Education Archives

Kon-Tiki & the STEM workforce

I don’t know if Thor Heyerdahl had Polynesian origins or Rapa Nui right, but he did nail the stovepiping of thinking in organizations:

“And there’s another thing,” I went on.
“Yes,” said he. “Your way of approaching the problem. They’re specialists, the whole lot of them, and they don’t believe in a method of work which cuts into every field of science from botany to archaeology. They limit their own scope in order to be able to dig in the depths with more concentration for details. Modern research demands that every special branch shall dig in its own hole. It’s not usual for anyone to sort out what comes up out of the holes and try to put it all together.
…
Carl was right. But to solve the problems of the Pacific without throwing light on them from all sides was, it seemed to me, like doing a puzzle and only using the pieces of one color.

Thor Heyerdahl, Kon-Tiki

This reminds me of a few of my consulting experiences, in which large firms’ departments jealously guarded their data, making global understanding or optimization impossible.

This is also common in public policy domains. There’s typically an abundance of micro research that doesn’t add up to much, because no one has bothered to build the corresponding macro theory, or to target the micro work at the questions you need to answer to build an integrative model.

An example: I’ve been working on STEM workforce issues – for DOE five years ago, and lately for another agency. There are a few integrated models of workforce dynamics – we built several, the BHEF has one, and I’ve heard of efforts at several aerospace firms and agencies like NIH and NASA. But the vast majority of education research we’ve been able to find is either macro correlation studies (not much causal theory, hard to operationalize for decision making) or micro examination of a zillion factors, some of which must really matter, but in a piecemeal approach that makes them impossible to integrate.

An integrated model needs three things: what, how, and why. The “what” is the state of the system – stocks of students, workers, teachers, etc. in each part of the system. Typically this is readily available – Census, NSF and AAAS do a good job of curating such data. The “how” is the flows that change the state. There’s not as much data on this, but at least there’s good tracking of graduation rates in various fields, and the flows actually integrate to the stocks. Outside the educational system, it’s tough to understand the matrix of flows among fields and economic sectors, and surprisingly difficult even to get decent measurements of attrition from a single organization’s personnel records. The glaring omission is the “why” – the decision points that govern the aggregate flows. Why do kids drop out of science? What attracts engineers to government service, or the finance sector, or leads them to retire at a given age? I’m sure there are lots of researchers who know a lot about these questions in small spheres, but there’s almost nothing about the “why” questions that’s usable in an integrated model.

I think the current situation is a result of practicality rather than a fundamental philosophical preference for analysis over synthesis. It’s just easier to create, fund and execute standalone micro research than it is to build integrated models.

The bad news is that vast amounts of detailed knowledge goes to waste because it can’t be put into a framework that supports better decisions. The good news is that, for people who are inclined to tackle big problems with integrated models, there’s lots of material to work with and a high return to answering the key questions in a way that informs policy.

Why learn calculus?

A young friend asked, why bother learning calculus, other than to get into college?

The answer is that calculus holds the keys to the secrets of the universe. If you don’t at least have an intuition for calculus, you’ll have a harder time building things that work (be they machines or organizations), and you’ll be prey to all kinds of crank theories. Of course, there are lots of other ways to go wrong in life too. Be grumpy. Don’t brush your teeth. Hang out in casinos. Wear white shoes after Labor Day. So, all is not lost if you don’t learn calculus. However, the world is less mystifying if you do.

The amazing thing is, calculus works. A couple of years ago, I found my kids busily engaged in a challenge, using a sheet of tinfoil of some fixed size to make a boat that would float as many marbles as possible. They’d managed to get 20 or 30 afloat so far. I surreptitiously went off and wrote down the equation for the volume of a rectangular prism, subject to the constraint that its area not exceed the size of the foil, and used calculus to maximize. They were flabbergasted when I managed to float over a hundred marbles on my first try.

The secrets of the universe come in two flavors. Mathematically, those are integration and differentiation, which are inverses of one another.

Continue reading “Why learn calculus?”

Out with the bad, in with the good

A while back Obama jumped on the fire-bad-teachers bandwagon:

“You’ve got to have radical change, and radical change is something that’s in the interest of students,” he said. “We’ve got to be able to identify teachers who are doing well. … And, ultimately, if some teachers aren’t doing a good job, they’ve got to go.”

Politico

This is all well and good, but some of what I’ve read about this idea seems naively linear. Bad teachers gone >> students learn more? Just contemplating the stocks and flows gives me pause. If we accelerate the outflow of bad teachers, what happens to the stock of teachers? Does it go down, causing class sizes to go up, inadvertently making things tougher on the remaining good teachers, who might then also leave? If not, where do we get the inflow of replacements, and what makes them any better? Is there an infinite source of potential good teachers out there, waiting to be exploited, or do we have to do something to create it?

Certainly there are some good reasons to think that getting rid of bad teachers is part of the solution. Anecdotal evidence of exceedingly low turnover rates in some districts suggests an opportunity. More importantly, there are positive feedbacks around quality. Good teachers make good colleagues, so a dolt-free school should be able to attract more good teachers. Good teaching reduces inspires, reducing behavior issues, so schools can focus resources on teaching, not discipline.

But at the end of the day, retention of good teachers has to be part of the picture as well. That means caring for them appropriately: giving them the flexibility to develop their own teaching style, not making evaluation obtrusive, providing slack time for development and continuing education, and – god forbid – paying them well. Many other education initiatives run counter to this purpose. For example:

Obama also said “nothing’s more important” than education, and he said if students stayed in class for one more summer month every year, they would retain more information. “I think we should have longer school years,” he said.

This is classic “get a bigger hammer” thinking. Is one more month of school that isn’t working going to help? Are underpaid teachers going to provide 10% more hours on a volunteer basis, or do we cut their effective pay to implement this? Could the resources instead be used to reduce class sizes 10%, or raise salaries 10% to attract better teachers? Again, there may be a kernel of wisdom here, but it’s hard to separate it from its systemic context.

My half-baked view is that it’s unreasonable to expect a revolution in education without providing more resources. That money isn’t going to come from poor school districts. The physics of the distribution of wealth suggests that it would have to come from the rich. At times, the rich have been willing to ante up for education, in recognition that wealth is unsustainable without civil society. But currently we seem to be in a social Darwinian phase, in which wealth is exclusively personal (in stark contrast to the view of achievement in science). So, perhaps the first step would be to make the problem salient: internalize the costs of uncivil society. Let’s pay for policing and the prison system with a luxury tax on McMansions, sports cars, yachts, first class air travel, space tourism, fine art, vintage wine and Viagra. Then we can tackle the really hard stuff, like anti-intellectual culture (since lotteries, our tax on ignorance, don’t seem to be depressing the supply).

Would you like fries with that?

Education is a mess, and well-motivated policy changes are making it worse.

I was just reading this and this, and the juices got flowing, so my wife and I brainstormed this picture:

Click to enlarge

Yep, it’s spaghetti, like a lot of causal brainstorming efforts. The underlying problem space is very messy and hard to articulate quickly, but I think the essence is simple. Educational outcomes are substandard, creating pressure to improve. In at least some areas, outcomes slipped a lot because the response to pressure was to erode learning goals rather than to improve (blue loop through the green goal). One benefit of No Child Left Behind testing is to offset that loop, by making actual performance salient and restoring the pressure to improve. Other intuitive responses (red loops) also have some benefit: increasing school hours provides more time for learning; standardization yields economies of scale in materials and may improve teaching of low-skill teachers; core curriculum focus aligns learning with measured goals.

The problem is that these measures have devastating side effects, especially in the long run. Measurement obsession eats up time for reflection and learning. Core curriculum focus cuts out art and exercise, so that lower student engagement and health diminishes learning productivity. Low engagement means more sit-down-and-shut-up, which eats up teacher time and makes teaching unattractive. Increased hours lead to burnout of both students and teachers. Long hours and standardization make teaching unattractive. Degrading the attractiveness of teaching makes it hard to attract quality teachers. Students aren’t mindless blank slates; they know when they’re being fed rubbish, and check out. When a bad situation persists, an anti-intellectual culture of resistance to education evolves.

The nest of reinforcing feedbacks within education meshes with one in broader society. Poor education diminishes future educational opportunity, and thus the money and knowledge available to provide future schooling. Economic distress drives crime, and prison budgets eat up resources that could otherwise go to schools. Dysfunction reinforces the perception that government is incompetent, leading to reduced willingness to fund schools, ensuring future dysfunction. This is augmented by flight of the rich and smart to private schools.

I’m far from having all the answers here, but it seems that standard SD advice on the counter-intuitive behavior of social systems applies. First, any single policy will fail, because it gets defeated by other feedbacks in the system. Perhaps that’s why technology-led efforts haven’t lived up to expectations; high tech by itself doesn’t help if teachers have no time to reflect on and refine its use. Therefore intervention has to be multifaceted and targeted to activate key loops. Second, things get worse before they get better. Making progress requires more resources, or a redirection of resources away from things that produce the short-term measured benefits that people are watching.

I think there are reasons to be optimistic. All of the reinforcing feedback loops that currently act as vicious cycles can run the other way, if we can just get over the hump of the various delays and irreversibilities to start the process. There’s enormous slack in the system, in a variety of forms: time wasted on discipline and memorization, burned out teachers who could be re-energized and students with unmet thirst for knowledge.

The key is, how to get started. I suspect that the conservative approach of privatization half-works: it successfully exploits reinforcing feedback to provide high quality for those who opt out of the public system. However, I don’t want to live in a two class society, and there’s evidence that high inequality slows economic growth. Instead, my half-baked personal prescription (which we pursue as homeschooling parents) is to make schools more open, connecting students to real-world trades and research. Forget about standardized pathways through the curriculum, because children develop at different rates and have varied interests. Replace quantity of hours with quality, freeing teachers’ time for process improvement and guidance of self-directed learning. Suck it up, and spend the dough to hire better teachers. Recover some of that money, and avoid lengthy review, by using schools year ’round. I’m not sure how realistic all of this is as long as schools function as day care, so maybe we need some reform of work and parental attitudes to go along.

[Update: There are of course many good efforts that can be emulated, by people who’ve thought about this more deeply than I. Pegasus describes some here. Two of note are the Waters Foundation and Creative Learning Exchange. Reorganizing education around systems is a great way to improve productivity through learner-directed learning, make learning exciting and relevant to the real world, and convey skills that are crucial for society to confront its biggest problems.]

Dumb and Dumber

Not to be outdone by Utah, South Dakota has passed its own climate resolution.

They raise the ante – where Utah cherry-picked twelve years of data, South Dakotans are happy with only 8. Even better, their pattern matching heuristic violates bathtub dynamics:

WHEREAS, the earth has been cooling for the last eight years despite small increases in anthropogenic carbon dioxide

They have taken the skeptic claim, that there’s little warming in the tropical troposphere, and bumped it up a notch:

WHEREAS, there is no evidence of atmospheric warming in the troposphere where the majority of warming would be taking place

Nope, no trend here:

Satellite tropospheric temperature (RSS, TLT)

Continue reading “Dumb and Dumber”

If your kids are boring, you're doing it wrong

The other day I ran across a blog post (undeserving of a link, though there is a certain voyeuristic fascination to be had in reading it) that described children as boring little wretches, unsuited to inhabit the cerebral stratosphere of their elders. The mental model seemed to be something like the following:

Bad parenting mental model

The policy response to the misfortune of having children implied by the above is to foist them off on TV and day care until they grow up enough that you can tolerate their presence. That leaves you plenty of time for more intellectual pursuits, like tweeting, or speculating about the romance of the person in the next cubicle.

This reminded me of an earlier perspective on children, now thankfully less prevalent:

Their Hearts naturally, are a meer nest, root, fountain of Sin, and wickedness; an evil Treasure from whence proceed evil things viz. Evil Thoughts. Murders, Adulteries &c. Indeed, as sharers in the guilt of Adam’s first Sin, they’re Children of Wrath by Nature, liable to Eternal Vengeance, the Unquencheable Flames of Hell. – Benjamin Wadsworth

Untitled, Ansel Fiddaman, Pastel

Continue reading “If your kids are boring, you're doing it wrong”

My Bathtub is Nonlinear

I’m working on raising my kids as systems thinkers. I’ve been meaning to share some of our adventures here for some time, so here’s a first installment, from quite a while back.

I decided to ignore the great online resources for system dynamics education and reinvent the wheel. But where to start? I wanted an exercise that included stocks and flows, accumulation, graph reading, estimation, and data collection, with as much excitement as could be had indoors. (It was 20 below outside, so fire and explosions weren’t an option).

We grabbed a sheet of graph paper, fat pens, a yardstick, and a stopwatch and headed for the bathtub. Step 1 (to sustain interest) was turn on the tap to fill the tub. While it filled, I drew time and depth axes on the graph paper and explained what we were trying to do. That involved explaining what a graph was for, and what locations on the axes meant (they were perhaps 5 and 6 and probably hadn’t seen a graph of behavior over time before).

When the tub was full, we made a few guesses about how long it might take to empty, then started the clock and opened the drain. Every ten or twenty seconds, we’d stop the timer, take a depth reading, and plot the result on our graph. After a few tries, the kids could place the points. About half way, we took a longer pause to discuss the trajectory so far. I proposed a few forecasts of how the second half of the tub might drain – slowing, speeding up, etc. Each of us took a guess about time-to-empty. Naturally my own guess was roughly consistent with exponential decay. Then we reopened the drain and collected data until the tub was dry.

To my astonishment, the resulting plot showed a perfectly linear decline in water depth, all the way to zero (as best we could measure). In hindsight, it’s not all that strange, because the tub tapers at the bottom, so that a constant linear decline in the outflow rate corresponds with the declining volumetric flow rate you’d expect (from decreasing pressure at the outlet as the water gets shallower). Still, I find it rather amazing that the shape of the tub (and perhaps nonlinearity in the drain’s behavior) results in such a perfectly linear trajectory.

We spent a fair amount of time further exploring bathtub dynamics, with much filling and emptying. When the quantity of water on the floor got too alarming, we moved to the sink to explore equilibrium by trying to balance the tap inflow and drain outflow, which is surprisingly difficult.

We lost track of our original results, so we recently repeated the experiment. This time, we measured the filling as well as the draining, shown below on the same axes. The dotted lines are our data; others are our prior guesses. Again, there’s no sign of exponential draining – it’s a linear rush to the finish line. Filling – which you’d expect to be a perfect ramp if the tub had constant volume per depth – is initially fast, then slows slightly as the tapered bottom area is full. However, that effect doesn’t seem to be big enough to explain the outflow behavior.

Bathtub data

I’ve just realized that I have a straight-sided horse trough lying about, so I think we may need to head outside for another test …

Update: the follow-on to this is rather important.