I was part of a grant last semester to implement a set of teaching materials that has been refined over the last decade. The materials use a teaching method called inquiry-oriented instruction, which I would say is a subset of inquiry-based learning (IBL). I used these materials in my abstract algebra class, although there are materials for both linear algebra and differential equations, too.

A very brief description is “intuition comes before definitions.” The materials introduce quotient groups by discussing Even and Odd integers, which students could easily see is a group at that point (using rules like “Even + Odd = Odd”). Once they got familiar with the idea that we could have sets of elements make up a group, we slowly backed our way into the definition of coset. It was pretty impressive to see students very naturally come up with definitions—having the right prompts helped a lot.

As part of the grant, I went to training at North Carolina State to use the materials. I also had funds to have student video my class, which will be used to analyze how well instructors who were not involved with the development of these materials can implement them.

We also used the class video as part of a weekly online working group. The purpose of this group was to prepare us, both in terms of pedagogy and course materials (not everyone was an algebraist), to teach the class. We discussed the purposes of the prompts, talked about what was going well and poorly, and watched video of each others’ classes. I found this immensely helpful.

I would use these materials again (in fact, I am planning on using the linear algebra materials next year). My sense is that my students had an abnormally good grasp of the definitions; previous students have struggled to understand what a coset means, for instance. My focus for the next time I use the abstract algebra materials is to work harder on the technical proofs—I think that my students did better on writing proofs than the previous time I taught the course, but not by a lot. Still, I think that the gains in intuition were worth it.

Links to the abstract algebra, linear algebra, and differential equation materials can be found here in the middle of the page.

### Like this:

Like Loading...

*Related*

Tags: abstract algebra, IBL, Inquiry-Oriented Instruction, Linear Algebra, math 331, Teaching, TIMES

This entry was posted on February 15, 2017 at 3:03 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed.
You can leave a response, or trackback from your own site.

February 16, 2017 at 1:23 am |

This sounds really cool. I really like the notion of students really defining things for themselves using their own experiences and vocabulary. I know some knock this type of approach in the physics world because it’s too slow. What would you say to that kind of criticism?

February 16, 2017 at 1:59 am |

Short answer: we started the semester slowly, but we ended up basically covering as much as anyone else.

Long answer: I guess that I would say that it depends on what you value. We were able to cover all of the topics that we normally do in abstract algebra, although we definitely did not cover all of theorems that one would normally cover.

I like this approach because I assume that students are absolutely going to forget the details, so I would rather they have a deep understanding of a couple of basic concepts rather than a shallower understanding of a lot of the details relating to the concept.

So if someone wants to be sure to cover every single theorem that is covered in the “standard” version of abstract algebra, I would say that this approach should not be for them. However, this curriculum is good for people who are interested in making sure that students understand the big picture.