October 2, 2011

Reflection and Self Assessment

This year's school-wide focus is writing.  Many math teachers groan or cringe or opt out of the reading/writing initiatives, but I've always had kids do a minimum of daily journaling; sometimes up to entire stories or paragraphs explaining projects.  Last year's school-wide focus was rubrics.  It was our NEASC evaluation and so we were supposed to all use the same rubrics so kids had continuity.  I would argue that students are more intelligent than we give them credit for and don't need that much continuity, but the idea behind the rubrics was okay and I was able to reformat them into something I find kid-friendly.  The result of these two foci is an ellipse (math joke!), okay, actually it's a double sided weekly reflection sheet.

Journal and CW Rubric

We operate on a block schedule, so if I collect these every Friday that's 5 days (barring schedule changes, which happen approximately daily, okay not really, but I do plan to count how many of the two week periods I get all 5 days filled in).  I used to carry around a clipboard all class and mark down any time a student was off task.  This, combined with attendance/tardies made up their classwork grade.  I'm still making occasional notes on my clipboard, and of course still taking attendance, but most kids are pretty honest when they fill in the rubric.  The original plan was to have them out on desks all class so every time a student was off task or doing a good job at one of the sections I (or my co-teacher) would mark that down on the rubric.  This turned out to be totally unrealistic.  If a kid is off task I don't want them to find their rubric for me to write on, I want them to get to work!  And several of them relate to behaviors when I am standing at the board.  Instead, I'm trying to use the language on the rubric when I reprimand or congratulate students on the behavior, and making a few notes so if my memory completely fails me for some reason they won't get an unreasonable grade.

The journal side looks boring now, but that's because the questions will be on the board.  Every day they will be asked "How did you meet the objective(s)?" and if they didn't to explain why.  There's also a second question that varies.  Some examples: to make a connection, to predict, to reflect (what are your goals for 2nd quarter? how should you study for the test?).  I expect a minimum of two sentences and they don't get credit otherwise.  The first week of past years I'd get quite a few "writing in math class?!?" exclamations, but this year there weren't so many.  It's a quiet way to close class and students will remind me that it's journal time if I get too caught up with a lesson.  The goal is to get students thinking about what they did in the hope that more of it will stick until next class (2-4 days away thanks to block scheduling).  The first question has changed year to year, sometimes asking what math they learned and other times about the objective.  I'm hoping that they will be more precise if they have to justify how they met the objective, although I'll miss the occasional comment about how someone did some really cool math in science class.


  1. I too have to ask the "writing in math class?" question—not because I object to writing, but because pointless writing does not help students.

    If you were teaching them how to write mathematics, using Halmos's "How to Write Mathematics" essay, for example, I'd applaud. But "how did you meet the objective?" is not a prompt that will lead to either good writing or good math. All it is likely to do is to turn off those students who are good at math but not good at writing (like the English language learners).

    There are some places in math classes where writing might be valuable, but journaling does not strike me as one of them.

    Disclaimer: my son is a very adept math student who would balk at this sort of exercise, and fail a class rather than do it, so I have a rather stronger than usual negative reaction.

  2. First, a student certainly won't fail math because they don't submit their journals; the point is not to penalize students, but to give them an opportunity to reflect.

    It was a particularly useful exercise in my pre-algebra class because that course was entirely context based math. Students studying the "dogs and buns" problem needed to tease out that we were studying multiples, not hot dogs, and directing them to the objective helped them to do so.

    This year I teach mostly Geometry, which is filled with vocabulary. The more students can use the vocab that we learn, the better. All the ELL trainings, SPED trainings and literacy workshops I have attended say the same thing: the more opportunities they have for writing, the better. Sure, journaling on its own isn't going to fill in all those gaps, but it's a start.

    If you have a suggestion for how to rephrase the "how did you meet the objective" question, I'd love to hear it. As I said, I've gone back and forth on how to phrase it; I want students reflecting on and sharing what they learned and what they're struggling with, but without requiring paragraphs each day.

  3. It would be better to ask them to write something that requires mathematical thinking related to the day's topic—like "why does AAA not prove congruence?" "If you draw two circles of different sizes, how many points can their intersection be? What about circles of the same size?"

    Asking them generically to reflect on the "objective" does little for their mathematical understanding. If you are looking for real-world connections, many (most?) people are turned off by discussion of "objectives", "mission statements", and other time-wasting exercises that managers inflict on people trying to get some work done.

  4. I do ask questions like those as a part of the daily journal. That's the "second question" which I didn't really go into. We also investigate and discuss those types of questions throughout class.

    I am rethinking the phrasing, and I get your adverse reaction to it, I feel the same way about the generic PD. But I still want students to reflect on what it was they were supposed to be studying today, and so far I don't have a better way to ask them to prove that they accomplished the goal.