May 31, 2012

Math Journals

The topic of writing in math is taking over blogs everywhere! (@samjshah: CEBDN and @druinokTeaching 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!

May 28, 2012

State Test Prep

I teach four geometry classes which are almost entirely comprised of sophomores.  Mid-May of sophomore year marks the point when everyone takes the state test in math.  I should say now that the MCAS isn't a terrible test.  In Massachusetts we have multiple choice, short answer and open response questions.  I rarely read a question and think "what a terrible question" or "that's a mean trick to play."  The multiple choice range from easy to difficult and the open response range from easy to difficult within the same question, which is awesome.  Every one of my students is able to answer part a) of every open response since it's usually very concrete; that low-threshold to high-ceiling nature within the problem is what I strive for in my classroom and it means that students usually do try the open response.  There is a requirement to explain your answer (showing work is an acceptable explanation) which echoes my emphasis on reasoning and justification.  Plus, you only need to get 17 points out of a possible 60-something to "pass."  So overall?  The test isn't terrible, unreasonable or insurmountable.

All that said, the first two weeks of May are still my least favorite weeks of the entire school year.  Why?  Because there's still a month of school and so we haven't gotten to circles or 3-D, I have to make a decision of what to rush through and what to take a gamble on skipping.  Last year I skipped circles and it showed up as an open response on the test (although I think it was a pilot question since they didn't include it in the released test- anyone know if that's valid reasoning?).  We rush through volume and surface area, by which I mean: I handed them the formula sheet and called it a matching game.  I hate doing that, but given time restraints I didn't have a choice.  Over the summer I plan on aligning to the common core standards and I'm hoping that will allow me to shuffle units in a way that surface area and volume get some quality time.  It's also frustrating that students have to take the test as sophomores since so much of the test is on Algebra.  While we use some Algebra in Geometry, there's quite a bit that needs refreshing.

Regardless of the pros and cons of the test, the students have to take it and since they take it my year, review falls on me.  So, here's what we do:

Over 4-5 classes, for the last 30 minutes (of our 90 minute blocks) they independently work on a complete practice test.  I refuse to answer any questions until after they have completed the test (real testing situation) and I instruct them to mark each answer they are confident about with a :) and each guess with a ?.  I check their answers as soon as they've finished a section, but I refuse until they have an answer for every multiple choice question.  It shocked me how many students were unwilling to guess- there's no penalty and a 25% chance of getting it right!  I wanted them to mark their answers so they could see if they were under or over confident (and not feel bad about getting something wrong if it was a guess).  For all of my other assignments, the deadline for corrections is the end of the quarter but I wanted them to be ready before the test, so they were welcome to correct as many times as they wanted- up to May 15 (the quarter won't end until June 20).

For the other hour of the class we had a different focus each day.  We spent one day on surface area and volume.  I cut up a whole pile of questions and instructed them to set up each problem.  They needed to: read the problem, identify the correct formula(s), write the formula(s) exactly as they were written on the reference sheet and then substitute in the given values.  No solving required!  The purpose of this activity was to read the problems carefully and expose them to a lot of problems.  Many of them get bogged down in the algebra which is okay on the test when you only have a few problems of this type, but the goal of the day was to see so many questions that they fit a pattern and looking at the reference sheet was an automatic reaction.  (Method taken from my Useful PD)

Another day I took last year's entire test (2 copies to have plenty of problems), sorted them by type, set up stations and sent students around the room to do at least 4 of each type.  There was also an extra-practice station where I included a list of all the topics that had been on recent tests and asked them to choose 4 that they needed to review.  I had a pile of questions to pull from and made some up on the spot.

I also asked students what topics they needed to review at the end of each class, based on the practice test they were taking.  I used those lists to come up with other problems to discuss, and methods to review for the other days.

The last class before the test I stopped 30 minutes early for a pep-talk and a confidence boosting activity.  I informed all of them exactly how few questions they needed to get right to pass- so no pressure, expressed my total confidence that they could all do part a) of every open response, reiterated the fact that they should write down something for every question- whether it was their gut instinct on a multiple choice or just writing down the given information and maybe a formula on the open response (that's actually worth a point!).  And then I announced the corny activity that I took from misscalcul8. Since I didn't have the time (or the patience, lets be honest, by this time I was spent) to handwrite each poster like she did, I printed a grid that said "I'm a fan of ____" in each box.  All the students names for a class were filled in, along with any teachers in that class.  Students filled in the boxes with something positive, cut out their boxes and made piles for each student.  By the end I figured out the best way to make the piles is to lay out all the posters alphabetically and have the students pile the small pieces of paper on top of the poster.  Then my co-teacher and I spent a lot of quality time with our glue sticks.  We had students write the names in big letters across the poster and I printed the boxes on colorful paper so in the end they looked rather awesome if I do say so myself.  I distributed the posters at breakfast on the first day of the test so they started the day reading all sorts of great things about themselves.  While I announced it as a corny activity and I got some groans and "we have to write something about everyone??" they really understood the purpose and the other students in the cafeteria were asking about them with interest.

I won't know until next year how well any of this really worked, but as much as I hate test-prep, this process wasn't awful, and I rewarded all of us with several fun activities (including dilating comics which they did immediately after the test).  Plus, I get to look at these wonderful posters every day!



May 24, 2012

The Classroom in May

Any teacher can tell you that by the end of May the classroom dynamic has drastically changed.  As teachers we are running low on patience and the students are ready to get out in the weather that's finally warm and sunny.  But we also know each other really well- I don't have to explain anything when I hand out progress reports; kids just get right to work identifying the assignments they want to improve.  They know where to find extra copies of handouts, where to get pencils and rulers and graph paper, and who to ask for help if I'm busy.  We can joke around, say "remember when?" and let the schedule slide a bit.  My geometry classrooms are even more relaxed than others might be.  Mid-May marks the state test that all sophomores must take and graduation hinges upon passing this exam.  We had major crunch time leading up to the test (I have a post in my head about that process, it's coming soon...) and now we're just doing a series of projects that involve plenty of thinking, but also some down time.

The toughest part of this last month is the students who have decided that they don't like me/my class.  One student in particular has been quick to put up his defenses all year and meets any confrontation with a negative attitude.  A couple weeks ago he asked "why do you hate me?"  At any other time of year the response would have been "I don't! How could you think that??" but on that particular day I was tired, and he'd been off task all class so instead I said "I hate when you don't do your work and have an attitude.  But I don't hate you.." at which point he cut me off while I was trying to describe hating an action vs. a person.  The next couple weeks were rough, and it was hard for me to continue to be positive with him when he was so negative, but that's my job- not just to encourage him to learn math, but also to be a role model of a kind, good person.  This week he stayed after school and we were able to chat without tension.  Today, he came into class and worked incredibly hard, asked me several questions and he told me he wanted to really understand trig, not just get a hint on the problem he was doing.  He continued working while several students around him had gotten sidetracked.  Today, he was my top student, and on my side.  Maybe by next week he'll hate me again, but that's okay.

The best part of the end of the year are the students who really get me and my class.  During class today one student told me that she and her boyfriend were watching a video, laughed, and realized that they sounded like me when they laughed.  The same student was after school and wondered aloud how anyone could not like me, and another student chimed in saying they stood up for me.  I also had students make fan posters a la misscalcul8 before their state test.  All of the ones about me are hanging next to my desk; they catch my eye when I'm tired of looking at my computer screen or grading.



Really, this post is to say: Congratulations, you've nearly completed May!! We finish June 20 so there is less than a month of school remaining.  Some days the outlook is a bit bleak (like, how is today not Friday?!) but the relationships we have built this year will last a lifetime.  Even if we don't often get to see the impact we make, I try to keep in perspective the critically thinking and genuine human beings that I am helping to mold.  I can't wait to start over and do it all again next year.

p.s. If you're here from either of the female math blogger lists- WELCOME! I will be updating a lot in the next few weeks as I catch up on all the reflecting I never got to do during crunch time.  Check back soon or just add me to your reader so you won't have to remember the url.