One of my high school teachers used to say that “Wikipedia is an enemy of research”. I have heard similar phrases throughout my university career, at OISE and at my teaching practicums. All those teachers were making valid points. First of all, Wikipedia is too easily editable. Many articles (especially historical or political ones) are biased or inaccurate. Moreover, we never know who the author of the article is and who the editors are, hence, we cannot be sure that they are professionals. The ready availability of Wikipedia articles might give the students a false idea of what research is, leading them to think that in order to understand a subject one just needs to click on several links. Over-relying on Wikipedia promotes poor time management skills because many students use it to cram before their tests, so it is understandable why many teachers would encourage their students to opt out of using Wikipedia altogether. Such an aggressive reaction always surprised me. I can certainly see how the overuse of Wikipedia can negatively impact students’ research skills and how inaccurate information may lead them astray but as teachers we need to face reality. As much as we want our students to consult reliable sources, they tend to consult Wikipedia when faced with anything unfamiliar.

I was reviewing the topics that would be presented at the CMS camp and I was shocked by their level of difficulty. I have taught a gifted math class before but the enhanced curriculum never covered game theory, advanced combinatorics or Diophantine equations. I thought it would be interesting to see what Wikipedia had to say about them (since the students probably looked all of them up already). I was pleasantly surprised. Most topics were covered in great detail and I did not spot any inaccuracies. Moreover, the descriptions contained links to interesting mathematical facts and theorems that could lead the students into interdisciplinary ways of thinking. For instance, after typing the word “Triangle” in Wikipedia search box I was expecting to see a one-screen description with a picture of a triangle. Wikipedia went above and beyond my expectations listing all interesting facts about triangles, related theorems and formulas, historical notes and more. There were at least 10 different formulas for finding the area of a triangle! (As a teacher I was lucky to meet students who knew one formula (A = ½(bh) ) and I was extra lucky if that student could explain why the formula is working.) There were other links to applications of mathematical concepts and numerous highlighted keywords linked to the relevant articles. Each page contained detailed diagrams, sometimes even the interactive ones. Many links made me regret that I did not think of consulting Wikipedia before preparing some of my lesson plans.

For me it is always important to motivate students to explore math in their own way and at their own pace. Wikipedia is a useful tool to get the student started on a topic. The first paragraph of a typical Wikipedia page is a concise summary that allows the student to quickly see if they are interested in the presented material. For instance, if a student heard an unfamiliar term he or she can quickly look it up and get a rough idea of what branch of math it belongs to, etc. Of course as teachers we need to be able to explain to the students which sources are suitable for effective research and which are not, but this part comes later, when the initial interest in a topic is present already. Wikipedia is just one of the numerous objects in our lives which have their designated uses but can be dangerous when misused. For instance, we never hear anyone calling a kitchen knife an enemy of human fingers. Wikipedia can be turned into teachers’ helper as well if the teachers will clearly define its role for the students. After all the phrase “Do NOT use Wikipedia” may cause more students to use it simply to ‘rebel’.

original at https://math.escalator.utoronto.ca/home/blog/category/points-of-note/

image from http://www.theage.com.au/news/web/fast-facts-found-online/2007/02/21/1171733770530.html