Today, I’ll continue with reblogging Scott Kim’s in-depth post about transforming mathematics education. You might want to read last week’s post to get caught up.
I will say that the discussion generated quite a bit of interest. Participants have been actively responding to each other in a very lively email thread. The comments and discussions are still ongoing — I am having a hard time keeping up with them! But in a later post, I’ll summarize some key ideas and observations made by members of the group.
But for now, I’d like to turn it over to Scott Kim. Again, if you’re anxious to read the entire post, please feel free to go to his blog. Or just be patient…. But you can see by looking at the heading that Scott is addressing a very important issue next. I can still recall — when teaching gifted high school mathematics and science students — really understanding where the question “When am I going to ever use this?” comes from.
The answer is pretty simple. Bright students want to know. When I first started teaching at university, I thought it was the students’ job to find motivation for doing mathematics — after all, they were paying a lot of money for their education.
But I eventually realized that there are only about three months between the end of high school and the beginning of college. Nothing magical happens to students to transform them into self-motivated human beings, hungering for knowledge for its own sake.
Actually, one of my goals is never to hear the question “When am I ever going to use this?” again. If I do a good job teaching and motivation concepts, students will already be able to answer that question, and won’t need to ask it any more.
Yes, it’s a more challenging way to teach. But I can tell you, for me, it has been worth it.
Now I’ll let Scott take over. Enjoy! We’ll look at the third level next week.
Level 2. Lack of MEANING (leaks)
The most common complaint in math class is “when are we ever going to use this?” And no wonder; the closest most kids get to using math meaningfully is word problems, which are typically dull mechanical problems, dressed up in dull mechanical narratives.
Traditional mathematics education focuses on teaching rote computational procedures — adding, dividing, solving quadratic equations, graphing formulas, and so on — without tying procedures to meaningful situations. Unfortunately most adults, including many teachers and administrators, think this is how it must be. But teaching only the rote procedures of math is like teaching only the grammar and spelling of English, without explaining what words mean, or letting kids read books. Mechanics without meaning is not just deathly boring, it is much harder to learn.
Here are three ways to plug the leaks of meaningless math.
2a. Use math. In our increasingly digital society, kids spend less and less time playing with actual physical stuff. All the more reason to get students out of their desks and into the world, where they can encounter math in its natural habitat, preferably integrated with other subject areas. My friend Warren Robinett told me “a middle-school teacher I knew would, after teaching the Pythagorean Theorem, take the kids out to the gym, and measure the length and width of the basketball court with a tape measure. Then they would go back to the classroom and predict the length of the diagonal. Then they would go back to the gym, and measure the actual diagonal length. She said some of the kids would look at her, open-mouthed, like she was a sorceress.”
Solution: use problems that kids care about, and excite student interest.
2b. Read about math. Before we learn to speak, we listen to people speak. Before we learn to write, we read books. Before we play sports, we see athletes play sports. The same should apply to math. Before we do math ourselves, we should watch and read about other people doing math, so we can put math in a personal emotional context, and know what the experience of doing math is like. But wouldn’t reading about people doing math be deadly boring? Not if you are a good story teller. After all, mathematics has a mythic power that weaves itself into ancient tales like Theseus and the Minotaur. My favorite recent math movie is a retelling of the classic math fable Flatland, which appeals as much to my 7-year-old daughter as to my adult friends. Here’s a list of good children’s books that involve math.
Solution: read good stories about math in use.
2c. Ask your own questions. In math class (and much of school) we answer questions that someone else made up. In real life questions aren’t handed to us. We often need to spend much time identifying the right question. One way to have students ask their own questions is to have them make up their own test questions for each other. Students invariably invent much harder questions than the teacher would dare pose, and are far more motivated to answer questions invented by classmates than questions written by anonymous textbook committees. Mathfair.com goes further to propose that kids build and present their own physical puzzles in a science-fair-like setting. Kids can apply whatever level of creativity they want. Some focus on art. Some on story. Others add new variations to the puzzles or invent their own.
Solution: Give kids freedom to ask their own mathematical questions, and pursue their natural curiosity.
If we plug the leaks of meaningless math, we will grow a generation of resourceful mathematicians who understand how to solve problems. But are we teaching the right mathematics? (To be continued….)
Creativity in Mathematics 
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