Stacking the Odds in My Favour

I'm currently teaching a grade 10 applied math class. I'm following @MaryBourassa's lead of spiralling the curriculum (Thanks Mary!) and I'm really enjoying it.

Today we had a quiz and a number of my students were quite nervous. Just before class started one girl said to me that she was going to fail the quiz. I reassured her that she was not going to fail. I told her that if she thought about the questions and wrote something down she would do just fine. She didn't buy it. Her response was "No I'm going to fail. I bet I fail. I'll bet you $5 I fail". I smiled at her and told her that I couldn't make that bet because she could easily make things go her way. I was glad to hear her response of "I would never fail on purpose".

As the class worked on their warm-up I thought about how I could guarantee a win on this bet I wasn't going to make. I didn't want to win to get $5 or to say that I was right. I wanted to win to help this student and others who were feeling the same way boost their self confidence. This course is typically comprised of students who don't feel comfortable in math and who don't think they can do math. Today, boosting their self-confidence was my number one priority. As I handed out the quiz I informed them that they would be allowed to use their notebooks. This made many of them feel more at ease and as it turns out, few of them used their notes. I will still get some good information on what they do and do not understand and I will have an opportunity to assess them again at a later date. I'm even toying with the idea of not including a mark on the quiz. I may just provide feedback.

Sine Law

Last semester I taught the Grade 11 College level math class. I was very disappointed to see that 12 out of 26 of my students had failed the course. Luckily, I get to teach the class again this semester. This means I can make some changes in the hopes of improving my students' understanding. This is a summary of my first change.

Friday I was teaching the Sine Law. I have in the past created a dynamic geometry sketch. I manipulated it and as a class we noticed how the ratio of the side length to the sine of the corresponding angle was equal for all pairs of angles and corresponding side lengths. For whatever reason, last semester I didn't even show the sketch.

This semester I decided to have the students do the investigating on their own to see what they could come up with. I provided them with a link to the simple worksheet below.



I wanted them to look at the ratios (mentioned above) from a number of different triangles so I had them complete this handout. We completed the first two entries in the table together before I turned them loose. I figured that the table would be fairly straight forward, but I was pretty confident that questions 5 and 6 (where students had to apply what they learned) would be a challenge. Sure enough I had a number of students call me over and say "I don't know what to do here". My response was to have them tell me what they discovered earlier and then tell them to use that information with what was given in the question to set up an equation. That was enough for a number of them to make the connection and do the problems...without any direct teaching. They figured it out on their own. I was blown away.

We had some guests in our class that day. During the activity, one of the guests said to me that this isn't an activity that would be typical in this type of class. I think he is probably right and I think that is part of the reason why the course has such a high failure rate. I challenged my students to learn something on their own and they did it. I think (at least I'm hopeful) that we have established the expectation that students will be active participants in their learning. Now I just need to find a way to maintain that expectation for the remainder of the semester.

The only disadvantage I saw to Friday's class was that many of my students were away. I will summarize the work we did on Friday and give everyone an opportunity to practice. We'll see how it goes.