This is actually about my own little experience, on a local level, with the confusion that comes from trying to explain the approach that I take. The mother of a student of mine called (first the school counselor and then my co-chair before finally calling me) to complain about my course. Her concerns were that her daughter learned math best by having the teacher explain each concept thoroughly (which means what exactly?) and then having the students practice the problems they learned. And why the hell wasn’t I doing that?
So I spent about a half hour with her on the phone telling her that we did do that sometimes in Geometry, but that it is really important for students to learn how to attack problems they have not seen before – and that they will not get good at it without having to do that. So I also ask the students to read on their own and try problems before we go over them. I do not do it all one way or the other. I also put a lot of emphasis on student questions – and primarily not the “How do you do number three?” variety. We have discussions about the material, we try different things – sometimes they work, sometimes they do not.
Another issue is the book that we are using. It is Geometry: A High School Course by Serge Lang & Gene Murrow. It is a great book for paring down the geometry curriculum to something that is manageable. Our school had been using a book that presented a theorem or postulate nearly every page – sometimes more than one! – and just plowed through topics. I love geometry, and I found many of the topics in that book fascinating, but the reality is that there was too much information for a typical geometry student to understand, much less master. And the truth? Most people probably forget 80% or more of the geometry they learned in high school unless they have a really good reason to know it – like they become a high school geometry teacher!
I went to a conference last winter on brain research and how it relates to learning. I do not pretend to be an expert by any means, but what I heard supports what I am trying to do. Students need to learn decision making – that part of their brain is beginning to really develop in high school – and they can only do that by making decisions. Learning concepts in any class divorced from a context the student understands nearly guarantees that the best they will be able to do is retain it long enough to regurgitate it on a test. Or that a student’s mindset can have more to do with how well they perform than their “natural ability.”
Now I do recognize that not all students learn the same way, but at what point to we sacrifice our desire to help them become independent learners who can solve novel problems so that they feel more comfortable? That is what I struggle with. At no point do I think that basic skills are unnecessary or unimportant, but without a context or ability to use them when it matters they are useless.
I do not want my students to leave my class unable to use what they learned.
In the end I think that the mother and I agreed to disagree, although I did ask her point-blank if I had addressed at least some of her concerns, and she said yes. I will be meeting with her daughter regularly to help her adjust to what is being asked of her, and give her as much of the support she needs as I can within the context of what she is being asked to do. Time will tell.
