Category: Education

Loopy

I just gave Loopy a try, after seeing Gene Bellinger’s post about it.

It’s cool for diagramming, and fun. There are some clever features, like drawing a circle to create a node (though I was too dumb to figure that out right away). Its shareability and remixing are certainly useful.

However, I think one must be very cautious about simulating causal loop diagrams directly. A causal loop diagram is fundamentally underspecified, which is why no method of automated conversion of CLDs to models has been successful.

In this tool, behavior is animated by initially perturbing the system (e.g, increase the number of rabbits in a predator-prey system). Then you can follow the story around a loop via animated arrow polarity changes – more rabbits causes more foxes, more foxes causes less rabbits. This is essentially the storytelling method of determining loop polarity, which I’ve used many times to good effect.

However, as soon as the system has multiple loops, you’re in trouble. Link polarity tells you the direction of change, but not the gain or nonlinearity. So, when multiple loops interact, there’s no way to determine which is dominant. Also, in a real system it matters which nodes are stocks; it’s not sufficient to assume that there must be at least one integration somewhere around a loop.

You can test this for yourself by starting with the predator-prey example on the home page. The initial model is a discrete oscillator (more rabbits -> more foxes -> fewer rabbits). But the real system is nonlinear, with oscillation and other possible behaviors, depending on parameters. In Loopy, if you start adding explicit births and deaths, which should get you closer to the real system, simulations quickly result in a sea of arrows in conflicting directions, with no way to know which tendency wins. So, the loop polarity simulation could be somewhere between incomprehensible and dead wrong.

Similarly, if you consider an SIR infection model, there are three loops of interest: spread of infection by contact, saturation from running out of susceptibles, and recovery of infected people. Depending on the loop gains, it can exhibit different behaviors. If recovery is stronger than spread, the infection dies out. If spread is initially stronger than recovery, the infection shifts from exponential growth to goal seeking behavior as dominance shifts nonlinearly from the spread loop to the saturation loop.

I think it would be better if the tool restricted itself to telling the story of one loop at a time, without making the leap to system simulations that are bound to be incorrect in many multiloop cases. With that simplification, I’d consider this a useful item in the toolkit. As is, I think it could be used judiciously for explanations, but for conceptualization it seems likely to prove dangerous.

My mind goes back to Barry Richmond’s approach to systems here. Causal loop diagrams promote thinking about feedback, but they aren’t very good at providing an operational description of how things work. When you’re trying to figure out something that you don’t understand a priori, you need the bottom-up approach to synthesize the parts you understand into the whole you’re grasping for, so you can test whether your understanding of processes explains observed behavior. That requires stocks and flows, explicit goals and actual states, and all the other things system dynamics is about. If we could get to that as elegantly as Loopy gets to CLDs, that would be something.

Tasty Menu

From the WPI online graduate program and courses in system dynamics:

Truly a fine lineup!

Not even wrong: a school board's discussion of systems thinking

Socialism. Communism. “Nazism.” American Exceptionalism. Indoctrination. Buddhism. Meditation. “Americanism.” These are not words or terms one would typically expect to hear in a Winston-Salem/Forsyth County School Board meeting. But in the Board’s last meeting on October 9th, they peppered the statements of public commenters and Board Members alike.

The object of this invective? Systems thinking. You really have to read part 1 and part 2 of Camel City Dispatch’s article to get an appreciation for the school board’s discussion of the matter.

I know that, as a systems thinker, I should look for the unstated assumptions that led board members to their critiques, and establish a constructive dialog. But I just can’t do it – I have to call out the fools. While there are some voices of reason, several of the board members and commenters apparently have no understanding of the terms they bandy about, and have no business being involved in the education of anyone, particularly children.

The low point of the exchange:

Jeannie Metcalf said she “will never support anything that has to do with Peter Senge… I don’t care what [the teachers currently trained in System’s Thinking] are teaching. I don’t care what lessons they are doing. He’s is trying to sell a product. Once it insidiously makes its way into our school system, who knows what he’s going to do. Who knows what he’s going to do to carry out his Buddhist way of thinking and his hatred of Capitalism. I know y’all are gonna be thinkin’ I’m a crazy person, but I’ve been around a long time.”

Yep, you’re crazy all right. In your imaginary parallel universe, “hatred of capitalism” must be a synonym for writing one of the most acclaimed business books ever, sitting at one of the best business schools in the world, and consulting at the highest levels of many Fortune 50 companies.

The common thread among the ST critics appears to be a total failure to actually observe classrooms combined with shoot-the-messenger reasoning from consequences. They see, or imagine, a conclusion that they don’t like, something that appears vaguely environmental or socialist, and assume that it must be part of the hidden agenda of the curriculum. In fact, as supporters pointed out, ST is a method, which could as easily be applied to illustrate the benefits of individualism, markets, or whatnot, as long as they are logically consistent. Of course, if one’s pet virtue has limits or nuances, ST may also reveal those – particularly when simulation is used to formalize arguments. That is what the critics are really afraid of.

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.

Algebra, Eroding Goals and Systems Thinking

A NY Times editorial wonders, Is Algebra Necessary?*

I think the short answer is, “yes.”

The basic point of having a brain is to predict the consequences of actions before taking them, particularly where those actions might be expensive or fatal. There are two ways to approach this:

  • pattern matching or reinforcement learning – hopefully with storytelling as a conduit for cumulative experience with bad judgment on the part of some to inform the future good judgment of others.
  • inference from operational specifications of the structure of systems, i.e. simulation, mental or formal, on the basis of theory.

If you lack a bit of algebra and calculus, you’re essentially limited to the first option. That’s bad, because a lot of situations require the second for decent performance.

The evidence the article amasses to support abandonment of algebra does not address the fundamental utility of algebra. It comes in two flavors:

  • no one needs to solve certain arcane formulae
  • setting the bar too high for algebra discourages large numbers of students

I think too much reliance on the second point risks creating an eroding goals trap. If you can’t raise the performance, lower the standard:

eroding goals
B. Jana, Wikimedia Commons, Creative Commons Attribution-Share Alike 3.0 Unported

This is potentially dangerous, particularly when you also consider that math performance is coupled with a lot of reinforcing feedback.

As an alternative to formal algebra, the editorial suggests more practical math,

It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted — and include discussion about which items should be included and what weights they should be given.

I can’t really fathom how one could discuss weighting the CPI in a meaningful way without some elementary algebra, so it seems to me that this doesn’t really solve the problem.

However, I think there is a bit of wisdom here. What earthly purpose does solving the quadratic formula serve, until one is able to map that to some practical problem space? There is growing evidence that even high-performing college students can manipulate symbols without gaining the underlying intuition needed to solve real-world problems.

I think the obvious conclusion is not that we should give up on teaching algebra, but that we should teach it quite differently. It should emerge as a practical requirement, motivated by a student-driven search for the secrets of life and systems thinking in particular.

* Thanks to Richard Dudley for pointing this out.

Is Algebra Necessary?

What drives learning?

Sit down and shut up while I tell you.

One interesting take on this compares countries cross-sectionally to get insight into performance drivers. A colleague dug up Educational Policy and Country Outcomes in International Cognitive Competence Studies. Two pictures from the path analysis are interesting:

Note the central role of discipline. Interestingly, the study also finds that self-report of pleasure reading is negatively correlated with performance. Perhaps that’s a consequence of getting performance through discipline rather than self-directed interest? (It works though.)

More interesting, though, is that practically everything is weak, except the educational level of society – a big positive feedback.

I find this sort of analysis quite interesting, but if I were a teacher, I think I’d be frustrated. In the aggregate international data, there’s precious little to go on when it comes to deciding, “what am I going to do in class today?”

 

 

Teacher value added modeling – my bottom line

I’m still attracted to the idea of objective measurements of teaching performance.* But I’m wary of what appear to be some pretty big limitations in current implementations.

It’s interesting reading the teacher comments on the LA Times’ teacher value added database, because many teachers appear to have a similar view – conceptually supportive, but wary of caveats and cognizant of many data problems. (Interestingly, the LAT ratings seem to have higher year-on-year and cross subject rating reliability, much more like I would expect a useful metric to behave. I can only browse incrementally though, so seeing the full dataset rather than individual samples might reveal otherwise.)

My takeaways on the value added measurements:

I think the bigger issues have more to do with the content of the value added measurements rather than their precision. There’s nothing mysterious about what teacher value added measures. It’s very explicitly the teacher-level contribution to year-on-year improvement in student standardized test scores. Any particular measurement might contain noise and bias, but if you could get rid of those, there are still some drawbacks to the metric.

  • Testing typically emphasizes only math and English, maybe science, and not art, music, and a long list of other things. This is broadly counterproductive for life, but also even narrowly for learning math and English, because you need some real-world subject matter in order to have interesting problems to solve and things to write about.
  • Life is a team sport. Teaching is, or should be, too. (If you doubt this, watch a few episodes of a reality show like American Chopper and ponder whether performance would be more enhanced by better algebra skills, or better cooperation, communication and project management skills. Then ponder whether building choppers is much different from larger enterprises, like the Chunnel.) We should be thinking about performance accordingly.
    • A focus at the student and teacher level ignores the fact that school system-level dynamics are most likely the biggest opportunity for improvement.
    • A focus on single-subject year-on-year improvements means that teachers are driven to make decisions with a 100% time discount rate, and similar total disregard for the needs of other teachers’ classes.**
  • Putting teachers in a measurement-obsessed command-and-control environment is surely not the best way to attract high-quality teachers.
  • It’s hard to see how putting every student through the same material at the same pace can be optimal.
  • It doesn’t make sense to put too much weight on standardized test scores, when the intersection between those and more general thinking/living skills is not well understood.

If no teachers are ever let go for poor performance, that probably signals a problem. In fact, it’s likely a bigger problem if teacher performance measurement (generally, not just VAM) is noisy, because bad teachers can get tenure by luck. If VAM helps with the winnowing process, that might be a useful function.

But it seems to me that the power of value added modeling is being wasted by this musical chairs*** mentality. The real challenge in teaching is not to decrease the stock of bad teachers. It’s to increase the stock of good ones, by attracting new ones, retaining the ones we have, and helping all of them learn to improve. Of course, that might require something more scarce than seats in musical chairs – money.

* A friend and school board member in semi-rural California was an unexpected fan of No Child Left Behind testing requirements, because objective measurements were the only thing that finally forced her district to admit that, well, they kind of sucked.

** A friend’s son, a math teacher, proposed to take a few days out of the normal curriculum to wrap up some loose ends from prior years. He thought this would help students to cement the understanding of foundational topics that they’d imperfectly mastered. Management answered categorically that there could be no departures from the current year material, needed to cover standardized test requirements. He defied them and did it, but only because he knew that it would take the district a year to fire him, and he was quitting anyway.

*** Musical chairs has to be one of the worst games you could possibly teach to children. We played it fairly regularly in elementary school.

Dynamics of teacher value added – the limits

In my last post, I showed that culling low-performance teachers can work surprisingly well, even in the presence of noise that’s as large as the signal.

However, that involved two big assumptions: the labor pool of teachers is unlimited with respect to the district’s needs, and there’s no feedback from the evaluation process to teacher quality and retention. Consider the following revised system structure:

In this view, there are several limitations to the idea of firing bad teachers to improve performance:

  • Fired teachers don’t just disappear into a cloud; they go back into the teacher labor pool. This means that, as use of VA evaluation increases, the mean quality of the labor pool goes down, making it harder to replace teachers with new and better ones. This is unambiguously a negative (balancing) feedback loop.
  • The quality of the labor pool could go up through a similar culling process, but it’s not clear that teacher training institutions can deliver 50% more or better candidates, or that teachers rejected for low value added in one district will leave the pool altogether.

Several effects have ambiguous sign – they help (positive/reinforcing feedback) if the measurement system is seen as fair and attractive to good teachers, but they hurt performance otherwise:

  • Increased use of VA changes the voluntary departure rate of teachers from the district, with different effects on good and bad teachers.
  • Increased use of VA changes the ease of hiring good teachers.
  • Increased use of VA attracts more/better teachers to the labor pool, and reduces attrition from the labor pool.

On balance, I’d guess that these are currently inhibiting performance. Value added measurement is widely perceived as noisy and arbitrary, and biased toward standardized learning goals that aren’t all that valuable or fun to teach to.

  • Increasing the rate of departure requires a corresponding increase in the hiring rate, but this is not free, and there’s no guarantee that the labor pool supports it.

There are some additional limiting loops implicit in Out with the bad, in with the good.

Together, I think these effects most likely limit the potential for Value Added hiring/firing decisions to improve performance rather severely, especially given the current resistance to and possible problems with the measurements.