Student Reflections

So one of my major goals this year was to make a push to help students realize different mathematical strengths and figure out where theirs lie.  I really wanted them to begin to see that mathematics is so much more than just being quick at calculations and seeing formulas, which was how most of them saw it (maybe quite a few still see it like that).  The one major way I’ve attempted to tackle this is via what I call the TARMADs:  Things All Real Mathematicians Are Doing; it is my acronym for the mathematician standards that I have students assess themselves on.

This year I’ve instituted trial round 1 of what I call Quarter Reflections.  At the end of each quarter, students fill out a reflection where they assess for themselves their level for each of the TARMADs side-by-side with where they were the previous quarter.  I stress to them that these are habits, and so one shouldn’t necessarily expect to grow in all of them (or any, in some cases).  They are then asked to discuss one of the TARMADs that they feel they grew in during the course of the quarter, and explain an instance where they remember noticing this growth.

This has been a blessing and a curse.  The blessing is definitely that students have become aware of important facets of being young mathematicians and that all of them have strengths in one or more of these areas.  They all have something to contribute.  The curse is that I realized that it actually holds me accountable to make sure I provide regular experiences in the classroom for them to have the chance to display their strengths!  Too many math classrooms only cater to the select few strengths, and I’m guilty of that much more often than my ideal.

Here are some responses after the most recent batch that stuck out to me:

This student had never really encountered true problems much before and is reflecting on his interest in math increasing because we’ve had a focus on that fairly often.


This student discusses connections and word problems


This one didn’t quite discuss the TARMADs as he was supposed to, but I thought it interesting to share his viewpoint on homework.  I agree with him in some aspects.  How can I make homework worthwhile?  I think I do aim for that, but I can always improve.


The next one simply changed in her view on making mistakes, which is great!


The last sample is great!  I love that things are making sense (as they should, eventually).  I was happy with the opportunity to give feedback on the fact that we forget most of the facts we learn, but my most important goal for students isn’t to remember all of what they learn, but to grow in the habits necessary to think like mathematicians (and educated human beings, for that matter).


It’s definitely clear that the messages are getting through via the various ways I make attempts to do so, though there will always be things to continue working on.  Next year, I’d like to be more direct with students about which of the TARMADs are highlighted during different activities we do in class so it can help them make more clear connections between our talk about the TARMADs and when they are actually using them.  I think this will also help those who have those strengths realize that they will be able to (and expected to) contribute.

4 Comments on “Student Reflections

  1. Matt – I love this quarterly reflection activity. Even if you can only address some of the needs, you are getting your students to think about themselves as mathematicians. And it is clear they are having some deep thoughts. Wonderful!

  2. Great idea! What’s on your list of TARMADs? I bet this works really well, and I’d love to try it. As i was trying to get kids work together and cite that interaction well, I ended up generating a list of sentence starters for them to use, which worked well too. Your idea makes me think of that, but more useful.

    1. So I replied to all of you within the admin site, but apparently it doesn’t post here. I’m still getting used to this. Thanks for being the first to post!

      Heather – The TARMADs say that a mathematician is a: mistake maker, tinkerer, model maker, pattern seeker, rose smeller, conjecturer, collaborator, and an identifier. I’m still working out the kinks, thinking if I should keep some or consolidate some, etc. Aside from my verbal acknowledgement and praise when students are using one of them, I would say that this has been the number one thing that has made a difference in helping my students to actually view themselves as mathematicians. Do you have any suggestions for adapting them? I think using sentence starters would be a great thing to use together with this. I am also really wanting to begin to use more writing directly in my classes, like journal prompts and actually writing out justifications and explanations in class. Do you have any experience with that?

      Wendy – Yeah that has been great to get students thinking of themselves this way! It is one of the many things on my ideal list of things to help address their needs and identities as young mathematicians. I’m still working on figuring out how to regularly give them chances to grow in each of these and have them identify when an activity highlights specific habits.

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