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!
If the interim test or the end of year state mandated test asks it this year, then we must teach them the meaning of this question — nutty or not. But of course, we can’t know that exactly because the teacher is not allowed to see the questions. Not a smart way to go, but no one asked me, a teacher. We also can use all those other ideas in the posts below, but students do have to know what that question means — if it’s on the test. But if we can never know whether that exact construction of the question is there — Catch 22.
I completely understand your struggle with end of the year testing. Being a classroom teacher for 19 years, I felt the exact pressures you addressed in your comment. I agree we want students to understand what a question is asking, however it must be a mathematically sound term. In this case, I am not sure “name” is something that holds up mathematically. I do think, testing or not, we must do what is right by the students mathematically, especially in these early PK-2 grades where testing is not mandated, at least in my state.
It’s really stretching “name” outside its normal use, isn’t it? Writers of questions should really try to use language in as natural a sense as possible.
I’m wondering what I would write if I wanted to ask that…? Maybe I’d just say, ‘Which ones of these are twelve?’
But it’s a shame we don’t see your question in textbooks. Write down what you know about twelve. Of course, you’d want the teacher to be looking at the answers and sharing them with the class – the ones she felt needed sharing, and the ones that surprised her. And then time to explore some of those avenues individually or in pairs and all together again. Something like that would jump out of the textbook into real lessons!
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Something which leaves me speechless is the way such questions are written into a program or a published scheme of work. By comparison ‘merely’ asking children to discuss and feedback, either verbally or as a poster: What we know about… (12, what ‘perimeter’ means, how to calculate 2+6×3, how many ways can we partition 10 into whole numbers, etc) is far, far more powerful. This is because as alluded to above, we find out more and more about the children we teach both in terms of what they understand and what misconceptions might exist.
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