The upper-school curriculum topic of quadratics—their algebra and their graphs—provides a profound opportunity to explore innovative problem-solving, to experience deep joy in truly understanding mathematics, and to practice the powerful art of thinking like a mathematician. This overview of the topic shows how to teach and experience just that.
Audience: These videos and notes are for educators looking for the true story of quadratics and their place in the 21st-century thinking classroom. Students who have had a first exposure to the topic will find these videos and notes of immense value too.
Professor James Tanton was a research mathematician who got his PhD from Princeton University and spent 10 years as a university professor before deciding to make an impact by focusing on pre-collegiate math education. He is currently the Mathematician-at-Large of the Math Association of America and has written several award-winning textbooks on middle and high school mathematics.
How to use these lessons: Each of the six lessons here is based on a 35-45 minute video made by James, in his home, as he shares his thoughts and experiences on thinking about and teaching quadratics. Each video is then divided into small, manageable segments, to make the lesson accessible and easier to digest.
Each segment comes with a detailed, downloadable essay explaining the content of that segment and sharing the practice examples (and a few additional examples) he presents in the video segment. In addition, Edfinity has student problem-sets to match each segment.
Educators: As an educator, watch each video and skim each essay. You will likely be surprised by the story that unfolds, seeing mathematics you thought you knew in a brand, new light. You will see how to adapt ideas to your natural teaching practice.
Share each video segment and matching essay during a class (or “flip” your classroom and have your students watch each video at home and try the problem sets) and discuss the ideas and practice problems with your students.
Students: Watch the videos (they might be fast for you, but that is okay!) Download the essays. Read them. Reread them. Watch the videos again. Try the Edfinity problem sets. And ask questions! Lots of questions! Ask your teacher. Ask your colleagues. Ask math professionals of all kinds. It is okay not to know, to struggle, and to take time in figuring things out. Be gentle on yourself and strive for deep understanding over quick memorization. This is an opportunity to learn how to think like a mathematician! Enjoy!