It is a well-known truth that assessment drives learning. Students will often not learn a particular topic or concept unless it is assessed by an assignment or exam. Fair enough — often students are not choosing to do a particular course for the sheer love of it, are they?
However, many lecturers take this truth just a little further and subscribe to the belief that assessment can actually teach. They put quite a bit of faith in what a simple assignment question can do for students: a lot of them believe that a well-chosen assignment question has the ability to teach students amazing truths about maths. They imagine the student doing the assignment question, struggling through it, and coming to an epiphany where suddenly everything makes sense. I have actually had lecturers in the past telling me about the great question they’ve written and how it will teach the students something cool. I think this is just a little unrealistic.
Through years of observation of students, it seems to me that actually, assignments don’t teach people, people teach people. Let me give you two examples from the last couple of days to illustrate.
The Maths 1B students are currently studying orthogonal projection and they have a MapleTA (computer-based) assignment due today. In it, there are some questions that give them a basis for a subspace and a vector and ask them to project the vector onto the subspace. The students need to do this and then type their answers into the computer. In the particular question I have in mind, there are two vectors to project onto the subspace, and the second one doesn’t change when you calculate the projection. What this means is that the second vector is already in the subspace, which is why projecting it into the subspace doesn’t do anything. I’m pretty sure that the writer of the question is hoping that students will notice this and wonder why it’s the same and remember that fact about vectors already in the subspace and feel the warm glow of learning.
But of course they don’t learn. Talking to students yesterday, they didn’t even notice the answer was the same as the input. They just noted their answer was correct and moved on. Luckily for these students, I was there to point it out and ask them why they thought that might happen and help them find the bit of their notes that discussed this concept.
My second example comes from last week’s written question. It asked the students to prove that each vector in a subspace can be written in terms of the basis in a unique way. This is quite a fundamental idea which is not covered explicitly in the lectures and it’s a pretty safe bet that the writer of that question was hoping that the students, through doing the question, learned this concept. And also, I reckon they also are hoping that the students learned how to prove that something is unique.
Only they didn’t of course. Almost every student who visited the MLC had dutifully written down the question, but the rest of the page was blank. They had no idea how to even start. Even those who had made a good start by writing down the definition of basis had no clue where to go from there. Since they had no clue how to start, they had no hope of finishing, and absolutely no hope of learning anything! Even those students who only needed a little prompting to solve the problem still had to ask about what was really going on.
See? The assignment question was certainly the fuel that was needed to learn those things, but it wasn’t the assignment question itself that did the teaching — it was me, or sometimes the students’ friends. It was the discussion with others that helped the students learn. They needed someone there to help them notice what was going on, and to help them turn it into a lesson.
I’m not saying you can’t choose good assignment questions that make it more likely for students to learn, I’m just saying that without also organising an opportunity to talk to someone as well, students will often not learn anything. Indeed, they often won’t do the question at all. So if you’re a teacher do remember: assignments don’t teach people, people teach peole.