kitchen table math, the sequel: new age education

Saturday, January 27, 2007

new age education

I found these nice circles with writing in them that are representative of educationist thinking about what's needed in education. It's hard to compete with the lofty rhetoric, especially when compared to the caricature of the alternative. It's also surprising to learn what is supposedly actually being taught, when I see constructivist stuff everywhere.


Tests are intended to ensure students have minimal foundational knowledge, unless they are watered down as is so often the case. Foundational knowledge is needed to achieve these ambitious goals. So railing against tests doesn't help the cause. If schools didn't waste so much time with discovery, there would be less of a need for cramming.

25 comments:

Catherine Johnson said...

aaaaaauuuuugggggghhhhhhh!!!!

Catherine Johnson said...

anthropomorphizing?

Catherine Johnson said...

This chart is delicious for me, because about the ONLY thing Christopher is learning in two years of Phase 4 math is "Short-term cramming."

He's not even picking up Useless facts or Outdated techniques.

Catherine Johnson said...

Oh dear.

This comes from Creating Passionate Users, a blog I like.

She's made the classic mistake of assuming that the mode in which experts work is the mode in which novices should work (and learn) as well.

You see this all the time with writing instruction.

Real writers do 'X'; therefore beginning writers should also do 'X.'

Of course in the case of writing educators' concepts of what real writers do is wrong, which compounds the horribleness of the instruction.

(Writing instructors seem universally to believe that real writers first construct detailed outlines of their entire work, then write the sentences & stick them in where they belong. I've seen "graphic organizers" based on this principle that made me feel faint.)

Why does engineering/math/science education in the U.S. suck?

Tracy W said...

Let's consider the list in the blue area.

"Short-term cramming" - this is a useless thing? This guy has never had to learn something fast in his entire working life?

I once got a call at 5.30 asking me to explain a piece of work my predecessor had done three years ago (and I'd never heard of). I did a presentation on it 10.30 the next morning.

"Useless facts". Notably, the guy has "Key facts" in the black area. Now, no one supports teaching "useless facts". But how do you tell which facts are useless and which aren't ahead of time? And for a class of perhaps a hundred students, who will likely pursue divergent lives.

"Outdated techniques" - every now and then people go back and look again at "outdated techniques". Eg neoclassical macroeconomics after the failure of Keynesian economics.

"Note-taking for test preparation." Ah, so this guy believes students will never need to learn something from another person once they've finished university. (I take notes several times a week for work).

"Problem-solving by recipe" is great. It means you can solve more problems faster. It's not like there's a shortage of problems out there.

"gaming the system" is always a useful skill (and how that's different from resourcefulness is another puzzle).

Tracy W said...

Hmm, now I'll consider the course in the red area against my engineering school (University of Canterbury, IEE and IEEE accredited).

Design - yep we did a lot of that.

Intuition - well, that comes with time. I'm not sure how anyone would teach it directly.

How to focus - yep, necessary if you're going to pass the course.

Multiple perspectives - yes. It was confusing for me for a while when I switched to economics and things like "zero" had absolute meaning. (Zero volts is just a reference point. Zero bread means you're going hungry. Big difference).

Curiousity - don't know how you'd teach that.

Visualisation - we did some tech drawing in first year. Plus all that graphing probably helps.

Ethics/social implications - ethics was covered. Social implications - how much time does this guy think students have?

Aesthetics - not covered.

Using metaphors - we're human. We do that since birth. Why not teach breathing while you're at it?

Learning theory - not covered. It's engineering, not education.

Wholistic thinking - huh?

Anthropomorphizing - amply covered for most NZ students by all those Beatrice Potter books and The Wind and the Willows and the like, long before anyone gets to engineering school.

Resourcefulness - as I said, heaps of design projects.

Practical applications - this is engineering school we're talking about.

Metacognition - not covered. Perhaps should be.

Storytelling - we're talking about humans here. What humans don't tell stories?

Instructivist said...

"She's made the classic mistake of assuming that the mode in which experts work is the mode in which novices should work (and learn) as well."

That classic mistake is an element of ed school ideology. In textbooks used in ed school prospective teachers are told that pupils should work the way historians and scientists work. Pupils are to be treated as young historians and scientists creating new knowledge. Foundational knowledge is not needed and valuable. Only newly created knowledge matters. This is the conceit.

These beliefs also inform the inquiry and discovery craze that has displaced foundational knowledge in science -- things like FOSS. Wherever I look, I see FOSS now. The Chicago school board forces FOSS on failing schools. The suburbs do FOSS. It's the sibling of fuzzy math and whole language.

SteveH said...

I looked at their web site. They are very "passionate" about their work and ideas. The problem is that passion and curiosity don't always get the job done, especially, as instructivist says, for the student.

On one hand they say that engineering school sucks, but then allow that many of them become good engineers. Life is tough when reality bumps into your hypothesis.

Tex said...

“If schools didn't waste so much time with discovery, there would be less of a need for cramming.”


This is a significant point for me because in our schools, and in many others, there is a lot of discussion about “teaching to the test”. Parents complain about so much time practicing for state tests, starting in 2nd or 3rd grade.

Part of the problem as I see it is the school spends about half its time in “discovery and exposure” and then the other half in preparing for the tests. Where’s the teaching?

Catherine Johnson said...

I once got a call at 5.30 asking me to explain a piece of work my predecessor had done three years ago (and I'd never heard of). I did a presentation on it 10.30 the next morning.

I love it!

Catherine Johnson said...

That classic mistake is an element of ed school ideology. In textbooks used in ed school prospective teachers are told that pupils should work the way historians and scientists work. Pupils are to be treated as young historians and scientists creating new knowledge.

Absolutely.

What gets me is that if we're going to base these ideas on looking what real scientists & mathematicians & writers actually do, why not look at how real scientists & mathematicians & writers got to be scientists & mathematicians & writers.

They weren't born scientists, mathematicians, & writers; they had to become these things.

How did that happen?

Why don't we spend five seconds taking a look at their learning process?

Catherine Johnson said...

Of course that would make sense.

Catherine Johnson said...

Part of the problem as I see it is the school spends about half its time in “discovery and exposure” and then the other half in preparing for the tests. Where’s the teaching?

good lord

that's appalling

SteveH said...

“teaching to the test”

Don't get me started on this. Either the material on the test is important or it isn't important. This implies that there are other things that are more important than making sure kids know the material on the test.

Actually, the material is so trivial that schools should laugh at these tests. There should be plenty of time left over to do whatever fuzzy, higher-order learning they want to do.

"Teaching to the test" is a huge copout for the education profession. If they don't like tests, just say so. However, even the fuzzies know how to give and grade tests, quizzes, and homework. They prepare their kids to take graded tests all of the time. They test the kids on the material they teach. They teach to the test. Their tests are no more trivial (at least they shouldn't be) than the state tests. What's the problem?

The problem is that they don't like standardized tests because they are also tests of the school and teachers. That's really what they don't like. Accountability.

Instructivist said...

"Teaching to the test" is one of those phrases the advocates of "critical thinking" repeat by rote.

"Actually, the material is so trivial that schools should laugh at these tests. There should be plenty of time left over to do whatever fuzzy, higher-order learning they want to do."

You can see sample questions from Illinois' ISAT math test for fourth grade here.

I love the comments in Extended-Response Student Sample 2C (p. 44) from evaluators for the problem on page 37 and the student's work on page 42.

The comment is:

MATHEMATICAL KNOWLEDGE 3 (out of 4)

This response shows a nearly
complete understanding of the
problem’s mathematical concepts
and principles. Drawing an
octagon with one side of
30 and seven sides of 10 meets
requirements of the problem.
However, the side lengths aren’t
labeled in feet.

Must see to believe it.

Catherine Johnson said...

Actually there's an excellent reason not to "teach to the test" even when the test is good, and that is that "teaching to the test" means random practice as opposed to coherent curriculum plus distributed practice.

Engelmann has some choice words to offer on this subject.

We are now entering Teach To The Test phase around here.

I printed out the 8th grade test; we're going to be doing brute force drill.

It's my only option, unless I want to drop everything and create a Brand New Life as a designer of New York State Grade 7 math curriculum.

Even then I'd still be using brute force because whatever I come up with would be a first draft.

So...I've typed up my list of STUFF Christopher has to know two months from now.

Now I'm finding problems in my gazillion workbooks.

It won't be pretty, but it might work.

Ben Calvin said...

The San Francisco public schools drop everything for a month or so and "teach to the test" before the state exams.

To me this indicates not a problem with the test, but with the curriculum taught the rest of the year.

I can't think of a better indicator to show that the subject matter covered on the test (i.e., the state standard) is not being taught effectively during the school year.

Instructivist said...

"I can't think of a better indicator to show that the subject matter covered on the test (i.e., the state standard) is not being taught effectively during the school year."

You can say that again.

The schools with fuzzy math are in real trouble to the extent that the state tests still have real math in them.

SteveH said...

I agree with Ben. My point was that school should always be about teaching to the test, meaning that you test what you teach. Every day should be about teaching important things, and the classroom tests should be testing those important things.

The pejorative use of "teach to the test" either means they don't think that the material on the test is important or that they did a poor job of teaching the kids in the first place.

I looked at instructivist's Illinois ISAT link for 4th grade math. Why would a school need to take a month to cram this material? Because they didn't do the job right in the first place.

In our state, it's even worse. They took a proactive stance about "Standards-Based Education" and got involved with writing the test. The result is that the education community defines the philosophy, the methods, the content, the test, and the grading cutoff. No outside force is doing anything to them except tell them that they have to test and that most all kids have to pass some minimal cutoff point that they define themselves. STILL, many complain. Our standardized tests are created AND the grading calibrated by teachers.

A big problem is assumptions. They want to keep all ability kids of the same age together. You can't do this if there are specific things kids have to know in each grade. They think that if kids don't learn the material, it's because they aren't ready for the material, not because they are teaching poorly or that the kids need clearly-defined expectations of content and skill mastery.

Full inclusion leads to being very lazy about expectations. It's always easier to expect less.

Instructivist said...

"I looked at instructivist's Illinois ISAT link for 4th grade math. Why would a school need to take a month to cram this material? Because they didn't do the job right in the first place."

My rough estimate is that half the questions are non-math (visuals) or minimal math like counting up to ten. Then the cutoff is probably 40%. So you don't even have to answer all non-math questions to pass. Still, most fail in this urban setting here.

Barry Garelick said...

A good test will result in teachers teaching the underlying concepts skills and facts that will enable students to be able to solve the problems on such test, rather than teaching how to solve particular problems. I.e., teaching students "When you see this type of problem, do A, B, and C., etc"

Interestingly, Fairfax County gave a state test (called SOL for standards of Learning) in math for 6th grade for the first time last year and newspapers reported that alarming numbers of students failed the test. Excuses included that teachers weren't shown the type of questions on the test, so couldn't prepare students adequately. On the other hand, when they released the questions, it was a perfectly reasonable test; the questions weren't too hard. In fact, if anything, it pointed up the fact that perhaps other SOL math tests were too dumbed down,raising other questions.

SteveH said...

"(called SOL for standards of Learning)"

Hee,hee,hee! Oops. It's not funny. I guess the students are SOL. I can't believe they chose that acronym.

Put Everyday Math next to Singapore Math. Show the exact tests to parents. Explain the exact cutoffs. Seeing is believing.

"On the other hand, when they released the questions, it was a perfectly reasonable test; the questions weren't too hard."

Did your papers pick up on this point? In our state, it goes like this. They give the test and look at the results. They're bad. The assumption is that there can't be a fundamental flaw in education. It has to be for lots of other reasons, like money, class size, external causes, you name it. The goal then becomes small relative changes to a problem that has fundamental issues.

LynnG said...

You all don't do Rallies? I can't believe we are the only state that does a pre-state test Rally!

Check the school budget and look for this new line item.

School districts can purchase a "Rally" from an outside vendor that will prepare a mock state test, provide materials to teachers, and then grade it so you can see how many of your students are in trouble.

It's ingenious. We spend a small fortune for curriculum, we purchase all the state test materials for the actual test, and now, despite a huge number of released items freely available (plus a highly trained crack teaching faculty) we must PAY for mock testing in November to get ready for the real thing (which we also pay for) in March. This whole state testing thing is really boosting the state economy around here.

PaulaV said...

Barry,

Hello neighbor! I live in Loudoun County. My son is in third grade and is gearing up for the Virginia SOL. I don't recall reading about the Fairfax 6th graders and the SOL. Was that in the Washington Post?

Catherine Johnson said...

School districts can purchase a "Rally" from an outside vendor that will prepare a mock state test, provide materials to teachers, and then grade it so you can see how many of your students are in trouble.

good lord