## Thursday, July 9, 2015

### Five Things I Learned at PCMI: Wednesday 7/8/15

1. There is a deep connection between transformation T(a+bi)=(a+bi)^2 and all sorts of algebraic geometry such as transformations, polar coordinates, Pythagorean triples, and hyperbolas.

2. There is an online companion to the text Principles to Actions (2014), called The Principles to Actions Professional Learning Toolkit. It consists of a modules containing videos, tasks, and student work designed to demonstrate the effective teaching practices. Fred Dillon, a math teacher and Teacher2Teacher Associate for the Math Forum, introduced it this morning during the "5 minute shorts". Take a look: http://www.nctm.org/Conferences-and-Professional-Development/Principles-to-Actions-Professional-Learning-Toolkit/

3. The "convince yourself, convince a friend, convince a skeptic" technique from Jo Boaler and Cathy Humphreys' book Connecting Mathematical Ideas (2005) is an excellent way to get students thinking about the reasonableness of an answer and practice delivering and analyzing arguments.

4. When asking a hinge question (aka quick check), it is important that the task be quick for students to complete (under 2 mins), easily gradable by the teacher (30 seconds), and crafted in such a way that students can't arrive at the correct answer accidentally. While multiple choice questions are a poor choice, "select all that apply" can be very useful.

5. The best people to be around are those who take their losses in stride. Today, we went tubing down the Provo River and what was advertised as a "lazy river" was full of rapids. We lost one pair of shoes, three water bottles (found one), two beers (found both), and one tube (found 15 minutes later). And yet, it was one of the most exciting activities that I have done all week - all thanks to the people I was with.

6. (Extra Credit) The best place to picnic is across from a grocery store. When faced with no dinner plans and no kitchen to cook in, we had to come up with an idea quickly. Fortunately, there is a small park complete with charcoal grills across the parking lot from the local grocery store.