Education: No Iron Triangle

I came from the corporate world, which invented the project management triangle. (“Fast, Good, Cheap: Pick Two.”)

Education has no triangle.

Money, of course, doesn’t work. Just ask Kansas City. Or Roland Fryer, who learned that kids would read more books for money but couldn’t seem to produce higher test scores for cash. Increased teacher salaries, merit pay, reduced class size are all suggestions that either don’t have any impact or have a limited impact….sometimes. Maybe. But not in any linear, scalable pattern.

“Good”? Don’t make me laugh. We don’t have a consensus on what it means. Most education reformers use the word “quality” exclusively to mean higher test scores. Teachers do not. Nor do parents, as Rahm Emanuel, Cami Anderson, Adrian Fenty and Michelle Rhee have learned. Common Core supporters have had similar moments of revelation.

So until we agree on what “good” is, what a “high quality education” means, we can’t even pretend that quality is a vertex of education’s triangle, even if it existed. We could save a whole lot of wasted dollars if people could just grasp that fact.

Time is an odd one. We never use the word directly, but clearly, politicians, many parents, and education reformers of all stripes believe we can educate “faster”. Until sixty years ago, calculus was an upper level college course. Once the high school movement began, fewer than 3% of students nationwide took trigonometry, between 10-20% took geometry, and the high point for algebra was 57%–over one hundred years ago–then declining to 25%. (Cite.) One of the little noted achievements of the New Math movement was to alter the math curriculum and make high school calculus a possibility. At first, just kids with interest and ability took that path. Then someone noticed that success in algebra I predicted college readiness and everyone got all cargo cult about it. By the turn of the century, if not earlier, more of our kids were taking advanced math in high school than at any point in our history.

And that was before kids started taking algebra in seventh grade. Sophomores take now take honors pre-calculus so they can get a second year of AP calculus in before graduation. Common Core has gone further and pushed algebra 2 down into algebra I.

Yet 17 year old NAEP scores have been basically stagnant for the same amount of time our high school students have been first encouraged, then required, to take three or more years of advanced math.

Not only do we try to educate kids faster, we measure their gain or loss by time. Poor kids of uneducated parents lose two months learning over the summer. CREDO, source of all those charter studies, refers to additional days of learning. Everyone comparing our results to Singapore always mentions the calendar, how much earlier their kids start working with advanced math. These same people also point out that Singapore has a longer school year. Longer school years don’t appear to work reliably either.

Except maybe KIPP, whose success is mostly likely due to extended school hours. KIPP focuses on middle school and has not really been scrutinized at the high school level. Scrutiny would reveal that the program doesn’t turn out stellar candidates, and while more KIPP alumni complete college than the average low income black or Hispanic student, the numbers are reasonable but not extraordinary when compared against motivated students in the same category who attended traditional schools. Particularly given the additional support and instruction hours the KIPP kids get.

So KIPP’s “success” actually adds weight to the NAEP scores as evidence that time–like money and quality–doesn’t respond to the project management constraints.

Kids learn what they have the capacity to learn. Spending more instruction hours will–well, may–help kids learn more of what they are capable of learning in fewer school years. But the NAEP scores and all sorts of other evidence says that learning more early doesn’t lead to increased capacity later. And so, we’ve moved 1979 first grader readiness rules to preschool with considerable success, but that success hasn’t given us any traction in increasing college readiness at the other end of childhood. Quite the contrary.

I probably don’t have much of a point. I was actually thinking about the increasing graduation rates. It’ll be a while until part 2. I’m swamped at work, moving again, writing some longer pieces, and really would like to post some math curriculum rather than detangle my mullings.

But the triangle thing is important. Really.

Take note: under 1000 words. Hey, I have to do it every year or so.


About educationrealist

25 responses to “Education: No Iron Triangle

  • James Thompson

    As you say, NAEP results at age 17 have not shown much change in the period 1971-2008. Over that period reading starts at 100 and ends at 100.3; Maths starts at 101.7 and rises to 102.5 This suggests that students take up the teaching offered to the best of their ability, but that there are practical limits as to what can be achieved by instruction. Of course, without any instruction the results would very probably be far worse.

    • educationrealist

      I hadn’t seen your comment until Vijay pointed it out. Yes, that has to be what it means. But for some reason, people tend to describe this interpretation as “teaching doesn’t make any difference”. I see it differently, given that we’ve dramatically increased the population at the low end of the cognitive scale, but teaching has kept up as best it can.

      • vijay

        I wish to amplify this response.

        The cognitive ability of the student population has extended on both ends; even if the left or lower side is much larger than the right side. The mean may have shifted left, and the SD has been increased. These changes in cognitive distribution is driven not only by the racial composition, but also by rising inequality. The response of test scores and graduation rates to this change in population distribution cannot be easily predicted. In a sense, it is similar to the male/female college graduation rates. Whereas the means are similar, the SDs are larger for males. As such, even as male admission and graduation rates have been lower than female, the graduation rates from Physical sciences, engineering, economics and other higher cognitive ability fields. In a similar manner, a reduction in HS graduation rates, increase in higher dropout rates and higher GED rates should have been anticipated. The flattening of NAEP scores and increase (??) in graduation rates may be an actual success story here.

  • anonymousskimmer

    If various classes such as math have been pushed down over the decades, then shouldn’t kids be awarded high school diplomas earlier once they’ve completed what used to be a standard high school curriculum?

    • educationrealist

      No, because that’s not considered a high school diploma anymore.

      • Vijay

        Is it the great psychologist responding? The education realist is moving on up!

      • anonymousskimmer

        I can’t tell if Vijay’s reply is snark directed at me or not.

        It is odd that a 60 year old can go to college on a 42 year old HS diploma when an 18 year old couldn’t on the same knowledge base.

      • vijay

        To Anonymous Skimmer:

        No snark. Dr. James Thompson is a famous psychologist from London who writes on cognitive capitalism and smart fraction.He was well known to people who were reading in the last century. I was commenting on the fact he responded to ED. Realist.

      • educationrealist

        I hadn’t seen it until this! Thanks for pointing it out. I’m a big fan of Dr. Thompson.

  • Floccina

    Kids learn what they have the capacity to learn.

    All the more important that we focus on what they learn. If how much they can learn in limited then it is importation that they learn the most useful stuff first. For example it is more important that one know that the Carnot limit exists than that he can calculate it.

    • Spare Armadillo

      “If how much they can learn in limited then it is importation that they learn the most useful stuff first.”

      Would it do any harm if we stopped trying to teach math beyond arithmetic to students in the bottom half of math ability? How many of them use algebra in later life? Almost none, I would guess. How many of them are “better educated” as a result of having had algebra, in the sense that they understand the world better? Probably almost none. Do even students in the third quartile really get much out of algebra?

      If we want to teach the dummies some math beyond arithmetic, I think a statistics course using this book would be about a thousand times more worthwhile than algebra:

      Even though the book is used as a college text, it’s written at a level appropriate for above-average 7th-graders. If a student finds this book too hard, then that student is probably not capable of understanding any math beyond arithmetic.

      • DensityDuck

        “If a student finds this book too hard, then that student is probably not capable of understanding any math beyond arithmetic.”

        The reformer says “nonsense, all children are equally capable of learning everything, we just need to find the right people and methods to teach them.”

        The progressive says “nonsense, all children are equally capable of learning everything, we just need to deal with the pernicious influences of clandestine white racism that cause people to unconsciously choose not to put effort into teaching minority students.”

  • countenance

    Explaining the paradox between harder math classes being taken earlier and earlier and flat NAEP scores? Maybe: Course title inflation. Or another possibility: Maybe the NAEP test in math is such that it misses all the increasingly advanced at younger ages math students.

    The increasing HS graduation rates? A lowered bar, affirmative action in grading.

    • educationrealist

      Um. Yeah. Did you actually read the essay?

    • momof4

      As far back as the mid-89s, it was widely recognized, in a suburan DC county, that the countywide course descriptions (not limited to math) really only applied to a group of very high-performing high schools, on a consistent basis – and that was because most schools did not have enough students prepared to do that levlel work. Most schools had some kids ready for that, but significant numbers of less-prepared kids (often pushed into the class for demographic/gender reasons) meant the section didn’t cover all the material. At some high schools, the prepared pool was insignificant Given last year’s results on the countywide math tests, it looks as if not much has changed.

    • DensityDuck

      “Explaining the paradox between harder math classes being taken earlier and earlier and flat NAEP scores?”

      Ever-groeing pools of low-performing test takers. If ten more students take calculus this year but twenty more students fail algebra, the net result is a reduction in average performance.

      • vijay

        Heckman, and jay Greene have been saying this for ten years; Mischel and Roy have been opposing that and saying (based on labor participation) that no more than 13% of the annual entrants into work force do not have a HS or GED diploma.

        The answer is somewhere between the two claims; in 2011 approximately 4 million students entered 9th grade; it is anticipated that between 3.1 and 3.3 million will actually graduate school this year. Both, claims of collapse in graduation rates, and rapid increases in graduation rates thrown out by Arne are wrong.

        GED: approximately 400 K to 500 K used to get GED every year. Diane Ravitch ( claims that the core curriculum aligned GED rates will drop to 55,000 this year. I think that is not that bad at all.

        Overall, about approximately 80% of those entering in 2011 are expected to graduate in 2015. Not bad; that is not bad at all. Given the composition of high school entering population.

  • Cooper

    “But the NAEP scores and all sorts of other evidence says that learning more early doesn’t lead to increased capacity later.”

    I understand this to mean that cramming down content to earlier grades doesn’t seem to increase “achievement” later on. I’m not sure how to explain this, but my guess is the same issue will explain the longer school years producing little effect.

    With that said, the quoted statement defies the laws of learning. Capacity to learn is geometrically related to what has already been learned.

    What’s going on here? I would love to hear more of your thoughts on why these changes never seem to move the needle.

  • cthulhu

    When I was a freshman in engineering at a mid-tier state school in the ’80s, almost none of my classmates had taken calculus in high school, or had taken it but were unable to pass the advanced placement test. Maybe I’m just a caveman, but this modern emphasis on high schoolers taking calculus – more than one year sometimes! – frightens and confuses me…


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