As teachers, we want students to succeed by arriving at the correct answer. It signifies an understanding of the material and can contribute to a student’s confidence. An emphasis on the “right answer” is particularly evident when studying mathematics. Unlike a subject like science where various theories can be entertained and justified, there is a rigidity in mathematics that increases the stakes for providing the one correct answer to a problem. The way in which a teacher responds to a student’s mistake can promote or discourage future participation in mathematics learning.
You are teaching a grade one class single-digit addition. You write the question 5+3 on the board and ask the class whether anyone can solve the problem. One child puts up their hand and says the answer is 7.
Here are three ways to respond while maintaining the student’s confidence and enhancing their learning.
1) Ask: How did you solve the problem?
This is one of my favourite questions because it provides insight into the child’s thinking, particularly where they went wrong. It’s a great question to ask intermittently – even when students get the question right! Sometimes, younger children have difficulty explaining their process. If so, try rephrasing the question: “If you were explaining this to someone who didn’t know how to add, say a younger sibling, how would you explain it?”
2) Make it obvious. Draw on previous knowledge.
Logically drawing on information students already know can help them realize they have made an error. In this scenario, you can have a child draw on math facts they already know. For example, ask a child to first solve 5+5. This a very familiar equation for many children, so they will likely provide the correct answer. Next, work your way backward by asking students to solve 5+4 and then finally 5+3. At this point, they will realize that 5+3 is 8, and 5+2 is 7. Breaking down these steps will allow your student to catch their own mistake.
3) When all else fails, try it together.
After asking students about their strategy to solve the problem, you may continue to be confused by their response. Try the problem together. For example, if the student says, ““I just added,” ask them to count up with you, beginning at the larger number (in this case, 5). For more complex problems, you may need to guess at what the child is saying and then find a way to communicate how you’re interpreting their understanding. I always find it helpful to write or draw as the child is explaining their thoughts. This way, you both have an opportunity to better understand the process. It’s also okay to nudge children toward the correct procedure! For example, a child may correctly begin, but get lost somewhere along the way. Encouraging a child to try to solve a problem, even if they don’t know how to finish it, increases engagement.
These strategies will allow you to better understand your student’s thinking, particularly whether the error was procedural or a lack of conceptual understanding. Moreover, these strategies help establish a neutral, inquiry-based environment where mistakes are recognized as a process of learning.