Computing Is the New Maths

Following on from What do we teach and why do we teach it?, I wanted to share a link to a post from a home school blog - Just SCRATCHing the Surface of Fractions where ther is an example of using programming to explore Maths:

Brute Force Solving in Scratch (screen cast) from Rhett Allain on Vimeo.

I have used a similar technique myself when my daughters were stuck with a problem in the Scottish Mathematical Council's Mathematical Challenge. Clearly it would have been unethical to solve the problem for them but often I'd suggest that they fire up a spreadsheet, plug in some sample values, then enter the connections between the numbers (from the problem specification) as spreadsheet formulae. Once they have built a model in the spreadsheet they could change the values and watch the effect. This gave them a feel for what was going on and often in working out the formulae in the spreadsheet, they had solved the problem. It was usually fairly straightforward to turn the spreadsheet formulae into an algebraic form for the official answer.

Learning Maths by learning programming... In this case programming a spreadsheet.

Perhaps I'm still infected by the disruptive ethos of the Learning Without Frontiers conference but I really like the idea that Computing should be a compulsory subject at school and Maths should be optional.

I suspect that many people can get through the day without directly coming into contact with Maths. (Arithmetic possibly, although even that can be avoided thanks to electronic tills and a host of other technological gizmos.) Direct, personal contact with Maths is unlikely but direct contact with Computing is almost unavoidable

So out with Maths as a compulsory subject and in with Computing instead. ...Or am I getting carried away here?

What do we teach and why do we teach it?

I taught Maths for five years from the age of 22 to 24...
-- Joke borrowed from Fred MacAulay

I usually describe myself as a Computing teacher but I wanted to make my Maths credentials clear right at the start for reasons that will hopefully become clear.

A couple of things started me thinking about this post: first was a conversation about the curriculum I had with a Chartered Teacher student; the second was a video of a TED Talk. The conversation with the student was about the balance between content and process. I asserted that much of what we teach in schools is taught because that's the way we have always done it. I also described how most years I deliberately wind up the Maths students (and at least some Primary students) by telling them we are wasting pupils' time when we get them to memorise their times tables; it is a completely redundant skill. I do this partly to annoy them but mostly to get them thinking about what we teach and why we teach it.

The TED Talk was from Conrad Wolfram and it is embedded below:

A couple of things in particular struck me about this talk. First, about halfway through he says that a great way to teach Maths is to teach programming. Second, towards the end, when he is talking about the radical changes to school Maths that are needed, he says that he is not even sure it should be called Maths any more. My immediate thought was: what he is proposing already exists... and it is called Computing!

I have posted before about the identity crisis school Computing teachers are facing (e.g. Computing: The Science of the Digital World) and it struck me that this call to shake up the Maths curriculum is one of the best defences of Computing that I have heard in a long time. So:

Computing is the new Maths

What do you think?

CAL 2009: Towards a naturalistic conceptualisation of technology integration in classroom practice: The example of school mathematics

Captured live at #cal09, posted late.

K.B.H. Ruthven, University of Cambridge

Innovations change schools but more importantly, schools change innovation. You have to look at the place of technology in the classroom. Project looked at the practical theory and craft knowledge that frame teachers action when using technology. Wanted to develop a model that would describe how teachers use technology.

Teachers saw "Assisted Tinkering" as useful but did not always connect this into their model of technology use. The project found a great deal of "craft knowledge" that had grown up around the use of technology yet there was very little research exploring this craft knowledge. For example using computer based tools and resources often involved changing teaching room and will more often require a shift in classroom routines - what effect does this have on experienced teachers who have built up successful routines and are then asked to change this because of the introduction of technology. Can be helpful to consider:

Activity Formats - templates for action and interaction.

Curriculum Script - the set of options a teacher has to help them teach a topic. They may feel under pressure to abandon a curricular script when adopting new technology but this does not necessarily make sense - their curricular scripts are vital.

Time Economy - how do teachers manage the rate of teaching. Also worth noting that new technologies very rarely completely replace older technology. Almost always they run alongside each other.

In response to question, there was an observation that teachers did not always connect what was done with (for example) hand geometry instruments (e.g. protractors) and dynamic geography tools. Curricular documents seemed to perpetuate this by listing ways protractors should be used to measure angles but not acknowledging role of dynamic geometry tools in doing this.

More maths stuff

Perhaps this should have been an addition to the previous post...

I've continued to play with ASCIIMathML and I realise I should have given a warning but I've also discovered some cool stuff that you can do.

I should have warned you that ASCIIMathML should work no problem with Firefox (and possibly other browsers) but you need to download a program called mathplayer if you want to see the formulae in Internet Explorer (and possibly other browsers). Also, the ASCIIMathML page says:

The STIX fonts (beta) have finally been released (download and select STIXGeneral as default font in Firefox).

From: http://www1.chapman.edu/~jipsen/mathml/asciimath.html

I've not found this to be necessary... but then I've not really pushed ASCIIMathML to try any particularly unusual symbols.

Now for some of the other stuff I discovered while I continued to play with this tool. I was pleasantly surprised to see that ASCIIMathML handles some of the graph drawing elements of LaTeX. For example:

`\begin{graph} width=300; height=200; xmin=-1; xmax=1; xscl=1; plot(x*sin(1/x)); \end{graph}`

I think that's pretty clever. :-)

Also, in the previous post, I mentioned a couple of programs that can export LaTex, but dgilmour sent me a Tweet that directed me to the Sitmo Equation Editor - a free, online tool that creates LaTeX code which you can copy and paste into your blog for ASCIIMathML to render. Excellent! Other useful pages I came across include the ASCIIMathML.js (ver 2.0): Syntax and List of Constants page (comprehensive but not particularly attractive) and the ASCIIMath Tutorial page (an stunningly useful tutorial that includes areas where you can type code and check straight away how it is rendered).

That's all for now. I don't know about you but I'm feeling a bit Mathed out now. I promise I'll try to stay away from maths for at least the next few weeks. :-)

Testing, testing, testing

{Note: I completely re-wrote this post once I got the ASCIIMathML version working. If you were here earlier, you may have found the not quite working version!}

I'm sure I did this last year when I was working with the Egyptian teachers... but if I did, I didn't write up how I did it on the blog and I had to work it out again. :-(

A maths student was wanting to show formulae in his blog but it has to be said that it is not easy to get the layout right - even for something as simple as a fraction:

$\frac{1}{2} + \frac{2}{3}$

If you want something more complicated, it is even more difficult:

$\int_{0}^{1}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}dx=\frac{22}{7}-\pi$

Last year I found jsTeXrender which is a javascript program that does the business and YourEquations.com explains how to use it. It uses a script to turn LaTeX gobbledygook into properly formatted formulae. It is fairly painful to use as you have to switch into the script view of your blog editor and type in some fairly obscure LaTeX commands. There is just about enough information in the above websites to make it possible to add formulae to your blog but it is a bit of a struggle.

However, I have now found an easier way - use ASCIIMathML. This script understands LaTeX, so you can create very complex mathematical formulae if that is what you need to do. Just surround the LaTeX with dollar signs and ASCIIMathML should do the rest.

For example, type \$\forall x \in X, \quad \exists y \leq \epsilon\$ to get

$\forall x \in X, \quad \exists y \leq \epsilon$

(Note that mathematical packages such as Mathematica and MathType can export in LaTeX format.)

However, ASCIIMathML's real strength is you can type a more or less readable text description of what you want and it will be rendered properly for you. Best of all, you do not have to switch to the script view to enter the formulae - just bracket the formulae with the grave accent, \` (not the apostrophe). For example:

For example, type \`int_0^1f(x)dx\` to get:

`int_0^1f(x)dx`

Type \`sin^-1(x)\` to get:

`sin^-1(x)`

Type \`d/dxf(x)=lim_(h->0)(f(x+h)-f(x))/h\` to get:

`d/dxf(x)=lim_(h->0)(f(x+h)-f(x))/h`

It was a bit tricky getting this working but the two sets of instructions I found most helpful were How to Post Math Equations in Blogger using ASCIIMathMIL and Equations in Blogger (and other HTML) Made Easy.

While looking for the jsTeXrender, I found a page on MathML which looked promising. I suspect that MathML is likely to be the most future proof solution, but I couldn't get it to work in Blogger at all! Help from scientific/mathematical bloggers who have already sussed this out would be greatly appreciated.