The NY Times recently ran an article by Andrew Hacker asking “Is Algebra Necessary?” He stated that in a typical day 6 million high school students and 2 million college students are “struggling with algebra.” His argument was that algebra, geometry, and calculus “prevents us from discovering and developing young talent” and in his opinion was the “major academic reason” that around a third of all students fail to finish high school. Consequently, he believes we should not “force them to grasp” these concepts.
I’m an engineer, and I’ve never been good at mathematics, but I believe his argument is flawed.
Firstly, why does the number of people who drop out effect whether a subject is valuable in education? The number of people who drop out is affected by many factors. If a subject is valuable, and people are dropping out because of it, don’t ignore the subject, find ways to improve the teaching of it so that the value can be passed on.
Secondly, he doesn’t relay how failure rates have changed over time, and consequently he doesn’t know what other factors may play into the current failure rate, he just jumps to a conclusion.
Thirdly, giving and receiving an education is hard work. The brain is a muscle much like the others in the body. Using it burns energy and oxygen, and leaves you tired. Learning mathematics, a foreign language, or music theory all require an effort. Some people are better at some subjects and worse at others. While we should exploit the things we’re good at, it is the subjects we are weakest at that need the most work, not the least, or worse, none at all.
Fourthly, mathematicians are an essential element in the advancement of society, much the same as entrepreneurs, shopkeepers, and the people who collect the trash. We need everyone to have a functioning and evolving society. He sites
“Of the 1.7 million bachelor’s degrees awarded in 2010, only 15,396 — less than 1 percent — were in mathematics.”
I don’t know if 15,396 mathematicians is enough for our countries needs or not, but from my experience I would say we need more mathematicians, not less. The fewer students we expose to mathematics, the fewer mathematicians will graduate.
Fifthly, the USA is one of the more expensive countries in the world for manufacturing. Apple’s “Designed in California” claim is almost the best we can assert for many products, because it “costs too much” to manufacture in the US. Mental capabilities will be increasingly valuable in the future. Skimping on “intellectual” skills is a disservice to future generations.
One of the concessions Hacker makes to mathematics is that
“young people should learn to read and write and do long division, whether they want to or not.”
I’d argue that teaching of the basic operators doesn’t need to be emphasized because of the fact that the calculator has been common for fifty years. It’s akin to using all your time learning to spell and ignoring sentence structure and the construction of stories (which education also tends to do). Which is more important when even your mobile phone has a spell checker?
What is more important in mathematics is to have a feeling for the form of equations, when they should be applied, and how. These things give a better idea of the purpose and use of mathematics, and when people see a purpose to something they are more likely to become engaged.
Ok, I’ve whined on at Hacker’s expense, but what could be done? There are probably lots of things, but the biggest single thing I think we can do is
Talk about mathematics.
We learn to talk English, French, Spanish and all the other languages of the world as babies, toddlers, children, kids, teenagers and adults. We do it for the most part not by classroom teaching, but by continual interaction with other people. Most people’s everyday conversations do not involve much mathematics. Consequently, our children learn our language, but not mathematics. Learning anything requires persistence and practice. Parents have the greatest opportunity to influence children. Expanding family conversation to include discussing maths practice and concepts could make a significant difference in our children’s ability to cope with it in a classroom setting. Gestation is everything.
Simple maths topics are all around. Let children work out how long a journey will take. Get them to explain the equations they use. Talk about the units of miles per hour, meter per second. Ask them how long it would take if you went twice as fast. Talk about the difference between lines, areas, and volumes. Talk about distance, velocity, and acceleration, and how they are connected. Talk about the parameters that yield the form of the arc of a ball. Talk about probability. Talk about symmetry. Talk about the difference between rotation and translation.
Talk about anything but that maths is hard – because even if our children don’t turn into college professors – life is much harder without it.
Ok, you’ve suffered my opinions, but I’m off my soapbox at last, so now’s your chance to set me straight!