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Mathematical communication Success

11/30/2014

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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!
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Christmas Wishlist 2014

11/30/2014

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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:
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reblogged from blogs.Disney.com
For my Classroom:
  • 6 iPads and 2 netbooks or laptops (for oh, how I would love to be able to regularly integrate some of the many fabulous tech bits I am learning about in various workshops I am taking!!!)
  • Math dictionaries: one more like this, and 2-3 like this; I have about 4, and they are always in high demand and students are working on various projects in math.
  • Kleenix and paper towel -- why these basics aren't provided has long been a mystery to me, but it sure adds one more daily annoyance to not have them!  I've already spent too much of my own money on this stuff this year, and I just bought new soaps for the sinks, so somebody, please, give me something for the kids to blow their noses into, already!!!
  • Blokus Trigon... because it's such a great geometry game!

For my Apartment:
  • My antique German, cherry wood, made-by-my-great-uncle-in-Kassel-about-100-years-ago dining room table, chairs and bench fixed/restored and reupholstered.  Truly, they are a masterpiece, with many fond memories, and I think a few more years left in them... but they are literally falling apart!
  • A few big, high-quality, sharp knives (a paring knife would also be welcome.  A sharp one!)
  • Four grapefruit spoons -- you know, the ones with the ridges on top?  My mother had two when I was growing up... they were always going missing.  Finally once they left for good. :(
  • Two new cutting boards -- a big and a small -- because ours have seen better days...

For my Back:
  • A new fridge -- apartment sized with bottom mount freezer (so I don't have to bend over and break my back every time I'm pulling out the eggs or cheese... and, hey, it would have the added bonus that it wouldn't freeze all my vegetables like my current ancient model!!)
  • Ergonomic chair from Herman Miller (like the AWESOME one my girlfriend recently got!)

For my Soul:
  • Flight for Tats to come visit or me and the boys to go visit her in Feb and again at March break.  It's been super hard to be separated for SOOOOO long this year while she works on PEI as the province's only flight instructor.  And after so many months apart, our upcoming 2.5 weeks at Christmas will be all too short, I'm afraid! :(
  • Gift certificate from Cheese Boutique (because truly, there is not much a good piece of cave-aged Gruyere can't fix!)
  • Roll of loonies for the laundry, roll of ttc tokens and/or a whole whack of children's TTC tix -- such a time saver to not have to run out and get this myself constantly!
  • 10 hours of Cessna 150 rental at Island Air -- because I REALLY miss flying!!!!
  • Books: Defying Gay Gravity, the Art of Coming Out, 3 copies each of Outing the Bible (to share with misinformed believers)
  • Gift Certificate at Freshii, cause I can't tell you how many times it's saved me on late nights at school!!

For my Face:
  • (Hey, I'm over forty, people!)  Cleanser, face mist, and night serum
  • gift certificate from Lush
  • Some kind of goggles so that my eyelashes don't freeze when I'm riding my bike in winter!!!

Oh, wait... that was a typo -- 
I'm just re-reading, and it actually says it's better to GIVE than receive!

Oops.  

Oh well, never mind.
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Sheet Music

11/30/2014

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Behind the scenes in the East Common Room at Hart House on Sunday afternoon, November 30th...
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Returning/sorting scores after our fall concert at Hart House on Sunday, November 30, 2014.
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How to do it without a plunger

11/27/2014

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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:
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Ms. Teschow's post-trauma toilet, recovering nicely. Assorted "tools" nearby.
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!
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Manageable Descriptive feedback on rotary

11/27/2014

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While it's true that I might be better off at home eating dinner or SLEEPING, seeing how it is after 9 p.m., rather than still sitting in my classroom marking, I do feel quite confident that at least one item I have generated this evening will save me a few hours of marking tomorrow night...

I'm having students submit a written piece from their geometry centers work tomorrow, their choice of a problem, a journal entry or their write up from the strategy games center.  Based on criteria brainstormed earlier in the year, I developed a marking sheet that will -- I hope -- allow me to provide specific, timely, descriptive feedback without my arm falling off from writing so much!

I plan to use this or a variation thereof with my grade 8 class and two of my grade 7 classes.  Behold:
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Growth Mindset... phase one

11/26/2014

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Attending this evening's ETFO Math Webinar on developing growth mindset I am reminded of the exit ticket I recently started having my Grade 7 and 8 students complete at the end of some math periods.

Someone asked me the other day how I choose which student(s) to conference with and about what, when I am teaching using a centers-based approach in math, and one of the ways I decide is through the use of this exit ticket.  I read each and every one, and write back to each student with direction, either "great, sounds like you have a plan", or "let's meet on such and such a date to talk about such and such", or, sometimes I will encourage them to challenge themselves further with specific learning tasks.  

While I do this, I keep a tally of who's working on what (usually on a sticky note), and then cluster similar needs, so that I can form some small groups in addition to planning for individual learning conferences.  I then transfer the groups and individual names over to a ppt slide which I project, along with the unit learning goal, at the beginning of each class, so that students know who will be meeting with me that period.

One thing I am still working on is getting students to be authentic in their self-reflections, and comment on something specific and relevant that they are mastering or still struggling with.  I'm hopeful that my individual feedback (and then my follow up with as many as possible within the next week) will develop a sense of accountability.

Growth mindset is tricky to develop in students already so far down the path.  Some have had conflicting schema in their previous school experiences, and it's certainly a work in progress to convince some of them that it's okay not to know everything... yet! :)

It's also a learning experience for me to retrain myself to notice and comment on effort rather than skill.
A teacher in my workshop this evening developed a series of simple posters she puts up in her classroom.  I share them here as a PDF, with her permission:
growth_mindset_posters.pdf
File Size: 81 kb
File Type: pdf
Download File

(And hey, if anyone wants to print me a nice set in colour, I'll post them in my classroom, too!)
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So, turns out it was a pretty good idea

11/25/2014

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While swamped with marking from a recent brilliant but "big" cross-curricular assignment a colleague and I embarked on with two grade 7 classes, I was second-guessing whether it had been a good idea to try something so, well, cross-curricular!  But seeing the enthusiasm of those groups who chose to present their ideas to their peers the other day confirmed it was just the sort of real life application that enriches student learning.

My colleague and I had assorted individuals and small groups set up shop in the locker bay area, then the rest of the students went around to "shop" the various field trip ideas and give their feedback on the creators' presentation of same.
It was neat to see the breadth of ideas students had come up with... everything from free lunch and a t-shirt to customized mini-maps highlighting the 6-minute walking route from the potential feeder school to our location... fun!
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Students Teaching Students

11/23/2014

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As a way of extending for enhanced learners, I've always found "helping others" to be a superficial task in class.  Without a specific goal, "go help someone else" is not enriching to students who may be ready for the next challenge. 

But with intention, this strategy becomes one that can benefit many.

Below are three examples of how I am attempting to integrate students teaching students into my math program this year:

1. Enrichment
Several students in my Grade 8 class are ready for the next challenge.  This past week, a small group of them completed a self-researched ppt on Pythagorean Theorem, and presented it for five minutes at the beginning of the class.
The group seemed to enjoy taking centre stage to share their learning, and their peers seemed impressed with their work.

If only there were more time... we'd co-construct a set of criteria for what makes an effective peer presentation, and have more students do it on a regularly basis!
2. Making it Stick
For some students, a mini-lesson needs a little extra support to take root. Recently I was working on classifying 3-D shapes (polyhedra) with a group of grade 7s.  At the end of the mini-lesson, I asked each student in the small group to share what s/he had learned with another person on my "to do 3D shapes with" list.

Not only does this solidify the learning for those in the original group, it saves me time as a teacher; rather than re-teaching the same lesson to a new group for 20 minutes, I can do a quick, 3-minute check-in the next time we have math, and then spend the other 17 minutes with students who require additional support in that or other areas! :)
3. For the Good of the Cause
The example I am most excited about is a student in Grade 8 who has made "effective communication" in math a goal.  I've enlisted his help with a student in one of my Grade 7 classes who could really benefit from some 1:1 support.

Although they have not met yet (scheduling can be a bit of a nightmare), I am hopeful that this opportunity will provide the Grade 7 student with the support he desperately needs (both academic and social/emotional), while giving my friend in grade 8 a chance to develop his mathematical communication skills.

If this works, I am going to try and expand the program to include more students; they'll meet once or twice a week after school in my classroom.

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Choose your own test

11/22/2014

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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.
rubric_summative_assessment_of_criteria.docx
File Size: 24 kb
File Type: docx
Download File

runbric_summative_assessment_of_criteria.docx
File Size: 23 kb
File Type: docx
Download File

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.
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Planting Birdseed

11/22/2014

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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!
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    About Vera...

    Vera & her Sons, April 2021
    After writing for several teacher and multiple birth publications, including ETFO's Voice Magazine, Multiple Moments, and the Bulletwin, Vera turned her written attention to prolific blogging for some years, including BiB,  "Learn to Fly with Vera!"  and SMARTbansho .  Homeschooling 4 was her travel blog in Argentina.  She now spends more time on her Instagram (@schalgzeug_usw)  than her blog (pictures are worth a thousand words?!) 
    DISCLAIMER
    The views expressed on this blog are the views of the author, and do not necessarily represent the perspectives of her family members or the position of her employer on the the issues she blogs about.  These posts are intended to share resources, document family life, and encourage critical thought on a variety of subjects.  They are not intended to cause harm to any individual or member of any group. By reading this blog and viewing this site, you agree to not hold Vera liable for any harm done by views expressed in this blog.
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Vera C. Teschow, OCT, M.Ed., MOT
Toronto, ON & St Peter's Harbour, PE
www.verateschow.ca 2021
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