Quadratic Motion Project

Math 2 is starting a unit about quadratics. Eventually they’ll be doing the standard solving quadratics stuff but first we’re familiarizing ourselves with parabolas. I remembered seeing this awesome art installation and wanted to try and recreate it. After all, whenever something gets thrown in the air, its motion is quadratic – that’s just math! Theirs didn’t turn out quite the same as the ones at the art museum, but we achieved the intended effect.

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I’m not sure what materials they had to work with at the Mustang Art Gallery, but in my class we were taping ping-pong balls to fishing line and dowel rods. There were some pitfalls with things getting tangled and un-taped, but my favorite mistakes were a little bit more process-oriented. To figure out the placement of the ping-pong balls, students plotted their quadratics using some type of grapher, either a calculator or Geogebra. I told them to decide what y-value the dowel rod was and find the distance from that to each point. This one has the dowel rod at y=5:

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Geogebra will just measure that distance for you. You can also just subtract whatever the point is from whatever the dowel rod is, which led to this interesting mistake here – can you figure it out?

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I think that the 2 points that should have been farther down were where the parabola crossed to be under the x-axis. For the example above, it’s pretty clear that 5 – 4 = 1 [C], and 5 – 2 = 3 [D]. It’s also entirely possible to get 5 – -2 = 3 rather than 7 [A].

The visual should make it clear that the math is off, but the frustration inherent in re-taping may have been a disincentive in fixing it.

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CHADD Conference Tabling

This week I spent some time representing the Howard Gardner School at the CHADD national conference. CHADD (Children and Adults with Attention-Deficit/Hyperactivity Disorder) is an organization supporting, advocating, and informing individuals with ADHD and their families. Each year they put on a conference, and luckily enough this year it was in Crystal City. Because of our school’s small size [48 students in the high school as of last Wednesday] and student-staff ratio [about 4:1], and our hands-on curriculum where we are out of the classroom 2 days each week, about 45% of our student body (as well as perhaps 20% of the staff) have been officially diagnosed with ADHD. Tabling at this conference was an excellent opportunity to meet some of the local professionals who work with our students or students like them, prospective parents, and rival schools – we were situated directly across from one of those. I asked them if they were interested in losing to our undefeated soccer team, and funnily enough they were not.

Conversations with parents reaffirmed what I strongly believe – the advent of high-stakes testing is extremely harmful to students with learning differences. Ironically, as awareness of ADHD, learning disabilities, and the autism spectrum increases, so does standardization. We clearly know that all students are not the same, yet we are embracing standards that leave few opportunities for differentiation because they call for teaching so many different topics. Gary Rubenstein wrote an excellent article about this. I’d strongly recommend reading it, but I will say I disagree with his second idea (an argument for another time). In his post, Rubenstein points out that we are teaching students too many specific skills to truly teach them the important parts of math – problem solving, reasoning, and generally thinking deeply about mathematics. This hurts students like mine the most. Teachers are forced to blaze through a series of disconnected topics, speeding through them before students with slow processing speeds, difficulty staying focused, or challenges with working memory (just a few examples!) even have the chance to understand. I’m extremely lucky that I’m able to pick and choose which specific topics I teach the students, spending enough time on each that they have a deep understanding. Most importantly, I can build a relationship with students so that math isn’t frightening and frustrating.

On the subject of other things I disagree with, near us in the exhibitors hall was a company purporting to improve concentration and focus through 5-minute sessions on a computer screen. The representative came to talk to us, and we gave her our standard spiel, something like this:

We’re a small, independent school with a focus on the environment and the arts. We use Gardner’s theory of multiple intelligences as a framework for viewing our students as individuals with unique learning needs. Our schedule has students learning outside the classroom 2 days a week, on field studies on Tuesdays and at an internship of their choice on Fridays.

She responded “it sounds like you’re working around their ADHD. What if you could treat the problem?” This statement has good intentions, but I’m rejecting it. Having ADHD or some other unique part of your learning profile isn’t a problem that needs fixing! Not to mention that our students are generally adept at doing anything extremely well for 5 minutes.

I’ll have more math to talk about next week. I have an idea for a visual way of adding finite geometric series that also reviews fractions, plus the math 2 students are doing a project with ping pong balls.