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Today's mathematics quote is from Lipa Bers who died on this day in 1993. Bers said,"... mathematics is very much like poetry ... what makes a good poem -- a great poem -- is that there is a large amount of thought expressed in very few words. In this sense formulas like
or 
are poems."I often talk about Rosie in my classes. We walk daily and we talk about life and mathematics. To be truthful, I talk, she listens. She wags her tail in agreement, pushes her head against my leg hoping for another treat, and keeps a wary eye out for the ever elusive squirrel. She is a good listener. She really likes my students. She will plead their case with those big, brown, empathic eyes and ignore me when she disagrees when I make a disparaging remark. She has convinced me of extending deadlines and sniffed out creative ideas for me to use in my teaching. She is quite the dog!
I have really come to detest school district meetings. Actually, most meetings. My assigned hell will be sitting in a meeting for eternity, filling out forms. This distaste is a recent phenomenon. For thirty years, I was tolerant of the meetings, looking for information that would enhance my teaching. I guess I am a slow learner. I have started to keep a small notebook to do math problems and to write down any math ideas that I would like to further investigate. During our most recent district meeting, I drew this graph of a walk with Rosie. I showed it to her that day during our afternoon walk. She licked it so I drew it again. "Ah", I thought, "She liked it so well, she licked it!" She wants me to show this to my class! With Rosie's inspiration, I assigned my students to find what mathematics, specifically calculus, existed within the graph.
The graph depicts my position from my home on a walk with Rosie. The vertical axis indicates the distance in feet that I am from my home. The horizontal axis is the time in minutes of the walk.
Here are the top ten of their responses:
1) "The derivative at (20, 50) is 0 because it* is a horizontal."
2) "From the time of 0 to 15 min you were walking at a rate of 3 1/3 ft/min."
3) "The interval [30, 45] has a slope of 20/3 ft/min."
4) "Kruger realized he was late so started slow then sped up until he got back to his house 15 min later."
5) "At the interval 15 - 30 minutes, Kruger and Rosie stopped walking, the graph shows this by staying at a horizontal line."
6) "At 45 mins Rosie and you ran/dragged home for some unknown reason. Obviously something changed, maybe Rosie saw Sam (her god) coming home and she started chasing him. In the last 15 mins of your walk your average rate was 10 ft/min. In the last 15 mins you double the average rate of your whole travel."
7) "Mr. Kruger needed some deep, philosophical questions answered from his loyal and trusty sidekick, Rose, so they decided to go for a walk, discussing life. Starting off, they walked increasingly faster and ended up walking 50 ft in 15 minutes. Mr. Kruger and Rosie were having a jolly good time, but then Rosie met a friend of her's, a Border Collie, so they stopped to chart for 15 minutes while Mr. Kruger sat down on a nearby bench and worked on math problems. Mr. Kruger had almost finished his 743rd problem when Rosie looked up and saw a radioactive ninja mutant squirrel terrorizing the local children! Rose got up and pulled Mr. Kruger along at a hearty sprint, speeding up. They ran 100 feet in 15 minutes."
8) "The slopes of the tangent lines of the parabola are positive, then zero at (45, 15), the negative"
9) "From (30, 50) to (45, 150), the slope rises quickly at an average rate of 20/3 ft/min. At the peak/maximum of the parabola (45, 150), the slope changes to an negative, downward, average rate of 10 ft/min.
10) "The biggest and most obvious fact shown on f(x) is that Kruger and Rosie walk extremely slow and don't get very far at all while taking breaks on their 300 foot walk. (0, 0)...(60, 300). Based on that, their average rate is 5 ft/min. At that pace, I wouldn't recommend a marathon. It would take you over 19 days!"
Another great idea Rosie! Thanks! Arf :-)
* I think it that is being referred to is a tangent line at that point.
