#WOLFRAMALPHA GRAPH HOW TO#

I would never do that now that I have a calculator that can do those things for me. I used trig tables and interpolation to find values of trig functions. I learned to compute logarithms using log tables. Why are we asking students to only do things that can be more easily accomplished with technology? Why aren’t we asking students to do things the technology cannot? If we are concerned about students understanding mathematical concepts, shouldn’t our exams include/focus on conceptual thinking? I am not 100% certain where I heard this line, but I think it was at AMATYC from the inspirational Fred Feldon ( follow him on Twitter) from Coastline College. If W|A alone can pass your exam, it’s a bad exam. I can remember many times in grad school where I had to work through a proof line by line before I could really understand what was going on, and the same thing can happen for our students.Ģ) We need to shift from “computational” exams to conceptual exams. And for a student who has no access to a tutor or other help, the Wolfram|Alpha student subscription gives a student access to all of the steps and that can help a student to figre out what is going on. And so can taking the answer and trying to work backward.

#WOLFRAMALPHA GRAPH HOW TO#

And while that does not mean having Wolfram|Alpha simply do your homework, it can mean finding a way to use Wolfram|Alpha to increase your learning.įor example, if a student does not know how to solve a problem, getting an answer from Wolfram|Alpha and trying to piece together a path to that answer can be an effective strategy. And we must discuss how students can get the most out of their homework. As instructors we need to let our students know why we assign homework: to improve student learning. Many students work under the point of view that homework is a way to accumulate points and improve their chances of passing the class. I feel that we often assume that students know why they do homework and that they will do it in the most beneficial way, but that is a mistake.

Here goes …ġ) We need to make sure that students understand that HW is a learning tool, not just something that earns points. The best strategy is to assume easy until easy doesn’t work, always try the simplest techniques first, and remember there is more than one way to solve an integral.Last week I came across a Wired article: Wolfram|Alpha (& AI) Is Making It Easier To Cheat, and reading the article brought so many thoughts to mind about teaching mathematics in today’s world. In some cases, you need to use multiple techniques. If none of the above techniques work, you should take some more aggressive measures advanced algebraic manipulations, trig identities, integration by parts with no product (assume 1 as a multiplier).Radicals: use trig substitution if the integral contains sqrt(a^2+x^2) or sqrt(x^2-a^2), for (ax+b)^1/n try simple substitution.Product of a polynomial and a transcendental function: use Integration by parts.

Rational functions: use partial fractions if the degree of the numerator is less than the degree of the denominator, otherwise use long division.If you can’t solve the integral using simplification or substitution, try to classify the integrand into one of the following: product of trig powers, rational functions, radicals, or a product of a polynomial and a transcendental function.Next, look for obvious substitution (a function whose derivative also occurs), one that will get you an integral that is easy to do.Not necessarily a simpler form but more a form that we know how to integrate. First, start by simplifying the integrand as much as possible (using simple algebraic manipulations or basic trigonometric identities).Let's start by sorting out the different techniques. Finding the 'right' technique for a given integral can be difficult, it requires a strategy.

Wolframalpha graph