Math Journals

The topic of writing in math is taking over blogs everywhere! (@samjshah: CEBDN and @druinok: Teaching Stat that I've seen so far)  I've been meaning to share more about how I do journals, and also do an analysis of the types of questions I ask.  Peer pressure did the trick, and I'm jumping into this conversation.

I spent a couple summers during college working at a math camp for high school girls called SummerMath which sadly is no longer in existence.  It was an awesomely individualized program with a series of problems that kids worked on in pairs- the series split, jumped and took tangents that we (the instructors) could choose from based on how the students solved each problem.  Given that, it was almost a necessity to have students write about each class.  After class we would read the journals and plan each student's next steps.  This experience, plus the writing initiatives that are so prevalent in schools, prompted me to carry this practice into my own classroom.  The structure has varied a bit each year, but I am quite content with the current state.

While this is a different kind of writing than I use to formally assess understanding (proofs, justifications, explanations and even lab reports), I believe it is important to ask students to summarize and analyze the math they learn each day. *

Five minutes before the end of class I get everyone's attention, make any announcements and then tell them to write in their journals and copy down the homework.  I read the prompt aloud for my auditory learners (and everyone else who can't see because someone is standing in front of that section of the board) and everyone thinks while flipping to their journal page, writes a few sentences and packs up.  This of course, is the ideal, it doesn't work exactly like this every day (today: oh! you have 30 seconds to write in your journals, I'm sorry!) but usually students remind me if I lose track of time and many students are already writing by the time I read out the question.

The first question is always the same; it changes in phrasing from year to year but always has the same aim: What did you learn in class?  I've asked "How did you meet the objective?" (when that was a district push) and currently it says "What math did you learn today?"  The purpose of this question is to have students reflect on the past 80 minutes, determine what they studied and record it in writing, which helps record it in their memories.  I started working on the phrasing when students would tell me they learned about hot dogs (the dogs and buns LCM problem) or did p. 45.  It still takes some explaining to get students to write about a math concept, but they're pretty much masters a couple months in.

The second question changes daily.  I just went through all the questions I asked my Fundamentals of Geometry class since November, and came up with the following questions and categories:


Metacognition:
  Which problem from today was the hardest?
  What do you need to review the most?
  How should you study for the test?
  Which part was harder today- writing the equations or solving the equations?

Prior Knowledge:
  Which formulas did you remember?
  What other special ratios do you know? (the day we studied the golden rectangle)
  Which of today's vocab words did you already know?

Vocab Analysis
  What does it mean to inscribe?
  Compare and contrast the definition of exterior in English class and Math class.
  List all the definitions you can think of for the word 'scale.'
  Do you think that we need names for any other types of quadrilaterals?
  What does the prefix quad- mean?
  What is a hinge? How does it relate to the hinge theorem?

Method Analysis:
  Which method is more accurate, shadow or mirror?  Explain
  Would you rather use a formula or break a shape into simpler parts?
  What does it mean for shapes on the coordinate plane to be similar?
  How can you tell if triangles are similar?

Non-Examples:
  Can you think of anything in similar triangles that wouldn't be proportional?
  Is the converse of a theorem always true?
  Is it possible to have a quadrilateral with 2 pairs of congruent sides that isn't a parallelogram?

Compare/Contrast:
  How do the similarity rules compare to the congruence rules?
  How are isosceles triangles and isosceles trapezoids similar and different?
  What are the differences and similarities between a rhombus and a square?

I also mix in some questions that can be personal or school related such as What are your goals for Q3?  Did you meet your goals for Q2? or How was your vacation?

I collect journals every Friday and give students a photocopy with Day 1: Day 2: etc. written down the page (mostly because they fill in a classwork rubric for the same time period on the back).  I enjoy reading them for the feedback and personal insights it gives.  The only thing I would like to change is how often I read them- every Friday on a block schedule means 2 weeks.  That's a long time to go without knowing that several students had never heard of something I assumed was prior knowledge, but I don't know that I'm willing to give up my convenient system.  Perhaps I could collect every Thursday or Friday and cut down to a half sheet.  Something to consider over the summer (I'll add that to my ever growing list)!  However, these are meant more for students than for me.  I hope to give them an opportunity to reflect and the second question is one that a reflective student might be asking him/herself based on the lesson, not something completely new to figure out at the end of class.  For that reason they also count as a tiny part of their grade.  While this is a different kind of writing than I use to formally assess understanding (proofs, justifications, explanations and even lab reports), I believe it is important to ask students to summarize and analyze, if even just for the practice of using new vocabulary.

*This was the last sentence I wrote, but after eating dinner I remembered my English teacher who told us to use our last sentence as the thesis since by the time you got to the end of your paper, you would actually know what you're talking about, true again today!