Reflection: Positive Reinforcement How Do You Know? - Section 2: Warm up


One word that, year after year,  has gotten in the way of communicating about integer concepts is "bigger". For example, my students will explain that the sum of -3 and 5 is positive because the positive number (5) is "bigger" than the negative number (-3). In past years I might have told my students that this statement is incorrect and then given them a counter example like -8 + 5 in which the positive number is still "bigger" (by definition) than any negative number, but the sum is not positive. Although my intentions were good this response never really had any great impact on their understanding. By drawing attention only to what was wrong my students assumed that their thinking was also wrong. 

I knew that what they were noticing was exactly right. It was just the word they using to describe it that was incorrect. I knew that they were recognizing that the number they were calling "bigger" was farther on the number line from zero, but I wasn't giving them any credit for their thinking!  

I recently started responding a little differently, in a way that gave them credit for their thinking, while at the same time addressing the precision in the speaking. I began saying things that gave credit for the thinking but called into question just the word:

  • "I think you are noticing something really important and helpful, but his word "bigger" isn't quite getting at it" 
  • "Bigger isn't the word he/she is looking for since all positive numbers are 'bigger' than all negative numbers. What is it he/she is explaining?"
  • "What does he/she mean by 'bigger'?"
  • "What is it he/she is noticing?" 

These questions still focus on precision while keeping the students thinking at the center. If we don't make misconceptions or miscommunications a specific focus students never get a chance to sort them out.


  Misconception or miscommunication?
  Positive Reinforcement: Misconception or miscommunication?
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How Do You Know?

Unit 4: Operations with Integers
Lesson 10 of 24

Objective: SWBAT explain and use evidence to support their explanation of when a sum will be positive, negative, or zero.

Big Idea: Students explain their reasoning so they better understand and internalize the relationships in positive and negative numbers.

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Math, Number lines , Number Sense and Operations, Integers, Operations and Expressions, Integer Addition, hot & cold cu, argumentation, questioning
  54 minutes
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