I had a second opportunity to see Steve Leinwand again with some more members of my department. I was reminded about the following:
Evaluate 16(.75)^x for when x = 8 in the exponential function
versus
You take 16mg of a controlled substance at 8am. Your body metabolizes the drug at a rate of 25% per hour. If you have to pass a drug test at 4pm with less than 1mg, will you pass the test?
Steve goes on to tell the story of how the Romain gymnast lost her gold medal because her coach didn't understand this problem. Well, I just so happened to be starting the chapter on logarithms in three days from this afternoon conference. Heck yeah, I'm so stealing this activity and having the kids get down and dirty with this function.
Three days go by and it's Friday... new unit day. I pose the problem, give the students 10 minutes to come up with an answer. Oh, and they had better be prepared to defend their answer and explain how they arrived at it. They didn't even blink. Bam, 15 minutes later I have kids telling to multiply by .75 not .25 each hour. Paraphrased from students: Well Mrs. Berg, it's because it's too much work to keep subtracting the 25%. You could, but this way was easier. (HECK YEAH! - trying to keep my excitement PG here) And no this person doesn't pass the drug test at 4pm. Almost, two more hours and they would have, but not at 4pm. Formula? Sure I wrote a formula for it. 16(.75)^x. (me in my mind - HOT DAMN - sorry for the French). Oh, I said at first they would pass the drug test because I just kept subtracting 4. But then I thought that was too easy, so I tried another way.
I could not plan for my students to astound me this way. They literally took over the conversation. And I hadn't even gotten to the good part of how this was a true story. They could google it when they got home, but a gymnast from the Syndey Olympics lost her gold medal because she took some over the counter cold medicine and the coach miscalculated the length of time on the banned substance. They were eating in the palm of my hand.
Then I said I had another real life story problem that involved exponential functions. Are they ready? They were ready as long as this one wasn't a sad story. I then told them about buying our first family vehicle. We were offered two choices $12,000 at 8% interest or $18,000 at 2% interest. Which should my husband and I take? I told them how we argued over it. He wanted the lower interest rate. I wanted the lower amount. I just so happened to have my graphing calculator in my purse (just like Batman would wear his utility belt). I worked the numbers. We took the higher interest rate. And then the bell rang.
I had assigned about 8 story problems. They all groaned when I said that. However, today, they came in without questions on those problems. I asked, any questions your groups couldn't answer? They said no. The homework was actually easy and they liked doing it! Ok, who are you and what have you done with my students?
Today we tackled graphing both exponential and log graphs. Easy peasy, lemon squeezy. Well, I hope. Those buggars made the connections they needed to on their own. I had very little to say today other than How do you know this? Please, convince the class. Do you agree with Suzy? Who can help John out?
Tomorrow we pursue the properties of logs. My goal: Shut my mouth and let my students take over the learning. After a small pop quiz. 1 story problem and 2 graphs... know or don't... show me.
Now, on to my other things I must attend to tonight. Felt good to brag and post again. Far too long I tell you.
Kelly,
ReplyDeleteThere is nothing more fulfilling than a math class full of motivated, excited students. You struck the heart of the matter with “These are not kids who love math and can't wait for the words to roll off my lips. But they love being in control of their learning.” Had you simply scratched out the equation 16(.75)^x, asked your students to solve it for eight and then drew out a few more abstract problems on the board, you would have had a class full of semi-attentive students waiting for the bell to ring. You introduced the concept with a practical application which fascinated your students. They were more in control of their learning, they were beginning to understand that mathematics helps them understand and take control of their lives.
I have a question for you. How did the quiet students do with this exercise? Was it a few of the overt students controlling the conversation, or were all of your students involved? Perhaps even more important, how did your math anxious students do with this exercise? Did they feel and catch the enthusiasm of their classmates? How was the peer to peer interaction? In cases like
This, where students are excited about the concept, those who grasp the concept quickly are right there with the students who don’t quite get it.
Thanks for the post. It is nice to read success stories like this in the math class.