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It is a bit sad that things like:

> The problem with mass-produced textbooks, Engelhaupt explained, was that they can cost $65 each and aren't aligned with Minnesota's math tests so the district would be paying for whole chapters that are never used.

and

> She said most high school textbooks are written to the requirements of Texas and California, the two biggest markets for the book publishers. It means often a third of the books go unused in Minnesota, she said.

appear to be the current state of things. Instead of targeting a good education in the subject, the norm today seems to be to teach k-12 students to pass the aptitude tests, not necessarily to learn the material itself.

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But isn't that... test-driven design? ;)

I mean, if the tests have 100% coverage, there's no problem with the education only covering what's on the test, right? It just means kids have to sit through exams that are perhaps eight hours long.

(Which is fine, really, if those exams get split up so that they're given one exam per unit, rather than one humongous state-wide test. And while they're at it, if those exams were also, say, given online, accessible at the student's whim, and able to be repeated indefinitely without penalty (because of some form of procedural question generation), they could even be used as gates to determine when the student was ready for the next level of material...)

This is kinda how Montessori schools do it - at least the one here where my partner teaches. They aren't online, but the student gets to chose to some degree what they are working on, however they can only move onto the next level of a subject once they've passed the 'works' that come before it. The grading of a work involves marking problems correct and incorrect. Note that this is 1st - 3rd grades

What you are describing in your last paragraph sounds a lot like Khanacademy...

Agreed. If the kids are being taught the wrong things, you don't get pissed at the teachers- you change the standards/tests. Same as with any good software!

I think the problem is that students should be taught to think, not to pass tests.

I was taught to think, not so much by school but by a select few teachers and especially my father. I learnt metric growing up. When I started construction everything was done in millimetres and meters. I moved from the UK to Canada, where the construction trade is solely imperial (it's not like the UK where you can get legacy tape measures that have inces and meters, I have inches and feet) and I didn't struggle. It was about a month before my boss said "Doesn't the UK only use meters, are you coping with the change?"

Of course I coped, I learnt to think. A foot is a generalised measurement so that multiple people can work to the same measurements. A meter is a generalised measurement so that multiple people can work to the same measurements. If someone calls out to me "cut at 1321mm" I cut at "1321" the same as if they'd just called "cut at 52 inch".

I've seen guys, high school graduates (in the UK I only did high school until I was 16, and the newbies I get given did it until they were 18) and they're confused by the mere notion that an inch is divisible up to a 16th on a tape measure.

I personally cannot comprehend how they don't understand. How lacking is your education that you can't find 9/16ths on a tape measure? How lacking is your education when you can't cut a 22.5 degree angle from a 16x16 square (measure up to the half way point and trace a line to the 0 point giving you the desired pattern)?

My work doesn't even require a high school education to get hired and we've had some phenomenal employees who failed high school. The irony is we get bucket loads of retards who graduated high school.

There's a big difference between learning and merely storing data. The problem is that we're creating a generation of databases. I'm sorry, but I have computers, and phones, and fuck a pocket book that can retain data for me. I don't need a million kids to do that. I need a kid that can read a tape and cut an angle so that I can train them.

I don't know how I'm supposed to train someone who's passed high school that should so obviously have failed.

Sure they should be taught to think, but do you have any good ideas on how that should be done?

Tests are used because a metric is useful for identifying weak schools so that they may be improved. Do you have a better metric?

Arguments for, or against, a topic chosen at random. Submitted as an essay, and graded by at least two independent readers. It may not scale, but it's a better metric.

So you learn how to game essay-writing competitions. Big whoop. The most brainwashed people I know are arts graduates, who think they know "how to think".

In reality, they know how to use hollow rhetoric to make a convincing case for their own prejudices, and present straw-man arguments to pretend you've covered both sides of an issue. They also find some way to "twist" the question, if it's easy.

The most important part of essay writing is not to be a perfectionist, and try to think too much. You come up with a few points (supported by examples, augments, or references - depending on the requirements), throw in some formulatic meta-discussion (i.e. '... though it may be more important to ask "why", not "if" ...') and get the fucker done. Don't worry to much if you're right or not, just make the bloody sausage. Oh, and try to predict what the markers (generally soft-left yuppies, who went from school to college back to school) will want to hear, or will get their attention - they have dozens (or hundreds) of similar papers to read and do not want to think.

My point isn't that essay writing is necessarily harmful. It's just another mostly useless technique to learn, and probably adds up to something if you can mix it with other techniques, and a little knowledge.

I'd say it takes a lot more thought to game essay-writing than it does to game multiple-choice.

The angle from the origin to the point (2, 1) isn't 22.5 degrees – it's arctan(1/2) = 26.6 deg. In fact, the slope of the point you want should be sqrt(2) – 1 = 0.414, not 0.5.

> I think the problem is that students should be taught to think, not to pass tests.

No one disagrees.

However, saying "students should be thought to think" is useless. We need to know to if they're being taught to think.

And no, "trust teachers" doesn't work. The testing fetish is a response to generations of kids who can't think taught by teachers who said "we're teaching kids how to think".

Are there bad tests? Yes. Are there perfect tests? No.

But that doesn't imply that testing is unnecessary. It just says that testing is hard.

"The testing fetish is a response to generations of kids who can't think taught by teachers who said "we're teaching kids how to think"."

Funny, I thought it was driven by too many politicians who'd taken management 101 and learned to "measure everything". Do you have a cite? (Honestly wondering).

The only way to administer tests at scale is with multiple choice and number 2 pencils. The easiest way to pass a multiple choice test is to memorize a bunch of crap and not bother thinking.

I'm not saying that all testing should be abolished, but it's pretty clear that testing is insufficient -- any real learning-to-think that goes on with a testing-dominated system is going to be the product of teachers going above and beyond, and totally unmeasurable so those teachers will never be rewarded (and probably punished).

"The only way to administer tests at scale is with multiple choice and number 2 pencils"

I think that there's an alternate way, but it comes at a cost: we have to de-standardize the tests. Here's how I see it playing out.

Jill is an eighth grade match teacher with thirty students in her class. When testing time comes around, she writes an exam for the state which she feels represents what an eighth grade math student should know. She sends a copy of the exam to the state. In return, she receives thirty different exams from the state, each written by a different teacher and assigned to exactly one of her students. She distributes the tests assigned to each student. At the end of testing, she sends back the completed exams. In return, the state sends her thirty answers to her exams, which she grades as she sees fit. Finally, she sends her grades in to the state.

The state then looks at how Jill's student performed on the assorted exams that they were given. The raw score isn't at issue, but rather how they performed compared to the other students who took that specific exam (e.g. how many standard deviations that they were above or below the mean). If most of her students scored above average, we're happy. If most of her students were below average, we question why.

Since the teachers don't know what will be on the test, they can't coach the students to memorize answers. Thus, the teachers who teach the students to think and handle unfamiliar situations will be rated higher by the test than students who simply regurgitate what their teacher taught them.

That's kind of brilliant, although I could see it being a clusterfuck in actual implementation, 30 isn't enough per-test to get meaningful statistics for one thing.

It also involves a total lack of control from the top-down, so it'd probably be resisted pretty strongly. I really like the basic idea, though.

> I think that there's an alternate way, but it comes at a cost: we have to de-standardize the tests.

Why do you think that "standardized test" means "same questions for everyone"?

Also, we're actually not that interested in the score at the end of the year but in the difference between what the kids could do at the beginning and end of the year.

>> "The testing fetish is a response to generations of kids who can't think taught by teachers who said "we're teaching kids how to think"."

> Funny, I thought it was driven by too many politicians who'd taken management 101 and learned to "measure everything". Do you have a cite? (Honestly wondering).

You haven't seen the "Asian kids are doing better" and "schools are failing" stuff? Really?

> The easiest way to pass a multiple choice test is to memorize a bunch of crap and not bother thinking.

How would "memorize a bunch of crap" work for an algebra test? Unless "crap" means "rules of algebra and how to apply them"....

How about three examples of this "learning to think" that can't be measured with a test? (Skill in playing a musical instrument is arguably one, but mostly at the extremes. However, ranking Carlos Santana vs Jeff Beck isn't the problem.)

I suspect that your definition of "test" is too limited, which says more about you than it does about testing.

"I think the problem is that students should be taught to think, not to pass tests."

OK. How do you propose to determine whether a student has been taught to think? Whatever your answer is, that's your test. Maybe it's questions like "build me a catapult with these materials and tell me how efficient it is" or "explain how so many Latin words came to be part of the English language and give examples". Answering those would demonstrate thinking ability. But that would still be a test.

Tests are important. If they are made well, teaching with the test in mind is fine.

Whether we're testing and teaching the right things is another question. But "students shouldn't be taught to pass tests" sounds to me like "buildings shouldn't be built using blueprints." How can you know whether you've succeeded if you have no stated goal or way to measure results?

I think every tape measure I have ever seen in Canada has had both inches and metres.

"I mean, if the tests have 100% coverage, there's no problem with the education only covering what's on the test, right?"

No. There are many books on the problems with high-stakes testing, and covering the 'right' material is only one out of many issues.

So what are the other issues?

Way too many to list. Also, there are many different types of standardized testing, and each has its own set of benefits and drawbacks.

If you want to read a more intellectual take on the issues with high stakes testing, Alfie Kohn has some good books on this. If you want to know the specific problems with No Child Left Behind, then Diane Ravitch's new book probably does a good job explaining it. But it's difficult to really understand the issue without reading a lot of different books on education in general, since testing by definition is designed to enforce its own normative preconceptions.

the root problem is that school funding and teacher's reviews are linked to the students' performance on standardised tests. another significant problem that this causes is that teachers who work with the kids who most needed it are harshly penalised by the way the metrics are structured (e.g. someone working with troubled kids from poor backgrounds, who manages to raise their standardised test scores from an F to a C, and, more importantly, taught them how to learn, will still be rated far worse than someone who has simply drilled a classroom full of bored upper middle class kids till they can do well on the tests (whether or not they have actually learnt anything))

this article, for example, is a good read on the subject: http://blogs.scientificamerican.com/guest-blog/2011/06/27/ed...

I don't understand funding based on performance on standardised tests. I mean it's one thing if you double-blind it, but who wants to be the parents of the kid in the control group who get zero education to see how well the teachers actually improved their students abilities.

The only reprieve I have for standardises testing in the UK was that a teachers opinion of you doesn't reflect on your ability to get grades. I was a d-average student in one of my classes. I never got marked well for my essays, etc. I took the exam expecting failure and received a B, comparing with friends I found I was only a few marks short of an A. The teacher never liked me, because he never liked my brother, because my brother was a cocky asshole. If I'd have been graded by him, I would have failed.

...someone working with troubled kids from poor backgrounds, who manages to raise their standardised test scores from an F to a C...

Such a teacher will receive a very high score according to most modern Value Added Modelling assessments (such as the one the article complains about).

In fact, it's the teachers of upper middle class kids who are hurt the most by VAM. If the VAM predictor says your student average should be 95/100, it's hard for your students to beat that by a significant margin.

Well at some point you are always teaching to a test of some sort. If I teach my students about X I will test them on X (either through extended pieces of work or through tests and exams) and not Y.

The trouble with many texts is that they aren't tailored to any particular course (mainly I imagine because courses vary so greatly even within countries). This is why it's really great to see lots of resources like Khan Acadamy out there where things are more focused on concepts rather than courses and you can pick and choose what you need to learn about.

One of the problems with teaching that I've seen since I started is that many people produce their own sets of resources, but there's very little sharing going on when you consider the total population. Considering the networks of really knowledgable people out there, we really don't need textbooks; we just need smart people willing to collaborate more and the technology to make that accessible.

Edit: With some afterthought, some of this is probably a systemic problem with the bureauracy which has large scale contracts with publishers and so on, and thus little interest in using the resource they already have (ie their teachers).

When implementing some new courses here in Westeran Australia the department of education implemented groups of teachers to produce sample material, but it wasn't particularly well funded or promoted nearly well enough to make it very successful, and it was only accessible to other government schools and not independent and religious schools (Catholic, Anglican systems etc). It would have been nice (and completely surprising) for the systems to work together or set up an independent body to manage something like this.

I'm curious what is so different in Texas and California math where a full 1/3 of the curriculum is different? Is it manifest in the difference when these students get to colleges?

I'm not sure, but it could be that the math text books are just plain bad. I did a rant about this a few years ago when a friend was homeschooling her kids: http://boston.conman.org/2004/01/21.1

Beautiful!

Great Feynman quotes!

Its the third that's bible-based maths. :-/

Why is the material taught different? Surely all kids should need to learn the same information.

Why is Minnesota cutting out so much of the math that California and Texas teaching? The students often end up going to the same colleges, where they will need to do the same work?

Off the top of my head: could be a breadth/depth thing, could be that the books are a union of California and Texas (in which case CA and TX also have the problem of unused chapters), or it could be that the time not spent on those chapters is spent on something that MN brings in with supplemental reading already or just teaches without a textbook.

It almost certainly isn't just that MN is a simple subset of the CA/TX material, or else the Byron district's scores wouldn't have gone up from the new material.

Perhaps Texas only teaches addition, California only teach subtraction - they used to also include multiplication and division but the kids tested poorly on those and it was dragging the grades down.

I went to school in Minnesota, and I think I know what they're talking about, at least when it comes to the math curriculum: we never had a trigonometry class. Sure we learned trigonometry, but it was never a dedicated class. Instead it was always a unit attached to what we were currently working on, whenever it made sense.

End result: we learned the same material, just in a different order.

Why is the material taught different?

States are the ones responsible for picking what material to teach their children. This is why material can be different.

There is so much that we could teach our children, there isn't a clearly defined set of "This is what is best to teach them", so different people will produce different sets of things to teach. This is why material is different.

Because no one actually knows exactly what the best things to learn are for human beings. Plus, it's constantly changing.

Secondly, different teachers have different experiences and teach differently. We're human!

How could it be the same? The only way I see is to remove as many human elements as possible (teachers most notably). Are we headed that way?

I suppose (well, hope) that the point of these statements is that their curriculum differs in some aspects. Maths (like all topics in school) is too wide to teach everything, so they had to pick their battles.

The 30% that aren't covered in the mass market books have to be provided by the teachers as additional material, while 30% of the books are not used in school. For $65, I'd expect more, too.

On the upside: Assuming that the additional material isn't provided centrally, these teachers who wrote the book have more exposure to writing course work than their colleagues in Texas, who get optimized books.

I think it's great that these teachers are taking initiative to make up for the system's deficiency (i.e. expensive textbooks targeted towards the biggest markets). However, I agree with this - I would hope that the goal would be enhancing learning, understanding, and appreciation of the subjects as opposed to passing the standardized tests. Granted, the two are not exclusive, but I think focusing on the first is more likely to lead to the second than the other way around.

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