Suppose a high school student cheats on a test. How harshly should a parent or teacher treat this offense? The efficacy of punishment in such situations has been controversial, and a new study sheds some light on the consequences of punitive control in moral matters.

When someone behaves immorally, a psychologist would typically say that the individual has not internalized the moral norm; that is, she may profess that an action is morally wrong, but she has not really taken that information to heart.

How can a parent or teacher encourage such internalization?

Attribution theories have been quite influential in how psychologists think about this matter. These theories hold that a parent should NOT ensure moral behavior through the use of harsh or punitive measures.

Doing so will gain compliance because the child will want to avoid punishment, but the child will not internalize the norm. He will attribute his "good" behavior not to his own belief in the moral precept, but to the desire to avoid punishment.

That theory would predict, then, that once the threat of punishment is removed, these children will engage in the forbidden behavior. That prediction is born out in research.

But another prediction of the theory is wrong. If children have not internalized the moral precept, they should feel no shame if they break the rule. But they do feel ashamed.

Sana Sheik and Ronnie Janoff-Bulman (2013) sought to resolve this paradox.

Their hypothesis: punitive parenting on moral matters does lead children to internalize the moral precept (hence the shame). But it also paradoxically makes children less well equipped to resist temptation (hence the tendency to engage in the immoral behavior).

Why would it be harder to resist temptation? Well, imagine that I say to you "Hey, it would probably be better if you didn't think about white bears." The idea of a white bear would flash in your mind, but you'd soon think about something else.

But suppose I said "FOR THE LOVE OF GOD AND ALL THAT IS HOLY, DON'T THINK ABOUT A WHITE BEAR, I BEG OF YOU." By making it such a charged request, I have paradoxically made it harder to not think about a white bear.

That's the theory. The experimental data seem to support it, although the logic is a little convoluted.

First, subjects were asked to fill out a questionnaire about discipline used by their parents. Responses were used to judge the extent to which parents were punitive about moral matters. (This use of questionnaires is common in this literature.)

Second, experimenters asked subjects to write out moral precepts; some subjects wrote about positive precepts (things that you should do) or proscriptive ones (things you should not do). They did this to prime subjects, that is, to get them thinking about these moral issues.

They varied the type of precept (positive or proscriptive) because harsh parental control is virtually always directed at moral proscriptions.

Third, they asked subjects to briefly describe the action depicted in some paintings. These paintings (like the one shown at left) are emotionally ambiguous--they are open to a wide range of interpretations. Crucially, subjects in the experiment were also told "Please do NOT use any words related to bad, immoral, undesirable behaviors, intentions, or outcomes (e.g., sneaky)."

Here's the idea. subjects who had first been prompted to think about moral proscriptions would be thinking about moral proscriptions when they saw the paintings, but they were told NOT to use those thoughts in describing the paintings. Inhibiting those thoughts would presumably "cost" them--their resources for regulating attention would be somewhat depleted. And that should be especially true for students whose parents were punitive about moral matters because such issues are hyper-charged for them.

How could you show that their attentional resources were depleted from the struggle to not think about moral proscriptions?

In the final phase of the experiment, the researchers administered a STROOP task--that's the task in which subjects are asked to name ink colors while refraining from mistakenly saying the color names spelled out. Doing so requires attention regulation, and the more tired you are from inhibiting the immoral descriptions of the paintings, the worse you'll do on the STROOP task.

And, as predicted, subjects whose parents were punitive were worse on the STROOP task than subjects whose parents were not.

But maybe kids with punitive parents are bad at the STROOP for other reasons. Maybe these just happen to be kids who lack attentional resources. In fact, maybe that's why they often got in trouble, and that's why their parents had to be kind of hard on them.

That's why the experimenters also included a condition where subjects were asked to think about positive moral precepts. Without that prime, everyone should find it easier NOT to think about proscriptive morality. And indeed, subjects whose parents were punitive don't have a particular problem with the STROOP in this condition.

As I promised, the chain of logic supporting the theory is a bit convoluted. Still, the basic account seem plausible.

If further data support the theory, the upshot for parents and teachers would be that harsh responses to moral transgressions won't work. They leave subjects feeling ashamed when they transgress, but paradoxically they make is harder to resist the temptation to transgress.

Shikh, S. & Janoff0Bulman, R. (2013). Paradoxical consequences of prohibitions. Journal of Personality and Social Psychology. Advance online publication: doi: 10.1037/a0032278

Most teachers t think that students today have a problem paying attention. They seem impatient, easily bored.

I’ve argued that I think it’s unlikely that they are incapable of paying attention, but rather that they are quick to deem things not worth the effort.

We might wonder if patience would not come easier to a student who had had the experience of sustaining attention in the face of boredom, and then later finding that patience was rewarded. Arguably, digital immigrants were more likely to have learned this lesson. There were fewer sources of distraction and entertainment, and so we were a bit more likely to hang in there with something a little dull.

I remember on several occasions when I was perhaps ten, being sick at home, watching movies on television that seemed too serious for me—but I watched them because there were only three other TV channels. And I often discovered that these movies (which I would have rejected in favor of game shows) were actually quite interesting.

Students today have so many options that being mildly bored can be successfully avoided most of the time.

If this analysis has any truth to it, how can digital natives learn that patience sometimes brings a reward?

Jennifer Roberts, a professor of the History of Art and Architecture at Harvard, has a suggestion.

She gave a fantastic talk on the subject at a conference hosted by the Harvard Initiative on Learning and Teaching (more here).

Roberts asks her students to select a painting from a Boston museum, on which they are to write an in-depth research paper.

Then the student must go the museum and study the painting. For three hours.

The duration, “meant to seem excessive” in Roberts’ words, is, of course, part of the point. The goal is that the student think “Okay, I’ve seen about all I’m going to see in this painting.” But because they must continue looking, they see more. And more. And more. Patience is rewarded.

Roberts gave an example from her own experience. As part of a book she was writing on 18th century American painter John Singleton Copley, she studied at length the painting A Boy With a Flying Squirrel. Although she is, obviously, an extremely experienced observer of art, Roberts noted that it was many minutes before she noticed that the shape of the white ruff on the squirrel matches the shape of the boy’s ear, and is echoed again in the fold of the curtain over his left shoulder.

If we are concerned that students today are too quick to allow their attention to be yanked to the brightest object (or to willfully redirect it once their very low threshold of boredom is surpassed), we need to consider ways that we can bring home to them the potential reward of sustained attention.

They need to feel the pleasure of discovering that something you thought you had figured out actually has layers that you had not appreciated.

That may not be the 21st century skill of greatest importance, but it may be the one in shortest supply.

Most everyone recognizes that talking on a cell phone while driving is a bad idea. It's distracting and so makes driving more dangerous.

It might seem that talking on a hands-free device would solve the problem, but it has been known for a while that's not so (e.g., Treffner & Barrett, 2004). Most of the distracting effect of mobile phone use is not due to looking away from the road to dial, nor the cost of holding the phone.

Talking on a phone is more demanding than talking to someone in the car: the audio signal is degraded, you have no visual information to rely on, your conversational partner doesn’t stop talking if the road situation becomes complicated, you may try to imagine being with the other person, and so on. (It is true, however, that driving is somewhat worse with hand=held than hands-free devices; Backer-Grøndahl & Sagberg, 2011.)

So what's the solution? Presumably, not answering your phone.

Now new data show that even that carries a cost.

A recent study (Holland & Rathod, 2013) had 27 young drivers use a highly realistic driving simulator, shown at right. Seven hazardous situations developed during the simulation (e.g., a pedestrian crossing the road, a car pulling out). Subjects had provided their mobile number to the experimenters, were aware that it might ring during the simulation, and that they should not answer it. The subject's cell phone rang during three of the hazards.

Seven dependent measures were collected, including crossings of the center line, collisions with other cars, and so on.

Ignoring the ringing mobile phone carried a cost. When their phone rang just prior to a hazard, subjects were more likely to hit pedestrians, to exceed the speed limit, and to cross the center line.

It is notable that these effects were more pronounced in subjects who said they usually answered their phone while driving than in subjects who said they did not. Hence, a significant contributor to the distraction may be the mental effort required to inhibit a habitual response.

What's the solution? The safest practice for drivers may be to turn the phone off, not just ignore it.

References


Backer-Grøndahl, A., & Sagberg, F. (2011). Driving and telephoning: Relative accident risk when using hand-held and hands-free mobile phones. Safety Science, 49, 324-330.

Holland, C., & Rathod, V. (2013). Influence of personal mobile phone ringing and usual intention to answer on driver error. Accident Analysis & Prevention, 50, 793-800.

Treffner, P. J., & Barrett, R. (2004). Hands-free mobile phone speech while driving degrades coordination and control. Transportation Research Part F: Traffic Psychology and Behaviour, 7, 229-246.

My Facebook feed today has lots of links to this article. The upshot: a new Pew study showing that Americans think that US 15 year olds rank "near the bottom" on international science tests, whereas the truth is that they "rank in the middle among developed countries."

I guess "the middle" covers a lot of terrain, but the way I look at the data, this assertion doesn't hold.

The international comparison in question is the 2009 PISA. Here are the rankings. (Click for larger image)

Most everyone would agree that it's not appropriate to compare scores of US kids to those of poorer countries with little infrastructure and funding to support education.

That's why the article specifies the ranking of the US among "developed countries," and by the author's reckoning, kids from 12 developed countries scored better, and kids from 9 developed countries scored worse. That would put US kids at the 41st percentile.

The US is ranked 30th on the list. Just eyeballing it, it's hard to see how 17 of the countries scoring better could be considered "not developed."

On measures of "developed" status would be the International Monetary Fund's definition of "advanced economies" which includes: Australia, Austria, Belgium, Canada, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hong Kong, Iceland, Ireland, Israel, Italy, Japan, Luxembourg, Malta, Netherlands, New Zealand, Norway, Portugal, San Marino, Singapore, Slovakia, Slovenia, South Korea, Spain, Sweden, Switzerland, Taiwan, United Kingdom, United States (Click image for larger image

By this definition of "advanced" US kids are 23rd out of 32 countries, or the 28th percentile.

It's true that "near the bottom" is too grim an assessment. But I can't see a way to put the 2009 PISA data together such that American kids are scoring about average.

I think of two very broad education reform camps. One calls into question the basic arrangement of institutions involved in U.S. education, arguing that the contradictory priorities in the system almost guarantee mediocrity. The solution, therefore, cannot be a nibbling around the edges of reform, but wholesale change: for some reformers, that means a market solution with greater parental choice, often coupled with more stringent human resources policies. For others the solution is a complete change—via technology—of the way we think of “learning.”

The second group of reformers argues that the system of education institutions is mostly fine, and that factors external to the system are responsible for our woes (which are, in any case, exaggerated). Some point to social and economic factors, others to the incoherence in curriculum (cf the Common Core), and others to the very reform measures (especially standardized tests used to evaluate schools and teachers) instituted by the other group of reformers.

In his new book Improbable Scholars,  UC Berkeley professor of education David Kirp offers an unusually readable account of what improved schooling would look like if you’re in the second camp. His explicit mission: to show that educational excellence is possible with the system as it exists now, even in districts that face enormous challenges.  He makes a fair case, given the limitations of the method he employs.

Improbable Scholars follows in the tradition of numerous education books by recounting time that the author spent in a school or district. Kirp tells the story of Union City, NJ, a city like so many others in the US: it has a great manufacturing past (“Embroidery Capital of the United States”) but was unable to find a new economic identity when cheap imports undermined its industries. Now most of its residents live in poverty, and a large percentage are recent immigrants who speak little English.

But Union City schools are unlike most districts with this profile. Despite the demographics, Union City students score about average on state tests. Ninety percent graduate high school, and sixty percent go on to college.

How they do it is Kirp’s subject, and in one sense this book has the feel of many others.  The account is told through stories. We meet Alina Bossbaly, a local legend of a third-grade teacher who is able to connect even with the most difficult children, and to make them feel a part of the classroom community, a process that has come to be known as “Bossbaly-izing” children.

We meet long-time Union City Mayor Brian Stack, strong supporter of education, savvy politico in a tough political town, and point man in the procurement of funding for the new 180 million dollar high school.  

Kirp is an academic, not a journalist, so although he’s an able writer, you’re not in the hands of a professional storyteller or fact-finder. But what you get from Kirp is a deeper analysis, a better-than-even tradeoff in this case.

So what is Kirp’s conclusion? He offers a list of key factors that he says must be in place for a district to thrive:

• District leaders put the needs of students ahead of those of staff
• They invest in quality preschool
• They insist that a rigorous curriculum is consistently implemented
• They make extensive use of data to diagnose problems
• The engender a culture of respect among the staff
• They value stability and avoid drama—they make a plan and stick with it for the long haul
• They never stop planning and reviewing the results of their plans.

When a district posts a remarkable record, it’s natural to ask “how did they do it?” The obvious problem is you’re looking at a single district. Maybe the real key to Union City is the Mayor. Maybe it’s the fact that many of the students come from countries with a tradition of respect for authority.

Kirp makes a case that other unusually successful districts have the same set of factors in common. It’s no substitute for a quantitative analysis, but KIrp at least shows that he’s aware of the problem.

And to be clear, I read the book in this wise, as something like an ethnographic study. Books like this offer detail and texture that larger scale, more rigorous analyses lack. In so doing, they ought to be inspiration to more quantitatively oriented researchers for what they are missing and where to turn their sights next. 

When it comes to criticizing methods he thinks are ineffective, Kirp is less sure-footed. He dismisses the notion that the relationship between school funding and student achievement is uncertain by noting that such suggestions leave administrators “shaking their heads.” There is an extensive and complex literature on the impact of funding, and the proper conclusion is by no means as simple Kirp would like us to believe.

Likewise, I’m rankled by Kirp’s assertion that “If you’re a teacher or principal whose job is on the line and your ordered to accomplish what seems unattainable, cheating is a predictable response.” This sounds an awful lot like a tacit pass to cheating educators.

The section of Improbable Scholars devoted to “what doesn’t work” left a bad taste in my mouth because it comes at he end of the book, but it is a mere five pages long.

If you’re curious about one vision of successful education that more or less maintains the status quo and actually gets into some detail, Improbable Scholars is a good choice.

What would you say if a major corporation took out a full-page ad in the New York Times to advertise a message that you thought was important and mainly agreed with, only to find that the text of the message was rife with misspellings, grammatical errors, and misused words?

That's the feeling that I get from the new video all over my Facebook feed (and with over 7 million views in 4 days) titled "Dove Real Beauty Sketches." If you haven't seen it, here you go. (I summarize it below.)

In brief, a woman describes herself to a forensic sketch artist, who cannot see her. He draws her portrait based only on her description, and then draws her again based on the description of a stranger who just met her. The woman then sees both portraits and recognizes that she has been rather hard on herself in her self description. (The process is shown for several women.)

The associated website calls this "a social experiment." But it's a terrible example of experimentation.

We are invited to draw the conclusion that women see themselves as less attractive than others do. I don't know the self-perception literature well, but I'm pretty sure this conclusion is right. But this experiment is a terrible way to illustrate that.

• The artist should be blind to condition. He knows when he's basing the drawing on the description of the subject vs. the stranger, and so could unconsciously bias the result
• The descriptions are not based on perception, they are based on memory. If you want to claim that it's about how women see themselves, not how they remember themselves, then each person should do their best to describe the woman based on the same photograph
• A the end the sketch artist tells each woman the source of each sketch. What would have happened if he had asked her to say which looks more like her, and to say which she thought was based on her description? If women's perception is really distorted, then the woman should see sketch based on her description as being more like her. An alternative hypothesis is that women more or less know what they look like, but talk about themselves in negative terms.
  
• The foregoing point raises another issue: social conformity. If the result is not due to perception but to people conforming to social norms, the difference in the sketches might be due to the women's reluctance to seem vain in their self-descriptions, and to the stranger feeling that he or she ought to describe the woman nicely.
  

How important are these criticisms to the overall message of the video? Not very. The point of the video is that women shouldn't be so hard on themselves in judging their looks. It's a good message.

That's why I draw the analogy to grammar, punctuation, and spelling in a written message. If Dove had published a print ad full of grammatical and spelling errors, I expect someone would have called them out on it.

Dove presents this as an experiment, but it's a terrible experiment. It would not have been hard to do a video making the same point with a better experiment. Any graduate student of social psychology could have improved this ten-fold.

I would have given the video 9/10 (subtracting one point for scientific sloppiness) if not for the statement made here in the video:

Well, I'd prefer a different message. Rather than "It couldn't be more critical to your happiness" and "be grateful for your natural beauty" I'd prefer a message amounting to "what you look like matters less than you think."

But I can't expect everything from a company selling beauty products. 8 out of 10, Dove.

A great deal has been written about the impact of retrieval practice on memory. That's because the effect is sizable, it has been replicated many times (Agarwal, Bain & Chamberlain, 2012) and it seems to lead not just to better memory but deeper memory that supports transfer (e.g., McDaniel et al, 2013; Rohrer et al, 2010). 

("Retrieval practice" is less catchy than the initial name--testing effect. It was renamed both to emphasize that it doesn't matter whether you try to remember for the sake of a test or some other reason and because "testing effect" led some observers to throw up their hands and say "do we really need more tests?")

Now researchers (Szpunar, Khan, & Schacter, 2013) have reported testing as a potentially powerful ally in online learning. College students frequently report difficulty in maintaining attention during lectures, and that problem seems to be exacerbated when the lecture occurs on video.

In this experiment subjects were asked to learn from a 21 minute video lecture on statistics. They were also told that the lecture would be divided in 4 parts, separated by a break. During the break they would perform math problems for a minute, and then would either do more math problems for two more minutes ("untested group"), they would be quizzed for two minutes on the material they had just learned ("tested group"), or they would review by seeing questions with the answers provided ("restudy group.")

Subjects were told that whether or not they were quizzed would be randomly determined for each segment; in fact, the same thing happened for an individual subject after each segment except that each was tested after the fourth segment.

So note that all subjects had reason to think that they might be tested at any time.

There were a few interesting findings. First, tested students took more notes than other students, and reported that their minds wandered less during the lecture.

The reduction in mind-wandering and/or increase in note-taking paid off--the tested subjects outperformed the restudy and the untested subjects when they were quizzed on the fourth, final segment.

The researchers added another clever measure. There was a final test on all the material, and they asked subjects how anxious they felt about it. Perhaps the frequent testing made learning rather nerve wracking. In fact, the opposite result was observed: tested students were less anxious about the final test. (And in fact performed better: tested = 90%, restudy = 76%, nontested = 68%).

We shouldn't get out in front of this result. This was just a 21 minute lecture, and it's possible that the benefit to attention of testing will wash out under conditions that more closely resemble an on-line course (i.e., longer lectures delivered a few time each week.) Still, it's a promising start of an answer to a difficult problem.

References

Agarwal, P. K., Bain, P. M., & Chamberlain, R. W. (2012). The value of applied research: Retrieval practice improves classroom learning and recommendations from a teacher, a principal, and a scientist. Educational Psychology Review, 24,  437-448.

McDaniel, M. A., Thomas, R. C., Agarwal, P. K., McDermott, K. B., & Roediger, H. L. (2013). Quizzing in middle-school science: Successful transfer performance on classroom exams. Applied Cognitive Psychology. Published online Feb. 25

Rohrer, D., Taylor, K., & Sholar, B. (2010). Tests enhance the transfer of learning. Journal of Experimental Psychology. Learning, Memory, and Cognition, 36, 233-239.

Szpunar, K. K., Khan, N. &, & Schacter, D. L. (2013). Interpolated memory tests reduce mind wandering and improve learning of online lectures. Proceedings of the National Academy of Sciences, published online April 1, 2013 doi:10.1073/pnas.122176411

Ben Goldacre is a British physician and academic, and is the author of Bad Science, an expose of bad medical practice that is based on wrong-headed science.  For the last decade he has written a terrific column by the same name for the Guardian.

Goldacre has recently turned his critical scientific eye to educational practices in Britain. He was asked by the British Department for Education to comment on the use of scientific data in education and on the current state of affairs in Britain. You can download the report here.

So what does Goldacre say?

He offers an analogy of education to medicine; the former can benefit from the application of scientific methods, just as the latter has.

Goldacre touts the potential of randomised controlled trails (RCTs). You take a group of students and administer an intervention (a new instructional method for long division, say) to one group and not to another. Then you see how each group of students did.

Goldacre also speculates on what institutions would need to do to make the British education system as a whole more research-minded. He names two significant changes;

• There would need to be an institution that communicates the findings of scientific research (similar to the American "What Works Clearinghouse.")
• British teachers would need a better appreciation for scientific research so that they would understand why a particular practice was touted as superior, and could evaluate themselves the evidence for the claim
  

As someone who has written shorter and book-length treatments of the role that scientific research might play in education, I'm very excited that Goldacre has made this thoughtful and spirited contribution.

I offer no criticisms of what Goldacre suggests, but would like to add three points.

First, I agree with Goldacre that randomized trials allow the strongest conclusions. But I don't think that we should emphasize RCTs to the exclusion of all other sources of data. After all, if we continue with Goldacre's analogy to medicine, I think he would agree that epidemiology has proven useful.

As a matter of tactics, note that the What Works Clearinghouse emphasized RCTs to the near exclusion of all other types of evidence, and that came to be seen as a problem. If you exclude other types of studies the available data will likely be thin. RCTs are simply hard to pull off: they are expensive, they require permission from lots of people. Hence, the What Works Clearinghouse ended up being agnostic about many interventions--"no randomized controlled trials yet." Its impact has been minimal.

Other sources of data can be useful; smaller scale studies, and especially, basic scientific work that bears on the underpinnings of an intervention.

We must also remember that each RCT--strictly interpreted--offers pretty narrow information: method A is better than method B (for these kids, as implemented by these teachers, etc.) Allowing other sources of data in the picture potentially offers a richer interpretation.

As a simple example, shouldn't laboratory studies showing the importance of phonemic awareness influence our interpretation of RCTs in preschool interventions that teach phonemic awareness skills?

Second, basic scientific knowledge gleaned from cognitive and developmental psychology (and other fields) can not only help us to interpret the results of randomized trials, that knowledge can be useful to teachers on its own. Just as a physician uses her knowledge of human physiology to diagnose a case, a teacher can use her knowledge of cognition to "diagnose" how to best teach a particular concept to a particular child.

I don't know about Britain, but this information is not taught in most American schools of Education. I wrote a book about cognitive principles that might apply to education. The most common remark I hear from teachers is surprise (and often, anger) that they were not taught these principles when they trained.

Elsewhere I've suggested we need not just a "what works" clearinghouse to evaluate interventions, but a "what's known" clearinghouse for basic scientific knowledge that might apply to education.

Third, I'm uneasy about the medicine analogy. It too easily leads to the perception that science aims to prescribe what teachers must do, that science will identify one set of "best practices" which all must follow. Goldacre makes clear on the very first page of the report that's NOT what he's suggesting, but to the non-doctors among us, we see medicine this way: I go to my doctor, she diagnoses what's wrong, and there is a standard way (established by scientific method) to treat the disease.

That perception may be in error, but I think it's common.

I've suggested a different analogy: architecture. When building a house an architect must respect certain basic facts set out by science. Physics and materials science will loom large for the architect; for educators it might be psychology, sociology et al. The rules represent limiting conditions, but so long as you stay within those boundaries there is lots of ways to get it right. Just as physics doesn't tell the architect what the house must look like, so too cognitive psychology doesn't tell teachers how they must teach.

RCTs play a different role. They provide proof that a standard solution to a common problem is useful. For example, architects routinely face the problem of ensuring that a wall doesn't collapse when a large window is placed in it, and there are standard solutions to this problem. Likewise, educators face common problems, and RCTs hold the promise of providing proven solutions. Just as the architect doesn't have to use any of the standard methods, the teacher needn't use a method proven by an RCT. But the architect needs be sure that the wall stays up, and the teacher needs to be sure that the child learns.

I made one of my garage-band-quality videos on this topic.

There's more to this topic--what it will mean to train teachers to evaluate scientific evidence, the role of schools of education. Indeed, there's more in Goldacre's report and I urge you to read it. Longer term, I urge you to consider why we wouldn't want better use of science in educational practice.

Illiteracy and its costs to individuals and to society has long been a focus of concern in public policy. A corresponding lack of ability in mathematics--innumeracy--has received increasing attention in the last few decades. The ability to use basic math is more and more important as modern day society grows more complex.

Some children have a problem in learning to read that is disproportionate to any other academic challenge they face. Some children have a corresponding problem with math. For some reason, the ideas just don't come together for these students.

In a recent article, David Geary (2013) reviews evidence that one cause of the problem may be a fundamental deficit in the representation of numerosity.

Geary describes three possible sources of a problem in children's appreciation of number.

To appreciate where the problems may lie, you need to know about the approximate number system.  All children (and members of many other species) are born with an ability to appreciate numerosity. The approximate number system does not support precise counting, but allows for comparison judgements of "more than" or "less than." For example, in the figure below you can tell at a glance (and without counting) which cloud contains more dots.

This ability --making the comparison without counting--is supported by the approximate number system. (Formal experiments control for things like the total amount of "dot material" in each field, and so on.)

The ability depends on not on the absolute difference in number of dots, but on the ratio. Adults can discriminate ratios as low as 11:10. Infants can perform this task, but the ratio of the difference in dots must be much greater, closer to 2:1.

Many researchers believe that this approximate number system is the scaffold for an understanding of the cardinal values of number.

So the first possible source of problems in mathematics may be that the approximate number system does not develop at a typical pace, leaving the child slow to develop the cognitive representations of quantity that can support mathematics.

A second possibility is that the approximate number system works just find, but the problem lies in associating symbols (number names and arabic numerals) to the quantities represented there. Geary speculates that regulating attention may be particularly important to this ability.

Finally, It is possible for children to appreciate the cardinal value of numbers and yet not understand the logical relationships among those numbers, to appreciate the structure as a whole. That's the the third possible problem.

Geary suggests that there is at least suggestive evidence that each of these potential problems creates trouble for some students.

The analogy to dyslexia is irresistible, and not inappropriate. Math, like reading, is not a "natural" human activity. It is a cultural contrivance, and the cognitive apparatus to support it must be hijacked from mental systems meant to support other activities.

As such, it is fragile, meaning it lacks redundancy. If something goes wrong, the system as a whole functions very poorly. Thus, understanding how things might go wrong is essential to helping children who struggle early on.

Gear, D. (2013) Early foundations for mathematics learning and their relations to learning disabilities. Current Directions in Psychological Science, 22, 23-27.

We are in the midst of an effort to explore what the new technologies enabled by powerful computing and reliable long-distance connection will mean to higher education. (There is, of course, a parallel effort in K-12, but that’s another topic.)

A new entrant is poised to make a bid, and it’s worth some study.

The Minerva Project was initiated by Ben Nelson, the man behind Snapfish (a photo website). His vision is of a university that offers an “uniquely rigorous and challenging university education." (At a price, we might add, that is a relative bargain--reportedly, the target cost is something like half of what the Ivys charge).

The idea is that classes will be delivered via video, and students will then engage in discussion and debate. Importantly, and in pointed contrast to MOOCs, class size will be limited to 25.

Because the university is virtual, students can live anywhere, but they will be encouraged to live in a different world city each semester, perhaps living together to gain some of the face-to-face interactions that many observers consider a significant advantage of bricks-and-mortar university life.

The curriculum will not rest on traditional academic subject divisions (some English, some math, some science) but rather on four essential skills: critical thinking, use of data, understanding complex systems, and effective communication. If that sounds squishy, be forewarned that the courses are planned to be demanding, and students who do not perform well will (gasp) fail the course.

Minerva is trying something quite different than other online higher ed options. Online universities exist, but their appeal has been their low price and low academic standards and, to a lesser extent, flexibility in scheduling. They claim to offer a degree that is comparable to a traditional degree, though few believe that they do.

It’s still not completely obvious how MOOCs (as implemented in Coursera and edX) will evolve, but no one thinks the long-term purpose is to give away courses. The interpretation I hear most often is that they will not seek replace standard degrees, but will offer more of an a la carte education; you take, say, 12 engineering courses (earning certificates showing that you’ve done the work) in the hopes that the reputation of the participating institutions will be enough to persuade an employer that passing the courses means you’ve got the chops for a job—and you’ve paid just a tiny fraction of what a traditional engineering degree would have cost.

Minerva seeks a third way. It promises an elite education, comparable to the most selective schools in the US. They are gambling that this option will appeal to students who were qualified to attend a big-name university, but didn’t get in.

It’s a darn good bet that there are plenty of frustrated students who thought they had the record for admission to Big-Name U; these places reject 75% or more of their applicants.

It’s no accident that the Minerva website notes that admissions decisions will disregard “lineage, state or country of origin, athletic prowess, or ability to donate.” In other words, "if you fear that you will be jostled by affirmative action targets, athletic admissions, legacies, etc., apply here."

The question is whether these students will see Minerva as a viable alternative to traditional schools.  

Naturally, that will depend on the quality of the courses and the curriculum. Minerva has not hired any faculty yet, but Nelson has some high profile members on his board (Larry Summers, Bob Kerrey) and they just hired Steve Kosslyn as the founding Dean of the College. Kosslyn has been a Dean at Harvard and was most recently Director of the Center for Advanced Study of Behavioral Sciences at Stanford. To lure someone that capable to devote all of his energies to Minerva bodes well for the project.

We may be seeing the first of new wave of elite colleges. In the colonial era and following, this country saw elite colleges founded to train clergy (Harvard, Yale, Princeton). Better than a century later there was another spate, as wealthy industrialists founded new schools or heavily endowed existing ones (U of Chicago, Stanford, Vanderbilt).

There may well be room for a new model of elite higher education, and Minerva, as the first one out of the gate, holds a significant advantage.  

Note:  Thanks to Chris Chabris, whose Facebook post made me aware of Minerva.