Wrong but not Crazy

pexels-photo-207756.jpegI’ve been reading a lot about formative assessment lately and one recurring theme that stands out to me is the importance of wrong answers. From multiple choice questions to class discussions, finding students’ misconceptions, incomplete understandings, over-simplifications and over-generalizations is so much more valuable than seeing how many questions students can answer correctly.

Intuitively, I think I have always kept an eye out for common mistakes so that I could warn students to avoid them. At some point, I think every math student makes mistakes like these:

  • treating 2^3 as equivalent to 3^2 because 2×3 is the same as 3×2
  • treating 3x^2 as equivalent to (3x)^2

Now, rather than preemptively warning students about such mistakes, I let students find them during the learning process. I now spend a lot more of my class time engaging students in discussions about answers that areĀ wrong, but not crazy. One of my favourite ways to do this is with multiple choice questions. Using a digital interface like Kahoot or a google forms quiz, I get a graph of how many students selected each option and I show this to my students. The graphs are anonymous, so no one sees who chose the wrong answers, but those who did answer incorrectly see that they’re not alone. I’ll point to the bar or segment of the pie chart that represents each wrong answer so we can discuss why that option is wrong but not crazy. Students can identify the misconceptions and suggests examples, reasons and explanations for clarification. I’m there to guide the discussion and correct, clarify or re-direct as needed, but most of the time the students identify the errors in reasoning and explain how to avoid them.

There are lots of things I think about this strategy:

  • it supports a growth mind-set: This classroom practice makes mistakes a normal and valued part of the learning process
  • it’s equitable: All students spend the time and effort reflecting on incorrect answers and all students benefit from that discussion.
  • it improves my practice: by forcing me to pay attention to frequently-made mistakes, I dig deeper into their root causes. I can address those misconceptions before moving on, and I can revise my approach the next time I teach that topic, concept or skill.

This is an iterative process. It takes time to discover, develop and refine prompts that will reveal students’ reasoning and give me insight into what misconceptions there are. To make sure I don’t forget what I’ve learned from one year to the next, I like to edit my resources as soon as I’m done with them so that they’re revised and ready for the next time I need them.




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