A couple of recent threads have got me thinking about mainstream US textbooks a couple online systems (ALEKS and Khan).
Problem 1. Has anyone else noticed that different books/systems have different methods of doing the same operations? And that every method requires a lot of instruction to teach the same simple idea?
Typical example. A Khan question asked, "You have a block that is 1 1/6 units long. What do you have to do to it to get a block that is 2/3 of a unit long?" DD twigged immediately that this was a subtraction problem. But she couldn't just type in "cut off half a unit." She had to go through a complex process that involved using the software to carve the original block into pieces of a certain length that could be removed. I swear, stuff like this just creates confusion. I see what Khan was trying to do, but IMO, the method has the exact opposite of the intended result and muddies the concept by forcing the kid to focus on WHERE TO CLICK TO CUT THE BLOODY BLOCK!!
Problem 2. Also, has anyone noticed that textbooks/systems don't present things in an orderly manner in which each chapter/section builds on the one before it and leads into the next one?
DD did the first two sections of the Khan algebra course. Section 1 had her solve for x, do basic decimal addition, plus exponents and square roots. When questions in a given topic came up again, they were
exactly the same as the originals, except with different numbers. This was a constant in ALEKS last year with DS14.
Similarly, Chapter 2 of her new Algebra book has the following concepts: rational numbers, the distributive property, "theoretical and experimental probability," and more properties of numbers. Not sure why distributive gets its own section, while nine others are squished into one section. Chapter 1 discusses basic expressions with variables, but has scatter plots and mean/median/mode tossed in.
It's a mashup of concepts --- and this book isn't even the worst I've seen. Like Khan/ALEKS, all the questions are basically the same. Online or print, the level of difficulty doesn't really increase until they throw something out of left field.
I compared with Brown and AoPS basic Algebra. Both start on a subject, move stepwise to the next one, and continue in the same pattern. The exercises are focused, and get harder as you go. Unlike the mainstream books, there are no
brightly colored pictures on every other page, nor are the margins full of distracting, irrelevant notes.
I've been studying algebra and other math books for a couple years now, and I've concluded that it's no wonder so many students are mathematically incompetent. How could they be anything else, given the material?
