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.

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:

Group Problems on Tests

This term, I have been giving group problems on my tests, and it has been fruitful.

Giving group problems as part of an assessment helps students treat group work during class time more seriously. In the past, I have tried to get students to work on problems in groups during class time, but they most often gravitated to working individually in the groups. This was because they knew that in the end, they were going to be tested individually.

This term, I noticed a point in time when there developed a resistance against group work. A colleague suggested that I try putting a group problem on a test to show that I value group work. I tried it, and it worked! No longer do I need to convince students to work in groups. Sure, there are still a few who just want to work on their own, but the majority have come to value working together and learning from each other.

I am still tinkering with the logistics. I have tried giving a problem for them to work on and then getting them to come up and ask for the rest of the test on which they will then write up the problem they solved together on their own. I have also tried giving a similar problem as the test for them to work on right before the test so that they will be ready for it when they complete their test. Finally, I included a group problem on the last midterm as described below:

Students were to in groups build a three dimensional object out of parts that I provided. They would then each describe and draw the object on their papers and give the object to another group to work on. The other group would then describe and draw the shape they received, and then work together to find the volume and surface area of the shape. Each student would then hand in a write up of the activity and then complete the rest of the midterm. The activity was graded as one of the midterm questions.

In giving such a task, I worried that students would just come up with simplistic objects in order to take the easiest possible route. However, the drive for most groups was quite the opposite. They challenged themselves with the most complicated shapes they could come up with! They even surpassed the outcomes of the unit in creating shapes such as:


Because they had created their own shapes, they had this drive to engage themselves in figuring out the volume and surface area regardless of how complicated it got! Many fruitful ideas and questions came out of their discussions.

If the stage is set right, group work can be very productive. However, I am constantly searching for new ways to switch up my group work strategies because too much of a good thing can take a hit. I have found that if I organize my class in the exact same way too many times in a row, students lose interest and it is no longer a novelty.

“Keep it fresh” is the advice I like to follow and remind myself of every time I plan a lesson.

Student Generated Examples

Since I have much more class time available for students to engage in learning material, I have been playing around with various types of tasks. One of which is getting students to generate examples of questions they may be asked. Any teacher who has developed their own questions knows that doing this is more difficult that it seems. A lot of knowledge is required to make a question to which a solution may be found using prerequisite knowledge. I was teaching a unit on using properties of exponents to simplify exponential expressions. I asked students to generate a question in groups and give the question to another group to solve. I also asked them to create a potential unit test in order to build study skills. I was afraid that students would choose to create extremely simple examples and that they wouldn’t learn enough from the task. However, I didn’t realize how difficult it can be for a student to create a “simple” example. In order to know that it will be simple to solve, they need to be fluent with their knowledge. In my class, all the students decided to try to make the most difficult problem they could think of! I was shocked. It led to a lot of good discussion and I was able to clarify several key points to them through analyzing how they would solve the problem. For example, a lot of them threw in addition signs but didn’t realize how much more difficult it is to simplify rational exponential expressions with several terms in the numerator and the denominator! This stemmed from the fact that they were still unsure of the difference between multiplying exponential variables and adding exponential variables. Other nuggets came out as well. This task was so useful that I ended up putting a question on their unit test to create an example and solve it. The fact that they had to solve it themselves forced them to try to stick to using properties they understood.

I’d like to share my favorite student generated example from the group work activity:


This is truly brilliant. Is it not?