Abstracting the Concrete

Jose VilsonEducation5 Comments

Last week in the classroom, I started dreading the idea of the two worst words for any regular teacher in this country: test prep. I hate it because it’s a contrived barometer of what they’ve truly learned, and en masse, becomes the data for metrics used to evaluate student progress, teacher competency, school preparedness, and demographic success rates. Unfortunately, only the people on the bottom of the totem pole ever address the malleability of these tests; they change at the behest of the emperor’s needs and not actually creating a standard for what certain grade levels should learn at any given part of their academic careers.

So instead, I decided to pull out the hardest questions from their predictive assessments (I’m a rebel) and help them understand how to do it. Let me show you. I took a problem like this:

Irregular Polygon

and actually made it more multi-dimensional.

Irregular Polygon 2

Nothing too shabby, but it’s interesting to see the kids’ faces of bewilderment. At first, only the more spatially inclined got how to do it. Then, as I started to show how the whole picture is nothing but a bunch of rectangles, the rest of the kids who were paying attention from the previous week’s lesson on the properties of a rectangle (it took a little reprogramming) were able to decipher the code on their own (for those not geometrically inclined, a hint: all parallelograms, including rectangles have 2 pairs of parallel and equidistant sides).

Of course, then I got really off-the-wall and gave them a similar figure and gave them completely off dimensions. Just to use the diagram above, the 10 was where the 7 is, and I mixed it up with some decimals, so the smart-asses in the class quipped, “But Mr. V, why didn’t you just put the measures where they belonged?”

I laughed, and like the quixotic teacher we’re used to seeing in the movies, I retorted, “It’s not about what you see. It’s about the idea behind what you see. Yes, the lengths are totally mixed up, and you’re already distracted by the mis-measurements. But if you understand that the longest length is the sum of the 2 shorter lengths parallel to it, then this should be no problem for you. Same goes with the the widths. Now, on the test, none of the lengths will be drawn to scale, so are you going to break out your ruler for every problem? I really hope not. I’m just making it obvious that you need to use your arithmetic skills to figure this out.”

Of course, one or two of them were still incredulous, but the rest understood. I was making them think for once. They couldn’t take anything for granted, and that’s important. Instantly, I found buy-in. I even differentiated by breaking the kids up in groups, and handing them cards with specially-made problems. Then they took it upon themselves to break out some chart paper and deliver how they did it to the rest of the class. I allowed for it only if I got to ask them critical questions to each and every student. Done and done.


Comments 5

  1. You gotta love those moments when it all clicks for the kids. I’m hoping my “hip-hop sampling = genetics” angle pays similar dividends for my biology students.

  2. Pingback: Carnival of Mathematics 1000 « JD2718

  3. I think it is important that you reminded them that the test will try to trick them with lengths that look different than they seem, like a figure that looks like a square but the test says is 7 miles by 8 miles. Coincidentally, I started teaching perimeter to my preschoolers this week. We used geoboards. I made a square with 3 “spaces” on each side. Then we counted 12 spaces or fingers around. Then I asked them to make their own shape with 12 spaces around it. It was definitely out of their league (they are 4) but if I do it 2 or 3 more times they will get it. THey thought it was so cool that I could make a T and a W and they still measured 12 spaces around.
    I wonder when most kids start looking at perimeter? Probably not soon enough, or then it wouldn’t be test prep would it? It would be review.
    I heard a story about a teacher in an affluent county who gives her biology kids a version of the state test the first day. They all score above 85% then she says so now we can go in the lab and have some fun with chemicals and microscopes and beakers instead of stressing about the test. Talk about a different perspective.
    I will start doing some combined adding/subtracting with my geoboards next week. At least if some of my students move to NY they will be ready for you.

  4. Post

    Nubian, if you put that down, I’d love to see how that comes out. Please post somewhere.

    Poor_Statue, and to think, this isn’t just something I’m pulling out at random.

    John, that’s wonderful. After the test, I want to do cool things like that, but upgraded for my 6th graders. I’ll think about it.

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