Last year, I stumbled across a video on Twitter in which Mike Lawler, a former math professor and homeschool parent, explains probability to his two sons by talking about the likelihood of choosing a perfect bracket in the NCAA Tournament. He first discusses the probability of choosing the winner in a single game and then in each of the three games in a four-team tournament -- when the probability of guessing correctly is 50% for each game. He next discusses picking the winners in tournaments with sixteen teams and sixty-four teams --- when the probability of guessing correctly is still 50% for each game. He then discusses how the probability of choosing a perfect bracket changes exponentially as the probability of guessing correctly in individual games changes. Finally, he discusses real examples from the 2014 NCAA Tournament in which individuals with perfect brackets after several games chose upsets differently than the population at large.
I not only appreciate his willingness to share his work and reflections on the process with others, but also how he uses his content knowledge to identify examples in the real world and adapt his teaching style to the ideas and needs of his students. While I would not suggest playing one of his videos for your own students, I do recommend using his work as a resource to strengthen your own content knowledge in math. Personally, I think I will improve more as a math teacher by seeking professional development in mathematical thinking, rather than teaching strategies commonly used during math lessons. I have organized several of his video series into playlists on my YouTube channel. You might also be interested in seeing how he explains place value and two-digit addition to his younger son.
Blogging my work as a teacher, educational consultant, speaker, and host of New Books in Education.