Do your kids find learning math hard? There may be an app for that!

If you are like me, you probably sigh and switch off when you read an article with a title claiming kids’ math scores show significant improvement after using some great new app for a few minutes each day.

In which case, you may have paid little attention when a news article came out in Science magazine recently, reporting a new study showing that after just one year of parents using a bedtime-story-telling app called Bedtime Math with their young children, those kids were three months ahead of fellow students whose parents were using an app to provide non-mathematical stories. In fact, children of math-anxious parents showed even greater improvement, ending up six months ahead.

If you happened to see the article, you likely assumed it was essentially a piece of marketing, where a bogus “study” was carried out to produce the “results” the marketing folks wanted. After all, there are no magic bullets in the math ed world, right?

My reaction was very different. I immediately wanted to know more. The reason being, as I recounted in last month’s column, the same thing had happened a few months earlier with a math learning app I had created, a mobile game called Wuzzit Trouble. (Actually, I should have written “we” there. Paul McCartney may have sung that he had “got by with a little help from my friends,” but the reality was it took a lot of work by all four Beatles to make them a global phenomenon, and in the apps business it usually takes a whole team of highly talented people to create a great product. My team are listed here.) A Stanford classroom study led by Prof Jo Boaler had found significant math learning after just two hours play of Wuzzit Trouble spread over four weeks.

The Bedtime Math study was unlikely to have been a bogus marketing “study”, I felt, since it had been carried out at the University of Chicago, which is a great university. True, as the Science article noted, the study was funded by an entity called the Overdeck Family Foundation, whose chair, Laura Overdeck, a former astrophysics major at Princeton, established the nonprofit Bedtime Math Foundation, which created and supports the app. Some might read that and smell a rat – as some did when they first read of the Stanford Wuzzit Trouble study.

But to my mind such a reaction says more about the reader than the researchers. We are talking about an educational app made and distributed for free by a nonprofit organization. Why would anyone want to fake data? Really!

In fact, even if the app were for sale – say for a mind boggling $4.99 – the idea that seven researchers at a major university would fake a study about a small children’s app is simply not credible. As a number of news articles have made clear, the price for a university researcher faking a scientific study is dismissal from the university and the end of their career. When it does happen, the motivation is invariably massive career prestige and fame, or a huge follow-up research grant (or both). Neither of which are likely to result from an at best encouraging, small scale classroom study of Bedtime Math, Wuzzit Trouble, or any other kids’ app.

If a foundation or a company wanted to run a fake study for marketing purposes, they could simply do it themselves, or else farm it out to an unscrupulous, individual researcher. Such people are to be found, sometimes associated with universities. (Google “intelligent design” or “climate change denial” for examples.)

Certainly, James Stigler, a well known educational psychologist at UCLA, is not skeptical. Science quotes him as saying, "I think it's a fantastic study. But it is just the beginning."

Another respected scholar, Andee Rubin, a mathematician and computer scientist at the nonprofit education R&D company TERC in Cambridge, Mass, has a similar reaction. Science quotes him as observing, "I'm interested in teasing it apart and seeing what makes this effective."

Those are pretty much the same as the reaction I had to Stanford’s Wuzzit Trouble results, which prompted me to draw up the list of possible explanatory factors I published in my last column.

With both the full paper and a cover article available in Science, all I will do here is provide a brief summary of the cover article.

The Chicago team recruited 587 first-graders from 22 schools in the Chicago metropolitan area. The parents of each child were given a tablet computer with which to read to the child at bedtime. 420 families were told to use it to work through word problems related to counting, shapes, arithmetic, fractions, and probability using Bedtime Math. Another 167 families were instructed to use a reading app. With a standardized test, the researchers assessed all the subjects' mathematics performance at the beginning and end of the school year.

As you would expect, use of the reading app made little difference to the children's math performance. In contrast, children who used the math app two or more times per week outpaced peers whose family rarely used it, ending up three months ahead.

Perhaps most important, use of the app brought students whose parents said they were anxious about math up to par with those whose parents were at ease with the subject. Among children whose family rarely used the math app, those with math-phobic parents made only half as much progress as the children of parents comfortable with math.

The researchers make some suggestions as to what may be going on. My own best guess, based on several months reflections on the Stanford and (subsequent) Finnish studies of Wuzzit Trouble, are consistent with what they think. Namely:

We have created a system where learning is walled off from everyday life. Particularly in math. The “math classroom” operates according to its own rules. Even with a truly great teacher – and I have met many – there are many restrictions on what can be done. Not least because of an incessant rhythm of performance testing.

Go into most math classrooms and what you see will most likely bring to mind a room full of clerks in the pre-computer age when companies employed large numbers of numerically-able people to crunch their numbers. (Young people will have to rely on old photographs or depictions in movies.) Which was, of course, what the system was set up to provide.

The classroom certainly does not look remotely like a room full of professional mathematicians at work. The first words that might come to mind if you were to walk into such a room would be “fun”, “engagement”, “argument”, “passion”, “social interaction”.

Nor does it look like the human activity that hundreds of thousands of years of natural selection have inbred into us to maximize learning in the young: play. (Some wise person once said that “play is the work of the child.” I agree.)

And there is something else that evolution hard-wired into is: our love of stories. Effective political speeches are usually laden with stories of individual people, and for very good reason. Because they are powerful.

At which point, it’s probably a good idea to do what we math instructors tell our student to do: look for patterns. Well, what do we see when we look at professional mathematicians at work and kids in their ideal learning activity?

Fun, engagement, argument, passion, social interaction, play, stories.

Those are all, I would argue, essential ingredients for good learning. Yet you would have difficulty finding any in many math classrooms.

Indeed, society seems to have gotten into a mindset that these items are distractions that you have to eliminate to achieve good math learning. Even when good teachers do their best to inject some of those valuable features into their classes, they have to operate within a system that disapproves. And everyone knows that, most of all the kids.

No wonder then, that when you have a well designed, engaging app – a game, a puzzle, a family-supporting bedtime story provider, or whatever – you will likely get good results. Because apps, if properly designed, create their own environment.

Though I labored long and hard to create Wuzzit Trouble, and I am sure Laura Overdeck worked equally hard on Bedtime Math, all to good effect for sure, my strong suspicion is our apps work as well as they do in such a short time primarily because of what they are not. Namely they are not the typical school classroom approach to mathematics education.

How else can you explain dramatic results after a few hours engaging with an app, other than it unlocking what had hitherto been shackled by the chains of an Industrial Revolution conception of mathematics learning? Learning something that is genuinely new takes time and a lot of effort. Freeing something that is already there – if only in embryonic form – is much quicker. If so, then this means that our received wisdom that it takes a lot of hard work, repetitive practice, frustration, tears, and pathological levels of anxiety to achieve competency in mathematics may simply be very strong evidence that our approach sucks.

Math MOOC – Coming this fall. Let’s Teach the World.

Higher education as we know it just ended. Exactly what will take its place is not at all clear. All that can be said with certainty is that within a few short years the higher education landscape will look very different.

That is not to say that existing colleges and universities will suddenly go away, or indeed change what they do – though I think both will occur to varying degrees in due course. What is changing now is what classifies as higher education, who provides it, how they provide it, who will have access to it, how they will obtain it, and how it will be funded. Distance education, for many years the largely-ignored stepchild of the higher education system, is about to come of age.

This is not just my opinion. My own university, Stanford, recognizes what is going on, and is taking significant steps to lead and stay on top of the change, and a number of Silicon Valley’s famed venture capital firms, who make their fortunes by betting right on the future, have sunk significant funding into what they think may be key players in the new, higher ed world.

Last fall, Stanford computer science professor Sebastian Thrun used the Internet to open his on campus course in artificial intelligence to anyone in the world with Net access, and 160,000 students from 190 countries signed up. Some 22,000 of those students finished the course, receiving “certificates of completion” signed by Thrun (and co-teacher Peter Norvig of Google), but no Stanford credit. (For that, a student has to be on campus and officially registered; annual tuition is $40,050 and entry is fiercely competitive.)

Demonstrating the entrepreneurial spirit that Stanford faculty are famous for, Thrun promptly left Stanford to found a for-profit online university, Udacity. With Udacity receiving financial backing from a large Venture Capital firm, the MOOC – massive open online course – suddenly came of age. A short while later, two more Stanford computer science faculty, Andrew Ng and Daphne Koller, secured $16M of venture capital funding to launch a second Stanford spin-off company, Coursera, a Web platform to distribute a broad array of interactive courses in the humanities, social sciences, physical sciences, and engineering.

Initial courses offered on Coursera include, in addition to several from Stanford, offerings from faculty at the University of Michigan, the University of Pennsylvania, and Princeton. Stanford president John Hennessy appointed a blue-ribbon panel of Stanford faculty to develop a strategy for developing, and delivering, online courses. For free. To the world.

Yes, you read that correctly. The faculty, the universities, and the new platforms are making the courses available for free. All the funding is coming – for now – from for-profit investors and the private universities themselves. Why are they doing that? If you have to ask the question, you don’t really understand the Internet and how it changes everything. Think Napster and the music industry or Skype and the telephone industry. Like the settling of the American territories in the nineteenth century, the initial focus is on establishing a presence in the new land; monetization can come later – almost certainly in ways very different from today’s.

Computer-assisted, distance learning is not new, of course. Stanford was one of the universities that pioneered it the 1960s; many universities have for several decades offered adult professional education courses for a fee, largely to raise funds; and there are the for-profit online schools like the University of Phoenix. More recently, led by MIT, a number of universities started making recordings of their regular courses, together with course materials, available online for free. So what has changed now?

The answer is the platform and the target audience’s experience and expectations have changed. What has been missing so far is the active participation of the distant student in a learning community. Building on technology developed at Stanford to support flipped classroom experiences for its regular students, Udacity and Coursera have secured the major investments required to build scalable, robust platforms that can take the small learning seminar and create a similar experience across the Internet.

A generation that has grown up on the Web has taken to the new online medium like fish to water. During the term when Thrun made his AI course available online, most of the Stanford students enrolled in his class stopped attending his lectures and took their information delivery online, at times convenient to them.

Is this the beginning of the end of physical universities? I doubt it. Though online courses are excellent for in-career professional learning, the absence of being a member of a physical community makes them a poor substitute – arguably no substitute – for a traditional college or university when it comes to providing first-pass education. But what about the millions (make that billions) in the world who do not have access to a university education? “Let’s teach the world” is a buzz phrase you hear increasingly among the Stanford faculty these days. And Stanford is putting resources into making this attractive dream a reality.

What makes it fascinating to a faculty member, is figuring out how to take a learning experience that works in a small-group setting on a campus, and re-creating a similar – or equivalent – experience online. Having decided last December that I would offer a math MOOC this fall, I found myself at once faced with a number of challenges.

By far the greatest problem is how to provide the personal, expert feedback that is essential to good mathematics learning. Web delivery is fine for providing instruction, but that is just a part of learning, and a minor part at that, as I discussed in the March Devlin’s Angle. At first, it seemed an impossible task. But with Stanford and the now independent Coursera building innovative new platforms, I began to see the glimmer of opportunities. Over the coming months, I’ll use this forum to write about my progress. And hopefully get your assistance.

My focus for this first foray into this new educational landscape is the high school to university transition. As every university mathematics instructor knows, many students encounter difficulty going from high school math to college-level mathematics. Though the majority survive the transition, many do not. To help them make the shift, colleges and universities often have a transition course. I myself developed one of the first transition courses in the late 1970s, when I was teaching at the University of Lancaster in England.

Such courses typically comprise a mix of some elementary mathematical logic, proof techniques, some set theory through to an analysis of relations and functions, with a bit of elementary number theory and introductory real analysis thrown in to provide examples.

Given the problems students typically have when they meet this material for the first time, doing this at a distance is a challenge. Even if they did well at math in school, most beginning university students are knocked off course for a while by the shift in emphasis, from the K-12 focus on mastering procedures to the “mathematical thinking'' characteristic of much university mathematics. Clearly, offering such a course as a MOOC is a huge experiment.

This is where you come in. (I hope.) One of the things we’ve learned at Stanford from offering MOOCs, is that a key component is the creation of a strong online community. Learning is all about human interaction. The technology just provides the medium for that interaction. In offering my math transition MOOC at the start of the fall term, when many colleges and universities offer their own transition course, I am inviting any instructor who will be giving such a course, together with their students, to join me and my MOOC students online, making interaction with other students around the world a part of a much larger learning community.

The result could be a total failure. I won’t know until I try. On the other hand, anyone who joins me might just find themselves at the start of something major, new, and exciting. The online learning revolution is going to happen, and existing educational institutions are going to have to adjust to it, just as the music industry did to the iTunes revolution. Why not jump on the train as it is leaving the station?

I’m going to make my course just five weeks long, starting in early October. By incorporating participation in my Stanford course part of your students’ learning experience, everyone could benefit. For one thing, your students are likely to be inspired by being part of an educational revolution that for millions of less privileged people around the globe can quite literally be life changing.

Because they will be supported by being part of a physical learning community, with the personal support of you, their instructor, your students will be highly empowered, privileged members of that online community. They can take advantage of your support so that they can help others. And as we all know, there is no more powerful way to learn than to try to teach others.

For that student half way round the world, trying to improve his or her life through education – by learning to think mathematically – the potential benefit is, of course, far greater. Helping that unknown young (or not so young) person make that step might just help inspire your own students to put in that bit of extra effort to master that tricky new transition material. Everyone wins.

If my Stanford MOOC draws a student body in the tens of thousands, which it might, based on the experience of my colleagues here, there is no way I and a couple of graduate TAs can provide individual feedback to every student. But if instructors and their students across the US join me, then maybe we can collectively achieve something remarkable.

I am making my MOOC deliberately short, five weeks, so participation will leave most of the semester open for participating instructors to concentrate on giving their own course, perhaps using their students’ initial experience in the MOOC community as a springboard for the rest of the course.

By the time I post next month’s column, I hope to have more details available. In the meantime, I ask anyone giving a transition course this fall to consider joining me in this experiment. The only cost is our time. There is no need to make any advance commitment to me or to Stanford. At this stage, all I ask is that you consider joining me. I believe we will all benefit. Let’s teach the world.