Comments on: Five Favorites â€” 101Questions [4/28/12]

By: lesanno

lesanno — Wed, 02 May 2012 13:52:40 +0000

@Jason Dyer I see your point and I’m certain my materials can be improved. But I also see that, not having experience in asking my own mathematical Qs as a student, I needed to be trained in this way of thinking by seeing others’ questions. Even as a young adult, I would not have asked, for example, “Which coin would be cheapest to carpet my home in?” Now I might. If a teacher can train students to ask these questions, can’t she train students in higher level courses to ask (and care about) higher level questions? Wouldn’t that be a major goal of the class?

By: lesanno

lesanno — Wed, 02 May 2012 13:14:00 +0000

@Kelly Holman 101qs is for the media part of the first act. Basically, the first act without the question. Dan publishes a collection of three-act problems here: http://bit.ly/IWOIos. Some of them have all three acts, plus a sequel; some of them only have certain pieces.

By: Mike

Mike — Wed, 02 May 2012 02:13:26 +0000

This is fascinating. I’m especially interested in hearing how to do this with the other 95% of the curricula, and who is building a repository of these student driven lessons, like Kelly and Jason asked. For instance, today I taught about finding the measures of a bisected angle, whose angles were arbitrary algebraic expressions. Bisected angles– sure! (mirrors, billiards) but angles of 6x-10 and 3x+5 makes it absurd.

I’m mainly posting to get notifications of the responses. :-)

By: Kelly Holman

Kelly Holman — Tue, 01 May 2012 22:05:10 +0000

I’m a little confused about 101 questions. Is it supposed to be only first acts, or are there complete three-act videos somewhere, that you can search for something to use? Is there such a website? I tried Better Lesson, but there’s an overwhelming amount of stuff, and I don’t see a category titled “engaging” or “WCYDWT”.

A related question: Do you manage to teach everything in math this way? If you do, I’m very impressed.

By: lesanno

lesanno — Tue, 01 May 2012 20:17:14 +0000

Michael P: Excellent question, especially since I have yet to contribute a single upload to 101qs. I am thus an amateur. The idea is still in the formulation stage, but here are my thoughts:
-There’s gotta be useful wilderness footage in some man vs. nature movie that involves navigating or estimating distances. I’m picturing adventurers stranded in snowy mountains.
-A bird’s eye view of a region with pins in the three relevant locations. The distance between locations 1 and 2 we know; we want to know the distance from 2 to 3; we can measure the angle.
-A picture along a line of sight between two somewhat distant objects and the simple question: “How far away is the ________.” I actually tried to construct this one on a faculty work day. I followed it up with video of me measuring the relevant pieces (a navigational compass for the angles, measuring tape for the side). It was workable, but deserves to be done better.

By: Dan Meyer

Dan Meyer — Tue, 01 May 2012 17:27:02 +0000

FWIW, I think Michael P's comment argues strongly for some kind of wishlist on the site. Like a stripped- stripped- stripped-down forum where you can say, "Is anyone in Philadelphia right now? I need a photo of the enormous domino piece." Or, "Struggling w/ related rates and cones." Or something. Jason:

Keep in mind the point here is to have an question just begging to be answered strongly enough that even the apathetic teenager becomes curious; if anything our mindset is too complex compared with how our students will think.

In general, I agree, and I try not to be too dogmatic about any of this, but check out the competition. You know? Just undertaking the exercise and asking ourselves, "What are students going to wonder here?" puts us leagues ahead of the typical student experience, which is more like, "Screw you, kid. Here's a dog in a bandana. Let's get our special triangles on."

By: Jason Dyer

Jason Dyer — Tue, 01 May 2012 14:56:28 +0000

I suspect that the supremacy of rate- and ratio-type results from 101qs is in part due to the questioners, not the uploaders. I think even if presented with a good trig opportunity, most of us pose algebra-type questions. Maybe because we’re just in that mindset? Or do Dan’s blog and 101qs appeal more to algebra-ers?

@lesanno: Keep in mind the point here is to have an question just begging to be answered strongly enough that even the apathetic teenager becomes curious; if anything our mindset is too complex compared with how our students will think.

Side note: Once I had a terrific lesson where I had a picture, a little extra context, and asked “what time of day is it?” No student would come on their own thinking answering the question was even possible, so it’s somewhat outside the 101qs format.

By: Michael P

Michael P — Tue, 01 May 2012 14:34:27 +0000

Lesanno, what media would you upload to 101qs to motivate a question that uses the Law of Sines?

By: lesanno

lesanno — Tue, 01 May 2012 14:24:56 +0000

Other ideas for trig problems: calculating distance (between two mountain peaks, say) using the Law of Sines. Then calculating distance when the Law of Cosines must be used. I can think along the lines of soccer players positioned on a field, tactical positions creating non-right triangles, etc.

As for right triangles, we once used Dan’s “How tall is the lamppost?” images (/?p=12620) to answer the question “At what angle is the sun hitting the lampost?” using SOHCAHTOA and inverse trig functions. I wouldn’t say the experience was award-winning, but it was cool. It would have been cooler if we could have calculated what time he took the photos based on the angle to the sun. Anyone know how to do that? Right triangle trig opportunities abound in architecture, shadows, just about anything that goes up from the ground. We just have to start taking the opportunities.

I’m hoping to come up with something truly awesome that uses logs or logarithmic equations. That would make my day.

By: Michael P

Michael P — Mon, 30 Apr 2012 22:22:43 +0000

There are other great applications, the constraints of 101qs don’t preclude them, they’re just kind of hard to capture.

To me, this is the exciting possibility of this project. Anybody have thoughts on the next batch of low hanging fruit?

Here’s what I’ve come up with:
Linear Equations Dan’s graduation problem is a start. Related: reading the dictionary. (ala http://www.youtube.com/watch?v=Q9DCoqMrKr8)
Systems of Linear Equations We should be able to nail this. Will the two things crash? Will the second gerbil win the race? Will he make the putt through the windmill?
Probability The challenge here is replicating the experience of a long-burning empirical experiment in a short video. Maybe a game show on the left side of the screen, with a tally of the results on the right side could create that experience?
StatisticsOpen with a bunch of short interviews of respondents answering a question. Would that be enough to provoke a question about the aggregate population?
Quadratics Dropping things out of windows? (I’ve got a couple of bouncy balls that I intend to drop out of my apartment window one of these days.) Racing things off of hills?
Trigonometry I’m thinking pendulums. Will the runner crash into the swing?

What else?