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Thursday, 19 February 2015

Many McGill Education Students Cannot Calculate an Average

This is a story about McGill education students that cannot calculate an average, and the professor who admitted he didn't care. Finally, I explain why this is important.

I hope that by telling this embarrassing story I will contribute to raising the standards at McGill and for Quebec teacher certification. I don't mean to unfairly target education students and I'm not calling anyone dumb. Some are just uneducated. But as a public institution McGill has a responsibility to fail these very weak students. Instead, in this case McGill handed out As.

The Story
The professor of an education course began one class explaining how to calculate a mean (average), median, and mode. I was surprised this was necessary, because according to the Quebec education plan, it's a basic concept learned in secondary cycle two (grade 8):

Feeling more like an anthropologist than a student, I sat back in my chair and observed. After twenty minutes (yes, twenty minutes) of decent explanations from the professor, he asked us a simple question: what is the average of these numbers:

One 100 and nine 20s. Or:
100, 20, 20, 20, 20, 20, 20, 20, 20, 20
(I'll save you some trouble if your mental math isn't snappy: the answer is 28)

What do you think happened in a class of 40 students? Did they hesitate? Maybe they got it right?

Nope! Six students in the class volunteered six different wrong answers before the professor stepped in. A reminder: Quebec teaches this to thirteen year old kids. It gets worse. I noticed several things:
  • Some of their answers, like 16 and 18, were lower than any value in our sample. This is like saying "all of my students scored higher than 60% on the exam, but my class average is a failing 42%! What's going on‽"
  • Some of their answers, like 120, were higher than any value in our sample. This is like saying "the class average on this exam is 132%, but I never gave bonus marks! What's going on‽"
  • Was it student tricksters? No. The answers seemed genuine, and the students who answered were not sitting together.
  • And the worst thing of all: this deluge of very wrong answers surprised no one.
Not a Smirk nor a Snicker
When a wrong answer was volunteered, each more wrong than the last, I never heard a snicker or saw a single smirk. If you're an optimist you may think that the students who knew better kept their mouths shut to encourage the learning of others. How nice! Except it's simply not the case. Compared to others, education students are far chattier during a professor's lectures and generally less respectful. Tact was not holding them back from snickering or mumbling.

I leave it to you to find irony in the fact that education students are disrespectful during a professor's lectures.

Anyway, had the bulk of students recognized how bad these answers were, nothing was holding them back from cracking a smile, given their usual behaviour. But as I said, no smirks and no chuckles. We can therefore conclude:
  • Many McGill education students cannot calculate an average. Or:
  • It surprises no one that some McGill education students cannot calculate an average.
I'm not sure which is worse.

The professor said we'd be tested on calculating an average and we never were.

Why this is Important
There are at least three major reasons why teachers should not be math illiterate.

Teachers Teach Everything
In their careers, Canadian teachers will teach many different subjects. The reasons for this are complex, but an English/History teacher typically must teach many subjects like Spanish, ethics, math, dance, and technology while climbing the seniority ladder. However being math illiterate means teachers would hopelessly fail high school tests on math and science. Yet sometimes they must teach the subject!

Understanding Education Research
In John Allen Paulos' fabulous book A Mathematician Reads the Newspaper, he shows us how math illiteracy is harmful and disrupts our perception of the world. How can we expect teachers to understand pedagogical research if they are math illiterate? They can't even "read the newspaper".

At McGill, education courses often ask students to read education research. These papers talk about significant figures, regressions, standard deviations... yet a student who has yet to grasp the concept of an average has no hope of critically reading any new research. The result is that a lot of education students get good at pretending they understand things that they do not. They may even convince themselves that they do understand the research. And so they reject and accept research on personal whim.

Too much school and not enough learning makes people confident despite their ignorance.

Interdisciplinary Lessons
We know that a great way to inspire students is to combine subjects in exciting ways. Sometimes chemistry can be taught in English class, or dance taught in math class. It's true! We have trouble believing this though because the teachers we had didn't know a diversity of subjects. Math illiteracy in teachers means there are fewer subjects we can combine. So math class remains boring math class, and nothing else.

As usual, instead of just complaining I'm also going to propose solutions.


Maybe the education program should have a mandatory mathematics course, like statistics? Or maybe not. But if education students can't calculate an average, then don't ask them to analyse articles with heavy statistics in them. Let's stop pretending education students understand these articles. Let's be consistent.

Everyone I know in the program skips the methodology and data analysis sections of their readings. They don't understand it! And then in class we criticize the articles like we know what we're talking about.

Too Many Teachers
It's not like there's some national emergency where we don't have enough teachers. There's a huge surplus of teachers in Quebec and all over Canada. This is a wonderful opportunity to raise certification standards. Lets start failing students who are math illiterate, tech illiterate, and humanities illiterate. But how will we know who to fail?

Teachers Must Pass All High School Exams
How about future teachers must take the provincial exams designed for high school students. If they fail even one, no certification. Try again! Why should someone be a high school teacher if they can no longer pass high school? These exams should be pass or fail, because there's no shame in a history teacher scoring 71% in math. That's adequate I think.

To some (and we can hope, most) bachelor of education students, these exams will be a joke. To others... they will be a crippling blow to their ego. Hurt feelings are unfortunate, but education is too important to let weak teachers get certified.

From what I've seen in my two years taking education courses... Yes, some McGill students would fail high school exams.

Tips for Employers
This advice is for employers who are not seeking certified classroom teachers.

Do not hire someone just because they have a bachelor of education degree. Instead, have a look at their portfolio (if they have one), their work experience, or their other degrees. If all someone has on their resume is a bachelor of education degree, I would view it as a net negative.

I plan on starting a business making education software. Presuming I'm one of the lucky few that succeed, I would never hire a bachelor of education graduate - unless they've accomplished a lot outside of school. I hope education start ups can take my advice so they have a better chance at succeeding. Or, maybe McGill and the ministry can raise the standards for teacher certification.

If you're a university student and you feel this way... please contact your professor, department chair, dean, whatever, about this problem. If you care, complain.