WolframAlpha, ChatGPT, and Desmos 3D

For the above expression WolframAlpha offers the result seen above, choosing to simplify only by removing the cube root of 64. 

Further down WolframAlpha offers the more simplified result seen above, but with the caveat that x and y must be positive. Yet the this is an odd root expression. Negatives "under the radical" are not imaginary. 

I asked ChatGPT to weigh in on this. As seen above ChatGPT, known to sometimes commit mathematical errors, concurs that x and y do not have to be positive. 

I then asked ChatGPT to simplify the same expression and ChatGPT went straight to the correct answer with no caveats. I say that round went to ChatGPT. 

Desmos 3D visually demonstrates that both x and y can be negative. 

All of the above screenshots are from a budget cell phone.

There is deeper question underneath this single example. In algebra classes students are still being taught to simplify expressions such as the above "by hand." Students are typically not permitted to use tools such as WolframAlpha, ChatGPT, and Desmos on quizzes and tests. 

In residential courses instructors permit calculators but ban cell phones. In online courses instructors turn to tools such as lock down browsers and cameras to control and monitor students in an attempt to prevent the use of such tools. And while ChatGPT sometimes "hallucinates," these are teething pains for a new technology (large language models) that will only improve in the coming years. By teaching students to use multiple tools to cross-check answers the issue of errors in any one tool can be exposed.

So why are we still teaching skills such as simplification? What is the goal or intent? Why not teach students to use WolframAlpha, ChatGPT, Desmos, and other mathematical apps accessible even from a cell phone, using the output of multiple tools as a cross-check on the output of other apps? Why do we take away the power tools of mathematics and have the students "build" every thing by hand? 

 

I am just convinced that I stand at the edge of the same cliff in algebra that I stood at in 1977. Banned in my 1976-77 Algebra 2 math class, permitted in my 1977-1978 Trigonometry class and now required by many instructors in algebra classes. 

The other day when a student asked if I had a calculator, I said yes. When they asked to borrow it, I said no, I don't loan my cell phone to anyone. They noted they couldn't use a cell phone in class. Felt like 1976 all over again. Mathematics is almost unique for hobbling students with thousand year old techniques. 

I see waves of change coming with WolframAlpha, Desmos, and AI. A series of waves that our students will have to know how to ride. And I don't know what to do to prepare them for that future.