I get asked a lot, what I recommend for assessing students’ math understanding. The answer is really based upon what you are using it for. I know that we have requirements for the types of math assessments that we have to give, but often those assessments really don’t give us any information that informs our instruction. That is really one of the biggest reasons we need to assess students.

I’m Christina Tondevold, the Recovering Traditionalist, and today we’re going to take a look at The Best Math Assessment Tool That Informs Instruction in our quest to build our math minds so we can build the math minds of our students.

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BMM PD site

Math Curse by Jon Scieszka

Now, honestly, I don’t like making this video, because educators are sick and tired of assessing kids. Everyone in education is sick of the testing for VARIOUS reasons, but I think that one of the main reasons we get sick and tired of the assessments is that they don’t give us information that actually helps us help students. 

The teaching style that I promote is student-centered instruction. In this style of instruction, you base your instruction off of what your students currently understand about mathematics, and you work towards building that understanding to the things that they need to build.  You start off with where your students are currently right now and the understandings they have, which does mean we need a way to assess what those understandings are. So if you’re wanting to teach in this student-centered way, you can’t just follow a textbook, because it needs to be based upon what your students are currently understanding. 

Student-Centered Instruction is Based off Your Students, Not The Textbook

The textbook is a resource. I’m not saying throw your textbook out, but we should not be following a textbook page by page by page.  We should instead be looking at our students’ understanding and then adjusting the lessons that are in the textbook based upon our students’ understandings or misunderstandings. 

So, for example, if your textbook has you teaching a lesson about ‘doubles plus one’, but your students have not built their understanding of ‘plus one’, then that time that you’ve spent doing the lesson about doubles plus one, will be a flop and it will be pointless. 

That’s why it’s so important to assess your students’ math understandings, because if they didn’t know about plus one and haven’t built an understanding about plus one, there is no sense in doing doubles plus one yet. That informs your instruction so you know how to best use the resources you have, which your textbook is a resource. 

If you are trying to do student-centered instruction, that uses your students’ understanding, the way that we learn our students’ understanding is through assessing them. 

What Assess Actually Means

The hard part is, is that typical math assessments that we have are, what’s known as summative. They’re typically given at the end of a chapter, or the end of a year, to give us a summary of what kids understand or don’t understand. And they’re often given on a computer (sometimes paper/pencil), but all we see is the end result. 

We see if they got it correct or incorrect. All we see is their answer. We don’t see anything about their thinking that led to that answer, that we should be able to then use to help inform our instruction. When we get the results we see they didn’t do well but we feel like we have to move on to the next chapter because that’s what I’m supposed to do in my textbook. 

If we’re actually wanting to use assessments to inform our instruction, we’ll give a pre-assessment.  But even those pre-assessments tend to only show us the answer that kids got. So it still doesn’t tell us anything about their thinking. 

I want to remind you, if you didn’t already know, what the Latin root for the word assess actually means. The Latin root for assess, which is assidēre, means to sit by. If you want to actually see what your students understand about mathematics, we have to sit beside and observe their thinking. Now, realistically, that ain’t happening. 

You can not sit next to every single one of your students every day to see what they are thinking. So it seems pretty impossible to be able to do that version of assess, but if we actually want to get information that informs our instruction, we need to observe our students’ thinking.

Observation Is the Best Math Assessment Tool

You don’t need to sit beside every student every day, but there are tons of opportunities to actually observe your students’ thinking. This might be as simple as, you’re standing in line, getting ready to head to lunch, and a student says something like, “we have 12 kids in our line, the other line has 10, we’ve got 2 more kids in our line than the other line.” You can make a note about what that kid understood; he was comparing, they knew two more than…You’re making all of these observations about that student in an informal observation setting. 

Now, it could be more formal. Like, you make a point that you’re going to go give students a story problem.  As they’re working to solve that story problem, you’re walking around and observing how kids are approaching the problem. What strategies they’re using to try to solve that problem. Let’s say that the problem is 32 + 45, and when you have the kids share their strategies, a kid says, “well, I added the 2 and the 5, and then I added the 3 and the 4.” Instead of just going on, you might stop and ask the kids, “so that 3 and the 4 that you added, is it really just a 3 and a 4? What’s the value of the 3?” and you’re trying to pull out that it’s really 30 and 40 that they’re adding together. That gives you a sense of their understanding of place value. So the big idea is that you’re just observing and you’re asking questions, you’re trying to dig out students thinking that can help you make decisions about where you need to go next with their instruction. 

You can even become really formal and create spreadsheets about what are some things that you really want to look for. Inside of the Build Math Minds PD site, we’ve created these for our members, but you don’t have to have formal spreadsheets.  Just start observing and noting what your kids are saying about numbers. Once you start doing that, it’s honestly kind of like the Math Curse book. Once you start observing your students and looking for what they’re saying about numbers, you will notice it all the time, and you won’t be able to stop. 

I hope that this video has helped you build your math mind so you can go build the math minds of your students. Have a great day.

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