Wildcard Wednesday: Wolfram|Alpha

Wildcard Wednesday: Wolfram|Alpha

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. Here goes …

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. Many students work under the point of view that homework is a way to accumulate points and improve their chances of passing the class. As instructors we need to let our students know why we assign homework: to improve student learning. And we must discuss how students can get the most out of their homework. 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.

For 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 so can taking the answer and trying to work backward. 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. 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.

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. And I think it’s a great line. 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 learned to compute logarithms using log tables. I used trig tables and interpolation to find values of trig functions. I would never do that now that I have a calculator that can do those things for me. Isn’t it time to make the next leap forward? Of course, students need to be introduced to topics and work through some examples by hand, but there needs to be a shift toward doing things in a more efficient way once a student understands.

In the workplace, who would be more valuable: an employee who can use algebra to solve assigned problems by hand, or an employee who can figure out exactly which problems need to be solved and can find an efficient way to solve them? I hear from many employers who let go of college graduates who struggle when it comes to problems they have never encountered, problems they were not trained to solve. We need to give students more opportunities for finding functions that model real world problems from actual data, let students use technology like Wolfram|Alpha (or Desmos) to solve any kind of equation that arises, and reason out whether their results make sense. This kind of student is truly a problem solver, and can make valuable contributions to their company and to society.

Maybe it’s time to shift from trying to find the right answers to trying to find the right questions.

This strategy is one that I use often in many classes, giving students time/space to discover rather than simply being told what to do. Give a problem, give the solution, and ask students to try to find a way to get from start to finish. Students can use this approach on their own while working on homework. They have a problem they are working on, they can get an answer from Wolfram|Alpha, and then some exceptional learning can happen while they are trying to find the path from problem to solution.

Wrap Up

So, there are two issues here. Can we get students to use technology like Wolfram|Alpha in a productive way? Can we change our focus to make our courses more beneficial?

Issue 1: I tell my students about Wolfram|Alpha, and I try to give them guidance about using it effectively. I use MyLab homework, and occasionally students will get a randomly generated problem that is difficult to solve, like a factoring problem. I tell my students that if they understand the concept but feel the problem is more tedious than it is fundamental, then they should feel comfortable using Wolfram|Alpha. I also warn them that using Wolfram|Alpha to do every problem might inflate their homework grade, but it will not result in learning or understanding, and that will be bad news when they are assessed.

Many of your students are going to use some sort of aid, whether it’s an app or a tutor. Don’t we want them to learn to use tools in an effective way that benefits their learning and understanding?

Issue 2: With all of the changes going on in developmental math, I feel we need to move math forward and create a more meaningful and useful experience for our students. We want them to be lifelong learners and lifelong problem solvers. Technology like Wolfram|Alpha and Desmos can play a vital role in tomorrow’s course. (The article focused on Wolfram|Alpha, but you could really fill in the blank with many other great tech tools.) We need to figure out what that course will look like, and what role technology will play.

I’d love to hear from you about this! – George

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