Peer- and self- assessment: what’s it all about?

If we simply try to memorize facts and procedures, mathematics doesn’t make much sense, and it becomes difficult to apply what we’ve learned. In contrast, when we can explain why the mathematics works, we make connections that help us apply mathematics to new situations. It’s a lot like putting together a puzzle; once you start connecting the pieces on the border it becomes much easier to fill in the middle.

Peer- and self-assessment helps us make these connections, which is just as important as (if not more important than) reaching a solution itself. The 3-step form is meant to help support this process. You will want to get in the habit of asking these questions even when you don’t fill out the form.

I. Big Picture

Looking at the big picture helps us see the problem as a whole, rather than getting lost in specific details. Don’t just recount steps, but ask what approach was taken and if it seems to make sense. Compare the responses:

  • I found a pattern.
  • I added 4 at each step.

which don’t say anything about how the pattern was found, to the response:

  • I noticed each arrangement added 2 tables to the previous one, and used that to find the number of people added.

In addition to stating that a pattern was looked for, it describes how the pattern was found. Unless you think about why something was done, it’s hard to determine whether or not it makes sense to do it.

II. Accuracy

After making sense of the problem and response, try to determine whether or not it seems to be correct. The key question to ask is: how could you know that the solution is right? If you get an answer, can you check it? (e.g. in the arranging tables problem, does the equation match up with what you counted in the patterns?)

III.Questions

Finally, ask yourself: “what’s really going on?” Are there things about the problem or response that were unclear or you didn’t understand? Make note of these questions – if you really want to understand the mathematics then you need to figure out how to answer them.

Also, ask yourself how the problem or response relates to mathematics more broadly. What can you learn that you can apply to other problems? Can you answer why the mathematics works the way that it does? If you understood the mathematics in the problem at a really deep level, what should you know? Asking these questions is a key part of learning from problems. In order to learn, you must first recognize what you don’t know, and what you could know.It’s important to be specific. Responses such as:

  • I’m confused
  • I don’t understand this

are not very useful, because they don’t tell you what to focus on. Compare these to responses such as:

  • I don’t understand why he added 4 between each arrangement.
  • Is there another equation that could work?

Which point out specific issues to try to understand in more depth.

Examples of questions one might ask (from homework 13)

Linear Relationship

  • How do we know the points are on a single line?
  • What would the table look like if the points weren’t on a line?
  • How could we find an equation for the line?
  • Does only one line fit these points?

Hexagons

  • Is there another equation that could work?
  • How do we visualize what changes between each arrangement?
  • How many tiles would be in an arrangement of 100 tiles?
  • What would happen if we arranged the hexagons in a different way?
  • What would happen if we had a shape other than hexagons?