Day Two

We have a lot of work to do in my class this year.  After Wednesday’s reasonably successful problem-solving activity, I thought I’d give the students a few problems to solve from the Marcy Mathworks PUNCHLINE series while I dealt with first week paperwork.  I intentionally chose a set of problems from the set that calls for students to “Draw a Picture” as a solution strategy.  My goal was to reinforce the idea that even as they enter middle school, drawing a picture can be a great method of making sense of a problem.

After watching the groups attack the medicine problem on Wednesday, I thought for sure that this would be a simple exercise…a warm-up…but I was dead wrong.  Although several students jumped right in and worked efficiently to solve the problems, the rest had that dear-in-the-headlights look.  I reminded them to skip any problems they were stuck on and come back to them later, and I think there were a few that just kept skipping problems in a big loop.  Sensing that, I asked students with good drawings to put them on the board for others who might not know how to draw a situation.  That seemed to get the others moving, but some were still lost.

Some sample problems:

So, knowing now that this group will struggle with interpreting “story” problems, I think we’ll be doing a lot like this.  Probably not 7 at a time like today; the students don’t have the endurance yet.  Maybe just 1 or 2 for bell work, but then followed up with justification and critique.  One thing is clear, these students don’t seem to have had much practice making sense of problems and so that is where we’ll start.

Day One

Wednesday marked my first day back in the classroom since June 2012.  I was nervous.  Did I still know how to do this?  Well, I might…but I couldn’t stand the thought of just doing what I had always done.  Not so long ago, the topic of discussion for Global Math Department was the First Day of School.  Reading about all the different ideas, I resolved not to spend my first 100-minute class period just going over rules and dress code.  So after some reading about whiteboarding in class and researching some different problems, I chose the “When Should She Take Her Medicine?” problem from Robert Kaplinksy.

Over 10+ years of working with gifted and high-achieving 6th graders, I’ve noticed that they really struggle with patience when they get to me.  They can’t wait to have the right answer…and they’re used to getting that answer FAST because they’ve almost never been asked to look past the immediate and obvious computation-based “problem.”  That’s why the medicine problem seemed perfect for the first day.

To introduce this activity, I created a slide to display the problem.  When I displayed the “situation,” their hands shot up immediately because they were sure the answer was 35.  I apologized for misleading them to think that I’d be asking them to give answers to any obvious questions this year.  Then I showed the “problem.”  Of course, they thought they had an immediate answer for that, too.  Then I walked them through the estimation process (high, low, best) and asked about assumptions being made (I had to define that term since they kept trying to tell me that they were assuming the answer was 4.5 hours).  As soon as we covered the waking and sleeping times, the hands shot up again and giant 3s were being written on the boards.  I asked them to convince me that their answer worked…show me with a timeline, schedule, list, something to prove they had a good answer.  That’s when they started to unravel.  They tried to show me that doses at 7a, 10a, 1p, 4p, and 7p worked, but then I’d ask them about the assumptions we made about the dose schedule.  I asked if everyone in the group was 100% behind their answer and every time there was the one kid that said they weren’t sure it was a good solution for the person to be awake for 3 hours without getting any medicine.  Then I encouraged the group to come up with a better solution that would address their teammate’s concern.  (My favorite student work-around for this was shifting the doses up 1.5 hours to break up the three hour gap.)

Here are some photos from the group that fascinated me.

1) This was the group that was the first to arrive at the answer of 3 hours (and most insistent their answer was correct.)  I told them I wasn’t convinced and suggested that they find a way to convince me.

  2)  This is when I asked them to explain their dose schedule and how they arrived at this solution (every 3 hours).  It didn’t take them too long to figure out that they actually had 6 doses, not 5.  (If they had only seen that they had 5 intervals!)

3) Making progress.  Notice the repeated addition…they knew they needed to extend the interval, but unfortunately they were trying to add 2 minutes, 10 minutes, 15 minutes, etc.  I found it interesting that no group tried converting the times to minutes to use a division algorithm.

The hardest part of the day was not helping too much.  These kids worked on this problem in earnest for almost an hour and still didn’t get to a “best” answer.  At times I felt like a member of the “Who’s Line is it Anyways” cast playing the questions game; the students asked questions and instead of giving them answers I just asked more questions.  There were some huffs and sighs, some frustrated grunts, but they kept working.  They kept going back to the problem.  The different solution strategies were encouraging.  It was good to see that they had some solid understanding of how to approach the problem, at least once they resigned themselves to the idea of not having an instantaneous answer.

One thing is certain; this problem threw these kids for a loop.  I don’t think they knew whether to love it or hate it.  I heard from one parent who works at the school that her daughter was talking about the problem all afternoon, telling them all about the problem, how I presented it, and how her group tried to solve it.  I think I’m going to like this class.  And it’s good to be back.

Let’s take this blog for a spin…

After lurking and Tweeting in the mathtwitterblogosphere (MTBoS) for just over a year, I’ve decided to push myself to reflect and grow through blogging.  I’ve been wanting to jump in for some time, but just didn’t think I’d have much to offer after taking a position out of the classroom last year.  So when it came time to talk about this year’s assignment I did something a little different; I asked to stay in my special assignment (80%) and also to teach one period of 6th grade math (20%).  Much to my delight, my proposal was accepted and yesterday I started the school year with 32 gifted and high-achieving 6th graders.  With an alternating day block schedule, it’s less crazy than it might seem…I go to the office every morning and then every other day I leave at 1pm to teach my 100-minute class.

Part of my special assignment is to help my district with the transition to CCSS in Math.  With that in mind I have several goals for this year, most stemming from ideas shared by other math bloggers for whom I have amazing respect:

1. Make sure the students are doing most of the talking, thinking, and working.  This is something our county office is hitting hard with administrators and teachers alike.  As teachers, we can’t work harder than the students and expect them to learn.  To accomplish this, I plan on the students doing a ton of group problem-solving this year.  I’m excited to use the 5 Practices for Orchestrating Productive Mathematics Discussions to guide my work with the students.  I’ve also invested in some 24×32 showerboard panels for groups to use as whiteboards when they explore problems.
2. Be less helpful.  So many of my students have learned to be helpless.  They don’t get it.  They don’t know where to start.  They have no idea if their answer is reasonable or not.  And these are high-ability learners.  Not any more.  I can’t continue to feed this disease of apathy and feebleness.
3. Move towards standards-based grading.  I’ve questioned the meaning of class grades for some time, realizing that there are always students who manage to earn As, even though I know they don’t understand the content at the highest levels.  There are also those amazingly intelligent kids who ace tests after being absent for three days straight.  How can I convince my colleagues to stop giving points for Kleenex donations because it doesn’t represent mastery if my system doesn’t seem to be consistent, either?  (I would have SBG as a solid goal, but my school is a letter grade institution.)

I’m excited to get some feedback from the greater math community, even though I’m a bit nervous to open up and share more about my teaching than I ever have before.  So, welcome and thanks for visiting.  I look forward to your responses.