This week’s online activity invited the participant to reflect about the online tools available for an instructor to use in addition to his/her (in class) lectures. Nowadays, many possibilities exist and the interesting part of this exercise is to have the participant think about the relevance of the such tools (course website, course notes in a blog style, online forum such as piazza, online blackboard such as WebCT Vista).

In class we saw a pleasant classical presentation about some basic theorems in number theory. One of the aspects of this presentation was to foster participants’ interest with interactive activities such as trying to find patterns and “re-discover” certain theorems. These interactions are in my opinion crucial. Indeed, some experiments indicate that the nervous system activity during a lecture (measured via electrodermal activity) is similar to… watching television; and lower than when studying or doing homework. It therefore seems crucial to have some interactive activities in class. This all the more since we currently see the emergence of online courses (with recorded lectures for example, think about coursera or Khan academy) which makes the fact of coming to class to simply listen at a teacher becomes obsolete. Indeed, in the future courses will have to offer more than what a recorded lecture does!

At this point in the program, things are in full swing. In addition to the reading and teaching dossiers, the participants are asked to challenge themselves and take the next step  in the classroom and online arena. This week, the two activities saw the participants take the next step in their teaching explorations.

The in class activity focused on the “integration” step highlighted in “How learning works” about how students developed mastery of material. Traditional first year calculus course focused on developing component skills and then application of such skills in word problems. However, the book suggests that there is a less known intermediate step known as integration, where the learners are given the opportunity to practice utilising multiple component skills simultaneously and in a controlled manner.

The emphasis on integration was highlighted through the context of Go. The learners were first introduced to the component skills of the game such as rules, valid moves, alive and dead positions. This then lead onto the integration step of determining whether a position can be killed. This task required an understanding of the component skills mentioned above as well as using them simultaneously. However, the local nature of this task meant that learners were able to focus solely on the position in question without having the burden of dealing with the rest of the board. It would be highly interesting (and educational for instructors) to see whether a similar task could be accomplished in the mathematical domain.

Meanwhile, in the virtual world, a highly interesting experiment is also taking place. This week, the participants are asked to create a Vlog to reflect on Chapter 3 of Bain. The use of blogs as a learning medium has recently been observed in several sections of first year calculus. However, Vlogs add a new dimension to the learning and it’s effectiveness will be the subject of this weeks experimentation.

For the second week, we’ve had one in class and one online activity.

The in class activity of this week was centered on differential equations. Instead of a usual teacher written on the board/student writing up notes, we experienced a guided way through a sequence of exercises. More precisely we were in two groups of two people and had to solve some problems on the board. After a little while the two groups merged into one. The whole process was guided by the teacher; he was giving hints about the exercises; summed up reflections and work and lead us through a series of problems.

As a participant I found this activity very engaging, I was definitely more active than in a regular class setting. I also have the impression that this interactive setting where the student does, in some sense, most of the work during the lecture and have time to reflect and discuss the questions made me more interested in these questions (in contrast to a lecture where the teacher says here is an interesting question and then solves it right away, or on the contrary never talks about it again and completely leave it to the students).

The general feedback on this activity was really positive. Of course some points could be improved. One such element would be to give a summary of the activity to the students (or ask them to do it themselves) both during the activity to see where we are and at the end in order to wrap up and reinforce was is the central point of the activity. Another point is to be careful about participation, in other words, to have everyone involved and active (something definitely difficult). One question that arose was how many people per group would be an “ideal” number. We felt that 4-5 people would be the maximum but without further evidence of why this number would give “better results”. Another point that seems difficult in such a setting is to encourage peer-teaching within the groups, an element that seems particularly important if the number of team members increases.

The online activity mainly consisted of a reflection on the system set up by the Khan academy, one of the main website for learning mathematics online. After trying “trying out” their online exercises, we reflected on the method’s strengths and weaknesses and then propose possible improvements. Indeed, the Khan academy introduced interesting ways for online learning and for organizing exercises but the level seems definitely too basic compared with the expectations of a first-year calculus course at UBC. Improvements are definitely possible though and I think that with the framework they have, it is definitely possible to set exercises for higher level math.