## A New Way to Teach Math

With the arrival of more advanced calculators (such as Wolfram Alpha), awarding points for correctness is becoming less feasible. What good does awarding points for a correct answer do if one could simply input the problem into a calculator and have the correct answer given to them? This issue is addressed in Teaching College Math’s blog post Shifting Assessment in a World with WolframAlpha.

In this blog post, a new form of assessment is suggested. Instead of asking students to arrive at an answer, simply give them the answer (along with the original question), and have them show how to (correctly) arrive at that answer. This takes the guess-work out of grading a problem with a correct answer and no work. This would also make problems more proof based and less computational, thus introducing proof concepts and integrating them into the work earlier in math curriculum.

I generally like the ideas presented in this blog. I think that having had the right answer before even starting the problem would have been helpful in seeing whether or not I was getting the right answer through my work. It would also force many students to take their learning more seriously, so they actually understand what is going on in their work, instead of simply knowing the shortcuts (in calculus, for instance). Finally, having been slowly introduced to proof techniques early on and building up to a class where proofs are the primary focus would have helped a lot (MATH 317 was not easy, for me at least).

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## Wolfram Alpha

In Stephen Wolfram’s talk Computing a Theory of Everything, he describes an incredible project that he has been working on called Wolfram Alpha. The talk begins with Wolfram illustrating how relatively simple programs can produce infinitely complex results. This inspired him to make all knowledge computational, and led to the creation of Wolfram Alpha.

Wolfram Alpha is a remarkable website that allows its users to type in any question, and generates a seemingly well-informed answer. It can even generate code based on the queries of its users. What I found to be most amazing about Wolfram Alpha is its capability to be used for simulation, experimentation, and discovery. Wolfram explains, “We can use the computational universe to get mass customized creativity. I’m hoping we can, for example, use that even to get Wolfram Alpha to routinely do invention and discovery on the fly, and to find all sorts of wonderful stuff that no engineer and no process of incremental evolution would ever come up with.”