Reflection: Student Feedback Integer Addition & Subtraction Assessment - Section 2: Warm up


When my students are learning new ideas and vocabulary their explanations are often unclear and imprecise. They use language that is accessible to them and I often don't understand what they mean at first. Anticipating ideas the students might come up with (including misconceptions) helps me recognize them in 'kidspeak'. The language they use doesn't always match their level of conceptual understanding.

For example, if I predict that students might notice the big idea that:

When we add integers with opposite signs, we find the difference and the solution will be positive or negative depending on which integer was further from zero.

I am more likely to understand and recognize this idea when my student says:

"If, like, the numbers are different, I minus them and then the bigger number makes the sign."

Then my goal becomes helping my students attend to precision and clarify their meaning. The imprecision in his language can lead to misconceptions and I definitely want to attend to this by drawing the students' attention to it. However, I don't want my attention to the imprecision to cover up the developing conceptual idea. So, my task becomes twofold: clarifying and correcting the language while, at the same time drawing out the mathematical idea. 

I might start by asking this student or asking the whole class to help clarify the words different and bigger:


  • "what do you (does he)  mean by 'different'/'bigger'?"
  • "Can you give me an example of what you/he mean(s) by 'different'/'bigger'?"
  • "different in what way?"
  • "could you show us using a number line/symbols?"


Then I would help the class rephrase this student's statement using more precise language.

Without first taking the time to predict how students might understand and explain the math in their own words I might not recognize the mathematical ideas they are approaching or see how to help them.

Anticipating doesn't mean I understand what a student is trying to say everytime. There are still times I can't make heads or tails of what a student is saying. In these situations the above questions can help me understand. I also might just ask the student to explain it again or the class if anyone can explain the idea in another way.

When I added these two questions to my reperatoire I gained so much more insight into my students' thinking:

  •  "what do you mean by that?" ("what do you mean by 'adding more minus'?")
  • "can you tell me more about that?"

  Why it's important to anticipate student responses
  Student Feedback: Why it's important to anticipate student responses
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Integer Addition & Subtraction Assessment

Unit 4: Operations with Integers
Lesson 19 of 24

Objective: SWBAT add and subtract integers mentally and/or using a number line.

Big Idea: Students demonstrate their understanding that subtracting is equivalent to adding the additive inverse.

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Math, Number Sense and Operations, Operations and Expressions, adding integers, subtracting integers, Additive inverse, integer operatio, open ended questions, lesson planning
  54 minutes
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