abstract representations
- Partial to complete solutions
- Least to most detailed
- Begin or end by sharing a common mistake or misconception.
It is important to vary the way in which student work is sequenced from lesson to lesson. For example, any of the above sequences may be shared in reverse when appropriate. Repeatedly sequencing in the same way can unintentionally cause students to think one strategy is better than another, especially if the most detailed or efficient strategy is always shared last.
Selecting and Sequencing in Action
Think back to Ms. Reames’ jumping contest task from previous posts in this series:
In order to move students toward the learning goal, the work Ms. Reames selects might include:
- Draw a number line and count down from 35.
- Write an equation with a missing number and count on from 18.
- Represent 18 and 35 with connecting cubes, and count to find the difference.
- Show 35 with 3 tens sticks and 5 ones, trade a ten for 10 ones, then remove a ten and 8 ones.
- Use known and derived facts by adding on from 18. Add 2 to get to 20, 10 more to get to 30, and 5 more to get to 35.
- Decompose 35 into 20 and 15 in a place value chart and then subtract 20 – 10 and 15 – 8.
Here is a collection of work Ms. Reames selected to highlight during the class discussion. How might she sequence these work samples? What story will the sequenced work tell?
Student 1’s Work
Student 2’s Work
Student 3’s Work
Student 4’s Work
Summary
Selecting and sequencing student work prepares us to have a productive mathematics discussion. Selecting and sequencing will vary depending on the learning goal, and there is not one right way to do this. The key is to sequence in a way that makes the math visible for all students and builds a storyline across the work samples. Ultimately, this storyline will be used to move students toward meeting the mathematical goal.
Whew, we’ve come a long way in our journey to orchestrate math discussions, but we’re not finished yet! Stay tuned for our final post in which we’ll examine how to make connections among the student work shared during a mathematics discussion.
Need help sequencing student work? These Progression Videos from Graham Fletcher might get you started. This series of videos shows how math concepts and students’ strategies build and grow through the grade levels.