A stab at American Education

I glanced over this book. It is another stab at poor math education of Americans. As you can expect, it talks about low scores and it hurts.... Poor textbook is one reason, the author says. I don't have time to read all the authors constructive suggestions to improve math education. I found the following interesting. Here is a quiz:

12/13 + 7/8.

What is it closest to? Here are the choices: 1,2,19,21.

Yikes, 13 and 8 are not nice to find common denominators.... I know how to do this... 13x8 = 104,....I am still working on it. The author explains: look, 12/13 and 7/8 are both fractions close to 1, so add them up the answer is going to be closest 2. Easy. Oops I didn't see that. Ok, gimme about 30 seconds I can do this problem even I don't see that. But it is alarming that 37 percent of 17-years-olds don't get it right. 17 year old should be almost ready for college, and that is just an elementary school problem? The problem is this: the students didn't understand fractions! Waita minute, did they have drills all the time? The problem is: they don't understand what they are drilling.

The next page the author interviewed a calculus student who says: I can find the limit by plugging the numbers in... but I just don't know what is it used for? I don't why I am doing this...

It seems like this student is on a Freudian chair by a psychologist expressing inner pain.

Unfortunately, my homework problems rarely ask me to evaluate limit by plugging numbers in. I usually get strange cases where infinity and divide-by-0 is involved... sometimes I may need the l'Hopital's rule. We should tell the students: RELAX, you probably don't need to evaluate limits in solving a real problem. BUT you need to know the derivative and integral are both defined by a limit. That epsilon and delta definition really shut many students off. However, math demands everything to be defined precisely. Informally, limit is simply "where are you going".

Students should know the amazing lim (x->0) sin x/x = 1... This is the key to derive many derivatives such as d/dx sin x = cos x.

I'd like to see that author write a math textbook. It is always easier to criticize than doing it right.