Saturday, January 26, 2008

Pink Dragons and other Real World Applications

In order to determine what would make science classes appear relevant to learners, researchers of the ROSE project actually asked the students. What they found was that teenagers care little for learning about plants in their local area, how car engines function, and how chemicals interact. They are significantly more interested in learning about how atomic bombs function, why stars twinkle in the night sky, and phenomena that science still can not explain. And the item of most interest to the young learners was the possibility of life outside earth.

So much for the mantra that science must be made "relevant to students' daily lives."

I should not be surprised. I can dutifully and with some determination work up a bit of interest for the functioning of car engines, but only a little bit. I majored in Physics.

Why do we think that math problems will be more engaging to students if they are about bake sales, CD shopping, and other real world applications? And those little vignettes in the textbook that purport to explain how useful and applicable all this math will be - why do they always seem so contrived? Who thinks that a note in the margin stating that "If you become an ornithologist, you may use polynomial functions to study the flight patterns of birds!" will be more convincing to the kids than it is to us? And if the value of high school math for students' daily living were so clear cut, why isn't the case made more forcefully after so many years of textbooks?

Svein SjĂžberg of the ROSE project argues that the reason why all students should learn science is not primarily that this knowledge will be so useful to them in their daily lives, nor should it be society's need for a sufficient supply of engineers and technicians. He instead emphasizes 1) the cultural argument and 2) the democratic argument. All citizens need to learn science because science, like arts and history and poetry, is a part of our common human heritage. Also, political decisions about issues involving science ought to be made by an informed electorate.

By the same line of reasoning, primary rationales for learning math could also be the cultural and political weight that this subject carries. Humans have calculated, devised and solved puzzles, and developed multiplicities of algorithms in all kinds of cultures throughout thousands of years. Accessing some of this heritage is part of the enculturation of a person in today's world - it is a privilege, not something we need to excuse or justify with awkwardly implausible future employment scenarios. As for the democratic significance of math, must not an informed electorate be able to interpret data displays and ask critical questions about statistical statements?*

There are times when I feel that my subjects are gatekeeper courses rather then essential components of a well-rounded education, as when I see a student aspiring to be a nurse struggling with logarithmic functions, and I wonder who ordered this, who has an interest in setting up this barrier between a dedicated and in many ways talented student and her choice of profession? On the other hand thinking of math in other terms than job training makes teaching it so much more interesting. I can happily create ridiculous word problems about pink dragons and syrup fountains, and remember that "relevance" for a teenager need not have much to do with usefulness in some narrow technical sense. The "relevance" of a math problem may have to do with the investment in completing it faster than the neighboring team, the joy of working together with a classmate on it, or the beauty of the graph when it is done in colored pencil.

*If we take the democratic argument seriously, maybe we should consider replacing most of Geometry with Applied Statistics as a graduation requirement and make formal, proof-based Geometry a college prep class rather than a course mandated for all citizens.


Anonymous said...


Thanks to your inspiration, last week when I was covering rate problems the questions were all about a dragon.

For the first problem, the kids laughed at the concept. By the time they got to the last problem, they wanted to know more, wanted to do another problem so they keep exploring the world this dragon lived in.

For all the real world problems I've given them this year, when I switched to a series of obviously fictitious problems was when they started to pay attention.

It's not about the real world, it's about telling a story that they can care about.

Now I need to decide whether the next set is going to be about ninjas, pirates, or zombies. I think it's going to be zombies. You've always got to be ready for zombies.

H. said...

Lovely. Let's post story problems that work as we go, aiming, ultimately, at a full fictional universe for the course. Actually... that's going to take years, realistically speaking. Anyway, the entry on rate problems that you linked to was the inspiration for this background for unreal world problems.

Anonymous said...

As I look back on these questions, I'm almost embarrassed by how really not interesting they seem.

All that really tells me, though, is how frakkin boring those other questions must be.

Here goes:

- It takes Gworghulm the dragon 7 hours to fly across the kingdom. If the Kingdom is 280 miles across, how fast does he fly?

- Gworghulm has 47,000 pounds of gold. If his cave has an area of 2000 square feet, how many pounds of gold does he have per square foot?

-Gworghulm destroyed 18 farms in the past month. If there are 30 days in a month, how many farms per day did he destroy?

- If Gworghulm abducts 0.75 maidens per month, how many does he take in one year?

- Gworghulm needs to eat firestone in order to breathe fire. He eats 83 lbs in 5 days. How much does he need for 4 weeks (28 days)?

- Gworghulm collected 39 lbs of gold this month (30 days). If he wants to increase his production by 1 lb per day, how much gold will he have to collect next week (7 days)?

H. said...

Thanks for more ideas! I'm realizing that it's too long since I actually read relevant (!) stuff - wouldn't have been able to come up with a convincing name for the dragon. Have even had an unread Terry Pratchett lying around for months (before teaching, that would not happen).

Anonymous said...

I agree what teenagers are interested in is not equivalent to "real-life examples", but I don't think there's no intersection either.

One of my best lessons came from my logarithm-frustrated class who I grilled about what professions they were interested in. The two big whiners wanted to do psychology and photography. So I wrote lessons based on both of those. In psychology I did an actual psychology experiment (using Stevens' Power Law) in class and then showed how we needed to use a logarithm to analyze the data. In photography I showed the "zone system" Ansel Adams came up with and we calculated f-stop sizes based on logarithms.

I actually had the psychology complainer excited, saying "this is what I get to be doing!"
(The photography complainer was absent the day I did that lesson.)

For your student who wants to be a nurse, try the book _Practical Statistics for Nursing and Health Care_. (It shows a probability distribution from a medical test compressed using logarithms.)

H. said...

Jason, that's fantastic.

I guess a reason why unreal world problems are nice is that they don't take forever to write - while real real-world problems would be very prep-intensive. Thanks for these ideas - developing a stock of such authentic problems would be well worth the time investment.

Oh, and your entry on the merit pay study in India was fascinating. It's been on my list of things to read carefully for weeks. Will do. Soon.

Anonymous said...

Thank you!

I do plan to post my psychology Powerpoint at some point and my plans so people can steal at their pleasure.

My photography lesson isn't quite ready for primetime, though.

Cav said...

It's quite ridiculous, some of the "real life" context that gets shoe horned into maths exams!