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 teachers thought you could just look at the number of questions the students got correct, and see if the students "score" went up.
My colleague pointed out that the questions on the 50-point test had twice as much weight as the questions on the 100-point test. One of the three other teachers realized their mistake - the other two just chuckled and said it didn't matter.
This isn't just frighteningly ignorant, it ends up having a devastating impact on many young people. One anecdote: I knew a bright young student who loved learning, but hated school. Why? He took algebra and french in 8th grade; he passed algebra and failed french. When he got to 9th grade he was placed in algebra again, and french 2. The school would not budge from its original placement; I don't know the rationale. He failed algebra because he refused to do any homework, and failed french because he couldn't make any sense of the class. I want smart teachers to take control of education so this s* doesn't happen nearly as often as it does.
Also, I've taught middle and high school math for 20 years now, mostly to students who struggle with math. I don't think I've had many groups of students who could come up with six different answers for a simple average problem.
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 different classes will have different questions and thus spend slightly different amounts of time on various parts of the material.
The trouble was that she would not give over 100% to the people who earned a higher score on the test than the curve. Her tests were not weighted, meaning that Test-A curved to 85 points was actually worth less than Test-B curved to 90 points. (Supposedly, the then-new district-wide computer grading system couldn't handle such arithmetic complexities.)
At one point, I received a score above the curve. Let's say I got 90 of 100 points, and the curve was 85. Later, when I saw my grades, I asked why I was only given an 85/85 on that test. She explained that she didn't give "extra credit," and she wouldn't budge. She would say things like "you got 100% of the points, so there's no reason to complain." I asked, then, if I could at least be given a 90/90, and she very confidently explained to me that 100% of the points on the test is the same regardless of the total number of points. She would not entertain the notion that a 90/90 is better than an 85/85, much less that a 10th grader might be able to correct an arithmetic mistake of hers. I even presented the example of changing a 100/100 assignment to 1,000,000/1,000,000 and noting the affect on the total grade, but she would have none of it.
As you can probably tell, I'm still bitter about that test.
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 student.
He scored 95% in the final exam. In NZ the end of year standardized tests are scaled to fit a curve across the entire country. He was scaled down to 43%. A failing grade.
Obviously in this case the only students that would bother taking Latin all the way up to 7th form are going to people who care enough about it to learn it well. The standard scaling method used doesn't make sense at all with this group of students.
He wrote a letter to the education minister of NZ complaining about this issue. Months later he got back a form letter explaining why test scores are scaled with no regard to the special circumstances.
Curving only makes sense when there's a normal distribution. Sounds like, at that point, the students were no longer in a normal distribution and therefore curving failed.
No it means the exam was way too easy. 90% of the questions were giveaways. If its ok to fail 400 out of 1000 students doing English, then its ok to fail 4 out of 10 doing Latin. Once you adjust for the easiness of the exam, he actually did not do too well.
Are you trolling? With a subject like Latin, the actual situation is that all the students are really good by the time you have only 20 students left in the whole country. The exam is probably not easy at all, and someone who didn't prepare well would get a much worse score.
You are assuming that it makes sense to make grading to a curve with a sample that is highly selective. It does not.
(I did not study Latin. Just as an item of curiosity, my country's public radio service YLE broadcasts regular radio news in Latin. You can listen and also read some of the stuff here: http://ohjelmaopas.yle.fi/1-1931339 )
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.
People often underestimate the bitterness that these experiences create in smart people. It's not a petty thing, either - it's life changing in many situations.
The road of life is bumpy. I would not seek to smooth out the few remaining bumps in school. We are already in danger of creating fragile people who shatter at the first bump.
All this, even if the teacher's idea were quite wrong - but it's not. By "clipping" the score, the teacher created a hybrid between curved and uncurved grades. If curved and uncurved are acceptable, why not the hybrid?
Neither curved nor uncurved grades remove points that a student earned from the student's score. Uncurved grades obviously just give you what you earned, and traditional curved grades give you more than what you earned. This "hybrid" gave me *fewer( points than what I earned.
> and traditional curved grades give you more than what you earned.
Traditional curves (mapping grades onto a bell-shaped curve based on the class average) do potentially give lower scores than standard 10% brackets (90% = A, etc.)
There is a common thing used in some places (particularly secondary -- don't know that I've ever seen it higher ed) often called a curve which just takes the highest grade in the class or the grade at a certain percentile point and calls it 100% and renorms scores based on that, and that system never gives people lower than the pre-adjusted score. That may be what you are thinking of.
Smoothing out bumps or making it "easy" and worrying about fragile stuff is totally unrelated to acting intelligent.
In early grades, I had amazing teachers. Plus they had "enrichment" where they pulled us out of less-useful classes, gave us a lab and a dedicated teacher who just said "hey, what are you interested in?" I excelled there.
After moving a few times, I unofficially dropped out of school in 7th grade (12 years old), after grilling my teacher and realizing she didn't really have a clue. Other teachers were worse.[1]
I attended for a few more years (partially coerced by illegal police force[1]), then at 15 dropped out for good by leaving the country.
Things turned out OK for me. But I lost a LOT by not getting a real education, not having a chance at college. Just the lack of maths alone takes a lot of effort to rectify. Yes, it's still my fault, but the system shouldn't be encouraging 12-15 year olds to make such mistakes.
Kids will have enough bumps with bullying and school life in general. Adding idiocy bumps that make a mockery of education and intelligence just make kids cynical and tune out.
(It also makes such graduates more OK with the idea of corruption, stupid bureaucracy, mediocrity, etc. - a shrug and a "that's how things work". Such things should be vigorously fought, not beaten into children.)
1: One "science" teacher: "Carbon-14 dating is a lie told by scientists that hate god."
2: Somehow there was enough of a "problem" to haul me in front of a judge who pre-emptively revoked my drivers licenses for 3 years. I told him I'd just get a pilot's license instead and enrolled in flight school the next month. I also found it hilarious how people in court used the term "infinite wisdom" when referring to the judge. Illegal part was that I am not a U.S. person so they didn't have jurisdiction for enforcing mandatory schooling any more than they'd have on any other B-2 visa'd tourist.
> Smoothing out bumps or making it "easy" and worrying about fragile stuff is totally unrelated to acting intelligent.
I stared at this sentence for a while and didn't quite decode it. Sounds like you've had your share of bumps. I don't know how old you are, but you may eventually decide you wouldn't change a thing.
But quite a few kids raised in good environments seem to have missed our on bullies (real, not cyber), and stupid, cruel authoritarian teachers.
This results in a naive and fragile person who is not equipped for the real world.
Have you read The Diamond Age? Neal Stephenson makes a similar point when the headmistress (really YT from Snow Crash) answers a complaint about a teacher.
Sorry, poorly written. I'm just making the point that there's a far cry from producing "fragile" people/overprotecting versus creating and defending a stupid system.
In the former case, it can be good to let kids have to get over some problems or deal with unfairness.
In the latter, encouraging or defending stupidity on the part of teachers or the school system only encourages cynicism or acceptance of such brokenness. School systems should try to encourage the ideals, teach people to stand up to bad things, not accept mediocrity, etc.
I'm 33 and have kids of my own, if that's relevant. I liked Snow Crash but don't remember those specifics.
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.
Perhaps you might object mathematically too. I think of a curve as fitting the test scores to a specific distribution as a corrective to testing error. It's not the fitting that's the issue, it's how justified the target distribution is. If you truncate it, you have to justify doing that somehow (all prior test results had that distribution?). Of course, if the sample distribution squashes it enough, you might end up clustered at 100% anyway, but...
Many comments here are anecdotal. Quebec outperforms other Canadian provinces in most math rankings (Programme for International Student Assessment). Globe and Mail on the subject:
> But there’s also good news. Canada’s declining performance in math isn’t equally distributed across the country. When results are broken down by province, there are shocking differences. And at the top of the class is Quebec.
> While the math scores in most provinces were sliding over the past decade, Quebec’s already strong results held steady. Students in Quebec outperform their rest-of-Canada peers in every mathematical category. Quebec students ranked sixth in the world, tied with Japan and Macao, and ahead of the Netherlands.
> There is no single, silver-bullet solution to solving the problem of declining math scores in the rest of the country, but Quebec is clearly doing something right. Exactly what is more than a matter of opinion. The OECD’s assessment teases out what appears to be working in those countries that perform best in the PISA survey. Quebec’s education system has a lot in common with them.
Having gone through the Quebec education system and now reflecting over it, I can relate to that student. It seems to me (of course I'm biased but...) that french and history were always seen as more way more important than math classes and that is very unfortunate.
I was very lucky to be able to skim through french and math for most of high school. I didn't have an interest in french grammar and thought I was just horrible at math so I just skimmed through it and assumed it was normal. It wasn't until my first year of CEGEP where I had a very good math teacher and a great group of friends help me catch up and discover the beauty and usefulness of math. I would've never thought in high school that I would end up becoming an electrical engineer.
I'm sure I'm not the only one from Quebec with a similar story and from your experience, it doesn't seem like things are going in the right way.
I don't think you went to the right school. It was made very clear to my classes from sec 3 onwards that taking "higher level math" (436, 536) would open a lot more doors in CÉGEP and university.
On the same topic, I firmly believe that CÉGEP offers the best general education in the world for 17 to 19 year olds.
I agree with you. I have a lot of friends in bot pre-uni (as myself) and in techniques and I find it awesome how a CÉGEP strikes a good balance between general education and specific classes.
Oh, the school/program I went to I was forced to take 436 and 536 (which is a good thing). However, just the general atmosphere was history and french is important, math, meh.
It's a bit sad IMO that in our current education culture, we portray the study of math and science as being somehow opposed to the study of history and culture.
I find the them inextricably linked. I'll never forget the human stories of mathematical discoveries from Erastosthenes to Newton, up to the present. And rigorous quantitative and symbolic reasoning is indispensable when discussing socio-cultural phenomena at all scales.
I wish math and science were taught with more historical narrative than they are, and likewise, that the humanities were taught with more mathematical/scientific rigor than they are.
I also think it would open up both to people who would otherwise have a hard time grasping them.
I think it's the idea that math and science are the same regardless of their history. You can learn the history of them, but the answers don't change when you do. On the other hand, your answers about historic and cultural questions can change drastically depending on how informed you are.
Also, the level of rote memorization required vs. logic and analytic thinking. You think math and science could be improved via learning their history; I think history and culture can be improved by learning more about the reasoning behind individual things. Less focus on when and what and where; more focus on why and causes.
> I knew a bright young student who loved learning, but hated school.
Of course. Any bright student realizes that school has nothing to do with learning, and furthermore often interferes with it.
If schools existed to provide food instead of education, they'd start by lining up all the kids at the beginning of the week and doling out a single crumb to each. And if those crumbs happened to be rat turds instead of crumbs of bread, they'd never notice. Every once in awhile, the school stumbles across the rare child that is starving, absolutely ravenous.
How long do you think it'd be before that child started to hate school?
> want smart teachers to take control of education so this s* doesn't happen nearly as often as it does.
Teachers aren't in control. They're prisoners of the classroom every bit as much as any child is. Maybe more so, they can't hope to be expelled or to flunk out or to graduate. Teachers will never be in control again, if ever they were.
>bright student realizes that school has nothing to do with learning
Depends on the high school and teacher. My high school (and primary schools) had really great teachers and they motivated me to learn things I otherwise would not have. Young people often need a push to learn things that they don't immediately see as useful. Schooling does interfere with learning, but when the stakes are high (getting into a top college) we might as well make the most of it if the privileges are afforded to us.
In the US, each student will have between 20 and 40 teachers by the time they graduate highschool.
Thus, you can't just hope to play the public education lottery and get all good teachers for your kid. Even if things work out better than could possibly be imagined, that's what, 10 or 15 good teachers, quite a few more mediocre and 2 or 3 bad ones?
Sorry. The damage that a bad teacher can do outweighs much or all of the good that the good teachers can do.
If your kid would have 40 doctors throughout his life, only 2 or 3 of which were quacks, would that make you happy? Would you say "but the quacks will probably be the dermatologist anyway and not the surgeon, so it's ok"?
I wouldn't say that.
The only way for any of this to work out is for the impossible to happen, for nearly all of teachers everywhere across the nation to be good teachers. The distribution is pretty natural, the various colleges of education don't act as a filter, and schools are co-opted to do too many non-education tasks for that to ever be possible.
> Sorry. The damage that a bad teacher can do outweighs much or all of the good that the good teachers can do.
> If your kid would have 40 doctors throughout his life, only 2 or 3 of which were quacks, would that make you happy?
I don't think this analogy is quite right, nor is the conclusion you are using it to illustrate. A kid, especially a smart kid, knows when a bad teacher is bad and can just coast through the class (bad teachers nearly always err towards teaching too little and therefore being easy).
The worst case scenario in most subjects is they have a hole there, which in the case of non-STEM subjects is not catastrophic because they (English, history) are more about general principles rather than specific facts that nearly all adults forget. In STEM subjects, it can be worse because they build on one another.
I guess a truly bad teacher can deny evolution or something like that, but that typically only happens in controversial subjects where a student should have prior knowledge that there's a controversy. If they aren't, they will figure it out soon enough.
But really, a bad doctor can kill you. A bad teacher leaves a hole that a self-motivated person with natural curiosity can completely fill. Take programming (I'll assume you're a developer). If one of your CS profs had just not bothered to teach a specific course, would you be able to live through it? Of course, as attested by the many successful developers who are self-taught. When you grow up, you have to take responsibility for learning for yourself. If some students have to do it sooner than usual, that has pros and cons.
> A kid, especially a smart kid, knows when a bad teacher is bad and can just coast through the class (
There are many sorts of "bad". Sometimes they're simply ineffective or uninterested teachers. Other times they're borderline mentally ill and abusive.
How many times does the child need to be mocked or called names for lasting damage to happen? Can you judge this before the fact? "Oh my boy Timmy, he can be called names at least a dozen times with no ill effects, and you look like you'll only do that 8 times, Mrs. Kuntzenheimmer."
> guess a truly bad teacher can deny evolution
Or lock them in a closet. Or tell them "girls can't do math" so many times they believe it, and roll their eyes derisively if any of the 9 yr olds object. Or fail them out of spite... or have them expelled without true cause.
Oh man, there must be a 100 different kinds of bad. And few children have the life skills to mitigate that (few adults, if we're honest).
I have a different perspective on this. School, especially in the later part of K-12 is many different things. There is a lot of bullshit, academically speaking. I'd say about 2/3 of my highschool teachers were pretty mediocre. Then there were the good ones. I actually liked studying math in high school because I got placed in advanced classes, and in a grade above my own. It provided a challenge, but also the teachers did a good job of explaining what I might use this math for: becoming an engineer or a researcher. The 10th grade algebra teacher actually had us do labs that would normally be reserved for physics classes: let's measure the swing of the pendulum and show that it's a harmonic oscillator empirically.
So I wouldn't say "I hated school", but I would say I hated my gym, art, and health classes for sure (don't get me started on sex ed. and I grew up in a fairly liberal state).
I enjoyed the learning part of school, apart from classes I had no interest in, and was terrible at.
The alternative to school currently is homeschooling, and, I do not feel that I would be able to teach my children the range of topics covered at school, and ensure they understood them, even with a university education in a STEM subject.
My role therefore is to pique their curiosity about life in general and the universe, and allow them to explore questions, and show them why the world is so cool. This then enables them to use what they have learned in school to form bigger questions and answer them themselves.
"If schools existed to provide food instead of education, they'd start by lining up all the kids at the beginning of the week and doling out a single crumb to each. And if those crumbs happened to be rat turds instead of crumbs of bread, they'd never notice. Every once in awhile, the school stumbles across the rare child that is starving, absolutely ravenous.
"How long do you think it'd be before that child started to hate school?"
I just wanted to tell you that was the-truth-that-hurts so much it literally made my eyes well up. I just... it's... sadness. Sickness.
This isn't just frighteningly ignorant, it ends up having a devastating impact on many young people. One anecdote: I knew a bright young student who loved learning, but hated school. Why? He took algebra and french in 8th grade; he passed algebra and failed french. When he got to 9th grade he was placed in algebra again, and french 2. The school would not budge from its original placement; I don't know the rationale. He failed algebra because he refused to do any homework, and failed french because he couldn't make any sense of the class. I want smart teachers to take control of education so this s% doesn't happen nearly as often as it does.
Sounds like passing a student with 80% grade, only with 60%. It's like passing a student who didn't master 40% of the content, and compounding it over and over again with each grade level, until eventual nothingness.
That's what it means to pass a student with a B, C, or an F. This is not quite the same thing as mastery of the subject, but it's a good proxy. Even an A student will miss some stuff.
I had a conversation with a math teacher from another school not too long ago. Both of our schools require a minimum of two credits of math to graduate. My school allows students to spread this credit out developing a deeper understanding of basic math, and beginning algebra. His school requires everyone to receive a passing grade in the equivalent of Algebra 2. The lowest passing score at my school is a B-; at his school it's a D-.
We have a reputation for being an "easy" school, so I asked him what the value of earning a D- in Algebra 2. His response: "At least they've been exposed to higher math." That's such an elitist answer, and it does such a disservice to students.
The interesting part of the story is that he started to question the value of a D- when asked in this way. He stopped comparing basic algebra to Algebra 2, and started comparing a B- in Algebra 1 to a D- in Algebra 2. It's an interesting comparison.
Sounds like your school is suffering from grade inflation. The average grade used to be a C. (At my college, it still was.) If you tell the teachers that a C is a failing grade, they will not give a C grade to a student who's doing an OK job in their eyes.
It's not grade inflation. We're a small alternative high school, and it's easier for us to do the right thing for students, even if it means going against existing bureaucracy. The smallest unit of credit in our traditional high school is 0.5 credits; at our school it's 0.25 credits. We grant passing grades for the parts of a class students demonstrate an understanding of, and grant partial credit for a class. This mitigates some of the issues involved with averaging over the course of an entire semester.
Usually, when someone earns a B-, they do have a basic understanding of the material they were learning. A student who earns a D- with 0.5 credit at the traditional high school will usually earn a B- and 0.25 credits from us. At the traditional school, they're "done" with that class. At our school, they've got to do something to demonstrate further understanding. It's not a perfect system, but it's not as simple as grade inflation.
Is it more useful for your grade to tell you how much of the topic you know in relation to the other students in your class (C = the average grade) or for your grade to tell you how much of the topic you know (A = you understand everything that was taught, B = you understand most of what was taught, C = you understand some of what was taught...)
If you fit an entire class on a bell curve and give out 1 A, 2 B's, 4 C's, 2 D's and 1 F but the highest grade was actually a 32% would those grades be useful information? Sure, the A student knows more than the C student ... but none of the students really understand any of the material.
Edit: by "how much of the topic do you know" I actually mean "how much of what was taught of the topic do you know"
Ie, if the teacher taught you how to graph a linear equation and you can graph a linear equation, then you should get an A. If you can't graph a linear equation, you should get some grade less than an A. If nobody in the class can graph a linear equation, then what use is it to give an A to the person who can't graph a linear equation, but does it less wrong than everyone else?
How much of the topic I know? That would be vanishingly small for any grade before college, and barely a blip for classes in my major at the end of college. No, I don't think that's useful.
'We have a reputation for being an "easy" school, so I asked him what the value of earning a D- in Algebra 2. His response: "At least they've been exposed to higher math."'
When you say Algebra, I assume you mean what most of us learn in pre-college schools? As opposed to what a mathematics major in college would call "Algebra"? If so, that's hardly even "exposure" to higher math, that's more just a demonstration that there is a such thing other than raw numeric arithmetic.
> That's what it means to pass a student with a B, C, or an F. This is not quite the same thing as mastery of the subject, but it's a good proxy. Even an A student will miss some stuff.
Grade might be a proxy for mastery in some situations but it's likely not in the majority. Grade is more often than not a combination of mastery, ability to take tests, willingness to do homework and an accounting of how often you show up.
I was working in a nightclub during my college years and I've met many, many people who loved learning yet hated school and dropped. There is an immense pool of potential being wasted out there.
I'm one of the lucky few who did drop out of school yet found a job as a software engineer on AAA games; the job I wanted since I was a kid with my first NES. I don't think having a degree would've made much of a difference other than wasting more years of my life and putting me even more in debt.
What made me get the job as well as keep it and rise faster in the company than those with actual degrees is finding the discipline to learn on my own every day and trying to understand how things work and why. In school I always felt slowed down by the rest of the class or by bad 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.
That's not necessarily true at all. It's a function of the difficultly of each question. Possibly it could be generalized to the difficulty of each test -- where perhaps the questions on the 50-question test were twice as difficult as the questions on the 100-question test.
The best way to resolve your concern is to never assign a percentage per test -- just assigned points to each question based on difficulty. Then accumulate points and take an average only at the very end. But, short of that, taking a weighted average of the two tests is not necessarily any more correct than just taking the average of the percentages.
I believe you might find this article very interesting. It is a discussion of how math education has changed over the years, and has strong words about the very problem you mentioned of the teachers being ignorant of math and passing that ignorance on to those they teach.
> My colleague pointed out that the questions on the 50-point test had twice as much weight as the questions on the 100-point test.
Actually there wouldn't necessarily be any correlation between the percentage of questions answered correctly and whether the students were making progress, and arguably that answer is even worse than just comparing the raw scores.
My friend's wife is an elementary school teacher and she's one of those really arrogant people who always has something more "intelligent" to say than everyone else.
She recently took over a project I was working on with her husband (my friend) so I've been emailing a fair amount with her. Her grammar is unbelievable for a school teacher. I mean, she doesn't know the difference between your/you're, their/there, then/than!
Imo, these results are not surprising (but sad regardless). There's similar studies in all fields. Economics is a prime example (with a couple of well publicized studies).
A little "closer to home"...I've listened to quite a few software developers who regularly A/B test and always implemented B if it had more whatever_unit than A. Significance be damned.
Statistics is pretty scary/best ignored on all levels I guess.
The very same thing happened in Portugal, where the Ministry of Education's guidelines for gauging teacher performance included taking the mean of a test graded in percentage points with another evaluation on a 1 to 5 scale.. by adding them and dividing by two!
Made even more embarrassing by the fact that the Minister is a mathematician.
Good example of out of context quoting of even a short post. He said it's not the teachers' job to have the type of control that the original poster was saying that teachers should seize.
He responded to a proposal that it should be with, depending on how you interpret it:
1) An assertion that it is not currently the case. (Probably true, but completely missing the point of a proposal)
2) An unsupported assertion that it should not be the case. (An unsupported opinion in response to a thought out opinion isn't adding much to the conversation. He may as well simply respond "No, your opinion is wrong." A better comment would explain why he has that opinion.)
My colleague pointed out that the questions on the 50-point test had twice as much weight as the questions on the 100-point test. One of the three other teachers realized their mistake - the other two just chuckled and said it didn't matter.
This isn't just frighteningly ignorant, it ends up having a devastating impact on many young people. One anecdote: I knew a bright young student who loved learning, but hated school. Why? He took algebra and french in 8th grade; he passed algebra and failed french. When he got to 9th grade he was placed in algebra again, and french 2. The school would not budge from its original placement; I don't know the rationale. He failed algebra because he refused to do any homework, and failed french because he couldn't make any sense of the class. I want smart teachers to take control of education so this s* doesn't happen nearly as often as it does.
Also, I've taught middle and high school math for 20 years now, mostly to students who struggle with math. I don't think I've had many groups of students who could come up with six different answers for a simple average problem.