Return-Path: <nifl-fobasics@literacy.nifl.gov> Received: from literacy (localhost [127.0.0.1]) by literacy.nifl.gov (8.10.2/8.10.2) with SMTP id iAGJcH016805; Tue, 16 Nov 2004 14:38:18 -0500 (EST) Date: Tue, 16 Nov 2004 14:38:18 -0500 (EST) Message-Id: <006601c4cc13$bac787a0$0200a8c0@wbrmfd01.mi.comcast.net> Errors-To: listowner@literacy.nifl.gov Reply-To: nifl-fobasics@literacy.nifl.gov Originator: nifl-fobasics@literacy.nifl.gov Sender: nifl-fobasics@literacy.nifl.gov Precedence: bulk From: "Lynne" <LynneT@comcast.net> To: Multiple recipients of list <nifl-fobasics@literacy.nifl.gov> Subject: [NIFL-FOBASICS:1159] Re: Long division --HELP!!!! X-Listprocessor-Version: 6.0c -- ListProcessor by Anastasios Kotsikonas X-Mailer: Microsoft Outlook Express 6.00.2800.1437 Content-Transfer-Encoding: 7bit Content-Type: text/plain; Status: O Content-Length: 5127 Lines: 85 I just recently had a long discussion with a student, older adult, who is really struggling with a required college math class. His comments were very similar to those of my daughter, also now in college, who is intellectually "gifted" but probably has a nonverbal learning disability and in any case has a terrible time with logical-sequential processing. My student said that his primary problem is that he needs to get the big picture first -- he can't build up to it by first learning all the little pieces. He needs to feel he understands what he is trying to do before he starts trying. Unfortunately, math is typically taught the other way. We teach lots of little pieces and then students are asked to put the pieces together. Once the pieces are assembled, there is -- one hopes -- an "aha!" when the student suddenly understands how it all works. For some students, no matter how highly motivated and even "bright", this simply doesn't work. At the same time, it's really hard to convey the big picture without dealing with the little pieces. (You think math is bad -- I had to tutor my daughter through both chemistry and AP chemistry in high school. A nightmare, but she learned it and is even signing up for another chemsitry course next semester.) I don't have a universal answer for solving this problem, but the general approach I've found that seems to work is to take a two tiered approach. On one hand, I do try to build the big picture and to help the student learn to tolerate a fairly fuzzy big picture because the thorough understanding just won't be there until the little pieces fall into place. On the other hand, I take an extremely mechanistic approach to the little pieces, linking fairly incomprehensible, to-be-memorized components back to the big picture. Don't even try to do conceptual work on the little pieces -- it's a distraction. Long division is a perfect example of this. How many people really understand why long division works -- we all just know how to do it. Some of us did have the "aha!" when we got good at it, but most just know what to do and know that the right answer magically appears at the end of the procedure. But for students with logical-sequential processing difficulties, just learning the steps without a sense of where they're leading is very hard. So it helps to stop pretending that the steps make sense -- and really, most people are indeed pretending -- just learn the routine. At the same time, these students have a very great need to keep track of where they're going, so you do want to keep linking back to the reason you're engaging in all these contortions in the first place, and also to track progress through the procedure. A related issue is that I firmly believe that very few students, even math students, know how to read a math book -- at least not until very advanced levels. In my experience, students first try to read it like a novel. In well-done math books, you read along saying "uh-huh, uh-huh" and everything seems to make perfect sense until you get to the problems. Then you can't do them and you just feel stupid. Once that tack fails, students start with the problems and their notes from class, if any. They look back through the chapter to find clues to the problems, but since they have no idea what the chapter actually says, never having looked at it before, they usually can't identify the clues. I work very hard on teaching students to read the math book the way a math person would -- with pad and pencil in hand, working every single example, checking back to confirm everytime the book says "as we have shown in chapter ___" or something of the sort. Don't even touch the problems (other than to estimate the level of the workload) until the examples are thoroughly understood. That means, often, working them several times -- first with open book, then with closed book. Finally, start the problems. Usually the first few match the examples and then everything goes haywire. But now we can start looking at aspects of the problem that match something in the chapter, hopefully an example, and we can start reasoning through. For studying for tests, I encourage students to once again start by working all the example problems, especially if the test covers several chapters. I also try to get students to keep clean copies of all assigned problems (worked correctly or at least corrected) and to use those for studying. Again, most students don't discover this on their own and don't realize it's what the math stars generally are doing. If they really want to test their knowledge, try working unassigned problems enough in advance to ask the teacher for help if they run into difficulty. Long division is sufficiently complicated that a modified version of all of this can be done just for this one operation. But only in the context of keeping an eye on the big problem (dividing large numbers of somethings into smaller groups and figuring out how many groups there will be and how many leftovers). Sorry for such a long answer -- this topic has been on my mind lately. --Lynne
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