Recently, a conversation on Twitter caused me to question my practice of sequencing student work when debriefing a math task.

After having attended NCTM 2016 in San Fransisco where mathematical tasks was a major theme, I have spent a great deal of time thinking about how one plans and implements a math task. One of the books that I used as a resource was this one:

I was so inspired by the ideas of this book that I took many of the concepts presented and tried them with students to see how theory would play in practice. I wrote about one of these experiences on my blog titled Fraction Math Task in Action.

One of the 5 practices is to sequence the student work to be presented to the whole class. The authors state that “the key is to order the work in such a way as to make the mathematics accessible to all students and to build a mathematically coherent story line.” (pg. 44) The authors go on to list ways in which a teacher might choose to sequence:

- Presenting a common strategy first to create more access to the task
- Sharing a common misconception first to create clarity
- Moving through the concrete to abstract progression, as these strategies will be ripe with connections to each other and will provide connections for student learning

After having an opportunity to try these ideas with students, I saw just how successful tasks organized in this way could be. Which is why the above Twitter Chat really caused me great cognitive discomfort. Is it possible that I was “taking the agency right out of the hands of students and making the processing time amost algorithmic” (pg. 140) as Humprhreys and Parker suggest in their book *Making Number Talks Matter*?

At this point, I felt compelled to go back to both these books with a new lens to determine which strategy is best when engaging students in math talk. During this rereading, I noted that Humprhreys and Parker worried that pre-selecting and sequencing can put students in the position of thinking that one strategy is better than another, especially if the most efficient strategy is always shared last in the sequence. Students are more keen observers than we often give them create for and are likely to pick up on this pattern over time. I think we can all agree that we want students to take pride in their mathematical thinking and giving more value to one strategy over another can be the kryptonite to a student’s mathematical confidence.

As I continued to grapple with these seamingly different practices, I was drawn to another of my favorite books, *Intentional Talk*. Kazemi and Hintz offer four principles for mathematical discussions and it is the first of those that shed some light on this issue for me:

Discussions should achieve a mathematical goal. The mathematical goal acts as your compass as you navigate the classroom talk. (pg. 3)

With this quote in mind, I see now that perhaps the ideas presented in both *5 Practices for Orchestrating Productive Mathematical Discussions *and* Making Number Talks Matter *are not so much different theories as they are different practices for different goals. As Principles to Actions states:

Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions. (pg. 12)

It’s really a matter of knowing what you are doing and why you are doing it. What is the learning goal for this talk and what approach will yield the greatest results for students? As we know, time is limited, so we must be intentional with all decisions we make to ensure that mathematical success can be found for all students.

Thanks for your post! In particular, I connected with your summary: “With this quote in mind, I see now that perhaps the ideas presented in both 5 Practices for Orchestrating Productive Mathematical Discussions and Making Number Talks Matter are not so much different theories as they are different practices for different goals. ”

Your post also inspired me to re-read chapters 1 & 2 of Intentional Talk. I was struck by this quote:

“[Open strategy share] is one way of getting discussion going in the classrooms; it is clearly directed by the teacher and generally goes back and forth between the teacher and one student at a time. This type of back-and-forth exchange can begin to show students what it means to share their thinking. But it’s also possible for some students to check out easily or lose trck of what is being discussed.” (p. 27-28)

I have certainly seen (and lead!) some open shares that have felt aimless, or had students check out. Disengaged students might be bored, or they might be rehearsing/waiting for their own chance in the “spotlight.” This means that the conversational thread is lost, as well as the thread of mathematical sense making. Obviously, this doesn’t happen all the time, but it’s one of the reasons I like to sequence with a purpose in mind. I do like that Intentional Talk outlines several purposeful structures, e.g. Troubleshoot and Revise, that can get teachers out of that “least efficient to best” rut of sequencing.

Also: isn’t student disengagement the enemy of student agency? So even though they are able to direct the conversation, it’s not achieving the desired effect…? Also: students have different levels of readiness when it comes to agency in the classroom. Some students may be able to synthesize information from an open share to make connections and deepen their understanding of the mathematics. For other students, an open share can feel “zoomed out,” and the teacher needs to apply a clear lens or focus. It’s like how some people shut down when given a completely open ended task. They may get something out of it, but not as much as if there had been some additional structures in place. Open shares are immensely valuable, but I think we need to balance using open shares with other talk structures.

Ultimately, I think it comes down to the ideas you addressed in your concluding paragraph: it’s all about designing an experience that meets your goals for your students.

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I appreciate your comment about student disengagement being the enemy of student agency. If a student isn’t involved in the task, there is no opportunity to exercise said agency.

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