There has always been a comfort to mathematics in knowing that there is just one right answer. You are either right or you are wrong. I am here to make that comfort a little uncomfortable.
Recently, I gave out a poll on LinkedIn and Twitter about the following question:
We can probably all agree that a correct answer to this question is 43 miles per hour. But would you accept anything else? 43 with no units? mph = 344/8? 43 miles?
On LinkedIn, 33% of my respondents said they would accept 43, and 67% said no.
Many comments mentioned the importance of units and that the answer “43” is incomplete without “miles per hour”. Someone else chimed in that if 43 was one of four multiple choice options on a test with no listed units, that it would definitely be the right answer.
On Twitter, we also found disagreements:
All of this begs the question, what really is the correct answer? I thought there was only one right answer to a math question. That is clearly not the consensus. So, how can we judge students strictly off of how many questions they get right on an assessment when we can’t even agree what the right answers are?
I believe there is a better way. There is so much information in every answer that students give us and it is information we can all agree upon.
Unlike the correct answer, everyone was able to identify that the answer 43 (no units) included evidence of proper computation, but did not show the units. We all agree on this. Breaking this answer down into its constituent parts allows us to find common ground so that we can treat both the answers and how to improve them in the same way.
In this question, there are 3 parts that students must complete to get “43 miles per hour”.
- 1 — Correctly compute.
- 2 — Understand the context of the question and know to divide miles by hours to get a rate.
- 3 — Make sense of and add the units to their answer.
With that said, there are many possibilities for answers. For example, students may correctly do some computation (Part 1), but nothing else. (Ex. 344 + 8 = 352).
Students may understand the context of the question (Part 2) and know to divide and include the units (Part 3), but incorrectly compute (Part 1).
Ex. 344 miles/8 hours= 45 miles per hour.
And inevitably, students will also do a variety of other combinations of these things depending on which parts they successfully complete and which they do not.
Breaking the answer down this way allows us to not only be more specific in our feedback, but also have a shared consensus across our beliefs about correct/incorrect so that we can focus on actionable next steps.
So, what next?
How can we best direct our efforts to support this student? Do they need help with their computational skills? Did they not understand the context of the situation or what to do? Did they just forget to add their units?
Each of these questions give us insights into how to re-engage with and support students in a meaningful, effective way; something a simple right or wrong does not provide.
At Math ANEX we are working to re-think how we view answers and what we can do with them. If we can utilize and organize all of the information students are giving us to help focus and direct teachers action, we will actually be helping move student thinking and understanding forward. And we believe this, rather than just reporting on right and wrong, will truly make a difference.