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Topic: RE: Should we teach computation? (fwd)
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Esther D Leonelli

Posts: 18
Registered: 12/6/04
RE: Should we teach computation? (fwd)
Posted: Jul 31, 2009 11:42 AM
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---------- Forwarded message ----------
Date: Sat, 25 Jul 2009 12:05:05 -0700
From: mmanly <mmanly@earthlink.net>
To: numeracy-approval@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
problem-solving 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: numeracy-approval@world.std.com
[mailto:numeracy-approval@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: numeracy-approval@world.std.com
Precedence: list
Reply-To: numeracy


XXXXXXXXXXXXXXXXXXXXXX

I have taught GED math . . .

Conventional wisdom says that the GED math teacher should teach
problem-solving 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 0896-0518; Volume 8, No.
4/5) advising GED teachers, as follows:

<<In my workshops, I present ways to teach math that focus on
problem-solving skills rather than on the rote strategies of computation.
the most common weakness in math skills is the inability to apply
computation skills to real-life 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 real-life
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 real-life situations, rather it is lack of skills and, more
importantly, lack of self-confidence 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 times-table, 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'
(McGraw-Hill). 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 three-week "intervention" or mini-course for such of
these students (the in-between group) as are interested. I would like to
open that course, in the first class session, by putting the students to
work constructing times-tables. 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 times-table
that they themselves create.

The reason for designing the course with a length of three-weeks 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 "drop-out"
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 times-table facts and given
flash-cards 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 Drop-Out 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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