Showing posts with label vnps. Show all posts
Showing posts with label vnps. Show all posts

Tuesday, October 17, 2017

MPM1D1 - Day 29 Interior & Exterior Angles

I started by having groups up at the board working on this Would You Rather problem.


This was the first time we've worked at the board in a little while. There were a number of people who were quite off task. Others got to work right away but the group dynamics were not what they should have been. Once they were done the activity I sent them back to their seats and we talked about contributing effectively to a group and how it benefits everyone in the group.

The main event for today was some geometry, specifically interior and exterior angles of polygons. I put the image below up on the board and asked students to work at the whiteboards to see how they would do without any instruction. 

The group work was much better this time around and all groups were able to answer all of the questions. A few groups needed some reminders about supplementary angles and a couple asked about opposite angles. They were doing great.

I brought them back together as a group and we summarized the different types of triangles, supplementary angles, opposite angles and began exploring the sum of interior angles. Everyone knew that the interior angles in a triangle sum to 180° so we began looking at other polygons. We did this by looking at the number of triangles in each polygon:

From this they were able to determine the sum of the interior angles. Next I had them fill out the table below to come up with an equation.


We've done enough visual patterns that to many this process came easily. They had no trouble finding the rate but had to think a bit about the initial value.  I had a couple of different results which was neat. The most common was that the sum of the interior angles = 180n-360 and the other was that the sum of the interior angles = 180(n - 2). It was exciting to see these different results.

We had just enough time to look at exterior angles. To do so I showed this video:




 We had a few minutes left which was enough time for me to handout the work for the day.

Thursday, September 8, 2016

Can We Just Take Notes?

Frustration by Sybren Stüvel
The first week of school is drawing to a close. After seven months off it's good to get back into the swing of things. I was greeted warmly by students (some I have taught, others I have not) and staff upon my return. My goal for the first week was to make it fun, or at least somewhat enjoyable. So many students hate math...or so they say. I wanted to destroy this notion during the first week.  I figure if I can tilt a student's perception of math in the positive direction at the beginning of the semester at least we'd be off on the right foot.

I wanted to minimize the amount of talking I did and maximize the amount of talking my students did. I had them working in groups, often up at the board. I was more interested in working on the mathematical processes and setting the tone for a collaborative environment than covering specific curriculum expectations.

We did some estimating, some visual patterns, some problem solving, some data collection and played a game. It was great for me to be able to spend most of my time circulating and listening to the conversations that were taking place and asking questions. I was enjoying it and it seemed as though most of my students were as well. Some of them would get frustrated at the problems we did. Many were able to overcome that frustration and feel the pride that comes from conquering tough problems.

Today I received mixed, unsolicited feedback from every class about how things were going. How did they know I wanted feedback? A couple of students from my grade nine class and one from my grade eleven class all said something along the lines of "You make math fun. Last year I hated math. Now I like it". On the flip side one of my grade nine students asked if we were going to be taking notes in the class. She looked relieved when I told her that we would eventually. Finally, from a number of grade twelve students today: "Can we just take notes? I don't want to do this group work and problem solving". As it turns out I was going to summarize some of the work we had done with a note towards the end of the class. I was dreading it. It was a boring note as the two people who fell asleep would probably attest to. Why would anyone want to do this rather than being an active participant?

The grade twelve comment is the one that had me thinking the most today. I kept wondering what we have done in our school system to make students want to sit around passively, hopefully, soaking up information. I couldn't help but think that we have trained these students to sit quietly at a desk, listen to a recipe and then follow the recipe a bunch to practice it. They would rather do this than think independently or solve interesting problems. It seems that some of my students don't want to experience productive struggle and the sense of accomplishments that comes with coming out the other side of that struggle.

Don't get me wrong. My students are great and I think this is going to be an excellent semester. I believe that many students are very accustomed to (and good at) 'playing the game'. You know the game I mean: show me what you want me to do, help me figure it out when I get stuck, test me on it and give me a good mark when I give you what you want. They know the game well and many of them are very good at it. When we as teachers change the rules of the game the students who are good at it (often the high achievers) get very nervous. They are still going to do well, but they're not as confident about it.

My grade twelve students are likely the students who will experience the most varied teaching methods when they go off to university next year. They will have lectures, labs, group project (formal and informal), open ended projects, etc. I really feel that they have the most to gain by experiencing different teaching methods and yet they seem to be the most reluctant.

One thing is certain. There will be more problem solving and group work throughout the semester! I can't wait.