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!

Personality in the Online Environment

As you may know, I’m teaching two online mathematics upgrading courses this term. It’s been quite an interesting journey in transforming my ‘regular’ classroom into a ‘flipped’ classroom, and now into an ‘online’ classroom. Essentially, I use my flipped classroom videos, and assign unit projects and online discussion boards. For the most part, it works well, but I still have to find a way to nail down increasing discussion board usage. Anyway, the main insight I recently discovered was the element of personality that students normally get when in a face to face class. You know when you don’t realize you have something until it’s gone? Yeah, well that’s how I came across this.

Normally, in a face to face class, there are so many more side conversations that build trust and community aside from the curricular content. In the online environment this term, I have found that some students still seem to lack trust in sharing their issues on the discussion boards (it’s already a month into the term). Many post, but there are some who will email me and tell me that they aren’t sure if they should post their question publicly. Others will post a question, and then a few minutes later, as if in shame, say that they are sorry for posting because they figured it out. My response is to ask them publicly to explain how they figured it out, because it will be helpful for others to see. Overall, I’ve seen some great posting going on, and awesome discussion among members, often leading to strong mathematical questions. However, there are still those who seem uncomfortable sharing in the online environment . . . and I can understand that too.

So, without thinking about any of this, I sent out a message to all my students yesterday telling them how I got sick this weekend and have fallen a bit behind with marking (an apology letter). The response to this was interesting. Because I shared something personal, I got several personal responses back!

This brings me to the question of how much personal sharing is necessary and appropriate, and how does one encourage students to develop an online persona as well?

Where to find the activities?

So often I have found myself marvel at how some teachers find the best activities. I always ask them, where did that idea come from!?! Recently, I discovered that there are SO MANY SOURCES OUT THERE! . . . and this is only because teachers take the time to share their ideas with the global mathematics teacher community online. I would like to see more connection between these seemingly single bloggers. Wouldn’t it be nice if we had a cohesive list of all the math bloggers? Well, it looks like someone’s already done that! I was so excited to find this link where there is a comprehensive list of mathematics teacher blogs! This means that at this point, there are 347 blogs chock full of potential teaching ideas. So why is this not visible to the average teacher, and why is it that teachers (like me) don’t have the ‘time’ to go through them? It’s overwhelming for me to think that I may never absorb all of those ideas that are out there.

However . . .

The time is now . . .

It’s time to be inspired.

In addition to the above link to blogs, here are some of my current favorites for teaching ideas:
Peter Liljedahl’s Teacher Resources
Dan Meyer Blog
Andrew Stadel’s Estimation180
Robert Kaplinsky’s Problem-Based Lesson Search Engine

Feel free to post your favorites in the comments bar:

Combating the constraints of time in the implementation of a flipped classroom

I have just embarked on a new term. This term I am teaching a fully online mathematics course for the first time, as well as a new course I haven’t yet taught before. I wanted to flip the new course, but with so much more on my plate this time around, I found myself short for time in making videos (in the same manner I made videos for my first flipped class). I have also received many comments and questions from other instructors about how much time is needed in developing a flipped class. At first, I did not think much of it, but now that I am in the situation myself, I have been forced to come up with a solution:

The solution is simple, I can still teach in the “guide on the side” manner without full blown videos! This is because I can give students the power to ask me to make videos for the things they need help with. The method I have implemented this term looks like this:


Student are given activities to work on in groups as well as assignments they can complete individually or with peers. They are also given opportunities to ask questions during class discussions about topics they have engaged in.


Students have access to content materials out of class time in an online environment. These materials include lesson summaries, photos taken from board work during class, links to recommended videos, and self-test online quizzes.

The videos are now much shorter than my first round. I usually go through one example per video, and I tell students to tell me which questions or concepts they would like to see explained in a video. This focuses my time on specific student needs rather than making everything available all at once. I post my videos on YouTube, so if you like, you can check out my YouTube Channel. I also sometimes link to videos made by others if I agree with their approach. Finally, I have also found it useful to record an example that I explain during class and post it on the course page.

These are just some time-saving measures, and I will post back in to let you know how it goes.

So far so good!