Five Things I Learned at PCMI: Thursday 7/2/15

1. Jo Boaler at Stanford University a website called youcubed.com that provides resources and online courses for teachers, parents, and students with a focus on growth mindset in the mathematics classroom. The site focuses on practices that promote depth over speed, equitable group work, and math efficacy. There is also a free set of videos and lessons for the first week of school that are designed to promote growth mindset, introduce the 8 mathematical practices, and set the tone for the year. Take a look here: http://youcubed.org/

2. There are multiple ways to complete congruence proofs with transformations. You could use transformations of the entire plane to map one figure onto another, starting with one point. Next, assume that the other points do not line up, and use properties of your figure and of transformations to explain why they do. Of course, this proof can take many forms, but there is another method too. You can express the properties of a figure by using circles to preserve distance and rays to preserve angles to create a locus of points where the vertices of the figure could exist. If there is only one set of vertices, then the figures are congruent.

3. Although there is some debate, the term "constant of proportionally" should generally be reserved for relationships between a domain and a range, and has the form y = k x. On the other hand, "scale factor" refers to a relationship between two geometric figures. It should normally be presented as one number, not a ratio. However, it can be useful to use ratios to compare lengths within one geometric figure. For example, we could say that two triangles with sides 4:6:8 and 6:9:12 have a 3/2 or 1.5 scale factor. You can thank Bill McCullen for that.

4. I can construct the incircle of a triangle using Euclid: The Game, level 15. And yes, I already knew the properties of an incircle and incenters, but the construction takes an extra trick.

5. The mountains in Utah are amazing. We took a 6 mile hike that turned into an 8 mile hike to Middle Mountain in Wasatch Mountain State Park. The trail was heavily washed out and it was a bit steeper than anticipated, but the view from the top and the experience was worth it.