Discovery Geometry

Back in college, I tutored math for three years. I quickly came to hate the discovery calculus that a few of the honors calculus classes were experimenting with. The students--good ones, these were honors students--often had no idea what to do and were needlessly frustrated. If "discovering" calculus on one's own were so easy, it wouldn't have taken until Newton and/or Leibniz in the 17th century for humanity to have come up with it.

This past week I've been helping a teenage boy who's being befuddled and deeply discouraged by his discovery geometry textbook. It makes the students figure out the "conjectures" and then requires them to apply the just-introduced conjectures in all kinds of novel, thought-provoking ways. Such a method sounds like a math prodigy's dreams come true. But I think it's terrible for average or below-average math students.

This boy has attention issues and Asperger's traits, so class lectures--where the conjectures get explored, explained, and supposedly compiled by the students into their own little reference notebooks--are less effective for him. This is a kid who, if he doesn't immediately know the answer to something, looks off in space, starts scratching at the side of his calculator, or enters numbers into the calculator without having a clue as to what mathematical operations should be done. His mom has worked hard with him; one year she pulled him out of school for two periods and "home-schooled" him in math. Under her tutelage, he did two years worth of math in just one. He seems bright enough and his attention issues disappear when he knows how to attack a problem. Discovery geometry is just wrong for him.

The mom corresponded with her son's teacher about the problems he is experiencing due to the book constantly hiding necessary information (formulas and such, the kind of things I grew up seeing inside the covers of my math books as ready references). The teacher responded by saying that some kids thrive and some kids struggle, but the book is in the syllabus and it's what he is going to teach. Great for the kids that thrive! And terrible for the kids that don't! Math is not a one-size-fits-all-endeavor, and when it becomes clear that a kid needs a different approach, that approach should be adopted.

When tutoring him, I've taken to letting him use a very basic geometry reference sheet like the one below:

http://stufiles.sanjac.edu/thea/theamathreviewforwebsite/geometry.gif

It's done wonders for his confidence. He can actually get through some problems on his own now. And he's not doing mere "plug-and-chug" work. He finally has an inkling of what he is expected to do and can go at it. Anyway, I'd rather see him doing "plug-and-chug" exercises correctly than cluelessly entering numbers in his calculator in flailing attempts to solve problems he doesn't comprehend.

I don't know yet what math text our family will use for geometry. Dd10, the oldest, only just started BJU's Math 5. BJU has a great incremental "mastery + review" elementary math program that has been pleasant for our family to use. But because of my math background, I'd like for my children to have more extensive experience with constructing proofs, and those are rather out of vogue in K-12 math. One thing is for sure: no matter what we end up doing for geometry for my Aspergery eldest, it won't be "discovery geometry."