Reflection: Joy Mistakes & Peer Instruction - Section 2: Warm up


The value in this lesson is really how it helps students change their minds about what it means to struggle in math class and helps take the sting out of making mistakes. The Common Core Mathematical Practices contain new expectations for kids that can be really uncomfortable and threatening for some of them.They are expected to struggle and persevere which may contradict their previous notions of what it means to be good at math.

  • If they have come to believe that arriving quickly at the correct answer using the single prescribed set of steps is what defines success in math class they may give up when faced with a problem that asks them persevere.
  • In this mindset mistakes expose their deficiencies and are to be avoided or hidden.

I wanted to normalize mistakes, make them part of the learning process and to foster the idea that dissagreement was not a competition about who is right or wrong. I wanted them to experience the struggle and then the joy of figuring it out.

This lesson also promotes the sharing and learning from multiple methods even if they are inefficient, and teaches my students to discuss options which is imperitive in order to persevere and make sense (mp1). One way to facilitate this is to ask probing questions that will uncover structure or connections in the math:

  • "How did Juan come up with the 300?"
  • "Why did he choose 300 and not some other number?"
  • "Will that always work?"
  • "What part of the fractions tells us whether the they are equal or if one is greater?"
  • "Why does that make sense?"
  • "When is Juan's method easier/harder to use?"
  • "When is Ben's method easier/harder to use?"
  • "Is there another method that might work?"

My student often recognize that Juan cross multiplied, but this is a procedure that they often use incorrectly. These questions help them understand why cross multiplying works by uncovering the equivalent fractions involved.

Even though most of my students concluded that Juan's method was not the best one to use here they experienced a lot of learning because of his inefficient method and I could point out "look how much math we learned from Juan's strategy!" I look for these opportunities to turn inefficient methods and mistakes into learning experiences in my lesson planning by anticipating student responses & misconceptions. I try to uncover the foundational math that may have been hidden in the procedures they have tried to memorize.

  Changing student mindset about struggle and mistakes
  Joy: Changing student mindset about struggle and mistakes
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Mistakes & Peer Instruction

Unit 5: Writing and comparing ratios
Lesson 13 of 14

Objective: SWBAT use peer instruction and error analysis to determine the most efficient strategies for comparing ratios.

Big Idea: Though there are multiple methods, certain strategies are more efficient for certain types of problems.

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Math, Number Sense and Operations, proportional relationships, common denominator, peer instruction, comparing ratios, error analysis, ratios, pattern, conceptual development, safety
  49 minutes
verifying juans work
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