Whatever all the problems are with adult innumeracy, using the current widely available junk commercial textbooks and the teaching that is similar to the junk in these books do not help solve the problem. Here are some reasons why (this is not an exhaustive list):
1. Little conceptual understanding is offered, and memorization is often encouraged either directly or indirectly. Yes, some memorization is needed, but even that memorization needs to come with understanding. And because textbook exercises and assignments never test directly the students' understanding (in that the questions on the assignments can be answered successfully by those who do a good job memorizing template questions without understanding), the ones who are simply trying to get by or the ones who want to try to understand but give up eventually because they cannot do so in the time allotted for the class then try to get by on memorization. Most will either fail in this attempt or just barely squeak by but then end up not really knowing that their lack of conceptual understanding is holding them back--not their memory, not because the math is supposed to be too hard for them.
2. Confusing language hurts students' understanding. Current curricular K-12 language is clearly included in college remedial and college algebra texts, and some of that language is a mess. And books often resort to using that language and symbolism so quickly and heavy-handedly that the students would have to learn the language and symbolism very well almost immediately to have any chance to read and understand the books. That is, the books introduce all this terminology and notation and then quickly use it to a level that requires good fluency almost immediately to understand what the book is talking about.
3. The math is taught in bits and pieces rather than as a unified whole. Many of the books don't really go anywhere and seem to end at some arbitrary place rather than at a natural final destination. These points are even more true for so-called "survey of math" courses. The so-called "survey of math" courses I have taught were not organized but instead had students wandering around aimlessly in various parts of Math Land. Where the course was supposed to be headed, why the course discusses these ideas, where these ideas lead, etc. have no answers because the course is nothing but a hodge-podge of mathematical topics. The ideas discussed rarely lead anywhere because, by the time a unit or chapter is over, the course never uses that stuff again.
But such a description can be said of algebra or arithmetic courses, especially when one considers that the courses do not give much indication to students where the course is headed or what the "big picture" of the course is. Books may say that they teach topic X because topic X has these applications, but that doesn't mean that students at the end of an arithmetic or algebra course--even if they learn these courses successfully--will end up seeing what the ultimate point of learning arithmetic or algebra is. Students end up focusing on the trees and lose sight of the forest (I normally try to avoid using cliches, but I can't bother right now on how to find a new way to say this). They end up not seeing what big ideas help bring all these topics together into a unified whole.
Even if one can argue that fixing these problems with textbooks won't help considerably, I don't see any good reason to continue using these junk textbooks because they don't give students any reasonable chance to learn the math. I don't have all the answers to fixing these problems, but I'm searching. And I definitely want to field test my books beforehand, but as of now, I do run into a problem with Argosy University: Argosy University's contracts with us give them the right to own any materials we use in teaching their classes. So as soon as I try to use my textbook in their classes to test it, they then own the book from that moment on. That might not be an issue at Florida Tech (I don't recall seeing anything that indicates this might be an issue), but I don't teach for them very often--usually just 2-3 quarters a year--because of much lower demand for online classes as compared to schools like Argosy and Kaplan and Dom Rosa's Post University. I will need to find alternative solutions.
One major challenge that makes such progress difficult is not only finding a way to fix these problems in textbooks so that we can write one that makes sense to students, we also face the challenge of teachers who will abuse such books and resort to teaching "show and tell" math as the current commercial junk books do, especially if enough of their students pressure them to do so. And we also face the challenge of helping students (and teachers) learn to see for themselves that trying to learn math via memorizing template examples and ignoring genuine conceptual understanding is exactly what holds them back from learning math--assuming that they have the ability to learn the math. Whether they do or not is controversial. I believe they do. And I'm sure that there are still a good number of students having the ability to learn math but are held back from learning for these various reasons I have mentioned. Finally, another challenge we face is what to do when students who take these helpful courses end up later taking math courses that continue to use textbooks and teachers teaching math in these same ways that hold students back from learning. The danger is that not only will the students be hurt in the current course but also that whatever good was accomplished in the previous courses will be undone partially or even completely.
And you had mentioned another good point a few days ago: many students' difficulties with reading comprehension. Though the books at their level are already unreasonably difficult for any student who needs that kind of help, poor reading skills will hurt them because any book at any level will be incomprehensible to one with poor reading skills. However, most math teachers are not experts on teaching this. I know I am not. Colleges and universities need an effective way to identify students with these difficulties and then have them take appropriate coursework on reading skills before progressing to regular college or remedial coursework in other subjects. But those developmental reading classes need to be taught effectively, and I am not one who has any idea how to make such classes effective.
I don't know how much of an impact I can make in resolving some of these problems, but I feel I must try. One thing we do need to do is to look at others' previous attempts and then figure out why they failed and how much evidence there really is for their failure. And we cannot forget that we cannot rescue bad teachers merely by giving them good textbooks just as we cannot rescue those with poor cooking skills by merely giving them good cooking utensils.
As for the history of math education, I will have to look further back into the history sometime, but I don't believe that these bad ways of presenting math have always existed. But they have existed in this country for such a long time that many students and parents and others falsely believe that math is supposed to be taught this way and without any exceptions whatsoever and even that math itself is this dry, mechanical subject full of meaningless rules for manipulating symbols. These prevalent attitudes did not arise because of the way ancient Greeks taught math or the way the ancient Muslims taught math or the way Europe or Asia or Africa taught math in such-and-such a time period but because of the ways math has been taught in this country for the past so many generations.
On 10/4/2010 at 7:10 pm, Haim wrote:
> Jonathan Groves Posted: Oct 1, 2010 4:48 PM > > >Again, I challenge you to find one of our statements > > >that makes the claim that we will fix all the > problems > >in math education with a single textbook. > > Jonathan, > > I am sorry for the misunderstanding. You do not > not claim to solve all the ills of math education and > I do not mean to imply that. With my hyperbole > (always a mistake in this forum), I mean to say that > you will not solve any problem with your textbook. > > I believe you will not solve the problem of adult > ult innumercay because a lot of people have been > trying very hard for a very long time to solve this > problem, with no discernible progress, and you seem, > not ignorant of this history, but indifferent to it. > I am persuaded, given the long history of this > s effort, that if there were a method for teaching > math to adults, it would have been found, already. > Whatever is going on with adult innumeracy, another > r textbook cannot be the answer. > > Perhaps the mistake you are making is this. You > You assert that math is taught in a dry, stultifying > manner that sucks the life out of what should be a > vibrant subject. However, you think this is how math > education began. Not so. Once upon a time, > mathematics was a very small community of people who > were motivated to learn and advance the subject and > mathematics was taught in a natural way. > > Only as the number of people learning mathematics > ics grew, did the style of instruction change. It is > the very mathiness of mathematics that most people > object to, and to make math more tolerable for them, > it was gradually transformed into what we have today. > Of course, the community of people who actually like > e mathematics and want to learn the subject and > advance it remains small today, as ever. > > Now, you and Schremmer want to turn the clock back > ack more than a century and inject the mathiness back > into mathematics, and you want to do it for the > masses. Good luck with that. > > Haim > We're buying shrimp, guys.