Path: utzoo!mnetor!uunet!lll-winken!lll-lcc!lll-tis!ames!killer!elg From: elg@killer.UUCP (Eric Green) Newsgroups: comp.edu Subject: Re: Learning arithmetic Message-ID: <3482@killer.UUCP> Date: 25 Feb 88 05:22:27 GMT References: <4643@ecsvax.UUCP> Organization: Bayou Telecommunications Lines: 77 in article <4643@ecsvax.UUCP>, hes@ecsvax.UUCP (Henry Schaffer) says: > Seriously - does anyone expect education to be completely free of boring > times? Drill in arithmetic (to the point that whatever desired performance > level is achieved and retained) is going to be boring, at least some of the > time. The question is whether some of the time devoted to rote memorization can be better used for other skills. Certainly there will be times that students feel bored (like, all the time in May :-). boring == bad only when boring == they're doing something that they know well enough that they could be moving on to new (more interesting?) topics. Personally, I have never learned anything by pure rote. There just isn't enough mental "hooks" to retain it for long. I learned multiplication tables by using multiplication in problems. I learned Spanish vocabulary by reading (and working) the exercises until I could translate the sentences "in my head". Reminds me of an article I read in, I think, _Phi Delta Kappan_, entitled "Dewey was right!". That is, we learn most when we are actually doing something. Or, from the Piagetian perspective, when we have a "cognitive framework" in which to place a fact... fancyspeak for "when we know what we're doing, and why we're doing it". > It is good when the students learn the principles behind arithmetic - but > I will claim that it is even more important that they learn the arithmetic > itself. This distinction is important when one is discussing students in > percentiles 60 or so and lower. In my experience with low-achievers, their biggest problem is that they really don't believe they can do it. That is, somewhere in their past, something important passed right over their head, and their teacher didn't notice it. So now, the subject seems mysterious, cryptic, and totally beyond their feeble abilities, because they've tried and tried and they just don't "get it". So they give up. At this point, even filling in the blank spot that gave them the problem won't help, because they truly believe that they are incapable of doing it -- and it's a self-fulfilling prophecy. The only way to break this vicious cycle is to show them that the subject isn't mysterious and cryptic, isn't difficult, and is really very simple... and that even they can do it. For example, giving an intuitive description of the counting process, and showing them how that relates to addition and subtraction, and so forth and so on until they have the self-confidence to sally forth & conquer it. One of the shameful things is that a low achiever usually won't ever get such help. Inevitably, it is the least-knowlegable teachers that get assigned to "low achiever" classes. Teachers who barely know the subject themselves aren't going to be much help in showing students how simple the subject is. > I think that this is one of the seldom > mentioned reasons why the New Math failed. Students who did have the > capability to learn arithmetic (well enough to make change, etc.) but who > didn't have the capability to do both that *and* learn place notation/base > seven/binary arithmetic - were spending all of their time trying to master > wierdo bases - and therefore coming out with *nothing* of value. I was one of the experimental dummies used in the "New Math". I remember 3rd grade, "clock arithmetic". "Duh, what's this?" But Mrs. Pear, the teacher, didn't know, either, alas. It took me 10 years to learn that the denotation of a number and the number itself were two different things, and that was only because I started programming 6502's in assembly language. All I ended up with out of that experience was the impression that math was something really weird and complex. Because the book was written in terms that a math major could understand -- not for a 3rd grader. Or even a 3rd grade teacher. I agree that place notation/modula 7 arithmetic/etc. probably aren't worthwhile topics to expect someone to learn in a vacuum. However, a brief explanation of the principles involved, and an actual APPLICATION (like the 6502 assembly language programming that I did 10 years later), can be quite useful when, later on, the student moves up to more complex subjects (I found my experience with computers to be invaluable when I took discrete math in college... it's easy to understand x V y, when you have experienced OR gates in real hardware). -- Eric Lee Green elg@usl.CSNET Asimov Cocktail,n., A verbal bomb {cbosgd,ihnp4}!killer!elg detonated by the mention of any Snail Mail P.O. Box 92191 subject, resulting in an explosion Lafayette, LA 70509 of at least 5,000 words