One of the wonderful things about studying and teaching mathematics these days is the ubiquity of software and web-based tools that can be used to bring math concepts to life and provide a framework for convenient and dynamic exploration.
One of these tools I use when helping students is Wolfram Alpha from Wolfram Research. Wolfram Research’s flagship software product is called Mathematica. Mathematica is a very sophisticated computation and analysis tool but a spin off tool is the web tool called Wolfram Alpha which is free for anyone to use. You just need a web browser.
Tools of this sort greatly enhance a student’s understanding of important concepts in all math courses in the high school curriculum.
Click here, and then click the play button, to see a demonstration of how Wolfram Alpha can be used by teachers and calculus students to enhance understanding of functions, their derivatives, and how their graphs relate to each other.
Happy computing! And remember: just because the square root of 2 is irrational doesn’t mean that you have to be.