First Day of a New Term – Neat Introductions Idea!

So I started my first Precalc 12 class (offered for adult upgrading students). The class had 17 people on the waitlist. It’s also a condensed course, so it’s basically two terms squished into one. FUN! I knew I had to minimize numbers a bit. So I decided to start off with a reality check. Here’s what it’s going to be like. Here’s an assessment for you to try in order to get a sense of the prerequisite knowledge that you will need in this course. etc. It worked . . . I think. A couple people gave up seats, and I let more into the class than I normally would because the energy in the room seemed to be working. Maybe it’s because my room is so NICE this term! It’s so big and spacious, and the best part is that THERE ARE TWO LARGE WHITEBOARDS ON THREE OF THE FOUR WALLS!!! The other one is filled with windows! This is extremely exciting. I believe that room ambiance has an effect on learning, but that’s a personal belief. Normally, I get rooms with way less vertical whiteboard space. So I have been resorting to using these:


However, students end up using them on their desks, and many students often resort to using their paper after a while. I don’t blame them, there doesn’t seem to be much difference other than the fun colors that can be used, and the fact that they are easily erasable. But also, they are easily erasable.

So students sometimes rather writing on something that will leave a record for them of their thinking. Anyway, this has worked well for the most part, but I really noticed the difference between flat non-permanent surfaces and vertical non-permanent surfaces! It’s true!

The engagement levels were much higher, and knowledge was more quickly mobilized around the room. This means that students quickly realized that I was encouraging them to look at what other groups were doing to guide them. One student expressed excitement that he is going to be able to look at other students’ work this term in this way. There’s something intriguing about that. Maybe it’s because for so many years, these students have been trained that it is socially unacceptable to “cheat” . . . but they have not always been encouraged to do this in a collaborative way.

So after giving these people a reality check on how demanding the course is going to be and how much they have to dedicate themselves, I gave them the following activity. It was inspired by a session I attended last August, where Dan Meyer introduced this similar tactic, but with coordinate points. Since my first topic is a review of sets, I decided to integrate it into a “let’s get to know people in the room” session. It seemed to really set the stage, and hopefully helps in creating that essential community aspect of classroom life. It also led us to some discussion around logical statements and key set related terminology. I actually tried this activity last term, and what I changed this time around was that I gave some prompts beforehand so that students had some examples of categories they could use for their set graphs.

So here it is.

First, I give my students slips of paper with these questions for them to answer. I gave them a couple minutes or so for this. The questions were rather obscure, and they probably wondered what this has to do with math class.

Census exercise photo

Next, I explained that I am going to group them, and that once I group them, they will be working on creating a Venn Diagram like this:

Venn Diagram

They will then be deciding on how to name each set so that they can then place themselves on this graph according to these categories.

I grouped them randomly using playing cards, and asking them to find the same number as them to form groups of 4. They were then to find some whiteboard space, and create their graphs.

Some groups were still confused. They drew two circles, but had no idea how to continue.

I gave them an example:

Say one category is a collection of those who hate cats. Then anyone who hates cats has to be in that category. But if someone hates cats AND bananas, then they would be in the intersection of the hates cats and hates bananas categories, and so on.

Here are some examples of what my students came up with:

IMG_0235.JPG (2)

IMG_0236.JPG (2)

And one group even created a way to make TWO sets of these on one graph :-0

IMG_0232.JPG (2)

Things that came out of our discussions included:

  • how do you label the categories so that the points make logical sense?
  • what is the “middle area” called? (intersection)
  • why would a point be outside of the two sets?
  • what’s a universe?
  • if a point is ON THE BORDER, does it mean that the person represented by the point is unsure? (lol, this was a cute idea)
  • what is meant by union and intersection?

This set the stage for more set related problems, and students got to present their categories to the rest of the group.

The one thing that I missed from this activity, that I would have liked to have in a student introduction activity, is the various reasons for why they have decided to take this class, and what they feel about math.

I am looking forward to working with this group, and only hope that I will be able to keep up with coming up with neat creative ideas for developing their engagement in mathematical thinking.

Student Autonomy: The Missing link – CanFlip14 Presession Materials

Here are a couple things that would be helpful for you to check out prior to attending my upcoming CanFlip14 session:

1. Watch the short clip I created (embedded below or linked here) on the key theory of autonomy that I draw on in my work on student experiences of flipped classrooms. We will use this as a basis for some of our discussions around classroom practice.

If you want more details on the theory, you can see my blog post here.

2. Read Dan Meyer’s blog post on the painted cube problem (found here) and consider how cognitive autonomy is being elicited by his approach.

3. If you still have time, think about what sorts of activities you can think of using in your classroom that give room for cognitive autonomy.

I look forward to seeing you at my session! See you at CanFlip14!

Student Autonomy in Flipped Classrooms

I was cleaning out my car yesterday, and I found a slip of paper from the ETUG presentation that someone had written on in response to my question of what teachers SHOULD be doing with class time.


Yes! Students often come with the expectation that they will be told everything and that they will figure it all out when they leave. I know I used to think this way! However, class time could be used so much more efficiently if students did the figuring out part during class instead of out of class. This is essentially the concept of a flipped classroom.

As I am just wrapping up my masters thesis on experiences of a flipped classroom, I am drawing more and more attention on analyzing the autonomy that students are provided in class and how that either motivates them to learn or motivated them to slack off.

In my research, I have found that autonomy can be classified into procedural, organizational, and cognitive autonomy. This classification is introduced by Stefanou, Perencevich, DiCinto, & Turner (2004) as shown below.


Stefanou et al. (2004) found that cognitive autonomy support was essential in student engagement. Further, Jang, Reeve, & Deci (2010) determined that not only is cognitive autonomy essential, but it should be paired with teacher provided structure. Structure, as defined by Jang et al. (2010), is a way of maintaining control over the procedural and organizational dimensions in an autonomously supportive manner.  This means that teachers should provide guidelines for these dimensions in order to maintain student engagement in course content. This is not to say that these dimensions should be controlled in a controlling manner, but rather in a manner that  leaves room for student input.

My current research has provided further evidence of the importance of cognitive autonomy in student engagement and how it is most effective when organizational and procedural dimensions are structured in a student friendly manner.

The implication here is that flipped classrooms should not be seen as ways to allow students to do anything they like. The role of the teacher as a facilitator rather than a dictator is absolutely crucial in fostering student learning. In essence, fostering student learning should be the number one goal of teachers. However, with a variety of external pressures, it is understandable that it is a difficult goal to pursue.

My research has also provided evidence that not all students desire a deeper understanding of the material. These students may not engage in meaning making activities no matter how interesting they are. However, providing opportunities for developing deeper understanding and eliciting cognitive autonomy in students allows those who strive for understanding to be able to attain it.

So, what will we do next to try to turn our students’ brains ON?

Jang, H., Reeve, J., & Deci, E. L. (2010). Engaging students in learning activities: It is not autonomy support or structure but autonomy support and structure. Journal of Educational Psychology, 102(3), 588–600.

Stefanou, C., Perencevich, K., DiCinto, M., & Turner, J. (2004). Supporting autonomy in the classroom: Ways teachers encourage student decision making and ownership. Educational Psychologist, 39(2), 97–110.