I haven’t taken the time to write, and I’ve barely been keeping up with all the great posts being written these days. Very big thanks to Dan for summarizing the many sessions at NCTM and NCSM.
I’m enrolled in a class titled Problem Solving for the MS Math Teacher. The class is great. We get three problems for each HW assignment, and they really forced us to justify everything about our solutions. If you set up an equation or a formula it needs to be justified, if you perform a calculation the theory behind it should be clearly explained. The emphasis on reasoning has been a great push, and it’s really valuable to see how so many others reason through the same problems. Here’s a sample of the problems we’ve been assigned
- Saved by Zero. How many zeroes occur at the end of the expanded numeral 999!?
- The Last Straw. Two piles of straws are on a table. A player can remove a straw from either pile, or a straw from both piles. The player who takes the last straw loses. If there are two players how should you play?
- The Case of the Grouchy Customers. Every morning at local cafes sleepy customers stumble in for their morning cup of coffee. One such cafe has a row of 10 seats at the counter. Typically, morning customers do not like to engage in conversation. How many different ways can three customers sit in those 10 seats so that no two customers are sitting adjacent to one another?
- Put Down the Ducky. A man selling ducks sold half his flock and half a duck to Amy. He then sold one third of what was left and 1/3 of a duck to Beth; then 1/4 of the remaining flock and 3/4 of a duck to Cathy, and finally he sold 1/5 of the remaining flock and 1/5 of a duck to Dina. He now has 19 ducks and he never cut a single duck (whew!) What was the size of the man’s original flock?
It’s been a fun challenge to figure out how best to explain myself as I approach these, and some of them have been good problems to have on hand for students.
I’m also taking Intro to Computer Science and Programming for no credit through the MIT OpenCourseWare offerings. As a model for online learning I love that MIT is doing this. I have already found myself applying python to multiple problems beyond this class in a more sophisticated manner than prior to beginning the lectures / readings / problem sets. It’d be great to be able to get credit for this, but you can’t beat the cost.
The entire offering is fantastic and well curated. A lecture I recently watched was entirely re-taped because technical glitches ruined the video of the original class session. The professor entirely re-did his near hour long lecture for the sake of OpenCourseWare. It is lecture based, so not for younger folk, but if you have the patience to really work through the materials provided you really could educate yourself with little more than internet access and time. Take a look at the offerings if you are interested!