# Mentoring interns is part of Proof School's commitment to serving the broader community.

For the last four weeks, I’ve had the pleasure of interning at Proof School. I just completed my third year at Quest University in British Columbia, where I study mathematics. Part of the curriculum at Quest is to do a work experience related to our studies, and because of my interests in math and math education, I was eager to intern at Proof School.

I spent my four weeks helping teach the Introduction to Number Theory class, assisting in Maker Studio, and helping plan the math festival. I prepared lesson plans and taught portions of the Number Theory course, usually when introducing a new topic.

I immensely enjoyed the time I had to work one-on-one with students. With more than one adult in the classroom, Dr. V and I could both work with smaller groups of students. This was particularly useful when students were at different levels of confidence with a topic. In the first week, I taught a lesson on number bases, and a few days later I worked with the students who wanted more review before the quiz while Dr. V worked with the rest on supplemental exploratory material. This was a nice way to avoid having students fall behind while also keeping others engaged.

One of the most interesting things for me to see was that writing is an integral part of the math classes at Proof School. I’m used to this at my liberal arts university, but I didn’t know it could be done at the middle school level. Dr. V does a fabulous job of setting students up for success. For example, he’ll start the class off with a sentence or two, then help everyone strategize about where to go from there. Proof writing isn’t easy, and it’s wonderful to see it successfully incorporated into a middle school curriculum.

I particularly enjoyed jumping in and teaching topics that were relatively new to me; one of the best ways for me to learn things is to teach them. One of my favorite topics to teach was continued fractions, which are nested fractions where each numerator is 1. The general form looks like this:

A few weeks ago, the students had a quiz on continued fractions, and the bonus problem was to determine the value of the following continued fraction:

While students were taking the quiz, I excitedly worked on this problem on my own. I find these types of algebra problems quite fun! A few days later, we had an extra 10 minutes to fill, so I showed the students how to do the problem. (Spoiler: it’s  2 ). I then gave them a similar problem using the continued fraction for  5 . The strategy is to call the whole thing x, and notice that x is also nested within itself! This was a conceptual leap that was understandably difficult for some. Periodic infinite continued fractions are funny like that; the whole thing is contained within itself. This way of thinking allowed us to turn it into a quadratic equation and solve it. I thought it was a really cool problem solving strategy, and I was happy to help the students master it.

I love learning math, and I love sharing what I’ve learned with others. It’s been a blast learning alongside these kids and helping them learn.

--Rose Johnson-Leiva