Comments on: [Makeover] Boat Race Preview

By: dy/dan » Blog Archive » [Makeover] Boat Race

dy/dan » Blog Archive » [Makeover] Boat Race — Thu, 22 Aug 2013 00:28:38 +0000

[…] Lindsay also asks her students to describe the path of the boat without yet knowing the vocabulary. […]

By: Dan Meyer

Dan Meyer — Wed, 21 Aug 2013 19:23:21 +0000

By: Nate Garnett

Nate Garnett — Wed, 21 Aug 2013 14:34:14 +0000

This would be a cool competition between students if they could then actually race their boats: program the vectors into a game that moves the boat as directed by the student at a set speed with a timer. The fastest student boat wins.
Any thoughts on what program to use? scratch? geogebra?

By: Mark Schommer

Mark Schommer — Tue, 20 Aug 2013 11:48:36 +0000

What about a cruise, …isn’t that exactly what they do, sail an circle? Identify points of interest and create the path to visit those points and have to port in (the red dots would be the “port” (I think I am a little off in terminology but I have never taken a cruise).

By: Lindsay

Lindsay — Sat, 17 Aug 2013 14:32:42 +0000

I am considering using something like this as an introduction to Vectors. Give the the students the image and explain a course that the boat needs to take (in words like the original problem) and then ask them how they could describe their exact course to someone else to follow. I would leave off the grid lines. My hope is they would then start measuring angles and a discussion could follow about convention of direction and polar coordinates vs. navigator method, etc.

By: Rob Liebhart

Rob Liebhart — Sat, 17 Aug 2013 14:05:19 +0000

My only idea for context help is to plan a boat race. Students could either be the race event planners–trying to pick a long/short, easy/hard, sharp-/gentle-turn course–or the races–trying to plan the most direct route around the race course.

Putting a finish line somewhere else could allow some students to be the white boat while other are the black boat, allowing for different answers, at least for the first leg of the ‘race’.

By: P. Nel

P. Nel — Sat, 17 Aug 2013 08:34:20 +0000

I don’t have as much problem with the question, poorly worded as it may be, as I do with the technological limitations of the textbook which the question appears in. Placing a piece of paper over the text book will not under normal classroom lighting make a traceable image and thus you will have students holding a textbook up to the light with one hand and trying to trace the boats with the other which is silly. This is a question which would make a lot more sense if the students were able to write on it directly.

By: William Carey

William Carey — Sat, 17 Aug 2013 03:16:24 +0000

> Computing bearings is something ship captains actually *do*.

In principle that’s true. According to the problem, I’m a ship captain. Why am *I* computing bearings? Context that aims the student’s perplexity at the *context* instead of the *content* is a type of insidious pseudocontext. Here are the questions that popped into my head while I read that question:

– If I want to end up at the black boat, why don’t I just sail directly at the black boat?
– Why do I have to go clockwise?
– What does “just past” mean?
– Why is there a green triangle in the upper left of the map? Does it mean anything?
– Where do I measure the position of my boat from? The front? The back? The middle? That *totally* matters for the answer.
– Is recording the bearings different from writing them down? What do I record them in? My log book? My phone’s voice recorder?

The last one might be directed at the content (though it’s really just about clarifying an ambiguous diagram). The rest are perplexity about the *context*.

I think there’s something like the uncanny valley for context in math problems. Good context embeds the mathematics in a narrative that fosters perplexity. That’s what the three act videos do so well. Total absence of context can work too. Are there as many fractions as whole numbers is a *really* perplexing question without any context at all.

My experience is that uncanny-valley-context is asking to be taken to task by my students. If the narrative is incoherent, they’ll figure out how and hammer away at that.

I’d say that “just enough context to make the context itself the focus of the perplexity” is a third type of pseudo context in addition to the two you point out here:

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Does that make sense?

(This is a salvageable pseudocontext. Actual ship captains do *measure* bearings and draw them on their charts, and we’ve made computer programs that compute them. There is interesting stuff going on there, but this problem doesn’t naturally lead to it.)

By: Jim Hays

Jim Hays — Sat, 17 Aug 2013 03:09:50 +0000

Why is the boat traveling around these red bouys? Why does it need to end up by the black marker? It seems rather arbitrary and contrived. Why should I (as the skipper) calculate bearings in this situation? Why can’t I just aim my ship at the first bouy, go around it, aim for the second, go around it, then head to the last spot? There’s no scale on this map, so the bouys might all be within sight.

By: Dan Meyer

Dan Meyer — Sat, 17 Aug 2013 02:34:19 +0000

@William, I don't understand how this is pseudocontext. Computing bearings is something ship captains actually do. How are you defining the term?