Teaching Circles

Inspired by this post, I wanted to share a little bit about how I introduce circles. When I pose the questions that follow, I usually use PollEverywhere to survey the entire class at the same time. I find this encourages table discussion. Keep in mind, when I show the students these equations, students HAVE seen the Pythagorean theorem, but other than that, this is the first time they have seen anything resembling the equation for a circle. The answer is not at all immediately clear and many students take a "guess and check" approach to finding the solution

Teaching Constructions

When I started my teaching career, I taught the constructions that were required on the state exams by providing my students with an overview of the conventional steps.  I soon learned my approach was completely ineffective. No matter how I varied my instructions, many students perceived constructions as little more than "pictures" that needed to be memorized.

In my fourth year of teaching, I completely abandoned my traditional method. On the first day of the constructions unit, I have students take out their compasses and given them one goal and a few rules:

Work Smarter, Not Harder, Ex. 2

For this activity, students must first be familiar with exam free response scoring rubrics. (I teach AP Computer Science A, which has plenty of resources available online for free response rubrics and scored samples.) When students have seen the rubrics enough to know how to earn partial credit on questions that would otherwise seem to difficult to approach, I turn it up the rigor: students work in groups to write their own rubrics and canonical solutions. The extra tasks turns familiarity into mastery.

Almost Perfect

The decision to allow students to retake exams and every conversation surrounding it should be based on the best path for learning. Always remember that.

Lately, I was grappling with the question: "Is a full exam retake necessary and effective for each student whose score is almost perfect?" The question came up because, invariably, every class has those  students who earn a 94% but still want to retake the exam and shoot for 100%. I will always allow this, but recently I was wondering if a retake is the best way to earn that extra 6%. I asked myself, "What would help this person increase his or her understanding from nearly perfect to perfect?" For such a student, I think retaking the exam is too mechanical, an trivial item on a checklist to achieve perfection. By contrast, I've heard it said you've never truly mastered something until you can teach it.

Sort-O-Mania

When I was new to teaching, a mentor challenged me to consider an strategy about the career that lay before me. He said that once a year, I should select the most boring or challenging unit of my curriculum and carefully craft it into something more interesting and engaging. He said even if I had to spend all of my creative efforts on revitalizing that one unit, if I could manage to do that once a year, with some time I would have a some pretty exciting curricula!

Whether or not you teach computer science, you can take my word: teaching sorting algorithms is not very exciting.

Testing Retesting

When I started teaching AP Computer Science A in 2015, it was easy to approach a subject that was new to me in a way unlike how I had been teaching mathematics. Initially, I allowed students to retake their exams simply because I knew I lacked the experience to write fair exams on my own first try. I kept the policy because it seemed almost natural, the course itself seemed conducive to a policy that allowed students to resubmit code until it worked. At that time, I could not see how the same policy could carry over to my math classroom and a discipline that is notorious as a harsh exam environment. Finally, in 2017, having grown frustrated with feeling that I was perpetuating a culture that rewarded exam performance over learning, (mind the distinction: it’s one thing to take an exam for the sake of one’s learning, I take issue when students perceive they are learning for the sake of their exams) I decided I could try what I was doing in C.S.

What High School Geometry Could Be

A project that is successful in that regard must embody at least three principles:

1. It must require student choice. More is better.
2. It must resemble a real life application.
3. It must be an end in itself. To superimpose exam questions on the project content is to dilute the meaning of the project itself and redirect the students' attention back to the very falsehood we meant to avoid in the first place: an exam is the ultimate end and indicator of success.

This year, I've come up with the "Geometric Dwelling" project.

Geometry Diagrams

Over the years I've made dozens upon dozens of geometry diagrams. Most were made for one-time-use. Eventually, I got the bright idea to simply post them online to optimize the utility of each one. All of these diagrams are free to use or revise without restriction.

Teacher Resource Index

After years of having my resources bookmarked, saved and otherwise scattered all over the place, I finally decided to draw them together into one location.