Friday, September 29, 2023
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# Using Positive Feedback in Math Classrooms

Providing math students with positive feedback can help them clarify their thinking, take risks, and apply concepts in new contexts.

If you were a “good” math student, your teacher may have filled your papers with a checkmark next to each correct answer. But handing back “perfect work” with a slew of checkmarks is a missed opportunity for math teachers. Every time we provide a student with feedback, we have a chance to send a message.

We can signal what we value and the strengths we see in the student’s work, providing insight into areas for growth and further learning. In math we value clarity and logic, creative solutions, perseverance, and curiosity. Used strategically, positive feedback can reinforce these cornerstones of the discipline. Although the examples I provide in this article are geared toward middle and high school math classes, positive feedback can be used at a variety of grade levels.

### Reinforcing Effective Communication

Math teachers frequently ask students to show their work. When students give us insight into their thought processes by writing enough on the page, we can provide positive and specific comments in return. Our reinforcement helps students learn what specific aspects of their work were effective at clarifying their logic.

Here are some examples:

• Your explanation here helps me see how you got from one step to the next.
• When you defined the variable before using it, I was able to follow your reasoning.
• The sentence at the end helped me to see that this is your final answer.

All of these comments acknowledge the time that students put into explaining their reasoning. Providing positive reinforcement when students effectively convey their thought processes helps them develop into effective communicators of mathematics.

### Recognizing a Mathematician’s Craft and Choices

Math teachers constantly remind their students that “there is more than one way to solve a problem.” This is true—the art of problem-solving allows students to discover elegant paths to a solution. Math talks have become popular because of their emphasis on multiple problem-solving techniques. The comments that we make on student work can reinforce the value of mathematical thinking.

You might write something like these:

• I didn’t think of this strategy!
• This is a clever implementation of factoring.
• This step reminds me of the example we looked at when _____.
• I like how you adapted the idea from _____ to this problem.

These comments will help students see their technique within the space of many pathways to a solution. When we reference the strategy that they used and contextualize it, we help them connect their problem-solving process to the content.

### Celebrating Growth and Perseverance

Math is hard! Math teachers must find ways for students to grapple with the content and engage in productive struggle. If we give students credit for their progress and perseverance, we can encourage them to push through challenges the next time they arise.

Here are some examples of how you might emphasize growth and praise perseverance:

• Great job catching the mistake here.
• I can tell this was a long and messy computation. By keeping your work organized and sticking to your plan, you persevered.
• I noticed that you had trouble with this skill in the last unit, but you have mastered it now! Great job sticking with it.

Students don’t always notice their own growth. When we can point it out to them, they see that their hard work and struggle is worth it.

### Encouraging Reflection

When students perform at a high level, positive comments can push their thinking beyond the standard content. With feedback, we can inspire their curiosity and encourage deeper thinking.

Here are some reflective comments you could make: