Geometry homework: Is this cheating?

Here’s a question for you…

Let’s say that my daughter’s taking Geometry and the homework assignment from her textbook asks her to prove that the three perpendicular bisectors of the sides of a triangle are concurrent (i.e., they intersect in a single point).

She tries. She’s successfully worked other Geometry proofs in the past. She’s even successfully done other proofs tonight. But she’s stuck on this one. Even after she tries again. Even after she takes a break and comes back to it. Even after her dad, whose high school Geometry-related memory faded long ago, takes a peek to see if he can give her a few tips. For whatever reason – she’s tired, she’s confused, she’s had it up to here with Geometry this evening, whatever – it’s just not clicking.

Now let’s also say that there’s a step-by-step proof available to her on the Web. The proof literally walks her through the steps needed to prove this theorem, with diagrams and explanations along the way. Is it cheating for her to get herself unstuck by consulting the proof on the Internet?

Argument 1: Yes, absolutely. She’s supposed to do it herself. Getting answers from someone (or some place) else is the very definition of cheating. If she can’t do it herself, too bad. Maybe she’ll understand it tomorrow after going to class and/or more practice.

Argument 2: No way. This should be about her learning and her understanding of important Geometry concepts. It doesn’t matter how she gets the information as long as she gets it. She should be encouraged to tap into outside resources (classmates, parents, other math books, the Internet, etc.) if they’re helpful.

Argument 3: Maybe. Argument 2 is somewhat persuasive. But at a gut-level it still seems like she’s cheating herself – if not her teacher / classmates / the discipline of mathematics – by consulting the online resource.

Argument 4: Who cares? This exercise is an inauthentic use of kids’ time and doesn’t result in true mathematical learning. She should boycott any and all homework assignments like this one.

Argument 5: ?? [insert yours here]

As educators (and parents), I think we need to have discussions – and try to come to some agreement – about whether or not we consider this ‘cheating’ or ‘taking advantage of the resources available to you to facilitate your learning.’ Because the quantity and quality of online aids to learning are only going to increase in the years to come.

Thoughts?