Halcyon Posted February 25, 2012 Share Posted February 25, 2012 (edited) Yes, another AoPS post :tongue_smilie: I think I need to more fully understand what is meant by "discovery" approach. I have the Pre-A book, and I have spent some time looking through it, but I am not 100% clear on a few things. Here's how one is to go through the book, as I understand it from reading the intro to the book: 1. Your child goes through the beginning-of-chapter questions, without having the "tools" necessarily to solve the problems in the most efficient way, or even how to solve them at all. Your student may (or may not) get frustrated as he struggles to solve some of the problems. Other problems may come easily to him. Either way, there is no assistance or help to be offered by the teacher. 2. The child then reads the chapter to see if his approach "matches" the approach taken by the teacher, or if it's different. If different, is the book's way more efficient? Why? If the child couldn't answer the question(s) at all, then reading the chapter serves to teach the child the best approach. 3. He or she then applies the approaches explained in the chapter to the Exercises, Review Problems and Challenge Problems. The Review Problems should be fairly easy for the student, as they are simply a review of the concept. The student should re-read the chapter if he cannot do these. 4. The student then attempts the challenge problems. Some of these, as the author mentions, are "very, very hard". If your child cannot solve these, he should continue to work on them until he can. He can use the hints in the back of the book only after working on the problem without success for a reasonable amount of time. 4. If your student cannot solve the problem, even with the hints, eventually he should be allowed to look at the Solutions book. Then he should return to the question in a couple of weeks to solve it without looking at the Solutions book, to confirm he retains and understands the approach. I think one of my concerns was that the challenging problems look.....challenging :tongue_smilie: But reading this intro, Richard seems to imply that some of the problems are very hard to solve, even for a child who is right for AoPS. I am used to my child being able to, eventually and without help, solve all the problems in a math book. I think I'd have to approach AoPS in a different way. Also, (and here's my main question): _NOT_ understanding, being able to "sit" with that "not-understanding", and being okay with it...this seems to be a huge part of AoPS. Most math books assume that the explanation (which comes first) will be VERY CLEAR, allowing your child to then DO THE PROBLEMS correctly. AoPS, otoh, almost welcomes the confusion as a way to force the child to find his own way through the fog. And the child has to be comfortable in the fog, at least for a little ways. And bit by bit, the fog is lifted as more problems are worked, and solutions are presented. With standard math problems, there is, ideally, no fog before questions are attempted. The concepts are explained AS CLEARLY AS POSSIBLE before problems are attempted by the student. And it's the teacher's (or book's) role to explain things very carefully to the student, so that ideally the problems can be done without too much struggle. AoPS seems to turn this on its head. The student needs to be comfortable with "not-knowing" and feeling his way around in the dark (or at least, low light :tongue_smilie:) and as more and more problems are worked on, the light begins to turn on. So when evaluating whether AoPS is right for one's child, simply looking at the text isn't enough, right? One needs to determine if one's child is comfortable with figuring things out for him/herself, but more importantly, are both you AND your student confident enough to sit in a place of befuddlement some of the time? Or will that make you or your child feel "we're clearly just not getting this!" I hope this makes sense. Edited February 25, 2012 by Halcyon Quote Link to comment Share on other sites More sharing options...
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