WCYDWT: Fare HIke

Reading the NY Times today I saw a blog post regarding the MTA's vote to raise the price for 30-day and weekly metro passes as well as individual fares. What caught my eye was that the article described one increase (for the 30-day passes) in terms of percent increase. That was all I needed.

Following the Meyer method, I got an image of the article and blacked out the percent increase answer for the students. I asked them to predict what the percent increase could be. We investigated the problem. I demonstrated how to find percent increase, which only a few of the students seemed to have learned before. Then, we checked our answer against a clean copy of the article that I printed later.

Overall, there was some learning and some excitement, but I can't help thinking that I could have done this better. What could I have done differently?

Before:

After:

Notes for next time:

• Next time black out the answer in Keynote, then print. My students spent a ridiculous amount of time trying to read through the dark splotch that I made with my pen before making copies.
• We tied in our steps for problem solving (Understand, Plan, Answer, Check) a bit too late. It would have really helped to direct their frustrations if we were introducing the structure earlier.
• The guessing/estimating gets a little distracting because the students attempt to revise their guess at each stage in our problem-solving process. It needs to be stated more clearly that while we can keep revising the end is to have a solution, not a guess.

No Wonder They Don't Like Math

I started reading Polya's "How to Solve It" this morning and found some tasty gems immediately:

• "Thus, a teach of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking."

• "... overhearing Polya's comments to his non-existent teacher can bring that desirable person into being, as an imaginary but very helpful figure leaning over one's shoulder."

• "Mathematics, you see, is not a spectator sport. To understand mathematics means to be able to do mathematics."

• "... to teach mathematics well, one must also know how to misunderstand it at least to the extent one's students do!"

• "Experienced mathematicians know that often the hardest part of researching a problem is under standing precisely what that problem says. [...] 'If you can't solve a problem, then there is an easier problem you can't solve: find it.'"