I am sure we have all seen it at one time or another – those math questions that make us cringe, furrow our brow, or just plain confuse us because we can’t figure out what is even being asked. Sadly, these questions are in math programs more often than they should be and even though they may completely suck, they do give us, as educators, the opportunity to have conversations about ways we could adapt them to better learn what students truly know. These conversations happen all of the time on Twitter and I really appreciate talking through why the questions are so bad because it pushes me to have a more critical lens of the questions I ask students. Through all of these conversations, I try to lead my thinking with three questions:
- What is the purpose of the question?
- What does the question tell students about the math?
- What would I learn about student thinking if they answered correctly? Incorrectly?
Andrew posted this question from a math program the other day on Twitter….
I tried to answer my three questions…
- What is the purpose of the question? I am not sure. Are they defining “name” as an expression? Are they defining “name” as the word? What is considered a correct answer here?
- What does the question tell students about the math? Math is about trying to interpret what a question is asking and/or trick me because “name” could mean many things and depending on what it means, some of these answers look right.
- What would I learn about student thinking if they answered correctly? Incorrectly? Correctly? I am not sure I even know what that is because I don’t know what “name” means in this case. Is it a particular way the program has defined it?
On Twitter, this is the conversation that ensued, including this picture from, what I assume to be, the same math program:
When a program gives problems like this, we not only miss out on learning what students know because they get lost trying to navigate the wording, but we also miss out on all of the great things we may not learn about their thinking. For example, even if they got the problem correct, what else might they know that we never heard?
The great thing is, when problems like this are in our math program, we don’t have to give them to students as is. We have control of the problems we put in front of students and can adapt them in ways that can be SO much better. These adaptations can open up what we learn about student thinking and change the way students view mathematics.
For example, if I want to know what students know about 12, I would just ask them. I would have them write in their journal for a few minutes individually so I had a picture of what each student knew and then would share as a class to give them the opportunity to ask one another questions.
After I saw those the problem posted on Twitter, I emailed the 2nd grade teachers in my building and asked them to give their students the following prompt:
Tell me everything you know about 12.
Look at all of the things we miss out on when we give worksheets from math programs like the one Andrew posted. I do believe having a program helps with coherence, but also believe it is up to us to use good professional judgement when we give worksheets like that to students. While it doesn’t help us learn much about their thinking it also sends a sad message of what learning mathematics is.
I encourage and appreciate conversations around problems like the one Andrew posted. I think, wonder, and reflect a lot about these problems. To me, adapting them is fun…I mean who doesn’t want to make learning experiences better for students?
Looking for more like this? I did this similar lesson with a Kindergarten teacher a few years ago. Every time I learn so much and they are so excited to share what they know!