It's one of the most familiar (and frustrating) problems teachers encounter. Students learn something new (say, a standard solution technique for a standard mathematical problem) but then fail to recognize the problem type when they encounter it again. For example, students may learn the idea of a "common factor" in equation form in an algebra class and fail to see that the same idea can be applied in a word problem. 

This is usually called the problem of transfer, and a classic laboratory problem was devised by Mary Gick & Keith Holyoak. 

It's a difficult problem, and most people are unable to solve it. If I tell you that this story may provide some inspiration, you'll probably get it. 

The interesting finding re: transfer is that if you simply ask people to read the military story and then to try to solve the radiation problem, most people don't see the analogy. They have no problem seeing it when told to look. But they don't spontaneously see it. And of course there's usually not someone around to give you a gentle elbow in the ribs, and drop a hint. You have to think of it on your own. 

This problem has proven very difficult to solve. One promising solution is to give subjects something to do that forces them to focus on the underlying structure of the problem. The underlying structure in the example above is "to avoid collateral damage, disperse your forces and converge at the point of attack." The underlying structure is expressed with tumors and rays in the problem and via a fortress and armies in the story. 

Dedre Gentner and her collaborators have tried (with some success) to improve transfer by asking people to compare problems. When you compare problems with the same deep structure, that obviously focuses attention on that deep structure and so you'll remember it better later.

A disadvantage of comparison is that the instructor must provide parallel versions for all problems. Ricardo Minervino and his colleagues sought a technique that would provide similar benefits, but might be more applicable to classroom situations.

In their experiment, subjects first read the fortress-army story (along with two other stories). At transfer, everyone was asked to solve the tumor-rays problem, but one group was also first asked to invent an analogous problem. Examples of the problems subjects invented appear below:

Subjects who invented an analogous problem were more likely to successfully solve the radiation problem compared to subjects not asked to invent a problem, 25% vs 10%. Independent raters judged the quality of the invented problems as analogous to the target problem, and further analysis showed that the better the analogy they created, the more likely they were to solve the target.

The experimenters also showed that it wasn't just the deeper thought required by the problem creation that made those subjects more likely to get the problem right. Another control group was given the tumor-rays problem and were asked to create an analogous problem before solving it, but they did not read the fortress-army story beforehand. Just 10% of these subjects solved the radiation problem.

In terms of the psychological mechanism behind this effect, it's not a huge surprise. Again, it's a technique that prompts people to focus attention on the deep structure, just as comparison does. What's nice about this technique is that, as the authors note, it removes the burden from the instructor to devise parallel problems. But that also gives students the freedom to create an "analogous" problem that isn't really analogous. So the instructor needs to check up on the problems students create.

Still, it's useful to know about the consequences when students create a new problem, and teachers may find it useful in some contexts

Maybe it's just on social media, but I often read this proffered solution to improve children's reading: "just get 'em reading" or "just surround them with books."

Certainly, there's some logic to the idea. We might hope that children's desire to learn about their world is natural, innate. That might mean that most of the problem is one of access. If we provide easy access to books, children will happily read. That's the idea behind book floods: flood a classroom with books, and kids will read, and will end up with better attitudes toward reading and greater motivation to read in the future.

​In a recent study, researcher Susan Neuman found that a book flood, even with a great deal of support, is not a guaranteed success.

​Neuman focused on information books in childcare centers for 3-4 year olds. They ensured there was a comfortable room with at least 500 books, child-size furniture, and a few puzzles and games. Even better, they had preschool specialists who read information books to the children, they made the books available to take home, and they had an outreach program for parents.

There was also a 20-hour per week librarian who used carefully planned sessions to draw kids in to book topics. Here's a description from the paper: "The librarian would begin with songs and rhymes, then read
three information-related books to the children, pointing out new words (e.g., considered essential to story understanding), asking questions, getting children to predict events, and holding a brief discussion following the general mnemonic of the INQUIRE model, described below. Children were then encouraged to check out a book after the reading (e.g., open choice) for the week."

At the end of the year-long intervention, compared to children in a control group, the intervention kids showed no improvement in receptive or expressive vocabulary, word naming, or knowledge of information text. Nothing.

What are we to make of these null results? 

Neuman has done book flood studies before that have shown positive effects, as have others...but there is at least one other null effect published. What might have made the difference here? 

As Neuman notes, there are several possibilities. She speculates that, although they tried to engage the children with read-alouds and other activities, perhaps more needed to be done, especially from a psychological point of view. She notes that the specialists doing the read-alouds were not the children's classroom teachers, and so didn't know the kids well, and might have had a harder time connecting with them. Neuman aptly contrasts physical proximity of books (which they provided) to psychological proximity of literacy (which they might not have provided).

That observation makes sense, and brings to mind Jimmy Kim's work on providing children with books for summer reading. Kim reports these programs don't do much good unless you ensure that kids discuss the books with their parents, or in some way interact with them. 

Taking this "it's not quite so simple" still further, it calls to mind Freddy Hiebert's observation that, for children to learn vocabulary for text, the to-be-learned word must be repeated. That's unlikely to happen by chance, and so requires some planning in the reading program. 

The same applies for background knowledge. As Marilyn Jaeger Adams has pointed out, even if you succeed with the "just get 'em reading" plan students are unlikely to bump into all the knowledge you hope they will (given that background knowledge is a key contributor to reading comprehension). What they need to read to gain the knowledge needs to be planned in a curriculum. 

There message here, I think, is that we should not underestimate the challenge of what we're trying to do. If we aim to raise children who love to read and who read well, we are taking on a significant challenge. It may look easier than it really is, because when it happens in families, we don't see most of the interactions that matter. And of course parents have many advantages over teachers in getting their children to love reading and to excel as readers. That should make us redouble our determination and our effort.

​Personalized learning is, of course, not new, but there is much greater urgency in evaluating its potential advantages and drawbacks, largely because of the promise/threat of two gargantuan funders (Gates & Chan-Zuckerberg) to make personalized learning a priority.

The RAND report (handily summarized here in Education Week) had a little something for the lovers and the haters of the idea. On the negative side, researchers concluded that enthusiasm for personalized learning was getting ahead of any research basis (i.e., we don’t know if this works), and the problem a lot of people pointed to when we used to call it “differentiated instruction” is 

​still with us—it seems like personalized learning will be very time-consuming for teachers. On the positive side, RAND researchers concluded the two most-feared bogey-men—school as an all-day screen-fest, and corporations gobbling up personal data—are not a problem, at least in the schools RAND evaluated.

The RAND report also mentioned a point that most of us already knew—there’s not an agreed-upon definition of personalized learning. I see the term used to highlight three possible features of a learning environment. These three are not mutually exclusive.

• ​First, it might represent a tailoring of pedagogical methods to individual children—one child might learn best like this, whereas another child learns best like that. “Personalized” means “personalized pedagogy.”
• Second, it might mean allowing children to learn at their own speed. There’s no differentiation of pedagogical strategy, but kids who understand move on, and kids who need more instruction get it. “Personalized” means “personalized pace.”
• Third, it might mean different content for different students, depending on their interests. “Personalized” means “personalized curriculum.”

Any or all of these seem worthy to me, but each carries a challenge that I’ve not seen discussed.

Personalized pedagogy. I can see two ways of doing this: theoretically driven, and theoretically agnostic. In the theoretically driven scheme, we have a theory in mind about different types of learners. For example, when learning an abstract idea, maybe some people learn best by exposure to many concrete examples before you hit them with the abstraction, whereas others learn best if they see the abstraction before the concrete examples. So education improves if we (1) have in hand distinctions like this that make a difference to learning and (2) have a reliable way to putting kids in the right category.

The problem is that we don’t have reliable theoretical distinctions in hand. (And yes, learning styles would be a subset of this idea.)

The theoretically agnostic version might work this way: you don’t pretend to know the differences among students. Instead, you let a learning algorithm figure it out for you. You note which lessons a child learns more quickly or more slowly, and keep a running tally. Over time, you should see which type of lesson each child learns more quickly. Then you can give the child that type of lesson more often (presumably still varying them some, so that you can continue to fine-tune your understanding of the child’s preference.)

This method is actually not theoretically agnostic. You still need to pick features that you’ll code for each lesson. The number of features we might attribute to each lesson is pretty big. That is not a problem for the learning algorithm, but may be a problem for creating lesson plans. The larger the number of features I code, the more likely I am to capture a set of features that’s a good fit to an individual student. But the larger the set of features, the longer it takes me to sample the feature space (i.e., the more lessons I need to administer to get an idea of what’s a good fit for the child).

But the biggest problem is that I’m greatly increasing the number of lessons I need to have at the ready. If you learn math best in a series of 5 brief lessons, with lots of ducks used as examples, with frequent review of previous concepts, and with the use of spatial metaphors, whereas I learn math best in a series of 3 slightly longer lessons, with examples from the solar system, and a moderate amount of review of previous concepts, and the use of number line metaphors. Now suppose everyone in the class has their own set of preferences. How are these specialized lessons going to be generated?

Personalized Pace: The challenge here is similar to the last point made about personalized pedagogy. In this plan we’re not thinking that different children will receive pedagogically different lesson plans. But, if you understand a lesson and I don’t, I will get another explanation, another set of problems to work, something. This decision to offer more instruction and support to me must be based on some decision about my performance to that point. So we have a bunch of decision points where kids either move to new content or review old content in a different way. As we add more of these decision points we have greater and greater opportunity to adjust the lesson based on the students current understanding.

What people often fail to realize is that each decision point also demands new material. A new explanation. A new metaphor. A new set of problems to work. With more decision points, the pathway through the lesson gets “bushier” and “bushier” and we greatly multiply the amount of high-quality instructional content we need. That’s a formidable challenge.

Personalized content: What if we allow students a greater voice in selecting the content that makes up their education? I’m ready to believe that there could be a benefit to student motivation, and that for some, that benefit could be significant.

But I also see a trade-off. Students will go deeper on X, and will slight Y. When student choice is to affect curriculum, advocates tell skeptics that breadth will still be assured. Choice represents a bonus, an “and.” I’m doubtful. I think it will be an “instead.” Even curricula with the explicit goal of breadth, of minimum competence in all domains, struggle to achieve it. If significant time is siphoned off for a particular domain, proficiency in others will suffer.

Practice matters. Students need time to work with ideas to really absorb them, make them part of their thinking. Even minimum competence requires exposure and thinking over the course of a few years.

If students become more narrow—that is, really good at what they are interested in, and less good at what they are not interested in--that’s not intrinsically bad. It’s a choice. It’s a way to reify an educational value. Your goal can be breadth or your goal can be depth. The personalized content approach is a depth approach. We should not kid ourselves that personalized curricula will give us both.

So, all in all, is personalized learning worth pursuing?
​
I’d rather start with changes that research gives us more confidence will help kids. But hey, that’s just my personalized point of view.

I've been very skeptical of 21st century skills (e.g., see here nearly ten years ago, and again here). My skepticism grew out what I perceived as a neglect of domain knowledge among the proponents of 21st century skills and (to a lesser extent) a sense that the truly new part of "21st century" is a relatively small part of what students need to learn: most of student time should be devoted to math, science, reading, civics, history, etc., much the way it the looked in the 20th century.

Sam Wineburg's recent research shows that I was wrong.

Wineburg has confirmed the suspicion that many have had regarding student's use of Internet sources. Students are too trusting of what they read on the Internet. Most striking, they implicitly trust Google to verify sources for them--whatever Google lists first, they figure must be a good source.

Even when asked to verify the accuracy of pages they read, they do poorly. They are suckers for a slick looking page, and for the self-description of the authors--i.e., if the authors say "we are a non-profit, devoted to the welfare of children," students are all too likely to believe them. 

I think my assessment of 21st century skills as a small part of what student need to know was inaccurate, because evaluating sources on the Internet is such a substantial part of student work today. 

In addition, I've always thought that the solution is for students to understand what the heck you're reading about. You won't fall for the Northwest Pacific Tree Octopus hoax page if you know even a little bit about cephalopods. I thought that because of work showing what I took to be the limited utility of reading comprehension strategies, and the decisive importance of content knowledge to comprehension. 

But Wineburg and his associates have shown that there's a useful, content-free strategy that could a big difference in student assessment of website accuracy. Through study of professional fact-checkers, Wineburg suggests that students be taught to 
1) read laterally. Instead of going through a checklist of features of the website in question (the usual advice) encourage students to get OFF the website to see what others say about it.  That's the way to discover that it's actually a front for a hidden organization, for example, or has some other agenda.
2) show click restraint. That's Wineburg's term for refraining from clicking on the first result from a Google search. Instead, students should peruse the short sentences accompanying each result to get a sense of what they'll find on each site
3) use Wikipedia wisely. There's more information on Wikipedia than the main article, and Wineburg specifically recommends the "Talk" page, which include ongoing conversation about more controversial aspects of the article topic and can be especially revealing. 

I'm not buying the whole 21st Century Skill bill of goods....but Wineburg's work on Internet search is hugely valuable, and I think all educators should know about it. 

Here's a free, recent article summarizing it from Wineburg, written with his colleagues Sarah McGrew, Teresa Ortega and Joel Breakstone.

I concluded that many teachers believe learning styles theory is accurate in about 2003. It was perhaps the second or third time I had given a public talk to teachers. I mentioned it in passing as an example of a theory that sounds plausible but is wrong, and I felt an immediate change in the air. Several people said “wait, what? Can you please back up a slide?”

Since then I’ve written a couple of articles about learning styles (here and here), created a video on the subject, and put an FAQ on my website. Last week I was on the Science Friday radio program (With Kelly Macdonald and Lauren McGrath) to talk about learning styles and other neuromyths.

I put energy into dispelling the learning styles myth because I thought that audience of educators was representative—that is, that most teachers think the theory is right. But with the exception of one recent study showing that academics often invoke learning styles theories in in professional journal articles (Newton, 2015) there haven’t been empirical data on how widespread this belief is in the US.

Now there are.

Macdonald, McGrath, and their colleagues conducted a survey to test the pervasiveness of various beliefs about learning among American adults (N = 3,048), and among educators in particular (N =598). Similar surveys have been conducted in parts of Europe, East Asia, and Latin American, where researchers have observed high levels of inaccurate beliefs on these issues.
Learning styles theory was endorsed by 93% of the public, and 76% of educators. Data regarding other neuromyths (common misperceptions about learning or the brain) are shown in the table below (from the paper).

As the authors acknowledge, there are limitations to the interpretation, in particular regarding the sample. The subjects were visitors to the site TestMyBrain.org, and so it’s difficult to know how they differed from a random sample. Still, neuromyths were endorsed at rates similar to those observed in other countries.

Why is acceptance of the idea so high? No one really knows, but here’s my tripartite guess.

First, I think by this point it’s achieved the status of one of those ideas that “They” have figured out. People believe it for the same reason I believe atomic theory. I’ve never seen the scientific papers supporting it (and wouldn’t understand them if I had) but everyone believes the theory and my teachers taught it to me, so why would I doubt that it’s right?

Second, I think learning styles theory is widely accepted because the idea is so appealing. It would be so nice if it were true. It predicts that a struggling student would find much of school work easier if we made a relatively minor change to lesson plans—make sure the auditory learners are listening, the visual learners are watching, and so on.

Third, something quite close to the theory is not only right, it’s obvious. The style distinctions (visual vs. auditory; verbal vs. visual) often correspond to real differences in ability. Some people are better with words, some with space, and so on. The (incorrect) twist that learning styles theories add is to suggest that everyone can reach the same cognitive goal via these different abilities; that if I’m good with space but bad with words (or better, if I prefer space to words), you can rearrange a verbal task so that it plays to my spatial strength.

That’s where the idea goes wrong wrong. First, the reason we make the distinction between types of tasks is that they are separable in the brain and mind; we think verbal and visual are fundamentally different, not fungible. Second, while there are tasks that can be tackled in more than one way, these tasks are usually much easier when done in one way or another. For example, if I give you a list of concrete nouns, one at a time, and ask you to remember them you could do this task verbally (by repeating the word to yourself, thinking of meaning, etc.) or visually (by creating a visual mental image). Even for people who are not very good at imagery, the latter method is a better method of doing the task. Josh Cuevas has an article showing this point coming out early next year: people’s alleged learning styles don’t count for anything in accounting for task performance, but the effect of a strategy on a task are huge. 

​A final note. I frequently hear from teachers that they learned about the theory in teacher education classes. I've looked at all of the well-known educational psychology textbooks, and none of them present the idea as correct. But neither do they debunk it. Teachers are, according to the survey, more accurate than the general public in their beliefs about learning, but they should be way ahead. Debunking these ideas in ed psych textbooks ought to help. 

Like so many other Americans, I am starting this week despondent about the weekend events in Charlottesville, Virginia. Yes, I work there and live nearby, so there was some poignancy in seeing events unfold in streets and near buildings I know so well. But more, it’s the bitter recognition of how far we have to go. Like others, I am certain that we’re not seeing a resurgence of racism, antisemitism, and chauvinism, but a more realistic look at what has always been there.

Educators might be particularly dejected. Have we not in some way failed? How can people believe ideas that are so self-evidently wrong? Are they that ignorant of basic facts? Are they that incapable of probing the soundness of the ideas they espouse?

Key tenets—at least those made public—of the organizer of Saturday’s rally are (1) white people are oppressed in America; (2) European culture is dying (3) the white race is “dispossessed.” (4) the solution to these so-called problems is what he calls “peaceful ethnic cleansing” which he apparently thinks can be squared with the Constitution. Readers of this blog will not need to be convinced that these ideas are factually laughable, so I won’t marshal evidence against them.

You can’t blame people for thinking that anyone who believes this nonsense simply closes their mind to facts and is motivated by ideology—an ideology that is plain evil. What good is education in the face of someone who closes their mind to facts?

I’ve put it crudely, but I think something close to this is right. Yet it’s worth trying to refine our understanding of the motivation of the Nazis* who gathered in Charlottesville.

People hold beliefs for multiple reasons. One—but only one—reason people believe things is in an effort to make their beliefs coordinate with reality, to be in line with the objective truth about the world.

People also hold beliefs to belong to a group, to maintain social ties. They believe things to regulate emotions. They believe things to promote and maintain their self-image. The believe things to protect values they consider important.

So for example, I might believe that a secret cabal of Jews runs the world economy because my close friends and family believe it; I hold this belief, in part, to maintain social ties. Now suppose I hear that some friends have threatened an elderly Jewish store owner in my neighborhood, which upsets a little, because he’s a nice old guy who has always been pleasant to me. I may adopt a new belief—the old man must be part of the cabal, or at least knows about it—as a way of regulating my emotions. I don’t want to feel bad for the store owner, and I don’t want to believe my friends are doing something wrong. So I start to have doubts about the old man.  

This is why persuaders work so hard to create doubt; doubt as to whether we know cigarettes cause cancer, doubt as to whether whether we know human activity changes the climate, doubt about whether we know GMOs are safe. If we doubt, that means there is not a settled reality out there in the world with which we must be sure our beliefs align. That allows the other influencers—emotion, social ties, sacred values—room to operate. We tell ourselves “no one really knows” and so we go with beliefs that feel right.

An important aspect of this situation is that is that we never admit to ourselves that we are influenced by anything other than facts. I may believe the science linking cigarettes to cancer is “unclear” because thinking that it’s clear, coupled with the fact that I smoke, makes me very anxious. But I’ll never say “I choose not to believe the science because doing so frightens me.”

This fact is our secret weapon. People actually want to believe what’s true. So if I could sit the Nazis down and present evidence that they are wrong about racial differences, they would change their minds? How much factual evidence is required to change an inaccurate belief obviously varies, depending the strength of the other motivators—to what extent to you believe something because it maintains social ties, is important to your identity, and so on.

It would be very very difficult indeed to persuade the people who marched in Charlottesville that their ideas about race, religion, immigration, history, the United States government, and many other things are wrong. But for each person who marched, there are likely hundreds or thousands who did not march but who read about these events and thought “Huh. Well, I see their point.”

These people might be reached. The children of these people might be reached.

The way to reach them is with facts, by building in them a habit of seeking evidence for their own beliefs, and with the skills to seek and evaluate that evidence. That’s the long-term goal of educators. So if you’re an educator, don’t lose heart. If you think your curriculum needs to do a better job on the history of the KKK, or Nazism, or the Constitution, or whatever, then work for that change. But in the main, keep doing what you’re doing. Every educator has learned, years after the fact, that he or she had a profound influence on a student, although at the time that was not at all obvious. The same principle applies here. You likely do not know the good you are doing.

In the shorter term, educators and non-educators can help by fighting fake news in all its aspects. Fake news stories are designed to provide what looks like objective evidence for a wished-for belief. Everyone has a friend or two on Facebook who reposts these stories. Don’t just roll your eyes. Let your friend know it’s not accurate.

Equally important, stand up for mainstream media sites that get it right. If you don’t already do it, support a newspaper you admire by paying for a subscription. Over the last decade I have been interviewed for hundreds of stories about education. With apologies to my friends in these media, my impression is that writers for television, radio, and magazines all, to a greater or lesser extent, worry about entertaining their audience. In my experience, newspapers are the only medium where truth is the primary concern. You know newspapers are struggling. Do your small part.

Truth is our greatest weapon against senseless evil. Fight with it. Fight for it. And don’t be discouraged.
 
*I’m aware that not all of the marchers would call themselves Nazis and I’m aware they varied in the degree to which they were coy about their veneration for Nazism. I tend to paint racist, antisemitic xenophobes with a broad brush. It’s a personal failing I’m not really working to correct. 

I was very pleased to collaborate with Daniel Ansari, (@NumCog) a renowned authority on the cognition of mathematics, for this blog. 

Just in case you have been away from this planet for the last few months, ‘Fidget Spinners’ are the latest toy sensation. Some have suggested (without any evidence) that this new gadget is "perfect for children with attention deficit hyperactivity disorder, autism, anxiety." Although there's no evidence for that, kids love them, which has prompted a flurry of interest in possible educational applications (see here), and educators have come up with creative ways of integrating spinners into educational activities (when they are not banning them, see here).
 
One such idea was the subject of a tweet by Dan on June 14th. The idea is simple: students use the spinner as a timer and try to solve as many math fact problems as possible while it is spinning.

This seems to us a simple, harmless and perhaps even fun thing to do, and most people on Twitter took it that way. Most, but not all.
 
Negative responses fell into two categories. One suggested that timed practice would lead to math anxiety. The other suggested that this kind of practice might legitimize the much maligned ‘drill and kill’ approach to teaching math.
 
If a teacher doesn’t like an activity, that’s obviously reason enough not to use it as far as we’re concerned—we’re not in the business of advocating for particular classroom work. But we can point to the research literature bearing on the two common concerns, and based on this research, we don’t think they have merit.
 
Regarding anxiety: This issue has been raised most prominently by Professor Jo Boaler of Stanford University. For example, she argued in a recent blog that  “…timed tests are a major cause of this debilitating, often lifelong condition [referring to math anxiety].”  
 
First, let’s note that the fidget spinner worksheet offers timed practice, not timed assessment, which Boaler mentions. It seems to us that in a zero-stakes situation like a worksheet, the main agent of anxiety would be social comparison, an issue that teachers have plenty of experience handling.
 
Second, when it comes to timed assessments, the evidence for an anxiety link is still lacking. Boaler cites Ramirez et al (2013) in her blog. This article examined the relationship between working memory and math anxiety and showed, perhaps counterintuitively, that math anxiety impacts students with high working memory more than it does those with relatively lower working memory capacity. The authors argue that because math anxiety affects working memory, through intrusive thoughts and ruminations (“I can’t do this”, “I am terrible at math”), that students who typically use working-memory-demanding strategies are hit the hardest. These data say nothing about speeded math practice--the measure of math achievement used by Ramirez et al was untimed.
 
In a review of Boaler’s book, Mathematical Mindset , Victoria Simms (@DrVicSimms) writes “…she discusses a purported causal connection between drill practice and long-term mathematical anxiety, a claim for which she provides no evidence, beyond a reference to ‘Boaler (2014c)’ (p. 38). After due investigation it appears that this reference is an online article which repeats the same claim, this time referencing ‘Boaler (2014)’, an article which does not appear in the reference list, or on Boaler’s website.”
 
Again, it seems obvious to us that if a teacher feels that this sort of activity would make her students anxious, she won’t use it. But it’s not accurate to claim that research shows that this sort of activity generally makes students anxious.
 
What of the second concern, that students should focus on developing a conceptual understanding of math rather than being able to recall math facts speedily?
 
Arguments for speeded recall of math facts are not arguments against building students' conceptual understanding of mathematics.  As @MrReddyMath  put it:

But cognitive scientists have long argued that there is an iterative, bidirectional relationship between the development of procedural math skills (such as being able to recall your math facts) and conceptual understanding (such as understanding the inverse relationship between addition and subtraction). That was the conclusion of the final report of the National Mathematics Advisory Panel in 2008.
 
It was also the conclusion of Professor Bethany Rittle-Johnson, a developmental psychologist at Vanderbilt who has extensively researched the relationship between procedures and concepts in math learning.  When asked about the debate regarding memorizing math facts vs. developing conceptual understanding in a 2016 interview she said “Actually, I think it's a silly argument because the evidence is pretty clear that children really need to do both things. Understanding is super-important, but understanding relies on knowing enough that you can understand it. If you have to spend all your time figuring out what two plus three is, then you can't notice relationships between number pairs, [for example].” Practicing math facts should be one of the methods used to help students build solid foundations to scaffold their learning of mathematics.
 
Fine, but why, you might ask, apply the pressure of timing practice? Does speed matter?
 
It does. When working a complex problem you not only want to pull simple math facts from memory, you want to do so quickly, so that the other work can proceed apace. Indeed, adults with stronger higher-level math achievement retrieve math facts faster (Hecht, 1999).
 
And speed matters not just in using math facts but in learning them. Methe et al (2012) conducted a meta-analysis of interventions for basic math in single-case research and reported “we found interventions involving practice under speeded conditions and a carefully controlled instructional sequence produced the strongest effects,” echoing results from Powell et al (2009) who reported that timed practice (vs. untimed) was crucial to an intervention for struggling 3rd-graders to learn math facts, and Fuchs et al. (2013) reporting similar results for 1st graders..  
 
It is clear, as is the case with any learning, that such speeded practice of math facts must be adaptive and appropriate for the level of the learning, and should be scaled gradually. And like everything else in a classroom, it will ideally be engaging. That’s challenging when you’re trying to develop automaticity, because it implies a certain amount of repetition. That’s why we liked the fidget spinner idea; it’s a little twist on a familiar task. It won’t be to every teacher’s taste, but we can say that there is no evidence it will prompt the problems that some feared.

There was a brief, lively thread on Twitter over the weekend concerning the definition of learning. To tip my hand here at the outset, I think this debate—on Twitter and elsewhere--is a good example of the injunction that scientists ought not to worry overmuch about definitions. That might seem backwards—how can you study learning if you aren’t even clear about what learning is? But from another perspective don’t we expect that a good definition of learning might be the result of research, rather than a prerequisite? 

The Twitter thread began when Old Andrew asked whether John Hattie’s definition (shown below) was not “really terrible."

I'll first consider this definition (and one or two others) as our instincts would dictate they be considered. Then I'll suggest that's a bad way to think about definitions, and offer an alternative. 

Hattie's definition has two undesirable features. First, it entails a goal (transfer) and therefore implies that anything that doesn’t entail the goal is not learning. This would be….weird. As Dylan Wiliam pointed out, it seems to imply that memorizing one’s social security number is not an example of learning. 

The second concern with Hattie’s definition is that it entails a particular theoretical viewpoint; learning is first shallow, and then later deep. It seems odd to include a theoretical perspective in a definition. Learning is the thing to be accounted for, and ought to be independent of any particular theory. If I’m trying to account for frog physiology, I’m trying to account for the frog and it's properties, which have a reality independent of my theory. 

The same issue applies to Kirschner, Sweller and Clark's definition, "Learning is a change in long-term memory." The definition is fine in the context of particular theories that specify what long term memory is, and how it changes. Absent that, it invites those questions: “what is long term memory? What prompts it to change?” My definition of learning seems to have no reality independent of the theory, and my description of the thing to be explained changes with the theory.

It’s also worth noting that Kirscher et al’s definition does not specify that the change in long term memory must be long-lasting…so does that mean that a change lasting a few hours (as observed in repetition or semantic priming) qualifies? Nor does their definition specify that the change must lead to positive consequences…does a change in long term memory that results from Alzheimer’s disease qualify as learning? How about a temporary change that’s a consequence of transcranial magnetic stimulation? 

I think interest in defining learning has always been low, and always for the same reason: it’s a circular game. You offer a definition of learning, then I come up with a counter-example that fits your definition, but doesn’t sit well with most people’s intuitions about what “learning” means, you revise your definition, then I pick on it again and so on. That's what I've done in the last few paragraphs, and It’s not obvious what’s gained. 

The fading of positivism in the 1950s reduced the perceived urgency (and for most, the perceived possibility) of precise definitions. The last well-regarded definition of learning was probably Greg Kimble's in his revision of Hilgard & Marquis’s Conditioning and Learning, written in 1961: “Learning is a relatively permanent change in a behavioral potentiality that occurs as a result of reinforced practice,” a formulation with its own problems.

Any residual interest in defining learning really faded in the 1980s when the scope of learning phenomena in humans was understood to be larger than anticipated, and even the project of delineating categories of learning turned out to be much more complicated than researchers had hoped. (My own take (with Kelly Goedert) on that categorization problem is here, published in 2001, about five years after people lost interest in the issue.)

I think the current status of “learning” is that it’s defined (usually narrowly) in the context of specific theories or in the context of specific goals or projects. I think the Kirschner et al were offering a definition in the context of their theory. I think Hattie was offering a definition of learning for his vision of the purpose of schooling. I can't speak for these authors, but I suspect neither hoped to devise a definition that would serve a broader purpose, i.e., a definition that claims reality independent of any particular theory, set of goals, or assumptions. (Edit, 6-28-17. I heard from John Hattie and he affirmed that he was not proposing a definition of learning for all theories/all contexts, but rather was talking about a useful way to think about learning in a school context.)

​This is as it should be, and neither definition should be confused with an attempt at a all-purpose, all-perspectives, this-is-the-frog definition.

Educators have been concerned about students' ability to vet information they find on the internet. Better put, the problem lies not just in students’ ability to vet information, but the extent to which they see the need to do so. This issue took on new urgency during the 2016 Presidential campaign, amidst charges that individuals and groups were willfully spreading false stories about candidates they opposed—stories that were accepted by readers and spread on social media.

​A new study indicates that people are somewhat more prone to be credulous when they think they are part of a group of readers.

​Subjects read purported headlines from a news organization. The headlines covered a variety of topics, and they were evenly split for veracity. Subjects were asked to mark them as True or False, or to “flag” the fact, which indicated they would find out the truth or falsehood of that statement at the end of the series. Subjects got a small monetary reward when they were right and a same-size penalty when they were wrong. Raising the flag paid nothing in one experiment and a small reward in another.

​The critical variable of interest is whether subjects thought they performed this task alone or with others, in which case they saw 100 or so other names of people they were told were doing the task at the same time. They were told their performance was not influenced by these other people; they just happened to be doing the task at the same time.

​Across 8 experiments, there was a small but consistent bias to check facts less often if subjects thought other people performed the task too. Of the 8, the most interesting experiment was one where researchers changed the presentation format to make the headlines look like part of a Facebook feed. In that case, it didn’t matter whether they told subjects they were alone; the format was enough to make it feel social, as shown on the graph below. 

The authors considered (and tested) several hypotheses about what’s going on.

1) Flagging something doesn’t signal “I want to know the answer.” It signals “I’m not sure.” So being in a group, you’re less sure of your answers because you unconscious think “in this big group, someone else really knows the answer, so I won’t pretend to know.” But the researchers collected confidence ratings when people said “true” or “false” and those didn’t differ between the answering alone and answerd with others conditions.

2)  Social loafing. When you’re in a crowd, you figure others are doing at least some of the work (in this case, checking facts) so you don’t feel the need. To check on this, the researchers tried to make subjedts feel like they stood out in the group by making the subjects name on the screen red. This had no impact on the effect.

3) The presence of others makes it a social context, and taking people at their word is a social norm. But you would predict this would also make subjects say that more statements are true and they didn’t do this.

The researchers of a safety-in-numbers interpretation. When people are in a crowd, they feels safe; “there are lots of people here, so there’s no need to be vigilant, to gather more information. If there were a problem, someone would notice it.” The researchers offer some evidence for this: they found that people performed worse on a proof-reading task when they believed they were in a group.

This theory is certainly plausible. It calls to mind Jerry Clore's theory about the impact of emotion on cognition. Clore suggests that negative emotions (anger, sadness) put you in a mode to collect more information—things are not going well (hence the negative emotion) so you need more information, and to focus on details, to figure out what’s going wrong. When you’re happy, in contrast, you’re content to do the sort of thing you usually do in the current circumstance, i.e., to rely on memory and don’t worry so much about collecting new information. Everything is fine, so you keep doing what you’re doing.

That’s all very logical, but it certainly seems to create a difficult situation. If true, the we are all of us slightly more ready to believe anything we read on social media. No, logging into Instagram does not turn you into a credulous zombie—spend five minutes on Twitter, for example, and you’ll see as much disbelief (and anger) as you care for in a day. But the social nature of social media may be one of many contributing factors.

​It highlights the fact that we are still working out the kinks in new media, trying to take advantage of the enormous increase in the our ability to create and to consume content while identifying and thwarting the drawbacks attendant to those increases. 

We cannot remind ourselves often enough that the predictions for education drawn from the learning sciences that obviously, 100%, HAVE to work…often don’t.

The latest example comes from a recent paper reporting a randomized control trial of adaptive vs. static practice in Dutch schools.

It seems self-evident that adaptive practice will be superior to static. In static practice, each student receives the same set of practice materials of graded difficulty: easy, medium, hard, with difficulty defined by the performance of a large cohort of students. In the adaptive algorithm, the proportion of questions correctly answered is factored into the probability of seeing a particular type of question: if a student is getting all of the easy questions right, what’s the point of posing more? Why not move on to more challenging content?

Adaptive practice is one of the reasons offered that personalized learning ought to lead to greater achievement.

The experiment tested 1,051 Dutch 7th-9th graders studying either Dutch, Biology, History, or Economics over the course of one academic year. Assignment to static or adaptive practice was assigned by classroom, and students were blind to condition. All students received the same instruction (a hybrid of a digital environment and traditional paper textbook) and all homework was the same. The independent variable was implemented only through extra practice; students were asked to practice at least 15 minutes per week, but any more practice than that was taken at their own initiative.  
We might expect that, because students are practicing at their own initiative, they will use the adaptive program less, given that the problems will likely be more difficult. The proportion of students who used the practice module did not differ between conditions, hovering around 90% in both cases. Students in the adaptive condition did indeed work more difficult problems and they also practiced a little bit longer per session…but they worked fewer problems than students in the static condition. Presumably, more difficult problems required more time per problem.

Nevertheless, they showed no advantage on a summative test. In fact, better prepared students (those who had passed the summative test before the experiment began) were slightly negatively impacted by the adaptive regimen compared to the static. (There was no effect for students who had failed the last summative test.)

Post-experimental interviews showed that students did not know whether their practice had been adaptive or static, and showed no difference in students’ attitudes towards the practice.

Why was there not a positive effect of adaptive testing?

One possibility is low dosage. The intervention was only 15 minutes per week and although students could have practiced more, few did. At the same time, the intervention lasted an entire school year, the N was fairly large, and an effect was observed (in the unexpected direction) for the better prepared students.

Another possibility is that the program was effective in getting challenging problems to students, but ineffective in providing instruction. Students in the adaptive condition saw more difficult problems, but they got a lot of them wrong. Perhaps they needed more support and instruction at that point, so the potential benefit of stretching their knowledge and skills was not realized.

Another possibility is that the adaptive group would have shown a benefit on a different outcome measure. As the authors note, the summative test was more like the static practice than the adapative practice. Perhaps the adapative group would have shown a benefit in their readiness and ability to learn in the next unit.

​This result obviously does not show that adaptive practice is a bad idea, or cannot be made to work well. It simply adds to the list of ideas that sound like they are more or less foolproof that turn out not to be: think spiral curriculum, or electronic textbooks. Thinking and learning is simply too complicated for us to confidently predict how a change in one variable will affect the entire cognitive and conative systems.