In addition to knowledge and understanding, thinking and application, communication is one of the skills we are asked to develop and assess in the Ontario Mathematics Curriculum.  And it's one of the areas that stands out as an area of need for many students across the province.

As part of my current unit in Geometry, I invited students to select one of three learning activities they had been working on, and submit a write-up on that activity.  Specifically, they could choose from a solution to a problem they had been working on, a math journal entry, or a written description of some of the thinking that evolved as they were playing Blokus, a strategy game involving various square-based polygons which I had featured at one of the centers for the past several weeks.  All three of these activities had enabled students to practice both their oral and written communication skills in math, and now it was time to show what they had learned.

Based on the math journal criteria we had co-constructed earlier in the year, I developed an assessment and descriptive feedback sheet.  I was looking largely for appropriate application of relevant math vocabulary, and use of diagrams to illustrate thinking.

To be honest, I was a little bit nervous to see the results... although I knew the tasks were curriculum-linked, rich and engaging, I also knew that some of the students had engaged only superficially with the food I had prepared for them in our math buffet, and so I wasn't entirely sure what to expect, especially when it came to the Blokus write-ups, since that was a somewhat more open-ended task.

But wow, were some of them ever good!

Below are two (the second is two pages long) that I found particularly rich.... (click to enlarge and see full dimensions)

I was intrigued to read of some of the problems the students developed to think about in relation to the game.  I was also interesting to see some of their thinking when it came to coming up with strategies for winning.

Although not all the explanations were as robust as the examples above, these nevertheless serve to set the bar high for other students, and I am pleased to have collected these as exemplars of what an intermediate student response might look like!

I just read somewhere that it is better to receive than give, so in addition to world peace and about $20K so I can finish paying off our year in Argentina and put some money back into my RRSPs, here is my wishlist for Christmas 2014:

Behind the scenes in the East Common Room at Hart House on Sunday afternoon, November 30th...

There is really something quite special about coming home after a long day at work to a clogged, stinking toilet... yes indeed, folks, in my excitement to get my science tests and math assignments marked, and clear some of the other languishing items off my to-do list at work, I left the house at my usual 6:45 am this morning and promptly forgot about our not-so-little problem in the washroom at home.  (In the panic of the moment, I had relegated "call building super" to some non-existent "to do later" list in my mind, and then never did it later.)

The issue, you see, is that for some reason, we don't seem to have a plunger in the apartment.

It's an odd thing, really... everyone ought to have such a tool, just in case, and I feel quite certain that in fact we had one at some point... but like so many little household niceties over the past year, our plunger seems to be in that nebulous "packed-up-when-we-left-for-Argentina-in-September-2013-and-never-found-upon-our-return-in-May-2014" pile somewhere.

Despite said hardship, however, and the skype-shared skepticism of my girlfriend, for whom I described in  disgustingly accurate graphic detail the gravity of the situation, I am happy to report that I have successfully solved the problem.  

With a little help from Uncle Google.  

Behold:

You see, knocking on people's doors at 11 p.m. is not really the sort of thing one does in my building, even to desperately inquire about a plunger.  But as it turns out, a little (well, a lot, truth be told) of baby shampoo and a big pot of hot water does the job.  Especially if one scoops out considerable amounts of preexisting clogged-toilet water and rummages around the clogged toilet with a coat hanger beforehand. (Yes, eewwww, but so very necessary in this case, I'm afraid.)

I would make one addendum to the advice provided online for such situations, and that is this: Upon successful completion of the job, do take care to either dispose of whatever tools you used to assist you in your endeavor, or spend considerable time washing same with dish soap and very hot or boiling water, lest your shitty (sorry, but come on, people, how could I not?!) evening turn into a week-long bacterial infection of mammoth proportions!

Having co-created the following rubrics with a colleague, based on the success criteria for our current geometry unit in Grade 7 & 8 math, we decided to design a test or performance tasks with specific questions that would allow students to demonstrate each of the criteria.

As I thought about how to build intermediate-student-appropriate differentiation into even a  pencil and paper test, I came upon the idea of building in choice:  There is such an excellent variety of potential test questions, I figured, why not pull out a few, and have the students choose their own?!

My plan is to create one page that everyone has to do, but then for each of the other two pages, have 2-3 options with different formatting and topic that address the same concept, which students can choose from, thereby customizing their individual unit test!

I'm hoping this novelty entices even the more reluctant test-takers in the class.

Along with my in-class observations of their work, as well as a few other specific quizzes and tasks, this "make your own test" will comprise the unit mark for term one geometry.

My math teaching has gone to the birds.  No, really! :D

I was invited back to Guelph yesterday to spend the day working with occasional teachers there again.  In the morning, I facilitated a session on "Math for Math-phobic Teachers".  Inspired by my own recent introduction to Fermi problems, I decided to haul along a bag of birdseed I had used with my Grade 8 class a few weeks ago for a TIPS4M lesson.

The 4 KG bag certainly did little to lighten my load, but I figured it would be worth it.  The other activities I had packed for the teachers to work on were some math monographs to read and discuss, and a cooperative learning problem comprising a set of six clues printed on little slips of paper, accompanied by a small baggie of cubelinks and colour tiles.  So I had space to spare. Thus, in went the heavy bag of birdseed, the open top held shut by a tightly wound elastic band.  I jammed a few math books on top for good measure, sat on the suitcase, and zipped it up.

When I arrived at my hotel, I unzipped the suitcase to pull out some clean clothes, and to my dismay, found birdseed everywhere -- it was in my clothes, wedged into the corners of the suitcase, jammed in between the pages of my Marian Small and in amongst the cubelinks and colour tiles!  It seemed the elastic I had used to wind around the opening of the bag was not so tight after all. :(

I tried as best I could to pick out the grains that had flown out of my luggage when I'd unzipped it and become lodged in the hotel room carpet, stuffed everything back into my suitcase, and zipped it shut, figuring I would deal with it in the morning.  

The next day at the workshop, I opened my bag to take out and set up the materials for my math workshop, and discovered the seed had spread.  There was now birdseed in, on and under every other item in my suitcase, including jammed in the staples of some of the handouts! 

Doing my best to not get too much seed on the floor, I carefully removed the morning's other materials, and tried to extract as much birdseed as I could, before setting them up for the teachers.

The bag of birdseed remaining was placed carefully on the presenter's table at the front, and the elastic readjusted lest more seed should escape before it was needed for the intended Fermi problem later in the morning.  I then took my nearly empty suitcase and dumped the seeds (and a few stray cube-links) unceremoniously into the snow out front of the building where it would hopefully be eaten by birds or will grow into crabgrass next spring. (Don't worry, bird enthusiasts, I did pick out the few plastic cubes.)

The rest of the bag was "planted", as it were, onto the impressions of the participants, and they worked eagerly to "measure" a cup of seed, and estimate number of seeds in the remaining bag.

Telling my tale of woe to the group at the beginning of the workshop, I threatened to leave the bag behind -- no way was I risking another escape attempt by 10 million tiny seeds!  And I made good on my promise:  At the end of the day, I sent the open but still useful bag of birdseed home with an enthusiastic young teacher eager to try out the problem in her own math class.

The things teachers do for the good of the cause!