End of Year Reflections: In Geometry I learned...

For the past few years, I've had students write reflections on the course and their year after they complete the final exam. The prompt is as follows:

• This year I learned…


• About myself


• About mathematics


• About studying/school/how I learn


• In this class…


• My favorite chapter


• The most interesting activity


• The hardest thing to learn

At the end of the year I'm spent, so I put these away until a day I'm ready to reflect. Today was that day. I'm getting geared up to prep for the arrival of students, take what I learned at PCMI and put it all together into a great new year. I pulled out the pile of reflections and they sparked fond memories of: my students, how much they grew over the year, and how willing they were to give meaningful feedback even after taking their final exam.

I compiled their responses for analysis of the year past, but also to remind myself on those tough days that even though it isn't obvious, they are learning and the ideas are sinking in. I'll divide this analysis into lots of posts so they don't get too long!

In Geometry College Prep I learned...

• I'm actually kind of good at math



• I'm good at geometry


• I'm not very good at geometry


• I'm not good at geometry, I'm a number person


• You can be very good at algebra but really suck at geometry or it can happen the other way around


• I am horrible at geometry, but if I just push extra hard I can do it


• I'm better at math than I thought


• I'm worse at math than I thought

• If you miss one class you can be lost forever!



• I need an explanation for everything


• I learn well from examples/book

• To work hard



• Studying is hard for math


• Studying really helps you become successful


• I don't do well in math unless I study


• If I study, I will do well


• Study sheets and flashcards help


• Doing the same problem over helps me understand

• You have to work to understand math



• I liked the experience


• I hated having to redo everything but it made me more conscious I should study hard before the first time


• I can figure out a lot of problems myself


• I am capable of doing all the work, I just have to focus


• I do my work well if I am alone


• I work better: not under pressure, by myself, when mad

• I learned who the real me really is



• I learned too much to put on paper


• I can achieve anything I want if I put my mind into it


• If I try I can do anything


• I never knew that we could learn so much about math in one year

It may have been the phrasing of the question, but I love that no one said 'I can't do math' or 'geometry is too hard' or 'I don't care about it.' And nearly every kid who said that they struggled then went on to say they should have worked harder, studied more or focused better. The fact that people learn by effort, not genetics or intrinsic understanding was a recurring topic this summer. I'm glad to see that most students internalized that message last year.

One comment that makes me really thrilled is:

I hated having to redo everything but it made me more conscious 

I should study hard before the first time

I worried that allowing students to correct their work would make them blow off studying the first time and just settle for whatever grade they could get with corrections. But, if going back over their assignments and having to re-work problems makes them wish they'd studied the first time around then I'm looking forward to continuing that option.

I shared these with a few friends before posting, and the one that jumps out at others is:

I work better: not under pressure, by myself, when mad

I won't pretend to understand exactly what this student meant. I can say that she was quite the talker, so the 'by myself' part makes sense. I wonder if the 'when mad' comment relates to the idea of 'struggle' that we all try to find a way to discuss. In the summer camp I taught at we talked about writing problems that would make students 'frustrated' or 'challenged.' We don't want angry kids, but the point is, that if a problem is too easy no one learns.  We need to give assignments that make students think and that they have to work to understand. I have no idea if that's what this student was trying to say, but it's interesting to think that students are having these same thoughts and are aware that they learn and grow through challenges.