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Responding to Student Understanding Guide: Secondary Math

What is It?

Select & Connect, also referred to as Show Call, is simply sharing a student's work with the class to discuss a misconception and highlight correct reasoning.   Since this instructional adjustment is only two of Smith & Stein’s (2019) five practices to orchestrate mathematical discussion, Select & Connect will look and sound familiar yet feel narrower in scope.  Why?  When used, Select & Connect is ideal for times when longer discussions aren’t required to clarify misconceptions; this adjustment could be mere minutes if questions about the selected student work intentionally lead students to clarify mathematical reasoning as a group.  To that end, these short examinations can center on any aspect of any of Holmes et al’s (2013) misconception types: the use of vocabulary; computational errors from incorrect processes; false beliefs about mathematics.

How to Do It

When showing a single piece of work to lead students to clarify a misconception, you must develop a narrative through questioning.  Below are questions that can help students connect to accurate mathematical reasoning when looking at a single piece of student work as well as consider social emotional dynamics when student work is analyzed.

Possible Question Sequence Intention 
[To all] What do you notice about their work that makes it strong?
  • Start with identifying correct mathematical reasoning
 [To the student] Please, talk us through your process.
  •    Allow the student themselves to control the narrative of the task
  •     Opens the opportunity to name a misconception and share it was common throughout the class
 [To the student] When you were solving this task, was there a point where you asked yourself some questions?  What were they?
  • Open the space for the student to share their thought process, which may open up discussion on the reasons why misconceptions exist
  • Continues to position the student as the expert of their own work
[To all] Let’s all lend our thinking now.  Consider the questions they thought about.  Which can we answer here together?
  •    Invites everyone to help answer questions the student themselves asked to make support meaningful
  •    Since this adjustment is ideally for a common misconception, the floor is also open to others who made the same misconception to engage.
[To all] Look specifically at this section of the task.  How does this impact what happens after?
  •   Promote connections within the work itself to highlight the impact of a misconception
  • Push students to consider the reasonableness of the eventual solution to pinpoint the misconception
 [To all] What would be the misconception we’re seeing here?  What should we do?
  •      Explicitly name the misconception
  •      Work to clarify it
[To all] How does the work we analyzed help us all?
  •     Summarize how the misconception was clarified promote transfer within and among concepts
  •     Acknowledge the power of collaborative problem-solving
  •      Show gratitude for those who allow their work to be analyzed

 

Considerations

  • Depending on the culture you’ve set up for analyzing student work, it's a good idea to ask students' permission to show their work before you do so, especially if Show Call is a new method.  Also, consider opening Select & Connect with, “What makes this approach strong?”
  •  Preface the selection of student work with, “We’ll now see a common misconception that we can all learn from,” to narrow the discussion and save time.  Again, ensure your classroom culture is strong enough to acknowledge that misconceptions are a normal part of learning and are valuable for discussion as a whole group.
  • Work a common misconception in real-time on a blank task that models the misconception from the class to make the analysis anonymous.
  • Have a student re-working their example in real time as you ask questions.
  • Engage in turn and talks during your questioning sequence and leverage strategic partner pairings to engage in dynamic ways.

Recommended Resources for Further Inquiry