Posts Tagged 'textbooks'

Overcoming the legacy of prior education

A real-time chronicle of a seasoned professor who is giving his second massively open online course.

We’re now into the third week of the course. The numbers are down on the first edition, almost certainly because the six months that have passed have seen the appearance of hundreds of other MOOCs students have to choose from. But the numbers are still huge. As of today:

Total registration: 27,014

Active students last week: 9,608

Total number of streaming views of lectures: 120,925

Total number of lecture downloads: 35,888

Number of unique videos watched: 87,155

Number of students submitting homework assignments: 5,552

Based on what we (my TA, Paul, and I) learned when I gave the course the first time last fall, I made some changes this time round. Paul and I discussed those changes in a video-recorded discussion we had with media host Angie Coiro just before edition 2 launched, that I referred to in my last blog.

Although the overall numbers are down by about 60%, the profile of the class activity is very similar. The most obvious one, the huge drop in numbers from the total number of enrollments to the number who are still active in week three, has been discussed ad infinitum, often being referred to as “a big problem with MOOCs.” As I observed in a recent blog in the Huffington Post, I don’t think there is a problem at all. The drop off is just a feature of what is a very new form of human experience. Old metrics are simply not appropriate, “retention rate” being one such. (Unless you pay attention to the base for the retention computation, in which case MOOC “retention” is not that different from retention in traditional college education.)

Some of the early research into MOOC participants that has been carried out by my colleagues at Stanford (including studies of my first MOOC) has already demonstrated what we suspected about why so many drop out of MOOCs: many people who register for a MOOC never have any intention of completing the course, or even getting beyond sampling one or two lectures and perhaps attempting one or two of the assignments. Some are motivated by pure curiosity into this new phenomenon, others just want to get a flavor of a particular discipline or topic, and doubtless others have different reasons.

For example, one reason some students enroll that I had not anticipated, reflects the fact that a MOOC offers a large number of eyeballs to be accessed. A very  small number of students enrolled for my course in order to advertise products. (At least, that was one reason they enrolled; they may also have wanted to learn how to think mathematically!) In the long run, this may or may not turn out to be a positive thing. Certainly, the products advertised in the discussion forums for my course (at least the ones I saw) were all education related and free. (Moreover, I also included my own course-related textbook in my short list of suggested – but not required – resources.)

Still, the very wide reach of MOOCs means we are likely to see new kinds of activities emerge, some of them purely commercial. The example I cite above, though right now a very isolated one, may be a sign of big things to come – which is why I mention it. There is, after all, a familiar pattern. The Internet, on which MOOCs live, began as a military and educational network, but now it is a major economic platform. And textbooks grew from being a valuable educational support to the present-day mega-profit industry that has effectively killed US K-12 education.

Talking of which (and this brings me to my main focus in this post), the death – or at least the dearth – of good K-12 mathematics education becomes clear when you look through the forum posts in a MOOC such as mine, which assumes only high school knowledge of mathematics.

To be sure, generalizing is always dangerous, particularly so when based on comments in an online forum, which always attracts people with something to complain about. (Case in point: See my Twitter feed when it comes to banks, United Airlines, and bigoted politicians.) But with that caveat in mind, some themes become clear.

First, many forum posters  seem to view education as something done to them, by other people who are in control. This is completely wrong, and is the opposite of what you will find in a good university (and a very small number of excellent K-12 schools).  “To learn” is an active verb. The focus should be creating an environment where the student can learn, wants to learn, and can obtain the support required to do so. There is no other way, and anyone who claims to do anything more than help you to learn is trying to extract money from you.

Second, there is a common view of education as being primarily about getting grades on tests – generally by the most efficient means (which usually means by-passing real learning). In education, tests are metrics to help the student and the instructor gauge progress. That does not prevent tests being used to assess achievement and provide credentials, but that is something you do after an educational experience is completed. Their use within the learning process is different, and everyone involved in education – students, instructors, parents, bureaucrats, and politicians – needs to be aware of the distinction.

Even worse, is the belief that a test grade of less than 90% is an indication of failure, often compounded by the hopeless misconception that activities like mathematics depend mostly on innate talent, rather than the hours of effort that those of us in the business know is the key. (Check out Carol Dweck’s Mindset research or read Malcolm Gladwell’s book Blink. Better still, read both.)

This is compounded by the expectation that a grade of 90% is possible within just a few days of meeting something new. For example, here is one (slightly edited) forum post from a student in my class:

Right now I want to quit this class. I don’t understand ANY of it. Hell I don’t understand anything regarding to math except basic equations and those barely. When asked to give a theorem on why something (let’s say a right angle) is that way my answer always was “it is because it is”). So now I don’t know what to do. I got 14 out of 40 … 14, and the perfectionist in me is saying might as well give up … you gave it a shot … there is no way to catch up now. The person in me who wants to learn is saying to keep trying you never know what will happen. And the pessimist in me says it doesn’t matter – I dumb and will always be dumb and by continuing I am just showing how dumb I am.

In this case, I looked at other posts from this student and as far as I can tell (this is hard when done remotely over the Internet) she is smart and shows every indication she can do fine in mathematics. In which case, I take her comment as an indication of the total, dismal failure of the education system she has hitherto been subjected to. No first-line education system should ever produce a graduate who feels like that.

Certainly, in learning something new and challenging, getting over 30% in the first test, less than a week after meeting it for the first time, is good. In fact, if you are in a course where you get much more than that so quickly, you are clearly in the wrong course – unless you signed up in order to fine-tune something you had already learned. Learning is a long, hard process that involves repeated “failure”. And (to repeat a point I made earlier) anyone who says otherwise is trying to extract money from you.

Turning to the third theme emerging on the course forums, there is a perception that the most efficient way to learn is to break everything down into the smallest possible morsels. While an important component of learning – if the breaking down is done by, and not for, the student – it is just the first part of a two-part process. The second part, which is by far the most important, and is in fact where the actual learning takes place, is putting it back together into a coherent whole. Textbooks and YouTube videos can provide morselized edubits (I just made that word up), and they do so by the bucketload. What they cannot do, is deliver real learning.

Suitably designed, I see no reason why MOOCs cannot be made to provide good learning, at least up to sophomore college level in many, if not most, disciplines. But a key to doing that is to leverage the power, not of machines, but of people. For fairly well understood evolutionary reasons, human learning is a social activity. We learn best from and with other people. That is how we are built!

Part of the benefit from learning in a social context is that it can offer the learner not just feedback, but also the – at a fundamental level, more important – human support that people need to succeed in education. You can find both of these in a MOOC. Within a short time of the student above posting her feelings, another student responded with this:

Hi. Don’t be discouraged. This course will give you the opportunity to think in a different way. I took the course last year and struggled with most of it. I am taking the course again as I find the subject of mathematical thinking fascinating. My scores this time round are better than the last time which indicates that given enough time even the most mathematically challenged can improve! Only have one caveat for you. If you don’t enjoy the struggle in trying to comprehend and feel that it is not worth the effort then maybe this course is not for you.

With that comment we can see one huge benefit of MOOCs. (At least, all the time they are free.) You can take them as many times as you need or want.

The one essential ingredient in order to take advantage of the huge opportunity MOOCs offer, is knowing how to learn. That should be the main ability graduates of the K-12 system get from their education. Unfortunately, with the current US (and elsewhere) system built around “being taught” and “being tested,” only a few students emerge with that crucial ability, and the ones who do usually say it is in spite of their school education.

The problem, by the way, is not the teachers. Certainly, most of the ones I meet agree with me, and are very clear as to what the problem is: a system that simply does not give them the freedom and support that is necessary for them to really help students learn. (See Jo Boaler’s excellent, well researched book What’s Math Got To Do With It? for a distressing account of how the current, overly micro-regulated system fails our students in the case of mathematics.)

Okay, that’s enough ranting for one post. Let me finish with a couple of examples where MOOCs are already working well. One student in my MOOC posted the following comment:

I have taken this course on a whim to get myself back in gear to return to school in the fall. I always despised the math classes that I was forced to attend in high school and early college. I was frustrated with the endless formulas and cookie cutter style problem solving. If you can solve one you can solve them all so being forced to endlessly solve these equations and proofs over and over seemed to be a futile act of nonsense.

Heading into week three three of this class, my mind has been completely changed. I not only enjoy this more logic based math, but have, in the course of some personal reading and problem solving, discovered i have a knack for it. I have found the challenge of solving more and more difficult problems from a few books i have purchased much more gratifying and interesting than any other area of previous study.

I would like you know that I now plan to switch majors to mathematics. I would like to thank you and your team for an eye-opening experience.

Oh, all right, I admit that included more ranting about US K-12 education. But, heavens, it is bad, and it is likely to remain so all the time that real, knowledgable educators are not part of the conversation, with all the important decision being made by people whose primary interests are profits or political career advancement. (BTW, I have nothing against the profit motive. Heavens, I have two for profit companies of my own and am talking with colleagues about launching a third. But financial ROI is not the same as educational ROI – and again, anyone claiming otherwise, as one head of a major textbook publisher did not long ago, is motivated by the former. I do have something against many politicians, but then I am an American citizen, so after what we have experienced in the past four years, I would.*)

Here’s the other example, this one sent to me in an email, rather than posted on the course discussion forum.

I am enrolled in your course “Introduction to Mathematical Thinking.” It is incredible. You have alleviated my fears that my college professors will have the same attitude towards mathematics that my high school teachers do. Mathematics is beautiful and certainly emotional. I am surrounded at school by people who believe mathematics is systematic. Through all of the videos you have posted so far and your archived NPR clips, I am now confident that mathematics is the direction I want to pursue. I am excitedly awaiting next week’s lectures. 

With tears in my eyes and more gratitude than I know how to express,

It’s that kind of feedback that makes teaching one of the most rewarding professions in the world. It’s why people become teachers. If society would just get off teachers’ backs and let them get on with what they were trained to do, what they know how to do,  and what they want to do, we’d all be a lot better off. (Check out Finland.)

To be continued …

*ADDED LATER IN RESPONSE TO A QUERY FROM AN OVERSEAS READER: The problem is the complete refusal of the Republican Party to cooperate with a now twice-elected President of the US, in governing the country as they are all elected and paid from public funds to do, choosing instead to drive the country, and with it most of the world, to the brink of financial and thence  social disaster.

 

How Facebook Made MOOCs Viable: MOOC planning – Part 2

A real-time chronicle of a seasoned professor embarking on his first massively open online course.

One obvious, but huge distinction between planning a physical course and planning a MOOC is that for the former, it is generally fairly easy to make changes — even major ones — once the course is underway. But MOOCs are different. It requires an enormous amount of time to put a MOOC together (video recording/editing and implementing all the online course materials are just two elements not present in a physical course, or if they are, those materials can usually simply be omitted if a mid-course adjustment is required). As a result, once the course launches, you are pretty well committed to running it through largely as planned.

If I were putting together a MOOC for which Stanford would charge (and offer credit), by now I would be getting decidedly nervous. But that is not how things stand at present. Everyone sees this sudden MOOC explosion purely as an experiment to see what the medium can offer. The courses are free, and since there is no credential at stake, there is no worry about unmotivated students or of cheating. An unmotivated student is not going to continue with the course beyond the first week or so, and the only person who loses by student cheating is the student. Presumably both will change if this experimental phase is a success, and MOOCs take their place alongside other forms of higher education, where there are payments and credentials.

My own view, as I’ve noted elsewhere, is that MOOCs are not a replacement of the traditional bricks-and-mortar university, rather they are the twenty-first century version of the textbook.

Widespread availability of textbooks did not replace universities. Indeed, they did not change university education very much at all. In theory, once every student could purchase a textbook, there should have been little need for professors to give mainstream content lectures — particularly if the professor had written the course textbook — but the basic content lecture continued to remain the dominant model.  Early in my professorial career, I tried to adopt a flipped classroom approach, based on giving students reading assignments from a book I had written, and using the class time to discuss the material. It proved to be a disaster; hardly any of the student read the assigned reading, and of those that had, few really knew how to read a mathematics text and learn by so doing. I soon ended up having to give classical lectures on the material that was expressed far better in my textbook — far better because I had spent time putting my thoughts onto the page and the resulting manuscript had been professionally edited.

I am not sure that, on their own, video-recorded instructional material will lead to much of a change in university education either. Video-lectures are not really very different from textbooks. At least, for most university-level material that is the case. For learning how to carry out maintenance around the house, to change a bicycle tire, to assemble a piece of furniture, etc., video is far better than text. But those are all simple procedural learning — the goal is to learn how to do something, and for that purpose, showing is more efficient than describing in words. In contrast, the main focus of much university education is understanding; the student is supposed to learn how to think differently. That is very hard to do at arm’s length, regardless of whether the arm involves a textbook or a video. It is by direct interaction with an instructor and with other learners that we can gain understanding and learn how to think a certain way. That is why I don’t see MOOCs as a threat to the existence of universities.

MOOCs may, however, do what textbooks and instructional-videos failed to do. They may finally give rise to flipped classrooms — a mere six centuries after the invention of the printing press give rise to textbooks. The reason is, MOOCs are far more than video-recorded instruction. In fact, video lectures are one of the least significant elements of a MOOC. The key to the educational potential of MOOCs are human-computer and human-human interaction —  the latter especially so for most subjects. In particular, social media are what make MOOCs possible, and it is the widespread familiarity with, and acceptance of, human-human interaction over an ethernet cable that led to the sudden explosion of interest in MOOCs. In short, MOOCs are a direct consequence of the growth of Facebook, which made interaction-by-social-media global.

[I should add that I don't see the degree of human-human interaction offered by social media in a MOOC being as educationally powerful as direct fact-to-face interaction. The unavoidable limitation in a MOOC is not the medium per se, rather is the scalability factor. In a physical class, the students get to interact with the professor -- the expert, the domain professional. In a MOOC, that crucial part is missing. I think good course design can get a lot out of social media, but that one factor means that we'll always need physical universities.]

The challenge facing a professor setting out to design and offer a MOOC, then, is to figure out how to take advantage of the (human-computer and) human-human interaction made possible on a global scale by social media, in order to provide students with a valuable learning experience.

In this regard, the experiment really begins with (many of) the 117 MOOCs currently offered by the MOOC platform Coursera. Coursera is a spin-off from a Stanford project in Computer Science to develop a platform to support flipped classrooms at the university. The first wave of Stanford MOOCs were basic level computer science courses, where there is a heavy focus on procedural learning and less dependency on reflection and peer interaction. (Those features come later in CS, and when they do, not a few Stanford CS students drop out and start their own companies, occasionally becoming millionaires within a few years!) But many of the second wave of courses now underway are in humanities and other areas, where the primary focus is on thinking and understanding, not doing.

To take just one instance of course design, in a basic-level computer science MOOC, it is possible to give machine-graded assignments. It would be possible to offer a math MOOC a similar way, provided the focus was on mastering basic computational procedures.  But in my case, where my goal is to develop mathematical thinking, I realized from the start that the key to making it work would be the social media factor. Just as it is for humanities courses.

That impacted how I would design, structure, and present the core material, as I’ll describe in my next post.

To be continued …

The Challenges of Online Education: MOOC planning – Part 1

A real-time chronicle of a seasoned professor embarking on his first massively open online course.

I’ve been pretty quiet on this blog since launching it on May 5.

Partly that is due to summer vacation and the start of great cycling weather. But a lot of my time got swallowed up planning and developing my fall MOOC. It’s now scheduled to start on September 17, and the registration page just went live on Coursera, the Stanford spin-off MOOC platform now offering online courses from a number of the nation’s best universities.

All my Stanford colleagues who gave courses in the first round earlier this year reported how much time it takes to create such a course, no matter how long you have been teaching at university level. Knowing that you won’t be in the same room as the students, where there is ongoing interaction and constant, instant feedback, means that the entire course has to be planned down to the finest detail, before the first day. In addition to the usual course planning, lectures have to be recorded written materials prepared, and interactive quizzes constructed well in advance, with the knowledge that for some students, you may be their only connection to the material.

In my case, my fall term was already pretty full, before counting the MOOC, so I knew I could not rely on having the opportunity to record material once the course begins. That meant I had to try to anticipate well before the course launch, the difficulties the students might have.

Of course, I would not have chosen my topic (introduction to mathematical thinking) if I had not taught it many times before. Many colleges and universities ask their incoming mathematics students to take a “transition course” to develop the all-important skill of mathematical thinking. I helped pioneer such courses back in the 1970s. So I did start out with a good idea of the kinds of difficulties students would encounter on meeting the material for the first time.

But the challenges I faced (and still face) in trying to provide such a course in a MOOC format were, and are, formidable. To be honest, I am not sure it can really be done, but the only way to find out is to try – and not just once either. (Like the Coursera platform itself, my fall MOOC will be very much a beta release.)

An obvious problem is that learning to think like a mathematician, which is what transition courses are about, is not something that can be achieved by instruction. In that respect, the learning process is similar to learning to ride a bicycle. There is no avoiding a lengthy, and often painful process of trying and failing (i.e., falling) until, one day everything drops into place and you find you can ride. At that point, you wonder why it took you so long. Instruction helps, though only in retrospect can you see how. During the learning period, riding seemed impossible – something others could miraculously do but that you were not capable of.

(As someone who came to serious road biking and mountain biking later in life, I can recall vividly that the same is true for “advanced cycling.” For instance, being instructed – many times – how to corner fast on a downhill did not prevent me having to go through a lengthy process of learning how to do it. And while the broken collarbone I sustained in the process was a result of a rear-tire blowout on a sharp corner descending Mt Hamilton outside San Jose, California, it is possible that with more experience I could have kept control. But I am getting off track, which is what happened on Mt Hamilton as well.)

The challenge facing anyone trying to help students learn how to think mathematically by way of a MOOC, is that the communication channel is one way, from the instructor to the student. The sheer number of students (likely into the thousands) prevents any reliance on even the highly impoverished forms of student-faculty interaction that are possible with distance education for a class of no more than thirty students.

The only option (at least the only one I could see) is to try to create an environment where the students can help one another, by forming small study-groups and working together. In particular, I felt the students in my transition mathematics MOOC would benefit greatly by having regular transition course instructors use my MOOC in a flipped classroom model, so that my MOOC students working alone would be able to interact with other MOOC students who in turn were interacting in-person with a professor in a regular class, and perhaps on occasion interact directly with one of those professors online.

This is why I decided to offer my MOOC at the same time (the start of the US academic year) as many US colleges and universities offer their own transition courses. If instructors of those courses get their students to take my MOOC as part of their own learning process, their participation in study groups and the online discussion forums could ensure that every student in the MOOC is at most just one step removed from an expert. For the students in regular transition courses, using my MOOC in a flipped classroom experience, there is the added benefit that we all learn very efficiently when we try to teach others.

Another advantage of trying to involve instructors and students from regular transition classes, is that those instructors could critique my teaching in their class. Contrary to popular belief, “experts” are not infallible beings who know everything. They are just regular people who have more experience in a particular domain than most others. Analyzing and critiquing expert performance is another powerful way to learn. (So feel free to tear me apart. I can take it; I brought up two daughters through childhood and adolescence to adulthood, and after that I was a department chair and then a dean.)

To make my course attractive to regular transition course instructors, I had to make it very short, and focus on the very core of such courses, so those instructors would have plenty of time to take their own courses in whatever direction they choose.

Once I made that decision, I decided to write a companion book for the course. My Stanford colleagues who were giving the first MOOCs reported that some students wanted a physical book to read to support the online learning. People learn in different ways, and we instructors should accommodate them as much as possible.

There are many transition mathematics textbooks on the market, but they are all fairly pricey (ranging from $60 to $140) and cover much more ground than was possible in a mere five weeks of MOOC instruction. Definitely outside the spirit of free learning for all. I decided to write a companion book rather than a textbook (insofar as there is a distinction), since my view is that MOOCs are actually twenty-first century replacements of textbooks.

(I don’t think there is any chance that MOOCs can effectively replace regular university education, by the way, and a school district, state, or nation that decides to go that route will be just a single generation away from becoming a new third-world economy. But if I were a major textbook publisher, I would see MOOCs as the impending end of that business.)

To remain close to the ideal of free education, I decided to make my text a cheap, print-on-demand book. I typeset it myself in LaTeX, paid for an experienced mathematics textbook editor to edit the manuscript, and sent it off as a PDF file to Amazon’s self-publishing CreateSpace service to turn it into a book that can be ordered from Amazon. It’s called Introduction to Mathematical Thinking, and it should be available by August 1. It costs $9.99 and comes in at 102 pages. (There is no e-book option. Given the necessity of mathematical typesetting, an acceptable e-book not possible – at least for e-books that can display on any e-reader. Besides, as I mentioned already, to my mind, the MOOC itself is the true digital equivalent of a textbook.)

Incidentally, the process of self publication on CreateSpace is so simple and efficient, I suspect that low-cost, print-on-demand publishing is the future of academic textbooks.

So add writing a book to the other tasks involved in creating a MOOC.

Still, the book-writing part was easy. Though many of my colleagues find writing books a major challenge – an insurmountable challenge for some of them – I have always found it relatively painless, indeed pleasurable.

In any event, books are an ancient medium that academics and teachers have long been familiar with. Pretty well everything else about the MOOC process was new. I wrote the book before I designed the course; indeed, the book constituted the curriculum. The only new twist for me was that in writing the book I was conscious of using it as the basis for a MOOC.

With the book written, the next question was, how do I present the lectures? After experimenting with a number of formats, I finally settled on the one I’ll use this fall. It’s not the one Sal Khan uses for Khan Academy. Given his success, I started out trying his format, but I found it just did not work for the kind of material I was dealing with. I’ll say more in my next posting. There were other surprises ahead as well.

To be continued …


I'm Dr. Keith Devlin, a mathematician at Stanford University. I gave my first free, open, online math course in fall 2012, and have been offering it twice a year since then. This blog chronicles my experiences as they happen.

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