Most teachers agree that learning mathematics is a process, and that process is not linear. Indeed, students make many errors as they learn. Those errors aren’t bad, they are a natural and critical part of the learning process.
We should use errors as points of celebration! Errors make for some of the best discussion points. If everyone does everything correctly, there’s not much to discuss. Errors also mean that students tried something! The desire and follow through to try something (even if it doesn’t work) is what many of us hope for from our students. We learn from our errors and reflecting on those errors leads us to more fruitful endeavors.
Although many of you may agree that errors deserve a place of glory in the mathematics classroom, students don’t always see errors as a good thing (shocking I know). One reason for this might be because we tend to ask for correct answers in the mathematics classroom. Also, we tend to only show our final, correct draft solution strategies rather than our incomplete, messy, rough drafts (shoutout to Mandy Jansen).
Here’s one simple idea to exalt the glory of errors: ask for them. That’s right, all I want you to do is ask for wrong answers. Here’s an example. Say you show students this equation to solve, x + 3 = 5. Don’t have them solve it, though I know you want to. Instead, ask them for some answers they know are wrong and have them explain how they know they are wrong. Here are some things they might say in our example:
- 0 is wrong because if you don’t add anything to 3 you won’t get 5.
- I know a negative number would be wrong because you have to add something positive to 3 to get to 5.
- I know a million is wrong because it would be way too big.
What’s so great about this? First, students feel very comfortable when they aren’t on the hook for a correct answer. Many students fear sharing their thinking because they don’t want to be wrong. Second, we have narrowed down the list of potential answers, we know it is positive and less than a million. This can help students further develop their number sense. Third, this encourages students to share their reasoning, something we can all get behind.
I hope you try out this strategy and let me know how it goes!
Love this idea! It reminds me of a similar strategy, when students provide a wrong answer, ask the whole class “what question is [student name] answering?” Also, as standardized testing season is approaching, we have been looking at test review questions. One of my students favorite things to do with multiple questions is to think about where the test authors got the wrong answers, which closely relates to this idea you are sharing. I will definitely give this a try!
Hi Joey, I like your ideas too! I will definitely mark these to remember for the fall when I am working with preservice teachers again. 🙂 I especially like looking at the distractors on multiple choice to see if we can think about why they may have put them there, it’s like a detective game 🙂