# 21st century computer algebra literacies

By Murray Bourne, 06 Jan 2008

There was an interesting response to my Twenty Global Problems and Twenty Years to Solve Them post. So interesting, in fact, that I thought it deserved its own post so I moved it here.

MariaD, from NaturalMath, wrote:

Zac,

I come to you for help. I’ve been enjoying your blog, and it looks like you may know something that may help with answering a big question I have.

When industrialization was taking place, universal literacy became important for progress. What “literacy” meant for math, back then, was basic arithmetic. Now it looks like the civilization needs, among other things, mass algebraic literacy to progress and to solve its problems. Governments have been working toward that goal, by their usual means (influencing school curricula). Despite this mass algebra instruction, we don’t see mass algebraic literacy.

I think one of the reasons why we don’t see mass algebraic literacy is that algebra isn’t viewed as something you MESS with. Kids doodle or compose texts for their myspace, but they don’t MAKE (construct, create, build) any algebra entities, ever. Algebra is something professionals have made in the past. Look at the software you reviewed: MS Math 3.0 or Algebrator are SOLVERS. For all the web 2.0 hype, you still see blogs, wikis, podcasts with kids re-representing already created math that they look up somewhere, or at best solving problems professionals pose.

Now for the question. Have you seen good technologies supporting kids in creating their own math entities? Something that would help kids doodle in algebra and compose in calculus?

## My Response

Hi, Maria

I come to you for help.

Sure, I’ll do my best. You’ve asked a great question.

I’ve been enjoying your blog...

Great! Thanks for the feedback.

Despite this mass algebra instruction, we don’t see mass algebraic literacy.

As you said, there has been a lot of effort put into improving test scores, but there is little real improvement in mathematical **abilities**.

I think one of the reasons why we don’t see mass algebraic literacy is that algebra isn’t viewed as something you MESS with.

I agree with you there. Math is seen as something that needs to be done for its own sake. It is something that is **imposed** from above. A lot of math educators also hold this view, so it is not surprising that many students and the public do also.

The ’normal’ situation is that students need to do the algebra (which usually means plugging a number into some formula), get the right answer, get a pat on the head, then move on in life. It is usually totally devoid of any application, any meaning or any connection to other things that they are learning. And it leaves most students wondering what any of it is about.

There are some **wikis** that I have come across where students are solving math problems collaboratively. There is a certain amount of "messing with" the algebra, but it is limited. These involve the use of a LaTEX-based image creator for mathematics. The limitation here is that students can’t **do** a lot with the algebra they have written. That is, the wiki doesn’t let them graph a result, or solve some system of equations, or whatever.

...you still see blogs, wikis, podcasts with kids re-representing already created math that they look up somewhere, or at best solving problems professionals pose.

Yes, this is another issue. There is always this feeling that mathematics has one neat answer that we can check in the back of the book. But ’real’ mathematical thinking and experience is often not like that.

Look at the software you reviewed: MS Math 3.0 or Algebrator are SOLVERS.

Yes, and they perpetuate the "math for math’s sake" mentality. There is so much more that can be done with computers to aid math learning than the ’automated tutor’ approach. Neither of them are Web 2.0, either.

Now for the question.Have you seen good technologies supporting kids in creating their own math entities? Something that would help kids doodle in algebra and compose in calculus?

My software of choice for such a task would have to be Scientific Notebook. It’s not Web 2.0, but it certainly allows the creation of ’user-generated content’.

The user interface for Scientific Notebook is similar to that of a word processor. You can easily enter math (one of the easiest input methods that I have come across) and manipulate it to your heart’s content. It *looks* like mathematics after you have entered it. It doesn’t look like computer code.

You can graph things (2D and 3D), solve equations, integrate and differentiate things, do matrix operations, etc, etc. You can also enter text, so adding explanations for the mathematics that has been "messed with" is possible.

You can output your work in useful ways, from TEX to image to HTML (which can easily be opened as a Word document).

A lot of the math software out there requires the students to manipulate something that some educator has designed before (including my own math manipulatives). But Scientific Notebook allows the students to start from scratch - and "mess with" the algebra as they go.

Of course, there are many other similar Computer Algebra Systems, but most of them have a steeper learning curve when it comes to math input. Cost is also an issue. The following 2 are free.

## Maxima

I am currently playing with the open source computer algebra system Maxima. It appears to be quite feature-rich, but at the end of the day, it has several shortcomings if you want to use it with students (math entry looks more like computer code than math, for example). Output options are limited - you can save what you have done as text, but that is all.

## Geogebra

I wrote about Geogebra in GeoGebra math software -a review. It is an interesting possibility for your application, but it is more geometry-based than algebra-based. Depending on how you design documents, it is possible for students to play around with ’what-if’ scenarios. A better possibility is to get *the students* to create their own documents.

## The Activity

I think an important consideration here is the activity that students are being asked to do. Are we aiming to just cover an algebra chapter in some textbook?

Or if the aim is to excite students in mathematics, to help them see the usefulness, to let them develop the skills to apply it, and to help them to think mathematically, then what is essential is to give them open-ended and authentic learner-centred activities where they need to solve at least part of the problem from scratch.

Some ideas:

**Augmented reality**- like the kind of thing done by the futurelab people and Harvard**Authentic data gathering**- and forming conclusions, speculating about future trends and the like**Modeling**- of a full range of variables**Problem-based Learning**- which is involved in each of the above and certainly in the Twenty Global Problems**Building things**- nothing like some construction to bring out the need for mathematics. The construction can be physical, or even the creation of computer games.

So Maria, I hope that helps.

**Endpiece:** I came across a discussion in the Physics Forums on computer algebra systems. One response went:

Learning how to use the computer for numerical calculations is all what the computer is about; I find the CAS [computer algebra system] to be pointless.

I don’t agree with him, but it is food for thought - does the importance of algebra shift a bit when we have powerful *numerical* tools available?

This goes to the heart of your question, Maria. What is the ’literacy’ that we are aiming for? I liked your question because you are looking for something that students can use to **build** mathematics, not just **do** a mathematics problem in a book.

And then **collaboration** is another aspect of 21st century IT math literacies that we need to think a lot more about...

**Update (10 Jan 2007):** Another possible solution is WebEQ, that claims that you can...

... create web-based learning environments that help educators engage students in math and science on the web.

I have played with this a bit in the past. Today when I looked at their site, the first WebEQ example I looked at completely froze up Firefox. While this is Web-based, it produces ’dead’ math at the end of the day.

See the 15 Comments below.