March 10th, 2014 by Dan Meyer
An ongoing question in this "fake world" series has been, "What is real anyway, man?"
Are hexagons less real-world to an eighth-grader than health insurance, for example? Certainly most eighth graders have spent more time thinking about hexagons than they have about health insurance. On the other hand, you're more likely to encounter health insurance outside the walls of a classroom than inside them. Does that make health insurance more real?
I'm sure they can help me here. Here are three versions of the same question.
Given an arbitrary point P on a line segment AB, let AP form the perimeter of a square and PB form the circumference of a circle.
Find P such that the area of the square and circle are equal.
When do the circle and the square have equal area?
Where do the circle and square have the same number of candies?
[suggested by commenter Jeff P]
You and your friend will get candy but only if you find the spot where there’s the same number of candies in the square and the circle. Where should you cut the line?
[suggested by commenter Mr. Ixta]
Imagine you were a contractor and your building swimming pools for a hotel. Given that you only have a certain amount of area to work with, your client has asked you to build one square and one round swimming pool and in order to make the pools as large as possible (without violating certain municipal codes or whatever), you need to determine how these two swimming pools can have the same area.
[suggested by commenter Emily]
Farmer John has AB length of fencing and wants to create two pens for his animals, but is unsure if he wants to make them circular or square. To test relative dimensions (and have his farmhands compare the benefits of each), he cuts the fencing at point P such that the area of the circle = area of the square, and AP is the perimeter of the square pen and PB is the circumference of the circular pen.
Which of these is a "real world" math problem? Or is none of them a real-world math problem?
If anybody else has a strong conviction either way, you're welcome to chip in also, of course.
- Kate Nowak says "real world" means "interesting to humans outside a math class."
- Ginny Stuckey asks if I'm trolling.
- Karim Ani is on vacay and promises a response when he gets back to business. [2013 Mar 22: He delivers.]
- Matt Lane asks, instead, if the task imbues people with joy for mathematics.
- Chris Lusto asks, "Is the question self-referential?"
These are the two ideas that seem to be confused here are just "real world" and "interesting". There seems to be an inherent assumption that they are somehow related when I doubt they even should be. Sometimes they will overlap, and sometimes not, but it is a bit random and quite personal in my opinion.
I caught the maintenance staff at my high school using "real-world math."
The problem probably lies in the many ways that one could define "real world".
What qualifies as "real world"?
- A problem simulating a project/job/task being performed by someone performing their normal job duties, such as the example of the contractor building a pool to meet municipal code?
- Is a problem involving objects or tasks that would be considered an experience students are likely to have "real world"(dividing up the M&Ms to be equal size)?
- Actual evidence of math in the "real world "(video or otherwise) being applied as a part of someone's job (the maintenance staff example above from @Kevin Polke) could qualify, or perhaps the application of math to a problem that is foreseeable in that person's job duties.
I think it's best to take the more pluralistic viewpoint on this one, as it would be quite a task to attempt to statically define the exact nature of "real world" math, as there are always countless more examples lining up to disprove whatever narrow definition you choose.
"Real world" is just a means to an end. The goal is interest.
What matters for a ‘good task’ is not whether it’s real, it’s whether
1) its meaning is clear right away
2) kids want to solve it
3) have the mathematical tools to solve it (even if not very sophisticated tools)
I’ll say again though: I don’t really care if a problem is real-world. There are so many great problems that aren’t, and so many terrible problems that are. I don’t think it carries huge added value. Everyone decides what’s “real” to them (as Jeff P said). Right now for my kid, 7-5 and 5-7 being related to one another is plenty real, even though there is no connection yet to physical objects or money or any of that.
— Cathy Bruce (@drcathybruce) March 11, 2014
@ddmeyer a missing aspect in the "Real-world math debate? "Nothing ever becomes real 'til it is experienced." – John Keats
— Micah Hoyt (@MicahHoyt) March 11, 2014
2014 Mar 26. Fawn Nguyen asked her eighth grade geometry students which version they preferred.