So we’ve all seen them, and we’ve probably all used them. These two kinds of extreme examples of practice activities and worksheets that we give kids where we have a ton of problems that we’re having them practice or we just have a couple.

I’m Christina Tondevold, the Recovering Traditionalist, and I hope that you will stick around as we investigate, when it comes to assessing math proficiency, how many math problems should kids get?  In our quest to build our math minds, so we can build the math minds of our students. 

Watch the video or read the transcript below:

Other videos in the series:

• Assessing Math Proficiency: Standard Based Grading
• Assessing Math Proficiency: Does the type of math problems you use matter?

Now personally, when I was in school, I loved problems like this where I could just zip through plotting, every single one of those points on the coordinate grid. 

It was just very procedural for me. I could do this, and I knew that if I just stuck with it, I would be perfectly okay. On the other hand, when I was given problems like this where it was a word problem and we had to go deep into this problem, I hated it.

I think that’s why I have to do the things I do now is because I’ve been learning a lot about the power of these kinds of problems

Different kids perceive these activities differently

Here’s the thing. You have students who are like me. You have students who are the complete opposite of me, who would rather spend a lot of time digging deep into one problem. We all have different learning styles.  When it comes to assessing our students, which one of these do we choose?

I’m going to be doing a little bit of a series here around how to assess mathematical proficiency.  In today’s vlog, I really want to focus on the number of problems. Because here’s one of the things that I see as an issue. I don’t think that one problem is the correct answer, but I also don’t think a hundred is the correct answer, right? 

If we only give one problem to assess a specific math concept, a student might guess it or they might make an error and get it wrong, but it seems like they weren’t proficient even though they had some great thinking and all they did was make one little calculation error. Versus a kid who guessed it, got it right, and they are seen as proficient, but really they aren’t. If we have a small number of problems that we’re giving kids, it doesn’t give us a full picture of that student’s mathematical thinking. 

However, if we have a hundred problems, what ends up happening in that kind of a situation is that kids start to lose focus.  They become more error-prone and basically productivity goes down when we have a ton of problems that kids are having to get through. 

How much does it take to show proficiency??

Think of it this way. Let me just caveat this a little bit, because another video I’m going to go deeper into this. But the way that we used to grade kids was basically, you give them a sheet and how many they get correct versus how many there were on the paper.  It was a percentage grade and they would all get averaged out. We are starting to do away with that, and in a future video I’m going to talk about that thing, and how we’re moving away, and what we’re moving towards. But for the sake of this video, I just want to keep this in mind. 

Let’s say we give kids a practice set that we are grading to tell whether or not a kid is proficient. And it’s got 10 problems on it. They only have to get 9 or 8 or whatever your cutoff is. I’m just going to say 9. Let’s just say 9 out of 10 makes you feel like the kid is proficient. Or maybe it was 8 out of 10. I don’t know, you pick. But if we increase the set that we are pulling from, and now we have 100 problems, that same child has to get 80 or 90 correct to get that same percentage. 

When we have a large set, that becomes harder and harder to do. So I just want to put this out here and pose the question. I don’t know that I have the right answer here. But I wanted to pose these issues so that we can start learning from each other. 

So down in the comments, what I’d really love for you to do is share with me: what do you do, what does your school do, when it comes to assessments. 

And in future videos, we’re going to talk about more in-depth about the assessments, but I’m just curious about the number of problems that makes you feel like, “Okay, we gave them 3 problems, and they got 2 out of the 3.” Or do they have to get 3 out of the 3? 

When you’re assessing kids, what is your basis for pulling items and deciding?  These are the set that we are going to give our students and this is how many they need to get correct for us to feel like they are proficient. Because, like I said, I don’t have the right answer. 

I think it’s interesting for us to learn from each other, to think about what other people are doing to help build our math minds so that we can build the math minds of our students. It’s not just about what I think or what’s happening at your school. I really feel it’s important that we learn from others to widen our minds about what is mathematical proficiency, how do we assess it, and in this instance, how many problems does it take for us to feel like they’re proficient. Okay, so again, drop that in the comments and I hope that you have a great day.