Month: October 2010

Total 19 Posts

Handle With Care

2012 Mar 09. This post references this task.

Greg Hitt put this image up in front of his class and couldn’t get them back:

So, anyways, they could see plain as day about the object’s motion, seeing the way that the vertical component of velocity goes towards zero, inspecting the horizontal component and seeing that it stays more or less the same. Again, the clarity of the image made it so they could see it, without me having to tell them. Good! Success! Time to move on! “Wait!” the kid yells. “Does he make the shot?

Sometimes the picture asks a question so loudly you have to answer it.

2011 Mar 09. Andrew Stadel:

Best quote from a kid: “Can we watch the video to see if he makes it?” No, we have to finish our graphs “It’s killing me. I gotta know!”

[PS] The Piano Lid

Geometry, Prentice Hall (Pearson), 2007, pg. 151

Pseudocontext

Kate Nowak gets out the knives and goes in:

I think Pearson knows that angles are hard to motivate. You would hope that the multi-jillion dollar conglomerate we paid multi-thousand dollars for books and associated peripherals would use all that money to help me. But they clearly punted on motivating angle measure. The lessons are dry and contextless and the exercises include this monstrosity.

  1. Yes people have to prop piano lids with sticks, but what could possibly happen that we would give a flip about the measures of those angles?
  2. The photo is not taken head-on. I bet that given angle isn’t even really 57 degrees.
  3. Superimposing a diagram of a triangle on a photo does not make it a real world application.
  4. Do “prop sticks” on all pianos intersect the lid at 90 degrees? Why? Is the prop-stick length and angle determined by the width of the piano? Yes, if the right angle is required, by hypotenuse-leg, and no, if it’s not, because it’s side-side-angle. I still don’t really care, but it’s at least a teeny bit more interesting.

Transcription:

The lid of a grand piano is held open by a prop stick whose length can vary, depending upon the effect desired. The longest prop stick makes angles as shown. What are the values of x and y?

A short prop stick makes the angles shown below. What are the values of a and b?

Assignment:

  1. Scan an example of pseudocontext.
  2. Email it to dan@mrmeyer.com
  3. List the textbook title, edition, and publisher.
  4. Give me your interpretation of the term “pseudocontext.”
  5. Let me know if you’d like credit (name, blog or twitter) or if you’d prefer anonymity.

Scott McRhee

Scott is usually a lot more subtle than this, but he overplayed his hand this round, and tipped the table to his low regard for classroom teachers. I encourage my readers (and his, to the extent that we overlap) not to forget this. Fair to say I’ve succumbed to his kind of contempt in the past but it became obvious to me, not long after, that I had a) underestimated my colleagues, b) overestimated myself, and c) seriously overestimated the effectiveness of contempt as a precondition of reform.

WCYDWT: Polynomials

Ha ha. J/k. There isn’t a picture for polynomials. That’s insane. The question about polynomials comes up, though, especially when we give into the fiction that students can’t enjoy math for its own sake.

Let me highlight two positive externalities of WCYDWT, which is to say, benefits of WCYDWT that don’t limit themselves to the time that we are actually WCYDWT-ing:

  1. The class understands that non-standard approaches are awesome.
  2. The class understands that failure is useful, not shameful.

You can capture those benefits using traditional curriculum but you have to work a lot harder at it and if you stop working harder, you capture the negative externalities: students come to understand that math is a right or wrong endeavor in which “wrong” is an destination unto itself rather than just another waystation to “right.”

The last two years of my career I facilitated classes that were often fearless and creative. That meant this: if they were really confident with trinomials like x2 + 7x + 6, I didn’t have to lecture. I’d just write on the board: 2x2 + 7x + 6.

Which would offend them. You know, like, “how dare you bring that weak stuff in here, Meyer? You didn’t see what we just did to the last trinomials?”

Because they were creative and because failure had little stigma attached to it, students would start putting answers down. They’d experiment. In math. Worst case, maybe one of them would throw down (2x + 7)(x + 6) — just banging the numbers from the question together, hoping to see some sparks. She’d call me over and ask if it was correct. I’d tell her to check it. “You know how to multiply binomials.”

She’d see she missed it — 2x2 + 19x + 42 — but we’d notice she nailed the 2x2 — “keep that!” — and ask her to experiment some more. My role in class was to help condense and summarize the findings of student experimentation.

This is how you maintain the spirit of WCYDWT even for concepts that seem to defy the spirit of WCYDWT.

[PS] Guitar Hero

Algebra I (Illinois Edition), Prentice Hall, a Pearson subsidiary.

Pseudocontext

Is there anything inherent to buying an electric guitar that would lead to that equation ever?

[via Ryan Buck]

Transcription:

A music store sells a copy of a deluxe electric guitar for $295. This is $30 more than 1/3 the cost of the deluxe electric guitar it is modeled after. What is the cost of the deluxe electric guitar?

Assignment:

  1. Scan an example of pseudocontext.
  2. Email it to dan@mrmeyer.com
  3. List the textbook title, edition, and publisher.
  4. Give me your interpretation of the term “pseudocontext.”
  5. Let me know if you’d like credit (name, blog or twitter) or if you’d prefer anonymity.