We’re now heading toward the end of the term and the conclusion of this course. This week has mainly been used for wrapping up the different documents elaborated during the term such as teaching dossiers and scrapbooks (i.e. list of concrete strategies to be used in the classroom).

Next week the participants will present the course and concrete tools they have gotten out of taking part in this course. This will also be the time for feedback and reflection on the whole term as well as planning for the future form of the TA accreditation program.

This week has been (again) pretty interesting. First we enjoyed an in class activity consisting of what I would call “supervised learning”. More precisely the teacher gave a sheet with a couple exercises and then let the students work on it for a while. He then guided the students to the solution and emphasized the important features of the exercises. As soon as the students had finished one sheet, another one was distributed.

One of the goal here was to have a form of teaching where the students are active learners trying to solve exercises. At the same time, the goal was to have a method that would work in a class of 60-70 students (unlike the activity described in this post that seemed to work only for small groups). As a participant I found motivating to work on concrete problems and being active. One difficulty though is to gauge the exercises correctly and in case some students are stuck, to give only only a little bit of help to get them started and not the full solution. Indeed, students who are not able to make progress at all on certain parts could easily feel discouraged (as it happened to the author on one section).

This activity seems to be easily scaled up to a whole class by forming groups. Then, of course, comes the always difficult task of having students actually working together and not just on their own and to help each other in case some are faster than others. To sum up this activity appears to be very attractive as it highly encourages students to be active during the “lecture”.

This week’s online activity revolved around possible alternatives for clickers. Participants were invited to reflect on the different alternative methods that exist to the use of clickers (the basic assumption was that slickers are helpful and that we would like to see what else is out there). Pros and cons of devices as simple as colored cue cards or the many instant polling software (such as Google forms, Socrative, Poll everywhere, or Learning Catalytics) were discussed.

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.

Next week we shall start the core weeks and we are all (I hope) excited to see what kind of activities the participants will come up with!

Today, I’d like to talk about one topic that came up during our class discussions. We were discussing the chapter of How Learning works on Student Development and Course Climate when the theme of stereotype showed up; indeed, mathematics is a field, with the other “hard” sciences and to some extend engineering, where stereotypes are pretty strong.

Even though this is nothing new this problem is still pretty hard to address; indeed, as illustrated in this recent study, faculty are sometimes unconsciously biased against certain category of students/people. Moreover students can also underperform due to what is called stereotype threat, the idea that they belong to a group that is not good at a given task. Here again, this can be an unconscious process and it is sometimes triggered in very subtle and by apparently insignificant actions.

During this discussion, two main views emerged: either talk about it in class in order to prevent such a threat to happen or be aware of it and act accordingly, namely, by being as impartial as possible but without directly talking about it with the students. The idea of talking about a possible stereotype threat is partially supported by this study, where students tended to perform the same when informed about the potential stereotype threat. One concern about this approach is that it could backfire and in the end have the opposite effect; this question remains open at the moment. Regarding the second view, acting as impartially as possible, this is of course desirable, and teachers should always do their best to act so.The difficulty here is that favoritism can be unconscious and thus pretty hard to control. As the first study mentioned above indicates, even people who think they are acting impartially can be biased. The question is then to know whether having measure specifically for that such as only having a number and no names on homework and midterms is useful and/or easy enough to set up. One could argue that just the handwriting give some information that could then lead to some unconscious favoritism. These last hypotheses remain to be tested.

As one would have guessed, there seems to be no miracle solution to stereotype threat. Hence, acting in good faith and being as impartial as possible seems to be the best one can do.

With the Prep weeks in full swing, the various components of the course are starting to fall into place.

We are currently nearing the end of our first book: How learning works. The in class discussions have been fruitful. The ideas generated, particularly regarding motivation and course climate, can be further explored during the Core weeks and concretely placed in the scrapbook.

In preparation for the core weeks, the various blogs and wiki have been set up. This will allow the participants (and the coaches) and share their thoughts, ideas and insights that they gain during the coming weeks. Within the rules and boundaries that the participants have set up (and also with their permission), I would like to give some highlights into the areas and activities that the participants have chosen the explore during the core weeks.

To assist the development of their core week activities, each group member will take on one of two roles: One person will be responsible for setting up the activity and the second person will be responsible to making sure the activities serve a purpose and to implement/facilitate feedback from the group.

The prep weeks conclude next Monday when we finalise the plans for setting up the scrapbook and from there the participants take full control of the course with the first round of in class and online activities. I am definitely looking forward to seeing what the participants have planned, what challenges they have set and what ideas I will be able to adopt into my own teaching.

Welcome to the blog of the Math Teaching Assistant Accreditation Program Course!

In this first post, we shall mainly describe what this “course” is about and how is will be ran this term. It has been a few years that the department of mathematics of UBC has an accreditation program for its TA’s. This term it will materialize as a course/seminar (we are actually not sure what the best terminology is, feel free to suggest one!). The main goals of this course is to give the opportunity to our participants to :

• study current educational/pedagogical texts and meaningfully interpret them in the context of teaching mathematics,
• practice and experiment the application of education theories to mathematics by creating and leading engaging learning activities, both in class and online,
• develop new tools and activities for the classroom.

In order to achieve this goal, this course is structured as follows :

• four weeks of preparation time during which the participants read the book How Learning Works, set up their own goals and framework, and are introduced to the different technologies to be used during the course,
• seven weeks representing the core activities of this course, with each week one in class and one online activity designed and lead by the participants. The in class activities will refer to material from How learning works whereas the online activities are linked to the book What Best College Teachers Do,
• one week or wrap up, feedback and public presentations of the work accomplished during the term.

We have four participants, divided in two teams of two and two facilitators. During the preparation weeks, the time is divided between presentation of online tools (such as wikis, blogs and so on) by the facilitators and general discussions about the chapters of How Learning Works. During the core weeks, each team is in charge of one activity per week (alternating online and in class).

Besides these activities, participants develop during the whole term both a teaching dossier and a scrapbook. For the teaching dossier, we follows the guidelines and structures proposed by the Canadian association of university teachers. The scrapbook is basically a list of ideas and concrete activities to be used in the classroom, the goal is to have engaging, interesting and research-supported activities and/or documents.

If you have any question about the course, feel free to contact of the the two facilitators (the author of this post and Tom Wong).