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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.


  1. I wish there was a way to popularize this more. This is a message that needs to be heard.

  2. Quick typo fix: John Allen Paulos, not Poulos.

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  4. heh reminds me of this peer reviewed medical article where they re-invent summing the area under the curve:

    1. That is fabulous :P

      What's actually pretty sad is they may have been really clever for coming up with such a thing. However their efforts are wasted because they are uneducated. Maybe not their fault :P

      They could have asked some mathemagicians though... but again, less likely to do that if you don't recognize that it's a very math-like problem.

  5. Excellent read.
    Not be unfair on teachers, but if you fail at something as simple as calculating an average you may also have a hard time marking papers.
    One of my final high school exams was supervised by one of our English teachers. The exam started at 11:17 AM and was supposed to last for 90 minutes. The teacher was supposed to write the start time, end time and duration in minutes onto a white board. It took her almost five minutes to figure out the end time of the exam, only to note down 1:43 PM.
    It was a final so I never had any lessons with her again, but I think I would have had a hard time taking her serious after this.

    1. Thanks. That's a very good point.

    2. An English teacher reading your reply would have a hard time taking you seriously.

    3. Why's that Anita?

      They either know how to calculate an average and this doesn't apply to them. Or, they don't, and therefore they can't understand how it's impeding them from teaching.

  6. I attended a community forum on education where I sat with a group that includes a prof responsible for teaching education students how to teach math. During a small group discussion, the prof mentioned that it was getting harder to teach education students to teach math because what they learned in High School did not prepare them for University. one of the community members in the discussion asked the obvious question, "What would it take to do a better job of teaching teachers how to teach high school math better?" Not even the prof was happy with her answer, "I don't know."

  7. I wouldn't interpret this as "education majors are stupid." I would interpret it as, all of us, even the best of us, are stupid in certain contexts with certain topics and certain time pressures. This partly due to how we are taught and how we learn in school. Our knowledge is inert (inaccessible in other contexts) because it is often taught without context. The technical term for this is "transfer" - our learning often doesn't transfer. An older term for this is "encoding specificity" - our learning is "locked" to the context in which it is encoded. For example the myth that if you are drunk while studying you should be drunk when you take the test.

    Here is a dramatic example that had a huge influence on reforming science education. On the bottom left of this page is a video clip of MIT graduates, in cap and gown, who, given a battery, bulb, and wire, can't make the bulb light. There's also a clip of Harvard students.

    The full videos that go into why this is happening (because of how they are taught) and how we can address it (contextualized and constructivist instruction techniques like problem-based learning, simulations, etc.) are "Minds of Our Own" and "A Private Universe", which can be viewed online here: and here:

    Another brilliant example comes from comedian Father Guido Sarducci's routine on the "Five Minute University" - how he can teach in 5 minutes what you remember 5 years after college:

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  10. I am not denying that the students did not know how to calculate an average, but the author makes a lot of unfair generalizations and assumptions about education programs specifically. Let's face it- standards in ALL university departments are lowering, and most students from ANY faculty would be useless to hire unless they have gained some real experience. At one time it was a challenge to get admitted into university; now, anyone who merely passes college can get in. The reason: universities are money making machines. Too many grads are not gaining employment upon graduation since too many are admitted in the first place, and standards lower year after year. Teachers give out 90's like they are 80's, and pass students who do not deserve to pass since mediocrity is now considered to be achievement. Furthermore, students everywhere are not taught how to think, therefore cannot transfer knowledge outside of a specific context. My greatest challenge as a teacher is trying to get students to do work where answers are not fed to them, or are not immediately obvious. Students want to regurgitate answers, and get upset when they have to think, since their main concern is doing well on a test- not actually learning and gaining real meaning.

    1. "Let's face it- standards in ALL university departments are lowering"

      Yes. However (and this will be covered in my next post) I have taken over fifty university courses in over a dozen departments, and this problem is by far most pronounced in the education department. And teacher certification is in a unique position because far more certified teachers are being produced than necessary, yet standards are not being adjusted.

    2. Yes, you are probably correct. I did my BEd. at Ottawa U. and the whole thing was quite a joke, and an embarrassment.

  11. But I do thank you, Mr. Spence, for making a fuss and for trying to make changes where they are deemed necessary. As for technology courses in eductaion departments, the funny thing there is that the government and school boards across Quebec have been pretending to be advocates for the use of technology in the classroom, so they bought a bunch of Smartboards, but half the teachers use them as mere projectors, and so it is a complete waste of money! Kudos to you for harassing your school's administration and trying to get something done. It is not lost, since your blog seems to be making some of these issues more public!
    Good luck!

  12. Although you make some good points you also make some awfully big generalizations. Just because that one class had difficulty finding the average, it doesn't mean every class will be the same. You're going to get people that are not as smart as yourself in ANY DEPARTMENT. Although, yes, it is unfortunate that they weren't able to calculate the average, that's what school is for. School is a place for you to make mistakes and learn. Nothing wrong with that. I do agree that schools in Canada need to step up their game when it comes to the education department. Some parts of Europe pays teachers almost the same salary of doctors. How is that done? It's because it is harder to get the degree and it's an honour to be a teacher because you are responsible for shaping the lives of many many people.
    Also, most students who willingly go into the education department is doing it out of passion AND has many QUALITIES a teacher need (patience, kindness, compassion, etc.)
    Do you know how many AWFUL teachers there are in university because employers hire those who have a higher level of education? Do you know how BAD these teachers are? Do you know how DISCOURAGING it is for those who have to sit and suffer through those classes? Most of these people who may be "smarter" than those with a bachelors of education have no compassion, no passion and no PATIENCE to teach students.
    So all in all, I want to say that you make some valid points regarding the program. The curriculum needs to be changed so that it is more challenging and more prestigious but don't start assuming that all these students won't become a great teacher. Don't be so narrow-minded, if you really want to solve a problem, consider ALL factors.

    1. "Some parts of Europe pays teachers almost the same salary of doctors"
      ... who in turn are sometimes paid almost the same as hairdressers.

    2. "it doesn't mean every class will be the same."

      Nope, and in fact I've had a couple very good education courses (though just a couple). But saying "that is what school is for" is missing the point. The students in this class did NOT learn how to calculate an average, despite it being required by the course, and they were given As.

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  14. Not news. The education system in Quebec is broken. Teachers teach subjects based on seniority and availability instead of experience and ability. The McGill Education department is especially bad, based on the conversations I have had with ex-profs.
    It just reinforces that adage: Those that can, do. Those who cannot, teach.
    The educational system is the only system I know of where it constantly introduces new 'improved' methods and still produces the same poor results. 'Differentiated Learning'? Give Me A Break.
    We have more bureaucrats in MELS (Minister of Education, Loisirs and Sports) than teachers.
    My advice: Fire all the bureaucrats and privatize the entire public education system. We spend billions and get bupkis.

    1. "We have more bureaucrats in MELS (Minister of Education, Loisirs and Sports) than teachers. "

      Shit, really? Do you have a source for that?

      I do not agree that education should be privatized.

  15. I get where this post is coming from, but I do think it's a little off in focus...

    Most everyone [not solely teachers] should know how to calculate an average, but I also know so many people who had such rough experiences with High School Math that they've done whatever they could to distance themselves from it. Sadly, math still has that stigma, but that's another issue for another day. In any case, many who decide they want to become teachers do show more interest in other subjects where math is not involved. Since it seldom comes up in their day-to-day lives, these skills no doubt fade away over time. Being caught off guard with a query they thought was out of their field isn’t just natural, it’s inevitable.

    At the end of the day, this was 6 students called in class to answer a question and doesn't prove anything. Everyone else being silent doesn't imply they didn't know [not everyone's comfortable speaking], and we can't conclude that if they were tested on it with paper and pencil and given ample time to think, that they would be incapable of solving it.

    But… that’s me nitpicking over specific details. I do that. The overall theme of this entry is to talk about a problem in the Faculty of McGill’s Education department. I have similar concerns, but for different reasons. I’ve met and had the pleasure to work with some brilliant education students who I’m confident will be fine teachers one day. Conversely, I’ve also had to deal with some who’d complain about having to attend class in the first place. Still, the tone of this blog seems to place blame more on the students, which I don’t think is entirely fair.

    The core problem with the education department at McGill is that these courses are just too easy… I don’t say that in a smarmy “I’m too smart for this work”, nor am I saying the theory and the practice of education are simple enough ideas to understand. What I’m saying is that I’ve turned in both really half-assed assignments and ones where I spent tons of time thinking/planning/composing assignments, and still got the same good grades for each. I tell others that I feel like I would have to go out of my way to fail some of these courses. There also doesn’t seem to be much discrepancy in the range of grades my peers get. I’ve had assignments where the professor flat-out admitted that everyone’s projects were so good, that they gave everyone in the class full grades. Whether said projects truly deserved it or not, it’s useless as a means of obtaining constructive feedback and to learn from your mistakes.

    That’s the worst thing this about this type of system. Not only do I feel like I’m missing out on learning opportunities, I feel like I’m being dis-incentivized from having to seek them in the first place. I take pride in putting in effort at what I do because I want to improve and be satisfied with my work whether it’s ultimately good or not. Nothing kills that motivation more than realizing you don’t actually have to try to get satisfactory results, and it just makes you complacent to produce unremarkable material. It’s not even a matter of becoming sloppy or lazy, but rather becoming more efficient by only investing your time in matters that do require your full attention. Either way, it’s not healthy, and that sense of challenge is severely lacking from the department.

    I don’t even want to lay blame at these Profs because most [if not all] have been extremely passionate about their job and clearly care about their students. Some of those educations students who do complain about them ought to spend a semester or two in an engineering/math department to see how much worse it can get. What I’m saying is they should raise their standards and expect more from us. Provided it’s fair and reasonable [avoid the cliché of the professor who automatically fails 80% of his class], it will bring out the best in us, and eventually the best for our students.

    1. I agree with most of what you've said, especially the second half.

      Certainly, 6 students failing to calculate an average after a half hour of instruction on averages doesn't prove the entire class cannot do it. In fact there were some really sharp students in that class. But it does however prove that these 6 could not do it though, and it is a grade 8 concept. Like you, I am concerned that they got an A in the course like everyone else.

      I've experienced exactly what you're talking about: turning in mediocre work, and turning in fantastic work you're proud of - only to see both get full marks and little positive feedback. It really is a bummer.

      You're right that the tone of this post blames the students more. But not entirely - and my other posts put a lot of responsibility on the administration, professors, and Quebec, actually.

      And like you said, other departments have their issues. My next post goes over some undergraduate survey data from a few years ago. Yes, science students are most likely to say their courses are sometimes designed just to fail them. Engineering students are most likely to say that their professors or incomprehensible. However... education students report having the most boring, most random, most tuition-wasting, and most impossible-to-fail courses. The worst - compared to everyone else. This and other things...

      I am only posting one thing a week, so that will be up sometime next week.

      I hope you're doing your best to make this bad situation better :)

  16. I agree that this is a very important matter to be attended to right away. If further certifications are needed to improve upon the quality of education, then so be it. While it may seem like a harsh decision for some, the consequences of not doing so is a much bigger concern. Thanks for sharing your thoughts on the matter, Stuart. Good day.

    Kent Gregory @ Armature

  17. Thanks for posting this. McGill should also raise standards for its future science teachers. Presently and shockingly they have no math-science requirements for future secondary teachers(only English and overall R-score requirements exist and are lower than any other faculty). In fact a B.Sc. should be an absolute minimum requirement for any math-science senior high school teacher.

  18. On the note for employers: Perhaps they could administer tests in preferred subjects for applying graduates.

    1. Maybe. But assessment is a major responsibility of schools. If they stop doing that I hardly know what the point of most of the classes are, especially the intro level ones.