Educational Achievement and Religiosity


educational achievement

I outlined a somewhat speculative argument that would support a prediction that increased religiosity at the social level should have a negative effect on educational achievement here, where I suggested that

Educators surrounded by cultures with higher religiosity—and regardless of their own personal religious orientations—will simply have greater exposure to concerns about moral and spiritual harm that can be wrought by science, in addition to the benefits it can bring.

Such weakened confidence in science may not only directly water down the content of instruction in both science and mathematics—by, for example, diluting science content antagonistic to religious beliefs in published standards and curriculum guides—but could also represent an environment in which it is seen as inartful or even taboo for educators of any stripe to lean on scientific findings and perspectives in order to improve educational outcomes (because nurturing children may be seen to be the provenance of more spiritual and less scientific approaches). Both of these effects, one social, one policy-level, could have a negative effect on achievement.

A new paper, coauthored by renowned evolutionary psychologist David Geary, shows that religiosity at a national level does indeed have a strong negative effect on achievement (r = –0.72, p < 0.001). Yet, Stoet and Geary’s research suggests a different, simpler mechanism at work than the mechanisms I suggested above to explain the connection between religiosity and math and science educational achievement. This mechanism is displacement.

The Displacement Hypothesis

It’s a bit much to give this hypothesis its own section heading—not that it isn’t important, necessarily. It’s just self-explanatory. Religiosity may be correlated with lower educational achievement because people have a finite amount of time and attention, and spending time learning about religion or engaging in religious activities necessarily takes time away from learning math and science.

It is not necessarily the content of the religious beliefs that might influence educational growth (or lack thereof), but that investment of intellectual abilities that support educational development are displaced by other (religious) activities (displacement hypothesis). This follows from Cattell’s (1987) investment theory, with investment shifting from secular education to religious materials rather than shifts from one secular domain (e.g., mathematics) to another (e.g., literature). This hypothesis might help to explain part of the variation in educational performance broadly (i.e., across academic domains), not just in science literacy.

One reason the displacement hypothesis makes sense is that religiosity is as powerfully negatively correlated with achievement in mathematics as it is with science achievement.

The Scattering Hypothesis

But certainly a drawback of the displacement hypothesis is that there are activities we engage in—as unrelated to mathematics and science as religion is—which don’t, as far as we know, correlate strongly negatively with achievement. Physical exercise, for goodness’ sake, is one example of such an activity. Perhaps there is something especially toxic about religiosity as the displacer which deserves our attention.

Maybe religiosity (or, better, a perspective which allows for supernatural explanations or, indeed, unexplainable phenomena) has a diluent or scattering effect on learning. If so, here are two analogies for how that might work:

  • Consider object permanence. Prior to developing the understanding that objects continue to exist once they are out of view, children will almost immediately lose interest in an object that is deliberately hidden from them, even if they were attending to it just moments earlier. Why? Because it is possible (to them) that the object has vanished from existence when you move it out of their view. If it were possible for a 4-month-old to crawl up and look behind the sofa to see that grandma had actually disappeared during a game of peek-a-boo, they would have nothing to wonder about. The disappearance was possible, so why shouldn’t it happen? This possibility is gone once you develop object permanence.
  • Perhaps more relevant, not to mention ominous: climate change. It is well known that religiosity and acceptance of the theory of evolution are negatively correlated. And it turns out there is a strong positive link between evolution denialism and climate-change denialism. How might religiosity support both of these denialisms? Here we can benefit from substituting for ‘religiosity’ some degree of subscription to supernatural explanations: If the universe was made by a deity for us, then how can we be intruders in it, and how could we—by means that do not transgress the laws of this deity—defile it? This seems a perfectly reasonable use of logic, once you have allowed for the possibility of an omniscient benevolence who gifted your species the entire planet you live on.

The two of these together seem pretty bizarre. But I’m sure you catch the drift. In each case, I would argue that the constriction of possibilities—to those supported by naturalistic explanations rather than supernatural ones—is actually a good thing. You are less likely to be prodded to explain how the natural world works when supernatural reasons are perfectly acceptable. And supernaturalism can prevent you from fully appreciating your own existence and the effects it has on the natural world. Under supernaturalism, you can still engage in logical arguments and intellectual activity. You can write books and go to seminars. Your neurons could be firing. But if you’re not thinking about reality, it doesn’t do you any good.

Religiosity or supernaturalism does not make you dumb. But perhaps it has the broader effect of making it more difficult to fasten minds onto reality, as it fills the solution space with only those possibilities that have little bearing on the real world we live in. This would certainly show up in measures of educational achievement.
Stoet, G., & Geary, D. (2017). Students in countries with higher levels of religiosity perform lower in science and mathematics Intelligence DOI: 10.1016/j.intell.2017.03.001

Bloom’s Against Empathy


I‘m on my way out the door to be on vacation, but I wanted to mention (and recommend) Paul Bloom’s new book, Against Empathy: The Case for Rational Compassion, before I do—you know, to put you in the holiday spirit.

Bloom makes a strong case that empathic concern acts as a spotlight—inducing a kind of moral tunnel vision:

Empathy is a spotlight focusing on certain people in the here and now. This makes us care more about them, but it leaves us insensitive to the long-term consequences of our acts and blind as well to the suffering of those we do not or cannot empathize with. Empathy is biased, pushing us in the direction of parochialism and racism. It is shortsighted, motivating actions that might make things better in the short term but lead to tragic results in the future. It is innumerate, favoring the one over the many.

In line with Bloom’s narrative, I would say that the short-sightedness of empathy is what makes students’ boredom more salient than students’ lack of prior knowledge. The innumeracy of empathic concern leads to a valorization of personalization and individualism at the expense of shared knowledge of a shared reality. And its bias? I’m sure you can think of a few ways it blinkers us, makes us less fair, maybe leads us to believe that a white middle-class definition of “success” is one that everyone shares or that everyone should share.

Perhaps next year we can talk about how in-the-trenches empathy is not such a great thing, and that perhaps we need less of it in education—and more rational compassion.

Instructional Effects: Action at a Distance

I really like this recent post, called Tell Me More, Tell Me More, by math teacher Dani Quinn. The content is an excellent analysis of expert blindness in math teaching. The form, though, is worth seeing as well—it is a traditional educational syllogism, which Quinn helpfully commandeers to arrive at a non-traditional conclusion, that instructional effects have instructional causes, on the right:

The Traditional Argument An Alternative Argument
There is a problem in how we teach: We typically spoon-feed students procedures for answering questions that will be on some kind of test.

“There is a problem in how we teach: We typically show pupils only the classic forms of a problem or a procedure.”

This is why students can’t generalize to non-routine problems: we got in the way of their thinking and didn’t allow them to take ownership and creatively explore material on their own. “This is why they then can’t generalise: we didn’t show them anything non-standard or, if we did, it was in an exercise when they were floundering on their own with the least support.”

Problematically for education debates, each of these premises and conclusions taken individually are true. That is, they exist. At our (collective) weakest, we do sometimes spoon-feed kids procedures to get them through tests. We do cover only a narrow range of situations—what Engelmann refers to as the problem of stipulation. And we can be, regrettably in either case, systematically unassertive or overbearing.

Solving equations provides a nice example of the instructional effects of both spoon-feeding and stipulation. Remember how to solve equations? Inverse operations. That was the way to do equations. If you have something like \(\mathtt{2x + 5 = 15}\), the table shows how it goes.

Equation Step
\(\mathtt{2x + 5 \color{red}{- 5} = 15 \color{red}{- 5}}\) Subtract \(\mathtt{5}\) from both sides of the equation to get \(\mathtt{2x = 10}\).
\(\mathtt{\color{white}{+ 5 \,\,} 2x \color{red}{\div 2} = 10 \color{red}{\div 2}}\) Divide both sides of the equation by 2.
\(\mathtt{\color{white}{+ 5 \,\,}x = 5}\) You have solved the equation.

Do that a couple dozen times and maybe around 50% of the class freezes when they encounter \(\mathtt{22 = 4x + 6}\), with the variable on the right side, or, even worse, \(\mathtt{22 = 6 + 4x}\).

That’s spoon-feeding and stipulation: do it this one way and do it over and over—and, crucially, doing that summarizes most of the instruction around solving equations.

Of course, the lack of prior knowledge exacerbates the negative instructional effects of stipulation and spoon-feeding. But we’ll set that aside for the moment.

The Connection Between Premises and Conclusion

The traditional and alternative arguments above are easily (and often) confused, though, until you include the premise that I have omitted in the middle for each. These help make sense of the conclusions derived in each argument.

The Traditional Argument An Alternative Argument
There is a problem in how we teach: We typically spoon-feed students procedures for answering questions that will be on some kind of test.

“There is a problem in how we teach: We typically show pupils only the classic forms of a problem or a procedure.”

Students’ success in schooling is determined mostly by internal factors, like creativity, motivation, and self-awareness.

Students’ success in schooling is determined mostly by external factors, like amount of instruction, socioeconomic status, and curricula.

This is why students can’t generalize to non-routine problems: we got in the way of their thinking and didn’t allow them to take ownership and creatively explore material on their own. “This is why they then can’t generalise: we didn’t show them anything non-standard or, if we did, it was in an exercise when they were floundering on their own with the least support.”

In short, the argument on the left tends to diagnose pedagogical illnesses and their concomitant instructional effects as people problems; the alternative sees them as situation problems. The solutions generated by each argument are divergent in just this way: the traditional one looks to pull the levers that mostly benefit personal, internal attributes that contribute to learning; the alternative messes mostly with external inputs.

It’s Not the Spoon-Feeding, It’s What’s on the Spoon

I am and have always been more attracted to the alternative argument than the traditional one. Probably for a very simple reason: my role in education doesn’t involve pulling personal levers. Being close to the problem almost certainly changes your view of it—not necessarily for the better. But, roles aside, it’s also the case that the traditional view is simply more widespread, and informed by the positive version of what is called the Fundamental Attribution Error:

We are frequently blind to the power of situations. In a famous article, Stanford psychologist Lee Ross surveyed dozens of studies in psychology and noted that people have a systematic tendency to ignore the situational forces that shape other people’s behavior. He called this deep-rooted tendency the “Fundamental Attribution Error.” The error lies in our inclination to attribute people’s behavior to the way they are rather than to the situation they are in.

What you get with the traditional view is, to me, a kind of spooky action at a distance—a phrase attributed to Einstein, in remarks about the counterintuitive consequences of quantum physics. Adopting this view forces one to connect positive instructional effects (e.g., thinking flexibly when solving equations) with something internal, ethereal and often poorly defined, like creativity. We might as well attribute success to rabbit’s feet or lucky underwear or horoscopes!

instructional effects

Searching the Solution Space


My reading in education has been a bit disappointing lately. This has everything to do with the relationship between what I’m currently thinking about and the specific material I’m looking into, rather than the books and articles by themselves. But Ohlsson’s 2011 book Deep Learning is so far a wonderful exception to the six or seven books collecting digital dust inside my Kindle, waiting for me to be interested in them again. The reason, I think, is that Ohlsson is looking to tackle topics that I am incredibly suspicious about, insight and creativity, in a smart and systematically theoretical way. The desire to provide technical, functional, connected explanations of concepts is evident on every page.

Prior Knowledge Constrains the Solution Space

Of particular interest to me is the idea that prior knowledge constrains a ‘problem space,’ or what Ohlsson wants to re-classify as a ‘solution space’:

A problem solution consists of a path through the solution space, a sequence of cognitive operations that transforms the initial situation into a situation in which the goal is satisfied. In a familiar task environment, the person already knows which step is the right one at each successive choice point. However, in unfamiliar environments, the person has to act tentatively and explore alternatives. Analytical problem solving is difficult because the size of a solution space is a function of the number of actions that are applicable in each situation—the branching factor—and the number of actions along the solution path—the path length. The number of problem states, \(\mathtt{S}\), is proportional to \(\mathtt{b^N}\), where \(\mathtt{b}\) is the branching factor and \(\mathtt{N}\) the path length. \(\mathtt{S}\) is astronomical for even modest values of \(\mathtt{b}\) and \(\mathtt{N}\), so solution spaces can only be traversed selectively. By projecting prior experience onto the current situation, both problem perception and memory retrieval help constrain the options to be considered to the most promising ones.

So, prior knowledge casts a finite amount of light on a select portion of the solution space, illuminating those elements which are consistent with representations in long-term memory and with a person’s current perception of the problem. It may even be the case that the length of the beam from the prior-knowledge flashlight corresponds to the limitations of working memory.

Crucially, this selectivity creates a dilemma. It is necessary to limit the solution space—otherwise, a person would be quickly overwhelmed by multiple, interacting elements of a problem situation—but, as is shown, prior knowledge (among other things) may restrict activation to those elements in the solution space which are unhelpful in reaching the goal.

It may be a goal, for example, for students to have a flexible sense of number, such that they can estimate with sums, products, differences, and quotients over a variety of numbers. Yet, students’ prior knowledge of working with mathematics can lead them to activate (and thus ‘see’) only ‘narrow’ procedural elements of solution spaces. The result can be that procedural mathematics is activated even when it serves no useful purpose at all.

This ‘tyranny’ of prior knowledge effects can be seen in the classic Einstellung experiments, a version of which is below—originally included in Dr Hausmann’s write-up on the topic, which I recommend highly. The goal below is to simply fill up one of the “jars” to the target level (the first target is 100). When you’re done, head over to Dr Bob’s site for the explanation. A similar obstacle to learning, described by S. Engelmann in his work, is called the problem of stipulation.

A: 21
B: 127
C: 3
Target: 100

But Creativity Theories Are Not Learning Theories

If one wanted to provide a slightly more serious intellectual justification for much of the popular folk-theorizing in education over the last decade—and then essentially replay its development, idea by idea—misinterpreting insight and creativity theories like Ohlsson’s would be an excellent strategy for doing so. (He never says, for example, that simply prior knowledge constrains the solution space, but that unhelpful prior knowledge does.)

It all seems to be there for the taking in these kinds of theories: the notion that solving problems is education’s raison d’etre, the idea that an unknowable future—rather than being just a fact that we must accept—can play a part as a premise in some chain of reasoning, the bizarre thought that removing instructional support can represent a game-changing way of restructuring the majority of learning time, a fluttering emphasis on collaboration and distributed cognition. All of this that has been humming in the background (and foreground) for a while in education fits comfortably and rationally inside creativity theories rather than learning theories.

From a learning-theory point of view, the problem of, say, thinking flexibly about number is primarily a problem of constructing better solution spaces—bring the goal within the flashlight’s view by instructing students (and thus making activation of ‘number sense’ more likely). Unfortunately, this requires a longer-term view, greater political will, and a bit of distance from everyday reality. Insight and creativity theories, on the other hand, assume that this number sense is already there but remains inert (students are only ever experiencing ‘unwarranted impasses’). The problem for insight theory becomes simply how to redirect the flashlight’s beam so that it uncovers the right knowledge. Along with the background assumptions listed above, these further assumptions of insight theories make them remarkably well tuned to the constraints of institutional teaching, both self-imposed and externally imposed. The practical work of teaching is still mostly a one-year-at-a-time affair, and sixth grade teachers, for example, do not have the time to remake solution spaces anew over the course of one year. What is within reach are redirection techniques suggested by insight theories. In this context, misinterpreting theories about insight for learning theories is practically inevitable.

Perhaps I’ll find out where Ohlsson makes learning theory and insight/creativity theory connect as I read further. But it’s worth noting that research Ohlsson himself conducted after the publication of this book has produced conclusions that run counter to certain predictions within it.

We’ll see!

Audio Postscript

Whited Sepulchres

A central—and remarkable—argument in Steven Pinker’s recent work, The Better Angels of Our Nature, is that a decline in collective moralization may be a significant cause of the decline over time in human violence. In other words, less morality (or rather, “morality”), less violence:

The world has far too much morality, at least in the sense of activity of people’s moral instincts . . . . the biggest categories of motives for homicide are moralistic. In the eyes of the perpetrator, of the murderer, it’s capital punishment—killing someone who deserves to die, whether it’s a spouse who’s unfaithful or someone who dissed him in an argument over a parking space or cheated him in a deal. That’s why people kill each other. . . .

The human moral sense does not consist of a desire to maximize well-being, to prevent people from harm. But it is a hodgepodge of motives that include deference to a legitimate authority, conformity to social and community norms, the safeguarding of a pure divine essence against contamination and defilement.

This idea helps me put some language around my discomfort with a lot of education discourse outside the policy and research levels. We moralize far too much about teaching and learning there. Or, rather, we moralize badly too often. Our “ought”s are not centered in the empirical, but in the ideal. Consider:

“Children, go get dressed for dinner. A family should look their best at mealtimes together” is moralizing. “Children, go get dressed for dinner. I have an important client coming over, and I want to impress her” is not. The reasoning attached to the second request is embedded in a real-world reality. He wants to impress a client, so he asks the children to get dressed for dinner. By contrast, the reasoning used to support the first request is rooted in “conformity to social norms.” The speaker wants the children to get dressed for dinner because doing so will bring them (and him) closer to an ideal he has in his head. Similarly, “Doctors are gentlemen, and gentlemen’s hands are clean” is moralizing—an idealistic “ought” (in this case, an “ought not”) untethered to reality.

In education, we have that students shouldn’t just sit in rows and listen to a teacher; that they should persevere and fail; that we should be less helpful; that students ought to create on their own, collaborate, and behave like real scientists and mathematicians do. To the extent that these are simply ideals for what students “ought” to be like, disconnected from evidence, they are moralizings: visions of a “pure and divine essence”; pictures in our heads of self-reliant, creative, free, and mature students; pictures that are, however well-intentioned, divorced from reality. It seems to me that in many ways the reforms inspired by these moralizings simply succeed in making children pretend they are accomplished, so that the adults can feel good about themselves.

If, as the research Pinker references suggests, our moral instincts are not as well calibrated as we think they are for modern life, and the population of “ought”s in our community is not controlled by predatory “is”s delivered by scientific thinking, we should be, at the least, increasingly wary of educational moralizing rather than increasingly comfortable with it.

Image mask: Ivar Gullord

Audio Postscript


Teachers Should Be “Poised and Articulate”


Resurrecting an old post from 2009 or 2007 or some year around then, about teachers being treated as Miss America pageant contestants (e.g., “poised and articulate”) rather than as professionals:

At the end of what seems like a long chain of events, I asked, and answered yes to, this question about professionalizing teacher practice:

Is there one or more cultural “teaching scripts” that might tend to stymie the practice of collecting and critically analyzing specific best-practice knowledge linked to academic outcomes?

Regardless whether yes is the correct answer to that question or not, I’d like to follow up and suggest one script that I think may be a significant culprit. Of course, in doing so, I will be making a solid leap away from firm ground, because cultural scripts are constructs that one can observe only indirectly, if at all:

[Cultural scripts] are not proposed as rules of behaviour but as rules of interpretation and evaluation. It is open to individuals in concrete situations whether to follow (or appear to follow) culturally endorsed principles, and if so, to what extent; or whether to manipulate them, defy them, subvert them, rebel against them, play creatively with them, etc. Whether or not cultural scripts are being followed in behavioural terms, however, the claim is that they constitute a kind of shared interpretive “background.”

One part of an “interpretive background” that I would suggest we share with regard to the idea of teaching is this: Teaching is “ethotic” and “pathotic” persuasion.

That is, the input of teaching is gauged in terms of the character of teachers (ethos) and their ability to navigate and control the emotional, cognitive-psychological, and interpersonal dynamics of learning (pathos). “Logetic” persuasion (logos)—which involves consideration of the presentation and organization of content in isolation–is really not part of the script for teaching or is, at best, completely overshadowed.

Consider these ethotic/pathotic selection criteria for the National Teacher of the Year award as a bit of indirect evidence for the existence of this script:

  • Inspire students of all backgrounds and abilities to learn.
  • Have the respect and admiration of students, parents, and colleagues.
  • Play an active and useful role in the community as well as in the school.
  • Be poised, articulate, and possess the energy to withstand a taxing schedule.

Poised and articulate. In short, we tend to view better teaching exclusively as a function of better people (more compassionate or caring or moral or humane, etc.), and almost never as a function of better technical information (“mere technicians”)–a script which makes the compilation and dispensation of best-practice knowledge nearly unimaginable.

Sophisticated Educators, Please Stand Up

sophisticated educator

People, sophisticated and not, have been talking about false dichotomies in math education forever, it seems. And so have I (as long as you think of seven years ago as “forever”). And so has Professor David Clarke! His paper, titled Using International Research to Contest Prevalent Oppositional Dichotomies, was published in 2006, and I wrote it up on my old blog in 2008.

In that old post, though, I only highlighted some good quotations from Clarke’s piece. So perhaps it’s time to talk about it again in a little more detail. I’ll do just that in the next post, I promise.

But before we get to Clarke’s dichotomies, I find myself compelled to anticipate the inevitable reaction that Sophisticated Educators (to repurpose Dr Coyne’s “trademarked” phrase) have when cornered by what seem like caricatures of their professional ideas.

You see, Sophisticated Educators do not dichotomize in the ways Clarke describes. They are flexible and open-minded. They can, for example, be advocates of a teaching practice or philosophy and even cite research and make solid logical arguments defending it, but they are also, with no loss of reasonable vigor for their own preferences, aware that there are narratives that compete—directly and legitimately—with their own. Sophisticated Educators find the discussion about dichotomies “tedious” because they have long ago learned to accommodate competing theories and practices into different contexts within their own work.

Problematically, however, the messaging of Sophisticated Educators often overlaps with batshit insanity. And we simply don’t have access to the reasoning that would help us tell the difference between the two.

There is an analogous situation in religion. Both a Sophisticated Theologian and a fundamentalist share a fervorous belief in the supernatural, but whereas the former has arrived at his belief through some process of semi-rigorous investigation or inquiry, the latter believes what he does because it says so in a book. When pressed, the fundamentalist may quickly scribble some syllogistic ransom note, cut and pasted from pieces of different arguments (helpfully delivered by his Sophisticated counterparts), but this is only a makeshift shield, employed to deflect scrutiny. The content of his belief is derived solely from an ancient text. If he had grown up with a different ancient text, he would have a different belief.

Similarly, a Sophisticated Educator and his less sophisticated counterpart may claim some common ground in their opposition to lecture, say. Yet, whereas the former stands this belief on evidence and knows where it begins and ends, the latter believes it because someone told them to believe it—because it’s popular to do so. (Note that over 40% of Americans believe that God created humans in their present form if it seems incredible to you that large groups of good, smart people can believe silly things in the face of overwhelming evidence to the contrary.) The fundamentalist educator runs the idea into the ground, into the absurd, as does the fundamentalist believer—because no one is there to stop them from doing so.

The problem, among both co-religionists and co-educationists, if you will, is that there is no price to pay within the group for having bad reasons or no reasons for your beliefs. It seems to be enough that their constituencies’ opinions are pointing in the same general direction, because there is no robust and widespread tradition of scrutinizing the value of evidence or logical arguments within either community. (See granfalloon.)

And as long as there is no internal policing of critical thinking and scientific reasoning within education, it will be imposed, annoyingly, from the outside. If Sophisticated Educators are tired of the tedium of dichotomous thinking in education, perhaps we should practice what we preach and demand more often of fellow educators what we ask of students—to explain their reasoning.