My Common Core Problem Based Curriculum Maps) has crafted a game plan for proceeding with reinventing how math can be taught in schools. He has collected activities and projects from his math blogging colleagues and organized them into a curriculum. When I was still at Stevens/CIESE I did a similar approach with the 6th Everyday Math curriculum since the teachers in the Elizabeth, NJ school district wanted more technology based activities that were not part of EDM. This kind of work requires support from the teachers, pedagogical change coaches (like I was there) and administration support to work. Unfortunately, my effort in Elizabeth has sat dormant since I retired from CIESE in 2007.
What we need is a curriculum (a modern textbook, if you like) that is written from a student's perspective. Most textbooks are written so that adults reviewing the books will find all the required checkboxes checked before they adopt. Why can't textbooks be written as engaging stories that students would buy into? I suspect very few kids would choose the books that are currently coming out of the textbook mills if they had a choice. Engaging stories should drive curriculum. Then students would actually want to do the activities in the book instead of being force fed by the teachers because they are "good for you."
Geoff Krall to his credit has listed links to interesting stories, but they are still on the sidelines in the curriculum game. Some day it will happen. The current technology makes it possible and the math blogging community is putting examples out there every day. However, the devotion to the Royal Road to Calculus continues to interfere with student engagement and genuine learning.
Thursday, November 14, 2013
1. Choose a number. Call it X
2. Add 11. Now you have X + 11
3. Multiply by 6. Result is: 6X + 66
4. Subtract 3. The result is: 6X - 63
5. Divide by 3. The result is: 2X + 21
6. Add 5. The result is: 2X + 26
7. Divide by 2. The result is: X + 13
8. Subtract the original number that you chose. The result is: X + 13 - X = 13
You are jinxed. Problem solved. Case closed. But what if we were teaching typical 6th graders then a more interesting twist on this story is to not assume the obvious (that it always works) and see whether these students could find a number that foils the Jinx Puzzle. Since testing numbers manually becomes quickly tedious a spreadsheet calculator can help with testing a wide range of numbers. There’s just one problem. If you use a spreadsheet you can get a result that actually foils the Jinx Puzzle! Try something like 3.0 x 10 to the 16th power as your number.
This is caused by the fact that the spreadsheet will round off numbers after a long string of numbers is entered or will send a bogus number because we have gone passed its capability to stay accurate.
Dan Meyer in a his 101 questions activity shows how Google Calc fails to handle a subtraction problem by printing 0 instead of the correct answer of 1 just because it doesn’t play well with very large numbers.
In an episode of The Simpson's called The Wizard of Evergreen Terrace, Homer appears to write a valid solution to defeat Fermat's Last Theorem which states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than two. But given that Fermat's last theorem is proven, is Homer's attempt a real counter example that Fermat and others didn't see? Look at the equation (above) that Homer used using the Desmos calculator to check his work. Looks like the real deal doesn't it?
The Simpsons and their Mathematical Secrets" calls Homer’s attempt at a solution a near miss. If you use a calculator that’s good to 10 places like Desmos, it seems to work. But the devil is in longer approximations. It’s close, but no cigar. And we need exactitude to proof the theorem. Andrew Wiles who proved Fermat’s Theorem in 1995 has nothing to worry about from Homer Simpson.