Abandoning ship on using Wolfram Alpha with Students
December 13th, 2011
I am really getting fed up tired of having to explain Wolfram Alpha graphs to students. For some reason, the default in Wolfram Alpha is to graph everything with imaginary numbers. This results in bizarre-looking graphs and makes it near-impossible to use Wolfram Alpha as a teaching tool for undergraduate mathematics, a real shame. Now that Google has entered the online graphing fray, I have a wary hope that the programmers at Wolfram Alpha might finally (after two years of waiting) fix the problem.
Here are a few examples. I’ll show you the graph in Wolfram Alpha, on a TI-84 Plus emulator (TI-SmartView), from Google Search, and from Desmos Graphing Calculator. These are all the “default” looks. Wolfram Alpha consistently shows this confusing imaginary view as the default whenever working with graphs involving variables in radicals.
Example 1:
Example 2:
Example 3:
I was hoping to really teach my College Algebra students to use Wolfram Alpha next semester. But, between the Logarithm Issues and this graphing issue, I’m afraid I’m going to have to abandon ship on using Wolfram Alpha as a teaching tool for students. Students simply don’t have enough mathematical sophistication to look at the graphs and realize that they aren’t seeing what they are supposed to be seeing and I’m seeing far too much confusion on assessments that are caused by the oddities in graphs and logarithms on Wolfram Alpha. What a shame that we can’t work this out, huh?
Possibly Related Posts:
- Navigating WolframAlpha Pro Features
- Timeline of the Rise of Data
- Wolfram Alpha in a Nutshell
- Giving up Calculation by Hand
- Shifting Assessment in a World with WolframAlpha
Posted in Wolfram Alpha
Any ideas why the real parts of some of these graphs are also different from their counterparts in the other software, like x^{1/3}*(x+4)?
Apart from those discrepancies, I can’t see why it wouldn’t be enough just to tell students, “Ignore anything orange”. That doesn’t take a lot of mathematical maturity, right?
That’s what I used to do … but upon seeing this bizarre case of the cubed root graph today, I can’t “in good conscience” keep doing that. It’s not just the graphing, it’s also the different interpretation of Logarithms – and in College Algebra, that’s about 4 weeks of class. The book and their calculator tell them there IS a difference between ln(x) and log(x) and Wolfram Alpha tells them otherwise. For calculus students, there might be enough maturity (although recent test mistakes tell me not) … but not for College Algebra.
Of course, all this nastiness could be put behind us if they would just FIX the two issues. It’s not like I haven’t asked before.
With the issue of log vs. ln, there’s no easy fix. It’s a question of context. For engineers and many scientists, “log” *always* means natural log and that’s why Mathematica, MATLAB, W|A, etc. do it that way. For computer scientists, “log” means “log base 2″. In fact it seems like mathematicians are in the minority when it comes to using “ln”. So I tend to think the textbooks bear the responsibility to update their language, not W|A to update its notation.
And yeah, that’s totally unhelpful for solving the pedagogical problem here. I tell my calc students that “log” means “natural log” unless they read it in a math textbook, and they seem to be OK with that. (We use Maple and W|A a whole lot more than calculators, so there’s that.)
I confess I’ve never seen ln “in the wild” outside of a high school / lower level college textbook or a calculator before. The last couple of math papers I remember having logarithms it was “log” and assumed based e.
Curious whether you’ve seen any logarithms “in the wild” outside of math conferences and math papers.
I think that’s a general “limitation” with WolframAlpha in classrooms: it gives too much information. I’m not sure WolframAlpha was designed as a teaching tool so we shouldn’t really have the expectation that it is one. Especially with GeoGebra, Desmos, and now Google out there, I think Wolfram fills a good “high-end” niche.
I don’t see “too much information” as a bad thing – as long as it’s understandable information. With events like “Homework Day” and conferences that tout Wolfram Alpha as a radical new teaching tool, I think they’d better fix it or stop promoting it to teachers.
Have you tried using geogebra? I think it’s a great teaching tool. Students can move graphs around and watch the equation change.
What would be an effective fix that adds usability for teaching without losing usability for scientists and engineers? Show both graphs? Store a preference on your computer?
Also, wow, what is going on with that cube root graph? I haven’t worked with graphs of nth roots enough to read what it’s doing.