Google your homework

By Asher Auel

I’ve noticed recently that students are increasingly using the internet as a key resource when working on homework assignments. In the wake of recent “cut-and-paste” and “contract” plagiarism scandals and an increasingly sophisticated industry devoted to plagiarism commercialization and detection, should we worry about this problem in math courses?

Here are three examples I’ve seen in my own classroom:

1. An abstract algebra take-home exam defines the Hilbert matrix then asks a few questions regarding it. A few students type “Hilbert matrix” into Google, find the corresponding Wikipedia page, and then essentially copy the contents from there, notations included. They neither make a reference to the Wikipedia article, nor seem to care that their solutions involve material far removed from the course content.
2. A slightly tricky problem on systems of differential equations moves one calculus student to find an on-line set of linear algebra notes where this case is dealt with, albeit in a quirky way. The student reproduces the solution, but makes reference to the notes.
3. A few students find a course website from another institution’s calculus course using the same textbook, where a TA has posted solutions to many problems. They more-or-less copy down the posted solutions, making various cosmetic changes in notation.

Here are some lessons I’ve learned from these:

1. My mistake was mentioning the term “Hilbert matrix.” Once there’s a keyword available, that keyword will be searched. It’s very difficult (at this moment) to enter an actual matrix into Google. From an academic perspective, the students’ only offense was not citing their source. From a teaching perspective, did they show a mastery of the course content?
2. The sought-after material was actually contained in the student’s own textbook. For the modern student, the problem with an old-fashioned textbook is that it’s not text searchable. Hundreds of on-line pages are easier to sift through than hundreds of paper pages. Should the student be punished for not reading the textbook, or receive some credit for learning a new method on his own?
3. There is clear misconduct in this activity. But how would you know that the solutions are from an on-line source? The students may appear to just be copying from each other.

As teachers, while making our own rules and guidelines about on-line resources, we should keep these examples in mind.

One possible rule: no consulting material outside the textbook and notes.
But with our increasingly tech-savvy students – especially after first year calculus – is this really desirable?

An alternative guideline: any material is fair game but you must reference your sources and your solutions must be understandable to the rest of the class (in particular use only the notations and concept from the class).
The key point here is transparency.

Clearly web searching is no substitute for problem solving. Nevertheless, I’ve noticed that seeing material from class appear in the “real world” (i.e. the internet) both encourages and excites students. Might there be a place for modern “digital literacy” considerations in our math courses?