think again!

We have come to trust that, given appropriate starting points, students will come up with all the mathematical questions we would want from a context. We have also realised, as we get more experienced in working with these tasks, that we are able to notice and hear more and so students seem to get further and into more complex issues each year. We find working in this way students become enthused and motivated by studying mathematics, and learn to view it as a subject which makes sense and over which they have control.

To find out how they are working to achieve these uncommon results, click here.

Watch the video.

… there are programs that can perform mathematics at the symbolic level, and some of them are free. This fact leads to an objection, heard with increasing frequency, that people will use programs like Maxima to avoid learning anything about mathematics at all, instead depending on symbolic math software to conceal their ignorance.  - More

“Determine which of (x - 3), (x - 1), (x + 2) are factors of P(x) = 2x^3 + 7x^2 + 7x + 2, and hence factorise P(x) completely.”

This was the first question on a recent test I gave. The students could have asked Maxima:

(%i1) factor (2*x^3 + 7*x^2 + 7*x + 2);

(%o1)                      (x + 1) (x + 2) (2 x + 1)

or asked the web site  QuickMath which uses WebMathematica:

http://www.calc101.com/ is a similar site.

Most of the problems we deal with in class can be instantly solved by free symbolic math software. So why don’t we allow the students access? Why do we insist they should learn what machines are far better at than humans and instead use the time to what the machines are poor at, namely problem discovery and problem solving?

There is a risk that we will use math software to become intellectually lazy. But the possibility exists that, in partnership with computer math software, people will learn much more about mathematics than they would be likely to do while using the older methods. Because we have computers to perform low-level computations, we can spend our time acquiring mathematical knowledge at a higher level. - More

I believe several universities now allow this kind of software, but at the pre-university level it is unheard of. At IB there is even an exam where calculators are banned. I fail to grasp why.

The film is about the extraordinary gifted students who represented the United States in 2006 at the world’s toughest math competition: The International Mathematical Olympiad (IMO). It is the story of six American high school students who competed with 500 others from 90 countries in Ljubljana, Slovenia. It shows the dedication and perseverance of these remarkably talented students, the rigorous preparation they undertake, and the joy they get out of solving challenging math problems. It captures the spirit that infuses the mathematical quest at the highest level.

The world turns on symmetry — from the spin of subatomic particles to the dizzying beauty of an arabesque. But there’s more to it than meets the eye. Here, Oxford mathematician Marcus du Sautoy offers a glimpse of the invisible numbers that marry all symmetrical objects.

Covering a span of sixty years, the graphic novel Logicomix was inspired by the epic story of the quest for the Foundations of Mathematics.

This was a heroic intellectual adventure most of whose protagonists paid the price of knowledge with extreme personal suffering and even insanity.  The book tells its tale in an engaging way, at the same time complex and accessible. It grounds the philosophical struggles on the undercurrent of personal emotional turmoil, as well as the momentous historical events and ideological battles which gave rise to them.

The role of narrator is given to the most eloquent and spirited of the story’s protagonists, the great logician, philosopher and pacifist Bertrand Russell. It is through his eyes that the plights of such great thinkers as Frege, Hilbert, Poincaré, Wittgenstein and Gödel come to life, and through his own passionate involvement in the quest that the various narrative strands come together.

Read more about it here and order it online here.

Kindly suggested by Daniel Brandt.

If you want to know more about the artist, his ideas and tools, click here.

Creativity: The Mind, Machines, and Mathematics: Public Debate

Two of the sharpest minds in the computing arena spar gamely, but neither scores a knockdown in one of the oldest debates around: whether machines may someday achieve consciousness. (NB: Viewers may wish to brush up on the work of computer pioneer Alan Turing and philosopher John Searle in preparation for this video.)  - More