There is an article here about how Ontario college students are barely making the grade in math.
A new study shows a third of first-year college students in Ontario are in danger of not graduating because they flunked or barely scraped through their math course.
Researchers at Seneca College who conducted the study say that equates to about 10,000 students.
About 67 per cent of students achieved good grades — As, Bs, and Cs — slightly better than last year.
The governing Liberals are focusing on post-secondary education as a way to pull Ontario out of a major economic recession.
Monday’s throne speech promised to increase the portion of the province’s population that has a university or colleges education to 70 per cent from 62 per cent.
The government also promised to create 20,000 new post-secondary spaces this fall and increase the number of foreign students to about 54,000 from 37,000.
The Seneca study focused on the math results of 30,000 college students, but also examined the records of almost 80,000 students who enrolled in college in the fall of 2008.
Is this really cause for worry? Or have things been blown out of proportion?
Last year, I remember attending an math-education talk at the British Applied Maths Colloquium. The talk, like many of the educational talks these days, was a long complaint about how today’s educational system is abysmal and about how mathematics as a field is suffering. The speaker’s examples were not taken out of courses taken by students majoring in mathematics, but rather math courses taken by a variety of students.
At the end of the talk, I raised my hand.
“Can you tell me,” I asked, “How much of an effect these trends have had on the number of research mathematicians produced by the school?”
The speaker didn’t answer the question particularly very well. He mumbled something about the fact that there probably wasn’t much of an effect (!) on high level research and moved on.
My point was simple: In today’s day and age, people may have lost appreciation for mathematics as a population, but the impact on actual research—that is, mathematics of the highest level—was minimal.
The first thing we have to address is the sample group in the above study.
In Canada, “college” doesn’t refer to undergraduate universities, but rather to post-secondary community or technical colleges.
With this in mind, it’s not a stretch to remark that the students who attend these colleges are usually not as academically strong as their high school peers who chose to pursue a university education—at least, in the sciences and mathematics.
How many of these college students will go on to pursue careers in Engineering, Physics, Mathematics, or one of the other sciences? Very few down to nil would be my guess.
Later down in the article, I see the problem:
Monday’s throne speech promised to increase the portion of the province’s population that has a university or colleges education to 70 per cent from 62 per cent.
Today, everybody wants numbers. It’s not enough to provide equal opportunity to education, we need the numbers to rise. And so we’re widening our net.
Now don’t get me wrong. This is not a bad thing. It’s good to push students to learn mathematics. But the problem is that we expect everybody to be good at it. The statistics are misleading because we’re opening our doors to the rift-raft and allowing pretty much anybody to get into colleges and universities. So of course when it comes to a subject like mathematics, the number of people who flunk the course is going to increase!
Some people might get offended by what I’ve just said.
The funny thing is that intellectual ability is not seen in the same light as physical ability.
That is to say that people freely accept the fact that a sports superstar like Usain Bolt is genetically designed to do things none of us are capable of—and yet, people are surprisingly resistant to the fact that certain intellectual activities may be beyond them.
The key [to solving a math problem] is often brilliant but difficult. There may be a psychological unwillingness to accept that there is a world of brilliance and of understanding which may exceed [the student's]. There may be a sudden revelation that some higher mathematics is beyond them completely and this comes as a shock and a blow to the ego.
[...]
It is commonly thought that there are “math types” and “non-math types”. No one knows why people take to math easily and others with enormous difficulty. For non-math types, resistance may be the honest reaction to innate limitations. Not everyone becomes a piano payer or an ice skater. Why should it be otherwise for mathematics?
Davis and Hersh in the mathematical experience
I wanted to talk about the very nice article “Recruitment and retention of mathematics students in Canadian universities” by Fenwick-Sehl et al. (available here for educational purposes). In the article, they make the following points:
1. The number of mathematics degrees at the undergraduate and graduate levels remained relatively constant between 1992 and 2005
and,
2. The total number of mathematics degrees as a percentage of all degrees awarded has slightly decreased over the same time period.
The explain this trend through various theories, among some of them:
A. Recruitment and retention are not at the top of the priority list for most mathematics departments.
B. There is a migration to other math-related disciplines, such as biology or medicine.
C. Self-selection out of mathematics: The very best students in mathematics may believe they have a wider range of career options outside of mathematics (such as in engineering, medicine, and so on).
And so just a quick glance at this article ‘confirms’ my suspicions: All this hubbub about the abysmal performance of students in mathematics is taken out of context. Surely in 2010, we’re getting significantly more people into higher education, and outputting significantly more math-related researchers.
The government needs to understand that these statistics are taken out of context. The fact that most community college students are failing math does not imply that the research output of mathematics-related disciplines has faltered.
If anything, it’s increased significantly in the last few decades.
And finally, my criticism about natural abilities stands firm. I’m not saying that we shouldn’t aim to improve mathematical literacy. I’m saying that simply increasing the number of students who are required to take a first-year Calculus course is not going to suddenly produce an explosion of mathematicians.
If you were to suddenly put every single member of a school’s population into a rigorous track and field program, you would not suddenly produce a dozen superstars, nor could you realistically expect every student to have the natural athleticism to make it through the program. It’s a good thing, of course. People are exercising more and you’re going to expose the sport to people who may not have normally had the chance to participate.
But you’re also going to have to deal with a lot more wheezing, fainting runners than usual.
It’s okay for people to admit that they can’t sprint a hundred meters in under 12 or 13 seconds. So why is it not okay for some people to admit that there are some intellectual sprints that are beyond them?
A good government will provide equal opportunity.
To expect equal performance is a step too far.
(Usain Bolt’s magical 19.19 in Berlin)
Bookish.Spazz says,
As a non-math person I’ve accepted the fact that math will always be something that I will struggle with.
I get what you’re saying. Increasing the amount of people who take university level math wouldn’t yield a higher success rate, but they’ve got to do something right?