>I have seen numerous articles addressing this issue that you have just >mentioned--the problem that "reform math curricula" often do not contain >any real mathematics content. <snip> >As of now, I don't have any way to really verify for myself how valid these >claims are. Experiences with students don't tell me much; most of >the students >at Kaplan and the other schools I teach for are older students who never went >through reform math classes. In fact, most of them had gone through boring >math classes that reduce mathematics to memorization and recipes, the kinds >of math classes that don't show any creativity or history behind mathematics, <snip> >"Because it's the rule. We're supposed to do it that way." So >something works >because it works or because it's the rule that tells us it works? That's not >reasoning but simply regurgitating a fact in which the student has no earthly >idea why it's true! These are the kinds of math classes I went through in >K-12. The mathematical content is fine and useful for learning more advanced >mathematics.
Exactly what you need to know in order to teach for Kaplan. Right?
>But it was taught without reasoning or motivation and was taught >via memorization. In short, no creativity, no ideas of how >mathematicians work, >no idea of how the subject is developed, no idea of how new mathematics is >developed, etc. No wonder such students have no earthly idea what >mathematicians do or how they view mathematics! These are the kinds >of classes >that are the persistent disease in mathematics education. Regardless of >actual mathematical content, classes that reduce mathematics to this kind of >abhorrent crap cause far more harm than good.
Such speculation sounds beautiful, of course, but I have yet to meet any mathematician who was taught in a full-blown "discovery" environment. Many of us correctly believe that we should have been taught more, and more quickly, but the idea of not learning as much as possible (ostensibly, from knowledgeable teachers and/or well-written mathematics books) before embarking on discovering new and exciting mathematics is purely the stuff of ed school insight, not professional mathematicians let alone (and statistically speaking, more important) those who need a strong mathematics background to pursue their areas of interest. For example, none of the seminal group who created Mathematically Correct word is mathematics per se (although some of us became involved very early). Two were PhD's from Stanford, one of statistics and another in genetics (later recruited as full professor with tenure to Brown), another was a PhD in geophysics from USC, another was an independent contractor electrical engineer, etc., united serendipitously one evening with a single common thread; all were teaching their children (and sometimes small groups of their children's friends as well) mathematics to compensate for their school's use of one of the better of the math reform curricula, CPM under the misnomer College Preparatory Mathematics about which I have had some experience: http://mathematicallycorrect.com/cpmwb.htm
Bringing this up to the present, one of this geographical region's very expensive private schools - complete with an avid supporter and sometimes contributor here with the same mathematics misconception as yours - adopted the newer version of this curriculum that supposedly has fixed those problems (that CPM never admitted that it had). Don't believe it for a minute; its creators and proponents are true believers. How's it working out at Chadwick? Here is the assessment of one parent and attached is the school's: response to what it is learning:
"Disappointingly, she has gone from a child who loved math to one that hates math."
>What teaching methods do you propose? Are the only kids doing well are the >ones Wayne and Company, including you, label as the "mathy" ones? I highly >suspect that these "mathy" kids are the only ones who do well under >the programs of Wayne and Company. I see no evidence so far that suggests >otherwise.