The OECD has just released a report on the success (or otherwise) of technology in education, at least in terms of PISA results.
This report is now being being widely quoted by media. For example, here's a BBC story on it, and another one from the Irish Times. The BBC story references a second BBC story from today, written by OECD Education Director Andreas Schleicher himself.
Conrad Wolfram has today responded that the report largely misses the point, which is that computers are being used to teach the wrong subject. You can read his post here: COMPUTERS IN EDUCATION: GREAT MACHINES, WRONG RESULTS
Having read a couple of viewpoints, where do you stand on this issue?
Hi, Richard, is there a link to the OECD report? I do not see a link to the BBC story either. For those who wonders PISA stands for Programme for International Student Assessment.
Thanks for pointing out the missing link, it's there now, and I have added a couple more! As for the original report, all I am finding is news stories quoting it, but yet to happen upon the report itself...
Thanks, Richard! Actually the BBC article you linked gives the reference to the OECD report - it is called "Students, Computers and Learning" and is free access. BTW you can click "Reply" to respond to a specific comment - Community has tree-structure of a discussion to see better who replies to who. Cheers, Sam.
I did read one of the articles. Of course, Mathematica ought to be a tremendous aid to learning mathematics, engineering and science. Here is the approach I would recommend.
1) Forget test generation, scoring and all that stuff for teachers. In fact, forget teachers.
2) Get Mathematica young and start learning it.
3) Write literate (with textual explanations) notebooks on whatever topics you find that interest you. But start with basic ones.
4) Write lots of notebooks.
5) You can make contributions and add value by using Mathematica's active and dynamic features to clarify existing math topics.
6) If you can find anyone to collaborate with or share notebooks that's great - but difficult.
7) Don't take no stinking PISA tests.
PISA does seem to be rather outdated - and as for Mathematica, couldn't agree more on making an early start!
I wasn't thinking so much of the specific PISA test, which I know nothing about, but the whole process of cramming facts and taking tests. Why not write a literate Mathematica notebook exploring some topic and be judged on the quality of that? Do math! I suspect that this isn't cost efficient for universities. Maybe it takes too much time. Maybe a teacher might not be up on the particular topic a student choose. Mathematica allows students to get their hands on much more mathematics and explore it, but it may not mesh well with the present university paradigm.
Cramming for specific test, or the culture of simply coaching students to pass exams, is one of the things CBM wants to re-examine. Agreed, the emphasis should be on skills and outcomes, rather than specifically on the test-passing process.
Bureaucracies run through a cycle:
Problem is recognized as new.
Problem is solved quickly in a makeshift way.
Solution is optimized.
Solution is given to a new generation who only understand the solution procedures.
Time passes. The problem changes. The current solution becomes less successful. This is denied, in part to avoid changeover costs.
Solution fails badly enough that it is abandoned. No solution exists.
And this continues. Historical example: British mathematics after Newton was paralyzed (according to C.P. Snow, Two Cultures) for perhaps a century after Newton because success in mathematics consisted of passing a standardized test in the Mathematics of Newton's time, and very few were the British contributions to mathematics. Eventually it was revised, and British contributions resumed. So says Snow.
That said, just turning a young person loose on Mathematica hasn't worked for me yet. The language is so, ah, persnickety, and requires so much knowledge of basic mathematics, that the young person can't understand it. ("There are different kinds of numbers? Why should I learn that? What use will this ever be to me?). Any successful approach will have to teach basic mathematics and present very specific Mathematica problems if it is to succeed. This should be a good thing, since an understanding of basic mathematics (at least of where numbers came from, and the problems that show why you need different kinds of numbers) makes things easier. It won't be easy to execute, however.
Remember how there were once tutorial languages such as Pascal? And note that Carnegie Mellon is now teaching only parallel algorithms to freshmen, with the single thread case taken as a degenerate case of the parallel case. Mathematica is comparably different from paper and pencil, hand calculators, and Excel, and will need just as careful a tutorial approach. If that approach exists, I don't know about it.
Very interesting perspective, Bill. Would you say we are currently in the 'denial' phase of the cycle? Costs are certainly an issue at this stage, but chats I've had with people in the know also remind one of how much influence self-interest and business has got in the educational status quo. The mention of computers and technology in education, for example, gets textbook publishers in a froth of protest. Many believe that teacher jobs would be threatened, although at Computer-Based Maths we've never suggested teachers be removed from the process.
Mathematica is behind some of the Computer-Based Maths modules but not in a scary way. It does remain a specialised tool, and CBM probably isn't aiming to achieve widespread Mathematica literacy any time soon. It's more about the concept of using applicable technology for the purpose of calculating.
Answering your question took quite a bit of work. The text below is a summary.
We have been in the “denial” phase for quite some time. My favorite example is Calculus. Calculus courses teach the original development of Calculus, using Leibnitz notation, using pre-1800s development and proofs. The idea seems to be that students should understand Calculus from the ground up, and therefore believe in their final results.
Only one problem: mathematicians in the 1800s thoroughly proved that the original derivations were invalid, and historians of the late 20th century have strong demonstrations that the derivations were bogus. Today’s usual summary of the early days of Calculus is that it was accepted because it gave testable solutions to long standing problems, not because its derivation was convincing. Fortunately, mathematicians of the late 1900s were able to develop a theoretical basis for Calculus (and for set theory also, another major foundation failure found about 1900).
So, in short, students spend their time learning bogus proofs that convinced very few back when they were new, and are not even told why they are doing so, or the holes in theory that each proof was originally intended to plug. That’s a bit worse than a waste of time.
The current situation is also much like the Tripos exam that C.P. Snow complained about. The examination was continued as long as it was because top scoring students were given secure academic appointments. The easiest way to quell complaints about fairness was, at the time, to give the same test to all applicants over both space and time, to follow tradition. Much the same is true for Calculus I today. It is a gateway course, and changing it will bring accusation from whomever fails the final exam. Political complaints have taken very seriously since the 1960s.
So: A crisis is building, but it is not here yet.
For something like Mathematica to succeed as a tutorial in elementary mathematics, it would have to be linked to a believable derivation of the theory it relies upon. That was attempted, for example, by K.D. Stroyan, who is currently offering his course under the Creative Commons license, Calculus: The Language of Change, University of Iowa, apparently current. I can’t evaluate that book, but back in 1993 he has abandoned the 1700s theory and was using 1900s theory.
In summary, much of mathematics education demonstrably does not make sense, as it does not incorporate theory agreed to be valid, or, for non-mathematicians, any theory at all. People with STEM careers are being worked hard enough to inhibit family formation and stability, which makes the industrial system that relies on STEM workers unstable over, say, three generations (~60 years). You would think that improved education and cognitive aids would be readily salable, but so far the educational and governmental organizations appear to be in the “denial” phase.
So, what does it take to break denial? Arguably, Newton’s work was possible because the English Civil War had introduced major changes to English society at about the time of his birth. The Tripos changes that Snowden mentioned came about right after another large change, the Napoleonic Wars and the start of the Industrial Revolution (c.a. 1800). It may be that something of comparable magnitude will be necessary to change the current educational status quo. However, there is also a great increase in home schooling, tutoring, and on-line education. That’s a start, and, should something discredit the educational establishment, I would expect all of those increasing activities to become very widely adopted, and very quickly (several years).
As for CAI threatening teachers:
Speaking from my own experience, much of mathematics teaching appears to be, ah, close to fraudulent to the student. It is ideal for a student who wants to disregard theory and learn to solve standard examination questions, but such a student encounters trouble when trying to solve non-examination problems. Understanding the distinction between easy and difficult problems, between what is known and what is not known, requires either years of work or a knowledgeable teacher. A curriculum helps, but you’d need more than IBM’s Watson to tell the student that there are limits to knowledge and how to recognize them, and then how to try to cross them.
If the teacher does not know that, then the mathematics will be of very use to the student only in solving problems that somebody else has selected and prepared. If the teacher does know that, and the CAI does not present mathematics as eternally unalterable rules, than I'd guess that the teacher could actually rely on CAI for job security.