Interactive Textbooks- And A Better Way To Learn Trigonometry

20 Jan

Posted by: Brian Armstrong in: Math Homework Help

I ran across this little flash widget which gives a great perspective on trigonometry:

Just playing with it helped me understand trig at a deeper level, and it didn’t even require any words.

A handful of companies are working on bringing textbooks to the iPad. Wouldn’t it be cool if they were interactive like this?

Like most new technologies, I think the first textbooks on the iPad will resemble their predecessors (paper textbooks). This happened with the first web pages (they were just paper documents published online) and even with the first cars (they resembled horse carriages). But after the first generation, new technologies are able to fully embrace their new medium.

What do you think – how else could textbooks be improved if they were based on the iPad or a tablet device?

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5 Responses

Christian Stapfer
20|Jan|2011 1

I think we should try very hard to keep all the advantages of textbooks and, yes, add some such interactive widgets, like dynamic-geometry widgets, too where they seem to be really useful.
But, in my opinion, it would be a terrible idea to try to do an appreciable amount of math “without requiring any words”, as you put it. The power of math is all in the words (and in the formulas, which is about the same thing as a language) and the very high level abstract thinking that a suitably chosen language and symbolism make possible. Much of advanced mathematics is not easily visualizable – and trying to do it is usually not worth the effort.
For me, as a student, the most important advantage of reading a textbook on a tablet-pc would be to be able to annotate the textbook freely with my handwriting, add cross-references and the like. Unfortunately, the iPad is not much use for that purpose at the moment. Maybe the Asus EP121 would be significantly more useful in this regard.

[Reply]
Brian Armstrong Reply:
January 20th, 2011 at 7:05 am
Thanks Christian and totally agree. Certainly didn’t mean to imply words wouldn’t be useful. Thanks for the comment!

[Reply]
Todd Kelman Reply:
January 22nd, 2012 at 12:06 am
Actually, the power of math is in the *application* and much of it *is* visualizable – see http://worrydream.com/KillMath/ for a very eloquent discussion of the topic by Bret Victor, including the visualization of non-linear a second order differential equation which *has no particular solution* (i.e. the visualization succeeds where the formula fails).

Implementing textbooks on electronic devices (e.g. iPad) as if we were simply making “electronic paper” – i.e. static with annotations/links – is a waste of time and resources. We need to teach math as it is practiced; unfortunately, in my 20 years of electrical engineering the math application looked nothing like how I was taught. The move to electronic devices capable of implementing *dynamic* systems is a fabulous opportunity to rectify that problem.

[Reply]
ödev
13|Jun|2011 2

Thanks Christian and totally agree. Certainly didn’t mean to imply words wouldn’t be useful. Thanks for the comment!
:)

[Reply]
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03|Jul|2012 3

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