Our current textbook is the Prentice Hall Mathematics Course 3 Common Core, 2013 Edition. There is a lot of good material in the book. Dad likes that it includes different ways of thinking and good problems. He is not happy with its sometimes vague or incomplete explanations. Nor does he (or Mom) like the way it is organized as a sequence of vocabulary lessons.
We use the textbook as a general guideline, for problems, and for tests. We dig deeper on some topics and fly off on a few tangents. One goal is to ensure that mathdaughter has a solid handle on the material at each stage. If there is weakness, we keep probing until we can identify exactly what it is. Dad was inspired by this terrific article about mathematical “ceilings.” The author warned
A student who can answer questions without understanding them is a student with an expiration date.
In other words, a student’s math gaps might not seem like much of a problem if they can work around them. But if today’s gaps persist they will eventually limit the student’s progress in math.
Another goal is to support mathdaughter‘s love of the subject by finding time for all of her questions and ideas. This feels like a luxury we are lucky to have. Dad tries to fuel her thinking with his own math ideas as well as external resources. Other resources have included:
Mike’s Math Page – The way this former math professor teaches his sons is an excellent model. He guides them gently and patiently through standard work while letting their ideas take them to unexpected discoveries.
These are some of our favorite YouTube channels for math:
Vi Hart – always fast-paced, funny, and thought-provoking.
Apps and Programs
DragonBox – fun algebra and geometry games.
Tesselations – a nice tessellation maker.
Beautiful Geometry by Eli Maor. We learned about Thales and his discoveries about angles in circles.