I wanted to point out that although it is not intuitive to use Shift + 6, for example, to write an exponent, Wolfram|Alpha with its free-form linguistic capabilities eliminates this problem and even helps teach users the proper inputs. Also, since version 8, Mathematica has incorporated Wolfram|Alpha’s free-form linguistics in its programming
environment, as noted in the blog post below:
http://blog.stephenwolfram.com/2010/11/the-free-form-linguistics-revolution-in-mathematica

Teachers can also reference Step-by-step math solutions (a feature of Pro) by visiting here:
http://www.wolframalpha.com/pro/step-by-step-math-solver.html

Best,

Amy Wolff
Wolfram Research

I guess the moral of the story is that doing hand written math to get an understanding of concepts is best, even for the most tech advanced. The power of computers come into play when we apply these concepts to particular data. Unfortunately many people confuse math with computation, but computation is just the often messy and tedious by-product of applied math and it can now be passed on to the computers.

So I think it is best to leave hand written math as the first medium, especially at lower grades. Once students get to a level where they can apply the abstract concepts to big numbers or excessive computations, they should turn to the computers. Basically I think computers should just be used as glorified calculators because if computer science professors still prefer hand written math to introduce and justify concepts, math teachers can too.

Only a few out of the hundred said they used mathematical symbology at all. Most said they did it in imagery and figurative terms, and an amazing ~30 percent (included Einstein) were down in the mud pies. Einstein said ‘I have sensations of a kinesthetic or muscular type’. The sad part is that every child in the US is taught Mathematics and Physic through this channel (using mathematical symbols). They (mathemeticians/scientists) use this channel to communicate, not to do their thing.

So why do we force them to go through a layer of symbols to understand concepts?”

This hits on several of the themes here — experts vs. beginners and doing vs. learning vs. communicating.

Experts are saying this as experts — however, were they taught mathematics using “muscular” methods or without symbology? I’m guessing that these sensations of math are WHY they are experts now — it was a subject that to them is multi-faceted, fully engaging, in their brains and bodies in pictures and feelings. What percentage of K-12 students have that level of engagement?

Was this the way that they themselves were taught K-12 level math? Extremely unlikely.

Are these the ways that they communicate math to one another?

The points made about learning basic skills of notation and not expecting students to learn two or more notations for one concept they have not yet grasped are key.

But tablet computers have changed how I //do// math (and how I teach.)

I’m much more likely to haul up Wolfram|Alpha to check a result (or get a hint, now it will show some methods); I’ll verify and illustrate a result in Geogebra or Cabri since I’m already at the computer; I’ll use animation, video or photography to explain including to myself. I might even do a simple bit of programming to search for particular results or counter examples. I’ve used various online tools to rehearse routine skills to gain fluency and get rapid feedback.

Above all, as I am doing now, I’m more likely to collaborate.

With pencil and paper, I think I was slower, more routine in my solution methods and relied more on following standard examples and doing standard problems.

I wonder if anyone else has found using computers to do math changed how they work?

Worth a try?

I’m in a similar boat. While I don’t usually teach math, I do teach chemistry. Computers are my bane when it comes to writing formulas and compounds. Besides superscripts, subscripts are also necessary, and if you’re doing nuclear chem, then all four “corners” can be used. My students are still figuring out where to put which number and what’s capitalized. If they also have to figure out exactly which keyboard strokes to do it, they’ll be awfully frustrated.

I think the bottom line is, computers aren’t much of a tool for learning if the students don’t know how to use them.