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Many McGill Education Students Cannot Calculate an Average

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Re: Many McGill Education Students Cannot Calculate an Average

#241

Post by mcherm »

amichal wrote: post #178
sly010 wrote: post #80

Real story: In Hungary students are rated from 1 to 5, where 5 is the best score and 1 is the worst. During the semester you have multiple tests (both verbal and on paper) each giving you a score between 1 and 5. Your final score is the average of these rounded to an integer. These final scores are the only important measure when you apply to study further, nothing else matters. I had a [5,5,5] and had to take a verb…

Not quite a straight up math error but my high-school english class had a weekly 10 question spelling/definition quiz. Each question was worth "10%" if you got both the spelling and definition correct and "0%" if you got either wrong. I typically got all the definitions correct but very few of the spellings (a major weakness of mine) scored typically 20-30 "%". At the end of the semester these tests were weighted equ…

Actually, this story makes me want to defend the teacher here.

Seems to me that this grading regime was explained beforehand and was a fair way of assessing your spelling and comprehension. Your complaint seems to be that you think the spelling should be a smaller proportion of the grade. While I agree with that, this appears to be a case of the teacher valuing skills differently not (as with so many other anecdotes being posted here) a case of the teacher not evaluating students fairly.

Re: Many McGill Education Students Cannot Calculate an Average

#242

Post by lotharbot »

jordigh wrote: post #228
lotharbot wrote: post #173

Earlier quoted context omitted.

> "It's not really about context ... [it] means different things to different people." The identities of the speaker and audience are part of context. As you correctly inferred, if I'm speaking, an unqualified "America" probably means "the United States". If you're speaking, it probably means "the largest landmass in the western hemisphere". If we're quoting Obama speaking to the Senate, or Morelos during the revolut…

> The identities of the speaker and audience are part of context. I cannot in general assume that information on the internet.

Depends on which part of the internet. (The context of the context ;) )

Re: Many McGill Education Students Cannot Calculate an Average

#243

Post by jpollock »

baddox wrote: post #229
Negitivefrags wrote: post #222

Earlier quoted context omitted.

Here is a story of something that happened to a friend of mine. This is from New Zealand. He was taking 7th form Latin. Latin has enough students in the 3rd form but by the time you get to 7th form (The final year before university) there were only 20 or so students in the entire country taking the course. He was taking the course by correspondence because the school obviously wouldn't provide a teacher for a single…

Can you clarify what you mean? How does a curve cause a 95% to get scaled down to a 43% failing grade?

You try to fit the marks to a normal distribution. It assumes that all classes/courses have the same distribution, with the same midpoint and that the only variation is that the test was too easy.

So, (simplistically) if the expected midpoint is 75, and everyone is in the 95-100 range, a grade of 97.5 would be shifted down to 75.

It does penalize students for having really smart friends and getting together to take a difficult course.

http://en.wikipedia.org/wiki/Grading_on_a_curve

Re: Many McGill Education Students Cannot Calculate an Average

#244

Post by aroman »

zaroth wrote: post #149
aroman wrote: post #91

Oh my god — I can't believe it. A professor of mine in college (I'm currently a freshman — this happened a few months ago) told me a story _exactly_ like this — just at the University of Pittsburgh Masters in Education program and wherein nobody knew (or cared) that 1 was not a prime number. I may be more dumbfounded now than I was sitting in his office during office hours... one is an anecdote, two is pattern.

I think knowing if 1 is prime is almost trivia compared to knowing how to calculate an average. The latter is incomprehensible to me. What age are the students in this anecdote?

From what my professor told me, they were almost exclusively in their mid-20s, having just finished undergrad degrees in math.

You're right — knowing if 1 is prime is kind of a trivial point, but this was a course for would-be math teachers specifically about how to teach _math_ to high schoolers. In fact, the specific context of the story was an in-class presentation about teaching kids about primes.

I definitely should have mentioned that in the OP.

Re: Many McGill Education Students Cannot Calculate an Average

#245

Post by aroman »

throwaway283719 wrote: post #109
aroman wrote: post #91

Oh my god — I can't believe it. A professor of mine in college (I'm currently a freshman — this happened a few months ago) told me a story _exactly_ like this — just at the University of Pittsburgh Masters in Education program and wherein nobody knew (or cared) that 1 was not a prime number. I may be more dumbfounded now than I was sitting in his office during office hours... one is an anecdote, two is pattern.

In fairness, thinking that 1 is a prime number (or just not knowing that it isn't) is in quite a different league to not knowing how to calculate the average of a list of numbers.

See my comment to the other reply. Ordinarily I'd agree, but these were all graduated undergrad math majors in a course about how to teach math (specifically prime numbers) to high schoolers.

Re: Many McGill Education Students Cannot Calculate an Average

#246

Post by ezy »

tshaddox wrote: post #197
japhyr wrote: post #3

I teach high school, and a colleague of mine went to an education conference a couple weeks ago. She was sitting at a table with three elementary school teachers. They were talking about how to gauge student progress when the students had taken a 100-question test, and a 50-question test. None of the three teachers realized that you had to scale the test scores before making a comparison between the two tests. These…

I've got a slightly subtler but similar story. I had a math teacher in high school who would curve her test scores to the lowest top score from any one class. In other words, if she taught three identical 10th grade Trig classes in a semester, for each test she would take the three top scores (one from each class), and curve the test to the lowest of those three scores. It's a reasonable enough idea, I suppose, since…

At the risk of sounding completely ignorant, what's wrong with what she did? In most classes I've been a part of, your total score was based on a weighted average of scores on particular tasks. The normalization here is a typical test curve -- a normalization that attempts to compensate for measurement error in one particular test, independent of the total class score. That's why she referred to "extra credit".

Re: Many McGill Education Students Cannot Calculate an Average

#247

Post by edtechdev »

I've seen this thing quite often. There's a famous video clip of MIT graduates, in cap and gown, who can't make a bulb light when given a battery and wire. I disagree with the blog author's interpretation that this is about the students being "stupid." I posted the comment below.

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 is 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 right 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. https://www.cfa.harvard.edu/smgphp/mosart/video_archive_2.ht...

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: http://www.learner.org/resources/series26.html and here: http://www.learner.org/resources/series28.html

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: https://www.youtube.com/watch?v=kO8x8eoU3L4

Re: Many McGill Education Students Cannot Calculate an Average

#248

Post by dpritchett »

mcherm wrote: post #241
amichal wrote: post #178

Earlier quoted context omitted.

Not quite a straight up math error but my high-school english class had a weekly 10 question spelling/definition quiz. Each question was worth "10%" if you got both the spelling and definition correct and "0%" if you got either wrong. I typically got all the definitions correct but very few of the spellings (a major weakness of mine) scored typically 20-30 "%". At the end of the semester these tests were weighted equ…

Actually, this story makes me want to defend the teacher here. Seems to me that this grading regime was explained beforehand and was a fair way of assessing your spelling and comprehension. Your complaint seems to be that you think the spelling should be a smaller proportion of the grade. While I agree with that, this appears to be a case of the teacher valuing skills differently not (as with so many other anecdotes…

If comprehension and spelling were decoupled but still equally weighted then the aggregate score would've been significantly higher. Let's split the difference and say that 20-30% on the set of [all answers simultaneously spelled correctly AND comprehended] becomes a 25% on the "spells things correctly" axis. If we weight that equally against the "comprehension" axis then you get

  let R = 25   # reading
  let C = ?    # comprehension
  let M = 40   # reported mean

  (R  + C) / 2 == M
  (25 + C) / 2 == 40
  (25 + C)     == 80

  C == 55      # implied comprehension grade from a 40% average
If comprehension was any higher than 55% - which this anecdote certainly suggests - then the 40% aggregate score awarded is an ineffective assessment of the holistic learning picture.

This is the grade school equivalent of tossing out resumes over a single copy editing mistake.

Re: Many McGill Education Students Cannot Calculate an Average

#249

Post by tshaddox »

ezy wrote: post #246
tshaddox wrote: post #197

Earlier quoted context omitted.

I've got a slightly subtler but similar story. I had a math teacher in high school who would curve her test scores to the lowest top score from any one class. In other words, if she taught three identical 10th grade Trig classes in a semester, for each test she would take the three top scores (one from each class), and curve the test to the lowest of those three scores. It's a reasonable enough idea, I suppose, since…

At the risk of sounding completely ignorant, what's wrong with what she did? In most classes I've been a part of, your total score was based on a weighted average of scores on particular tasks. The normalization here is a typical test curve -- a normalization that attempts to compensate for measurement error in one particular test, independent of the total class score. That's why she referred to "extra credit".

This was explicitly not the case in this class. A test curved to 85 points was worth less than another test curved to 90 points.

And honestly, even if each test was normalized to 100 points after the curve, I would still object (on ethical grounds, not mathematical) to not being given >100% when the test is curved to below my score.

Re: Many McGill Education Students Cannot Calculate an Average

#250

Post by baddox »

sgk284 wrote: post #240
baddox wrote: post #229

Earlier quoted context omitted.

Can you clarify what you mean? How does a curve cause a 95% to get scaled down to a 43% failing grade?

If you have 10 people who score: 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98% 99%, 100% and scale the grades from 0-100, those students' curved grades are: 0%, 11%, 22%, 33%, 44%, 55%, 66%, 77%, 88%, 100% In other words, they turn the students' grades into their ranked percentile within their cohort. It's an absolutely brain-dead decision.

Oh, I see. Essentially curving from both ends, to fit a desired distribution.

That idea has never made sense to me, at least if the class is using a system where having a score less than some specific percent implies failure.

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