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Computers in Math Education AMS update

Posted 2 years ago
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American Mathematical Society (AMS) Blog recently published an article "Computers in Math Education" which goes over Conrad Wolfram's ideas about impending fundamental changes in the math and STEM education. To learn more please visit the Computer-Based Math (CBM) website that aims "to push the reset button on the school subject of math so it truly reflects today's real-world subject of math, with its vitally important applications".

AMS Blog is run by math graduate students. It is inspiring to see CBM ideas are getting picked up by a younger generation, people who will reshape the future. It is also exciting to see that ideas that originate in Europe (with Conrad Wolfram based in Oxford, UK as the founder of Wolfram Research Europe) are having impact on thinkers oversees. While many education issues are specific to a country, the general imminent changes in education due to engulfing computing technology growth are universal and understood by many independently of age or location.

I encourage you to read the article and see the student perception of the subject and interesting sources mentioned that echo the CBM ideas.

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I've read Kyle Cluver's article, watched again Conrad Wolfram's Ted talk and Dan Meyer's talk.

This is a very difficult topic. We might say: "Computers are the future of mathematical education - and always will be."

Conrad Wolfram's talk had many good points but I think he failed to jump the chasm. (Of course it wasn't difficult to make an animation that jumped the chasm!) For example, what form is Mathematica going to take in the educational setting? He seemed to imply that Mathematica would do the calculations and students would do all the conceptual thinking. It rather looked like students might be given models with dynamic displays and they might adjust parameters to fit some problem. That doesn't sound like mathematics to me and maybe he was speaking against that. He didn't say much about symbolic calculation or doing derivations and proofs. His comparison of driving a car as compared to servicing a car was meant to contrast getting the computational results of a calculation against doing it by hand. But otherwise the analogy is weak and points in the wrong direction. We really should teach what goes into designing cars and not just how to drive them. I believe Mathematica can help teach conceptual thinking but we don't yet know enough about how to do it.

There is a form of Mathematica that might be suitable in the educational setting. It's not just basic Mathematica. It's not CDF documents. The students can't calculate with CDF documents; they can only push buttons and slide sliders, which is not doing mathematics. It's not displays like in the Demonstration Project, as nice as many of them are.

When Edison first invented the movie camera it was used to show things that moved. Trains pulling into stations, horses running, streetcars moving on their tracks, men jumping. That's what it was for. Things that move. It took some time before people started to think: "Hey, we could use this to tell a story." (The movie Hugo tells the story of one of these pioneers.) We should be using Mathematica to tell mathematical stories to students and giving them the tools and incentives to make up their own mathematical stories. We should not just be making dynamic displays that move.

The proper instrument for this is a Mathematica application with all its possible resources - routines in packages, stylesheets, palettes, documentation, and literate notebooks that read like a story and encourage a student to make some of his own mathematical constructions. The point is that this is a structure that is robust enough to encompass many different approaches to the education problem along with experimentation and development. I don't believe anything else really will be.

The trouble is that WRI has left the Mathematica or Wolfram application project uncompleted. The most uncompleted part at the moment is that only a small set of users can document. All users must be able to document. Most users are not even aware of Wolfram applications or what can be done with them. For the most part, they don't know how to set them up, even through it's relatively simple. WRI can't just leave it to users to discover them, there needs to be some promotion, and interest at WRI on applications.

One of the areas where Mathematica applications might work well is in the Math Circles. They seem to concentrate heavily on getting interested students to think about and solve actual mathematical problems in a rather free-form manner.

Mathematica and the Wolfram Language are relatively new. People are barely aware of Wolfram applications. They are a completely new communication medium. How to apply them to education is basically an unsolved problem. I'm a fan of the Edward Tufte books on data graphics. He shows lots of examples of things that don't work, but are commonly used. He talks about "computer junk" that gets thrown into displays. Applying the Wolfram Language and applications to education is much more difficult; there are many more ways to go astray. One problem might be: how do you prevent students from being overwhelmed by the technicalities of the Wolfram Language?

I like to watch the lectures on physics by Leonard Susskind. I like to think about whether they could be improved by using Mathematica. Sometimes equations get lost. The writing isn't always legible. Questions come out of the blue that perhaps need examples. Could Mathematica be used, partly spontaneously, and still preserve the personality and approach of the lecturer? This is not a simple task and would require a lot of development and many trials.

I feel certain that Mathematica can make significant contributions to technical education. But I'm saying it's a difficult problem. The solution does not already exist ready to hand to the schools on a plate. I'm also certain there are many users who frequent Wolfram Community who could and probably have made important contributions. Better than I.

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