This is somewhere in the neighborhood of What Can You Do With This? except I have no idea what to do with it.

Reaching a beach in Trinidad, [Jennifer Figge] became the first woman on record to swim across the Atlantic Ocean – a dream she’d had since the early 1960s, when a stormy trans-Atlantic flight got her thinking she could don a life vest and swim the rest of the way if needed. –

Associated Press, 2009 February 8

Figge swam 2,100 miles from Cape Verde to Trinidad in 25 days, sleeping nights on a catamaran that drifted alongside her.

Sort of. *Outside Magazine* has printed a retraction.

I know this is worth our class time because a) the situation is objectively interesting, and b) the situation is inherently mathematical. I *don’t* know how to maximize its interest to my class or how to make the mathematics as rigorous as possible.

Here is a hazy look at how I plan this sort of activity. Please step in at any point to save me from myself.

**I’ll tell them that a woman has claimed a distance swimming record.**I’ll ask them to guess which body of water she crossed. I will project a world map on the wall. Somebody will eventually suggest the Atlantic, a suggestion which other students will shout down as impossible, at which point I’ll confirm it.**I’ll ask them what route**Each of my students is a pretty quick study in contract law and will find the loophole or shortcut if one exists. I’m not sure how many of them will find Figge’s*they*would choose across the Atlantic.*exact*shortcut, however, which had her swimming between two of the closest islands on opposite sides of the Atlantic. I’ll pass out world maps on paper so that the students can draw on themduhn duhn DUHN. .**I’ll ask them how long they think it took Figge to cross the Atlantic.**At this point I’m*pos*itive they’ll ask the right questions (how long was she swimming each day? was she swimming all day, every day?) at which point I’ll quote the relevant passages from the AP report. (She swam, at most, eight hours in a day.) I will give the distance between the islands only when they request it.**I’ll challenge their guesses.**“I don’t think a human can swim that fast.” They will either have to defend their answers or alter them.**We’ll sample some data points for comparison**– Michael Phelps’s 100m gold medal at the Beijing Olympics (4.4 miles per hour); Petar Stoychev’s record-setting swim across the English Channel in 2007 (3.02 miles per hour); then there’s Figge’s presumptive trip the Atlantic (10.5 miles per hour).

Again, we lower the mathematical framework onto this situation *slowly*, only as the kids give me the nod to bring it closer, only as they invest themselves into the problem in small ways like guessing the route or the duration of the trip. Bonus exercise: imagine how efficiently your textbook publisher would crush the life out of this problem.

I’m running out of ways to illustrate my frustration with curriculum design’s status quo. Time to get the jihad going, I guess.

## 9 Comments

## Nick

February 17, 2009 - 5:18 pm -I wonder how they’d do if you set up some sort of standard distance in the classroom and had kids walk through it at the different rates (Walk the speed that Michael Phelps swims, and compare that the Figge). I have some swimmers who would be easily engaged in keeping everyone realistic about how fast swimmers swim. Lots of us aren’t so good at estimating the velocity of moving objects that we see. To make things easy you could plot a course in the room that’s about 52.8 ft long, that converts to around 52’10.” This would nicely allow quick and fairly accurate approximations of velocity.

It’d also be cool to try to have two kids do it at the same time to really hammer home the point about Phelps vs. Figge.

One little oceanic point to bring up is the speed of the currents. Figge might have only swam .5 mph but if she were riding an easterly current drifting at 5 mph then she’s already beating Phelps who doesn’t get the advantage of a current.

Good ‘ol Glenn Elert posted some approximations – Gulf Stream moves at 1.5 m/s which converts to about 3.4 mi / hr. Another site has the Gulf Stream at between 3 and 4 knots (4 knots is about 4.5 mi/hr – see google).

My final thought – it should be much easier to get every student to see and accurately describe how ridiculous the initial claim is (10 mph * 8 hrs * 25 days is unreal). However, 250 mi / 25 days = 10 mi / day, as her retraction claims, is no small feat. I think it would be hard to get the kids to respect those numbers, if in fact they are somewhat close to true.

## Allison

February 17, 2009 - 5:27 pm -What about the currents? Would this be more or less plausible going the other way?

I want more data points in Step 5– what kind of relationship exists between the distance of the swim and the speed at which the fastest human can swim it? What does this predict about our presumed trip across the Atlantic, especially under varying assumptions about the amount of the day actually spent swimming? (Besides that if I try to swim for 24 hours at a time I’ll drown, of course.)

Can we use some information about average current speed and water temperature to find the “best” route to swim across the Atlantic? Would the route change if we assumed the swimmer would stay in the water more or fewer hours a day? If we allowed drifting with the current at night versus anchoring the boat?

## Kate

February 17, 2009 - 8:44 pm -Oooh can we ululate?

## Chris

February 18, 2009 - 8:45 am -I found this today which matches up nicely with this post and how text books do the thinking for students. I don’t know how accurate it is for older decades, but it is interesting nonetheless.

Can the level of math education sink any lower?

Teaching Math In 1950:

A logger sold a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit?

Teaching Math In 1960:

A logger sold a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit?

Teaching Math In 1970:

A logger sold a truckload of lumber for $100. His cost of production is $80. Did he make a profit?

Teaching Math In 1980:

A logger sold a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Your assignment: Underline the number 20.

Teaching Math In 1990:

A logger cut down a beautiful forest, because he is selfish and inconsiderate and cares nothing for the habitat of animals or the preservation of our woodlands. He does this so he can make a profit of $20. What do you think of this way of making a living? After answering the question, the topic for class participation is: How did the birds and squirrels feel as the logger cut down their homes? (There are no wrong answers.)

This is from: http://www.cs.elte.hu/~ewkiss/education.html

## kevin

February 18, 2009 - 2:20 pm -Dan,

I’ve been enjoying your posts recently as they’ve given me a fresh perspective on the pointless ‘applied’ problem of textbooks. I love what you’re trying to build with these ‘pictures’ that build math. Just lovely. Brilliant even, I’d say brilliant. So there’s my hat tipping.

So something like this, where would you work it in? Average rates of change? I often feel like beautiful ideas like this succumb to the realities of curriculum. Is the goal to build enough of these to ‘illustate’ the math (i.e. cover what needs to be covered and then do this, or use this as an introduction the material?) Just curious.

Again, this is just brilliant.

Kevin

## Meghan

February 18, 2009 - 2:35 pm -I always enjoy installments of your “What Can You Do With This” series and I really liked how you outlined the Q & A process in this post. It’s very empowering for the students to be able to create the mathematical framework around a single image or idea.

That led me to thinking about empowering your students even more. Why kill yourself scouring the internets for images and videos when you can empower your students to do the same thing? And for double bonus points, the image/video/news article must already have relevance and cultural context for them to want to choose to study and explore it. This way you’re not just teaching how to “do the math”, but really think critically about their world.

Maybe this would work more along the lines of a project/presentation setting… just a thought.

## Dan Meyer

February 18, 2009 - 5:15 pm -@

Kevin, I’m not exactly sure how to account for my class time. We discuss one miscellaneous question per opener, one photo set per class, one interesting video twice a week, and one of these investigations once a week (contingent on supply of course).In spite of all that, my kids meet the same pace as their friends in other classes and we set the school curve on the semester final.

My classroom management is solid enough that we don’t waste time getting started or getting ended or getting into disciplinary confrontations. We don’t waste time on long, unwieldy assessment. We don’t waste time reviewing homework. That frees up a lot of time.

I think it’s possible, though, that the critical thought we develop through these WCYDWT conversations helps us gun through material a lot faster than before. For instance, I find myself introducing new material in a lot less time lately, relying on students to use old skills in new ways. This may be an effect of WCYDWT.

@

Meghan, I have no trouble accepting that students can demonstrate content proficiency by taking photos or videos and explaining them, as an alternative assessment, if you will.Personally, I find it

verydifficult to capture an image and present it in such a way that my students will develop as critical thinkers, in such a way that they will engage in rigorous mathematics.I know that other teachers find it difficult too (eg. Ben Wildeboer’s attempt and our conversation in the comments) so I’m open to the possibility of student contributions to this project but unhopeful that they will be as rigorous as what I can create.

## Ben

February 24, 2009 - 5:29 pm -It’s not that curriculum design has a stranglehold on the status quo. It’s easy to see that when you’re young like we are, have as much free time as we want to plan, think, react, and re-evaluate whenever we want. Curriculum design seems almost clunky, slow, and glacial.

The problem arises when you start to grow older; love interests become spouses, children enter the picture, commitments to projects and life outside of school begin to take up more and more time. It’s scary to admit this, but eventually the curriculum starts to look not so much like a huge lumbering iceberg to steer clear of out in the North Atlantic, but more and more like a life preserver tossed out to keep your head above water.

This isn’t to say I’m this pessimistic about teaching, and my ability to find time to prep for it; just a viewpoint from someone looking to the horizon and realizing just how much time I honestly have to spend preparing for class, and how much more time I know I’m going to want to spend with my family.