Groupprops:Introduction for teachers
This is a first-person article written by: Vipul
First-person articles give opinions of their authors, as long as these opinions are broadly endorsed by the wiki
Dear teachers!
A very warm welcome to Groupprops. Most of my knowledge of, and passion for, group theory comes from the great teachers I've had, some who've taught me personally, and some who have taught me through their books or other indirect support. I appreciate the crucial role you play in developing an understanding and passion for mathematics for your students. I hope you find the content and organization of this wiki interesting.
Wikis and Groupprops
What the wiki model means for you
How does Groupprops affect your teaching activities? I've been working hard for the last few months to figure out how Groupprops can be made a better resource for teachers. A lot of resources and ideas are still in a development stage, but I'm convinced that the impact on your teaching activities can be a lot.
One of the problems I faced as a student, attending a lecture and trying to take notes, was that when I came back from the lecture, I sometimes couldn't make sense of my notes. What could I do? Read the textbook -- the textbook is long, and covers things in a somewhat different order. Or bother the teacher or teaching assistant? Not for every little thing.
Another problem was remembering the little examples and counterexamples, and looking up references. Teachers make painstaking efforts to look up references for students, but despite my best intentions, I've hardly ever looked up the references for the little examples and counterexamples. It's too much work to locate a book in the library and find the relevant page. Besides, I've to do that every time I need to look up the little example or counterexample.
Yet another problem is that of problem sets and exercises. A huge amount of preparation time for teachers goes into preparing and grading assignments. And students also don't have quick access to a nice common problem pool. Each book has its own problems, but the problems are localized to the books; hopping between books, assignments and other sources for problems is a pain.
I've tried to use Groupprops as a solution to these problems at two, somewhat different, levels. At one level, the structure and organization of the wiki itself means that after the lecture, the student can go back, look at the lecture notes, and check whatever was unclear on the wiki. Didn't understand a proof? No longer a need to open up a book and be told that the proof follows from Lemma 2.3, Proposition 4.1 and Corollary 4.3. Instead, just type the name of the theorem in the search bar, and read a fully detailed article on the proof, with links to all relevant references in books and perhaps even to papers written about the theorem!
To see the way things are organized here, check out definitions like characteristic subgroup or permutable subgroup or proofs of facts like characteristic implies normal. Or a counterexample page like normality is not transitive. Many of these pages are undergoing significant reworking, but I think the current state of these pages shows how easy it is to look up and cross-check facts.
The second level at which I've been trying to solve this problem is the creation of add-ons. Loosely speaking, I'm working on articles that are not part of the main wiki but that use content on the wiki to provide resources useful to students. Some of these developments are:
- Problem sets: These are huge lists of problems in relevant topics in group theory. You'll see that many of the principles of instructional design have been merged smoothly with the organizational principles on the wiki. The solutions not only give a quick explanation but also link to relevant term and fact pages so that the student can take the opportunity to read more about things as he or she solves the problems. see, for instances, problems in elementary group theory (still in development).
- Entertainment: Entertainment is important, and I've been working on some ideas of how entertaining articles can help cement a student's love and understanding of group theory. See, for instance, what on earth is a group? (still in development).
- Dynamic guided tours: Here, students are taken through truncated versions of pages in a select sequence, with summaries given periodically. In between, entertainment pages are shown for short breaks, and problem sets are administered regularly. Learners arealso encouraged to take detours into related articles to get a better feel of what's going on.
We're different from Wikimedia projects
Further information: Groupprops:Groupprops versus Wikipedia
We differ significantly from projects like Wikipedia, Wikibooks, or Wikiversity. For one, we are very few right now -- this wiki has approximately 15 registered users and most of the edits are done by one person (that's me). Moreover, our policies differ significantly.
What you may find odd
Too much nonstandard material and too much content per page
It could be extremely confusing for students to go through the Groupprops wiki without guidance, because we have a lot of nonstandard terminology (terminology local to this wiki). Moreover, even the pages on simple topics often contain details that the student might find distracting.
The first problem can be solved somewhat, through the dynamic guided tours, and by encouraging students to concentrate on these categories: