Tuesday, August 17, 2010

Some articles about math education.

The standard view is that American kids aren't as good at math as kids in other countries and are learning less than we did "back in the day", but from my own experience I can say that our educational system currently expects more people to know more math than at any time in history. AP Calculus was pretty rare in my era, and expecting high school students to get through statistics or a beginning programming class was absolutely unheard of back before 1973 when the integrated circuit started the computer revolution. When I teach linear algebra at Berkeley City College, I can expect a lot of kids from Berkeley High School sitting in on what is still viewed as a sophomore level college class. Some material has been "dumbed down" without question, most notably reducing the emphasis on proof in geometry. As someone who was actually pretty good at it, I'm not exactly sure when we should ask students to sink or swim with the concepts of proof, but I think it's probably not something we should force on all kids at the age of sixteen with the threat of not graduating high school.

Friends send me links to articles about math and math education. My friend Ken sent me an interesting article from the New York Times quite a while back about the correlation between mathematical success in school and an early talent for estimation. As the article states, the skill of looking quickly at a picture and deciding if there are more blue dots or red dots is math brought down to the level where the test could be administered to lab rats, but people who show an early skill at this tend to do better in math than people who don't.

My friend Art sent a link to a paper done by some researchers from his alma mater Texas A&M that states American students somewhere in their early education are not grasping the concept of the equal sign as well as students from other countries. If the problem is stated as 3 + 4 + 2 = (____) + 2 for example, many students will add all the numbers from the left side and put a 9 in the blank, when the correct thing to do is just add the 3 and 4 to put 7 in the blank. I see things like this in my classes that appear to me to be about reading comprehension, especially on tests. If the instructions say "round to the nearest tenth of a percent", I will invariably have some students ask "Do you mean to the nearest tenth?" It's almost as if they run out of gas before they get to the end of the sentence.

It raises a question relevant to all education, not just math education. Most people who teach a subject decided to do this job because they are good at the subject, and with disciplines like math, music and athletics, innate talent means some people will be better than others even though they put in about the same amount of time in study or practice. It can be hard for the innately talented to get ideas across to people who don't have the same gifts, much in the same way as it would be for a person without colorblindness to explain green to someone who can't tell green from blue.

The struggle continues.


namastenancy said...

I wish I'd had a teacher like you back in high school. I don't remember any of my math teachers presenting things as clearly as you do on this page. I wasn't very interested in math; unlike anything in history, art or the humanities, I needed a good math teacher and as a "girl" in the 50's and 60's, I didn't get one. Of course, being a Navy brat and moving every year or so didn't help.

But expecting all high school kids to understand calculus or statistics seems unnecessary. If you are going into science or medicine, yes - it's necessary but is it necessary for other professions? Maybe having kids understand how to balance a checkbook and how the interest is calculated on credit cards would be more useful - and a lesson on using math in the real world.

But that's just my humble opinion. YMMV.

Matty Boy said...

Nancy, calculus and statistics are Advanced Placement classes, so it's not every high school student that is expected to get through them. The NCAA has decided that every student-athlete needs stats now, and a lot of them aren't prepared.

ken said...

I think that they should probably push basic statistics and probability, rather than pre-calculus, at least for "average" kids. Scientists and engineers need calculus, but everybody needs to be able to deal with probabilities and statistics, at least at the level where "How to Lie with Statistics" makes sense.

Matty Boy said...

Very good point, Ken. A lot of people both in and out of academia haven't completely accepted the value of technology in math education. Without technology, statistics is a very daunting topic. With knowledge of how to use a good calculator or a spreadsheet, the class becomes much, much easier and the real life skills are more applicable than calculus or differential equations are to the vast majority of students.