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RE: Should we teach computation? (fwd)
Posted:
Jul 31, 2009 11:42 AM


 Forwarded message  Date: Sat, 25 Jul 2009 12:05:05 0700 From: mmanly <mmanly@earthlink.net> To: numeracyapproval@world.std.com Subject: RE: Should we teach computation?
Charles seems to be trying to spark a discussion on this list and I applaud him for that. However, in doing so, he has overstated our differences.
His first sentence states: "Conventional wisdom says that the GED math teacher should teach problemsolving and NOT computation."
He then goes on to suggest that my remark that "I suggest you start with word problems" is the same as saying that I would not teach computation.
I have never said that one should NOT teach computation in a GED class, but I will always say that one needs to teach MORE than computation in a GED class. After all, the GED test is not a test of computation skills.
Charles knows (and quotes elsewhere) that I am one of the authors of a paper, "The Components of Numeracy" which stresses that context, content, and cognitive/affective aspects are critical. With that in mind, from the first class session, I would strive to engage learners with meaningful contexts where knowing the facts and procedures of arithmetic would be helpful in solving problems. Computation is thus a tool, not an end in itself. (quoting Lynda Ginsburg)
It would seem that the disagreement between Charles and me is more style than substance. I would not start a GED class with everyone reviewing naked multiplication facts.
Myrna Manly
Original Message From: numeracyapproval@world.std.com [mailto:numeracyapproval@world.std.com] Sent: Thursday, July 23, 2009 9:28 PM Subject:
 Forwarded message  Date: Thu, 23 Jul 2009 18:49:30 EDT From: Charles Roll <chasroll@my.wgu.edu> To: numeracy@world.std.com Subject: INTRO: Should we teach computation? Sender: numeracyapproval@world.std.com Precedence: list ReplyTo: numeracy
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I have taught GED math . . .
Conventional wisdom says that the GED math teacher should teach problemsolving and NOT computation.
[NOTE: this isn't in my INTRO, but it's relevant: Myrna Manly has written (September/October 1991 issue of GED Items (ISSN 08960518; Volume 8, No. 4/5) advising GED teachers, as follows:
<<In my workshops, I present ways to teach math that focus on problemsolving skills rather than on the rote strategies of computation. the most common weakness in math skills is the inability to apply computation skills to reallife situations. Rather than reviewing computation, I suggest that you start with word problems. . . . Q. 'Many students come to our center for just a quick review of math, because they need to take the GED Tests within four to six weeks. What are the most important things to cover with these students?' A. 'The most common weakness in math skills is the inability to apply computation skills to reallife situations. Rather than reviewing computation, I suggest that you start with word problems.>>]
However [Manly's advice notwithstanding], a big problem that I have seen in teaching GED math is that students start out at radically different points in their math development. If the problem is ignored, less confident students  comparing themselves to others  will likely get discouraged and drop out. [For many students, there is no way that they can pass the GED Math test within 4 to 6 weeks. For these students, the biggest problem CANNOT honestly be described as inability to apply skills, that they already have, in reallife situations, rather it is lack of skills and, more importantly, lack of selfconfidence respecting skills and a perceived inability to learn them: if you start by giving these students practice GED Math tests in the first class session, that first session may well be their last!]
A few students are really no where near where they need to be in order to start work in a GED class: for example, they have forgotten how to subtract and don't know even the easy facts from the timestable, e.g., 2 X 7 or 3 X 6. These students need special attention. Some are just 'rusty' and, if willing to work, can systematically fill in the gaps in their arithmetic skills; but others may have dyscalculia and need more specific special attention. [Many have been or could be diagnosed as with dyslexia, never addressed in a numeracy context in all their schooling years before they dropped out.]
On the other end of the spectrum, there are students who can do all the basic four arithmetic operations, except (usually) long division. These students are ready to go into the GED math curriculum  which I consider to mean studying the various GED problem types, as in 'Contemporary's 50' (McGrawHill). As for long division, that's another matter altogether, but just to state my opinion, it's surprising how many GED math students want to learn long division, so I think it's valuable for those students in three ways: (1) building confidence (a huge consideration for GED students!), (2) as a review of multiplication facts, and, (3) for understanding the concept of algorithm. However, the truth is that long division isn't a skill likely to be used either in real life or on the GED.
Then there are all the students who lie between the two extremes, maybe 50% or 60 % of all those who make it to the first class session. These students generally need some review and refreshing of what are known as the "difficult" basic multiplication facts, such as, 7 X 8 and 9 X 6. I am working on creating a threeweek "intervention" or minicourse for such of these students (the inbetween group) as are interested. I would like to open that course, in the first class session, by putting the students to work constructing timestables. Ideally this would be done on computers. A spreadsheet could be used, but most of these students would probably do better with a specialized CAI application that would allow them to practice the facts they don't recall automatically in the context of the timestable that they themselves create.
The reason for designing the course with a length of threeweeks is that students who don't know all their basic arithmetic (not including long division) are likely to drop out during the first three notorious "dropout" weeks. I think this is still an issue even now, a decade after publication (in Focus on Basics, Vol. 2, Issue A, 1998) of "The First Three Weeks: A Critical Time for Motivation" by B. Allan Quigley. These students, if identified as deficient respecting basic timestable facts and given flashcards as the primary or only intervention, are likely to drop out without even discussing the matter with their teachers (Quigley, at fifth para. under "The DropOut Weeks").
In connection with this project (which I am doing in the context of a Masters of Education in Instructional Design program at WGU), I am asking for comments from GED and ABE math teachers and tutors.
chasroll@my.wgu.edu
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