Minnesota demands that juniors pass a demanding math test to qualify for graduation. Or they can flunk three times and get a diploma. Rather than drop the questions, which really are difficult, and write easier ones next year, the Legislature decided on the three strikes and you graduate plan.

Via Education Gadfly.

I applaud their honesty in doing this rather than continuing to make the test easier until the desired pass rate was achieved.

-Mark Roulo

This really is a goofy deal, and it illustrates the poor judgment of the people who put these tests together and mandate that everyone must pass them. Our math teachers say that this really is a tough test and it requires that a student master Algebra II to pass it. It’s easy for someone living in an ivory tower to think that that’s the way it ought to be, but I can tell you one thing: Those people in those ivory towers have never worked with my Basic American History students or even with some of my lower end regular American History kids. I might not be a math teacher, but it’s not too hard to figure out that there are some kids who will never pass that test.

This is true for almost any test with a cutoff.

Charles Murray has recently (last few years) pointed out that:

1) Typically, the spread of talent/ability is *wide*. Consider the athletic ability of the worst 10% of students in a school (or state) compared to the best 10%. Same for music. Academic subjects like math and literature have the same spread.

2) To get a 90% pass rate on a test, you need to set the cutoff point low enough that 90% of the testees can pass. This is math, not ideology.

3) The people who are paying the most attention tend to be at the top end of the scale in academic ability.

Because of (1), it is not unreasonable to expect that the senior year kids in the bottom 10% of a *state* in math will be several *years* behind the average (and the top 10% may be several years ahead of the average).

Because of (2), you will then need to set the pass level at several years *below* grade level if you want 90% of the kids to pass.

The people who are constructing and calibrating exit exams thus have two very unappealing choices:

A) Make the test appear to be embarrasingly easy to the people who are paying attention. *These* people do just fine when trying to perform at grade level. Setting the test several years below that seems absurd, but will allow 90-95% of the students to pass. Or,

B) Set the test at about grade level and expect to see some large percentage (30%? 50%?) of students fail it. The percent who fail will depend on the cut off point.

If (1) and (2) hold, there just isn’t any way around the choice between (A) and (B).

-Mark Roulo

Mark–a wide disparity between top and bottom is not a given. Finland and Canada (just to name two) illustrate both high average performance and a smaller than average spread from top to bottom on international tests.

It may not *have* to be this way, but in the US today is *IS*. I don’t see this changing any time soon either.

So, yeah, things might be different. But they aren’t, so in the US we still get to choose between (A) and (B) or somewhere in the middle.

-Mark Roulo

Margo/Mom…

Mark didn’t give an absolute size for the range of ability. In essence, he’s describing the normal distribution (the ‘bell curve’) and it does in fact apply.

The width can vary between populations, and excellent education can (but rarely does, in the United States), skew the curve. Modern U.S. education, sadly, tends to skew the curve to the left.

True, but I was trying to convey that the spread was “large enough to matter.”

I’m also trying to avoid a discussion on whether the ability is inherent/innate/genetic/whatever. My point is simply that the ability of high school seniors to do, for example, math:

1) Varies, and

2) Varies a lot [my example was maybe 4 ‘grade levels’ between the top and bottom 10% of students in a state]. This would work out such that the best 10% of high school seniors were taking Calculus and the worst 10% were struggling with Algebra. Since the worst 10% have probably dropped out by senior year (and, my guess is that they weren’t doing so hot at math, either), this seems reasonable. Calculus to struggling-with-Algebra is a 4 year spread.

Actually, my point doesn’t depend on the shape of the underlying distribution, only the fact that it is “large”.

Also note that one can have a normal curve, but with a small standard distribution. In this case, there is no nasty tradeoff between (A) and (B).

-Mark Roulo

Let me put it this way. Even though I teach social studies rather than math, I am constantly getting opportunities to see kids thinking skills at work and to see them handling complex information. Some kids are really, really poor at this. I have to believe that handling any upper level math courses would be nearly impossible, unless like Mark indicates, the class is watered down to the point where it’s not really upper level math anymore. Do we really want to set up a system where those kids can’t graduate from high school even if they’re making a reasonable effort? I don’t think that’s a good idea.

Yes. They may be great at plumbing, or carpentry, or selling things, but dealing with lots of complex, abstract information just isn’t their strong suit.

We probably don’t, although we are heading that way (as a society).

But … and there *has* to be a “but” or there isn’t any problem … if we graduate the kids who are making a reasonable effort, but don’t know “the material” (for whatever we define as “the material”), then what is the H.S. diploma supposed to mean?

*THIS* is the problem:

How do we construct/define a H.S. diploma such that we don’t exclude some large percentage of kids who are below average (like about 1/2 of them will be) at dealing with complex, abstract information, while not turning the diploma into something that people complain “means nothing?”

I think that there are solutions, but as a society we aren’t going very near to them.

-Mark Roulo

We could (but won’t) return to the system used with great success in past years, where there is a “academic” track and a track aimed at those whose skills do not match the abstract thinking, symbol manipulation skills.

But as long as we pretend that all of us are above-average in academic ability we won’t, and we’ll continue to waste money failing to teach those who lack those abstract abilities.

This is not a new problem…I learned in the early ’60s that a High School Diploma was no guarantee of ability to do simple arithmetic. But today it all too often fails to indicate any degree of functional literacy or numeracy.

I don’t know that the questions are particularly difficult, but #3 is wrong on its face.

The equation for the height of the ball above the ground after

tseconds is:h = -20t2 + 20t – 2

I think it should be:

h = -20t2 + 20t + 2

At time t = 0, we know that the ball is 2′ above the ground, so the last term has to be + 2, not – 2.

If this is the way the test was administered – and I really hope not – then the authorities did a very poor job.

Ragnarok,

I checked and found that it is correct on the test itself. The Star Tribune goofed.

Diana,

You’re right.

These are relatively easy problems, at least in comparison to the O-levels.

Mark, I don’t know whether you’ll come back and see this, but I think a high school diploma should indicate work the student did rather than what the student supposedly now knows. Shouldn’t kids with legitimate and significant learning disabilities be able to earn high school diplomas?

Saying that a high school diploma should indicate that the student “knows” a certain body of knowledge sounds good, but is it really practical? I use a lot of basic math for various things, but I certainly don’t use high level math even though I passed those classes back when I was in high school and one class when I was in college. Give me the test our state is having our kids take now, and I’ll be in the hurt tank. Does that mean they should take away my high school diploma?

No.

I don’t think anyone is proposing that the H.S. diploma be something that gets withdrawn if one doesn’t keep one’s skills current.

Now for the more interesting bits!

I’d like for kids with learning disabilities to be able to earn a H.S. diploma.

I’d also like for the H.S. diploma to “mean something” other than a certain number of hours of “seat time” plus “tried hard.”

It is the tension between “means something” (e.g. knew Algebra at the time of graduation, or could write a coherent 1,000 word essay at the time of graduation) and “significant learning disability can earn diploma” for which we as a society don’t have a solution.

While I do *NOT* think that the only point to a H.S. diploma is to help one get a job, this is one aspect of it.

Except that today a H.S. diploma doesn’t signal much that is of value to an employer. This is one reason (of many!) that kids who don’t belong in college go there … they are trying to get a piece of paper that indicates that they are worth employing.

So … we wind up back where we started:

*) Easy to pass, almost everyone graduates and the diploma is seen as close to worthless.

*) Diploma “means something”, but lots of kids are unable to earn one.

I am actually *FINE* with either choice … but this is a cop-out because my kid will be going to college no matter how we define a H.S. diploma. In a very real sense, I just don’t have a dog in this fight.

We are, however, as a society going to be making a tradeoff between the kids in the bottom 10% of the ability level being able to earn a H.S. diploma and the diploma signaling a specific, moderately high level of skill/talent/ability/whatever. We just can’t have both (or, at least, I don’t see how we can have both).

Do you see a way out of this tradeoff?

-Mark Roulo

Mark, I think high schools should demand that students be responsible (consistently show up for their classes and show up on time, bring their materials, etc.), be at least somewhat conscientious (consistently do their assignments, make some effort to study for tests), and make reasonably good use of their abilities. I believe there is real value in those things, and I think a high school diploma should mean that a student has done those things. A student who has done those things might not end up winning any Nobel Prizes, but he or she will be capable of making positive contributions to our society even if their scholastic ability levels are not very high.

And you might not have a dog in this fight, but it’s fun to be bantering with you again!

I think we need to recognize that those kids who are not REALLY deserving of a diploma, either academically and/or behaviorally, are very likely to have problems that go back to their first few years of school. High school is not the only problem; k-8 is creating seriously unprepared kids. The exception would be those kids who come to this country as teenagers, with little or no prior education and poor-to-nonexistent English.

I think the 8th-grade algebra is a fine standard for college-bound kids, but not for all. We need to do much better by those kids whose ability and/or inclination is much better suited to a good vocational program. Of course,some of those kids, especially those going into building trades and medical fields etc, would definitely benefit from solid algebra/geometry skills, and should be able to take as much math as they wish. I’d be happy if the basic graduation standard was solid knowledge of the manipulation of fractions, decimals, percentages, interest etc. Right now, large numbers of kids don’t have that. For the rest, everyone should be able to read at newspaper/news magazine level, understand basic civics and history and write well enough to do well at sbusiness letter/job applications/resumes//giving directions etc. There could be an honors option, with higher test standards (different test), for those who so choose.

We also need to realize that some kids will never be able to pass a significant test, despite all the touted glories of mainstreaming/differentiated instruction/diversity/group projects etc. Some kids should not be in an academic setting at all and some should be in programs aimed at basic life skills and entry-level job preparation. I know several such people, whose parents chose to send them to a special-ed school (now closed, of course) and who have been doing well in the workplace ever since. Their parents recognized that their needs would not be met sitting in a room listening to other kids discuss Shakespeare or algebra.

Quoth Dennis Fermoyle:

Maybe that’s the wrong question. Maybe there should be different grades of diplomas with levels of achievement listed, and those students’ achievement in math should be given as “below basic”. Different regular and honors diplomas would be good too.

College is an extremely expensive and often wasteful way of getting a meaningful credential, and the more we can eliminate the need for it by going back to what a diploma used to mean, the better off we’ll be.

I think that Engineer-Poet has the best solution, and incidentally the one now used by the HS I attended. I don’t know the exact details, but basically there is a “Basic Diploma” and an “Academic Diploma,” with different requirements for each.

But even when I attended school with one diploma, there were signals available to separate those who took challenging classes from those who attended. Being an “honors” graduate was the clearest signal; in those days before AP classes were offered at the school, certain classes were designated “Honors Classes” and the GPA number for that class was increased by one (i.e., an A in an honor class was worth 5 points, a B worth 4, etc.). The main purpose of this scheme was to deter people interested in college from getting a “perfect” 4.0 by taking home ec and consumer math instead of trig, physics, etc. Consequently none of the honor graduates (top 10%) had a GPA below 4.0.

Momof4, I agree with you. Not everybody is geared for the academic route. Yesterday, I went to breakfast and was waited on by a girl I had as a student last year. As a student, she was horrible. Her academic ability was low, her effort was minimal, and her bahavior was horrible. As a waitress she was wonderful, and I told her so. Putting that girl into some sort of work program would make a thousand times more sense than telling her she must take Algebra II.

I think the 8th-grade algebra is a fine standard for college-bound kids, but not for all.So you think that kids should be knocked out of the option of going to college by 8th grade?

I am in favour of vocational training. But people change their mind all the time about what they want to do in their lives – and the one thing I know that prevents the most people from doing what they want to do is a lack of sufficient maths preparation. One of my parents’ friends left high school at age 15, got a job at the post office, one year later chucked it in, over his father’s objections, and went back to high school (had to sell his motorbike to do so as his father refused to fund any more education), now is a scientist. A friend of mine did his technician engineering qualification (non-uni) and now wants to do his bachelor of engineering, and is having to go back to high school for some more mathematics. My mother burned out of maths at age 15, and avoided it right through uni, until she needed some help with her honours year thesis, and met Dad, but she found herself needing more maths when she started a business with a friend even more maths-phobic than her.

Plus the advantage of taking algebra is that practising algebra helps engrave arithemetic more and more deeply into your brain, without the dullness that sheer drill entails. In Dan Willingham’s book “Why students don’t like school” he presents evidence that what matters for long-term retention is practising something beyond the point of knowing it. On page 89 of the book he shows a graph of how much people remembered of algebra, given the number of intervening years since they’d studied it, the lines in the graphs are broken down by how many maths courses the people had taken. The people who had taken maths courses beyond calculus didn’t forget their algebra. Even 55 years after their last maths course, they still remembered as much algebra as people who had taken their last maths course 5 years ago.

Meanwhile students who had gotten an A in algebra and then never taken another algebra course again forget algebra as quickly as students who took a C and never took it again. They remember more at any given year, because they knew more to start with, but the forgetting curve is there.

This indicates that if you want students to be able to do arithmetic like percentages, fractions, etc, 10 years after leaving school they need to keep practising it. And what’s wrong with teaching them algebra as a way of maintaining attention while getting the practice in?

“So you think that kids should be knocked out of the option of going to college by 8th grade?”

Taking Algebra in 9th grade does not eliminate the college option. I took it in 9th grade and did well in it, eventually “acing” calculus in college, and ended up getting my BS in Finance and Economics.

Dennis hasn’t said that it should not be offered. He’s pointing out (I think) that *requiring* it is a ‘whole nuther kettle of fish.’

-Mark Roulo

Sorry Lori, I misread the words “college-bound” and thought that if you weren’t doing algebra in 8th grade you weren’t going to be able to go to college and do maths there. My mistake.

Mark Roulo, I think that algebra should be required because there’s always the chance that a kid will change their mind later on and want to do something that requires the maths background. Also, doing algebra means repeating the more basic maths skills, which looks to be valuable for long-term retention of those skills.

Okay … but required in 8th grade??

[Yes, I realize that 8th grade algebra appears to be what the rest of the world would consider to be a remedial track, but the US has typically had algebra in 9th grade for a long time … do we think that moving it up a year will create *more* success for kids doing math? (Actually, it might if the main problem was that the kids were bored … I don’t think this is the primary problem).]

I’d be very happy to see 9th graders consistently learning algebra well.

-Mark Roulo

Oh, Okay Tracy. And I agree with you that Algebra should be required for high school graduation for any student… for the reasons you state, and also because it seems to help a student think logically.

I’m sure I’d be in the minority on this… but for the same reason, I’d also require at least a semester of Geometry (with proofs, not the watered-down “integrated” geometry at our local high school) for every student, not just the college-bound.

If you required geometry, I suspect that you would find that a large fraction of the US population cannot handle the required abstract thinking.

Yes, I’m cynical. But am I cynical

enough?