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Mathematics: Art vs. Application

4/3/2016

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I recently rediscovered my love for Pattern Blocks.

While preparing to explore fractions with my Grade 6 students, some colleagues and I co-planned a lesson from the Pattern Block volume of the ETA Cuisinaire Supersource Series, an oldie but goodie when it comes to constructivism in math.

I had been introduced to pattern blocks and other manipulatives early in my teaching career, and found them helpful in teaching myself math concepts, never  mind introducing these concepts to students!  



​So I was eager to see what the text had to offer.  

We selected a problem that would require students to work in pairs to calculate the "value" of a design they had created using a baggie of pattern blocks (based on the wide range of needs in our classrooms, we decided to prepare baggies ahead of time, so that some students would have either fewer pattern blocks to work with, or no blue rhombi, or both fewer and less variety of blocks, in order to scaffold and make the task more accessible-- this turned out to be a very wise choice in my room!!)  Depending on which block was worth "one whole", the design would have differing values.

The idea was to introduce improper fractions and mixed numbers through a constructivist stance, in a way that would appeal to both the hands-on learners, and those more math phobic students who enjoyed patterning in art.

And it worked! Students really engaged with the math, and using the pattern blocks as thinking tools allowed them to explore concepts that would have been foreign using merely standard notation in the abstract.  Even with the blocks, many students had to be prodded to move beyond a superficial examination... but the blocks helped them to do so in a wide range of ways, as evidenced below...
After creating and calculating the value of a particular design, I asked students to use pattern blocks now to build a design to specs (e.g. if the red trapezoid is worth "1", build a design that is worth 15 and 1/3).

Some of my students found apps or virtual pattern blocks online, and created screenshots of their annotated work to post on our Edmodo site.  A few got so excited about the work that they even shared photos of their designs with students from our collaborative class in Australia!
As the students worked on these assignments, I was able to get a much clearer insight on what they understood, and what gaps still needed addressing, mathematically.  We also had the opportunity to extend students' thinking as they themselves noticed and wondered about patterns in the math they were playing with.

One of my goals this year has been to integrate more equity and social justice issues into my math program, and while that endeavor has been going reasonably well, I worry that sometimes my focus on "real life application" comes at the cost of just engaging students in the beauty of mathematics.
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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
Photos used under Creative Commons from Sean MacEntee, Studio Paars, Bengt Nyman, zeevveez, GoodNCrazy, CJS*64, Accretion Disc, CharlesLam, Courtney Dirks, CJS*64 "Man with a camera", Accretion Disc, Bobolink, Ian Muttoo, BioDivLibrary, Alaskan Dude, IsabelleAcatauassu, runran, Transformer18, jglsongs, Create For Animal Rights, david_shankbone, Paul J Coles, foilman, Newport Geographic, Photo Everywhere, kevin dooley, Claudio , Alex Guibord, Tscherno, f_mafra, Terry Madeley, musee de l'horlogerie, BobMacInnes, wwarby, jonathangarcia, amboo who?, chimothy27, Elin B, cliff1066™, Grzegorz Łobiński, Rennett Stowe, Farhill, Phil Manker, Guitarfool5931, airguy1988, dierk schaefer, Rob Stemple, katerha, StockMonkeys.com, Ramotionblog, andrewk3715, charlywkarl, AJC1, rachel_titiriga