Five Things I Learned at PCMI: Monday 7/6/15

1. There are many ways to explain why the slopes of perpendicular lines are opposite reciprocals. One way is to recognize that perpendicular lines are just a 90 degree rotation away from each other. Since the algebraic function for a 90 degree rotation is R(x,y) = (-y,x), the slopes of the two perpendicular lines will be y/x and -x/y. Of course this is only a rotation about the origin, but a rotation around another point would just add a constant to our function, and would only effect the y-intercepts of our lines.

2. The Dekker & Querelle method (2002) can help students analyze worthwhile tasks. After students have completed a short task, they should analyze a number of sample solutions (more than just a few). Then, either ask them to pick one incorrect and one correct to discuss in depth, or use some sort of critiquing rubric (I have a 4 point one). This technique works well after working on open middle problems. Speaking of open middle: http://www.openmiddle.com/

3. It is difficult to caramelize a large amount of onions in a high-walled stock pot. If there is too much moisture and not enough surface area, then the onions just end up steaming themselves.

4. There is a high level of variance in standards based grading across schools. Some schools have standards set for teachers by administrators, others ask teachers to come up with their own. There is also a debate as to how many standards you should have, if they should follow through the entire year or just one unit, and if practice standards should also be included. The most interesting one was a hybrid SBG system where 50% of the final grade is given to content standards, 30% is given to practice standards, and 20% is given to scholarship standards (homework, participation, etc). I also learned about Easy Grade Pro, a program for standards based grading. It’s pretty neat, although I’m not sure how it would fit into our existing grading structure. Take a look here.

5. I can now create an origami augmented dodecahedron.

6. (Extra Credit) I learned some math chants:

Rah rah sis-boom-bah!

2, 4, 6, 8, Even numbers are really great!

1, 2, 4, 8, We can exponentiate!

Ski slope: lots of fun! Math slope: rise over run!

Our love for America is IRRATIONAL!

Count off PCMI! 1! 1! 2! 3! 5! 8! 13!

M-A-T-H M-A-T-H! MATH!

Pictures below are from the 4th of July weekend: the Park City parade, lunch at The Bridge, dinner at the Wasatch Brew Pub.