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:

- 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.
- 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.
- 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:

- 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?
- 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?
- 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?

Interesting topic, really grabbed my attention. You may have come across students copying stuff directly from some website like Wikipedia and then pasting it as it is with even the tags such as citation needed! Although math is a subject that still it the hardest to copy off from the webistes if the problems given are unique as solution to text book problems could be found with the right keyword and a few searches but unique problems are not so easy to find unless of course they copy each others work. Sure it’s great to see students acting out of the box and being tech savy but it all comes down to this, whether all this would help in their finals, where the results greatly impacts their future. My teacher had the habbit of giving surprise test to the class, that always kept me on the toes knowing no outside help is going to help me and this also helped the teacher gain a broader insight into what everyone was putting down in their progress and then use the results to act accordingly. Sure copying stuff does make the students seem brighter but in the end of the day does that help them in the finals or later in life?

I’m clearly not arguing that copying math homework from the web will help the students on their final exam. But one possible question is whether searching the web to find a solution (or something close enough) is akin to preparing a “cheat sheet”? It’s usually not the cheat sheet that helps in itself, but the preparation that went into creating it. -AA

In the past student did not have that much resources to complete their works. The hardcopy books and libraries were only the single resources. Butas of today internet in under their hand. Very basic. Copy paste functions. Now either the teachers will have to be carefull on those homeworks or student will think of their future an try to learn actually as those stuff are being asked toimprove themselves and not only copy paste work. Anyhow this is a result of technology world.

In the past student did not have that much resources to complete their works. The hardcopy books and libraries were only the single resources. Butas of today internet in under their hand.

You may have come across students copying stuff directly from some website like Wikipedia and then pasting it as it is with even the tags such as citation needed! Although math is a subject that still it the hardest to copy off from the webistes if the problems given are unique as solution to text book problems could be found with the right keyword and a few searches but unique problems are not so easy to find unless of course they copy each others work.Sure ı have the sama idea.