Like responding to mathematical mistakes, addressing misconceptions requires that we take back the least amount of responsibility from students as necessary and release it as soon as possible. Yet, misconceptions require additional intentionality to deconstruct inaccurate frameworks and reconstruct correct ones. The construction of understanding requires the use of methods that lead to meaningful mathematical dialogue. Since you respond because original methods did not lead to student understanding, your adjustment must recruit a different method to promote this dialogue (as opposed to “doing it over” in the same way, slower, in a smaller setting and/or with a louder voice). The following table presents a high level guidance for methods to use when your original was not successful.
| Method | Use Cases | Considerations |
| Think Aloud | Communicate a cognitive process to teach how to think, wonder, compare, analyze, etc. |
Think Aloud's are dynamic. They can model any thought process and focus students’ attention on any conceivable aspect of what we do when thinking through mathematical content and at any aspect of mathematical rigor. Suitable for:
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| Select, Sequence & Connect | Generate an awareness of misconceptions, analyze how they impact mathematical decisions, discuss the false mathematical beliefs, and illustrate correct mathematical reasoning. |
Structured discussion using student work is versatile enough to achieve the ends of a Think Aloud yet rely on students themselves to clarify misconceptions that exist (or may potentially exist) at a class-level. Ideal when the evidence of inaccurate inaccurate thinking leading to the misconception is clear. Suitable for:
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| Select & Connect | Pinpoint and discuss a specific misconception focusing on a single work sample. |
Show calling work can be thought of Select & Connect to focus your adjustment on specific aspects of student (or teacher) work to quickly highlight misconceptions. Suitable for:
More on how to implement Select & Connect |
| Multiple Methods & Representations | Use a variety of instructional methods and mathematical representations to draw connections between concepts when confronted with a misconception. |
Multiple methods and representations help students connect between the ways in which we perform mathematics and the mathematical content itself. In doing so, we position students as sense-makers accountable to monitoring their own conceptual misunderstandings and, eventually, to reflect fixed ways of approaching mathematics. Suitable for:
More on how to implement Multiple Methods and Representations |
| Model the Process | Model a process that requires two or more stages while highlighting the underlying concepts embedded in the process itself. |
Akin to “Naming the steps,” this method deepens the focus on concepts embedded in the “steps” themselves. Suitable for:
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