Ugh, it’s getting hard to keep up this blog. I’m working hard to keep trying new things in class, while still making my tutorial videos, and now I’ve got the Daily Desmos blog taking up half my planning time! So this one’s gonna be short. Here goes:

I have an assessment that basically asks students to describe the effects of the variables “a” “h” and “k” on the graph of the function y = a(x – h)^2 + k. I was thinking that this would be great because it is so open ended (I’ve heard this type of thing referred to as a “goal-less” problem). The idea was that students would have to not only know what the effects of the variables would be, but also be able to describe it to me using graphs and charts.

For some students it worked out great. They clearly understood what I was asking of them and were able to demonstrate that understanding by comparing several graphs and their equations. But then some students were completely stumped. I’ve figured out that they were afraid of this assessment because they didn’t understand the basic principles.

I think the solution is to create a separate assessment that is lower level. Maybe a few multiple choice questions where they have to compare two graphs, or even a constructed response, but one where I give them the graphs to compare. That way, students who only *sort of* understand the skill can at least show what they know.

So I feel like the lesson on this one is that having a “goal-less” problem as an assessment is great, but it shouldn’t be the only assessment of that skill.

What do you think? Do you use goal-less problems?

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This sounds like a skill that some kids won’t have right off, but could develop. I bet if you asked them to do this multiple times in a low stakes situation before putting it on an assessment again, you might have better luck.

I try to make all my assessments low stakes 🙂 But I agree, I think more development of this skill was necessary (the skill of explaining things I mean).

I love goal-less problems in classes, but I understand how they can be intimidating. I feel like some of the students might see a problem like that and have some anxiety over the grading. It might appear ambiguous to them. That’s such an essential math skill, though, and it’s absolutely essential for students to be able to analyze and interpret functions. They need to be broken of the common misconception that mathematics is rigid and primarily dependent on calculations, and recognize that all the numbers and symbols have significant meaning.