I don't get it! Why is this discussion list organized as it is! Why all the "no subjects" -- even when the post clearly states a subject? E.g., Mark Schwartz clearly states a subject: "Rosen's interest in brushing up on math" but we don't see it in the topic list under the subject column????
Apparently, I am not the only contributor here who doesn't get it!
According to the rules (rather more complicated than need be) for joining this list, we must each send an introductory message to introduce ourselves before we can join. Okay, I did that. Then I went to find it only to see it listed as "no subject" even though I had entered "Introductory message" into the subject field??????
Why couldn't I have been given a way to supply not only the subject of, say, "INTRO" but also something more like "INTRO: Should we teach computation?" Or, by default, it could be: "INTRO: Hello"
Here's my introductory message . . . without my personal intro info and my survey announcement (survey closed now!), which I have edited out here so as not to bore anyone:
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.