Monday, November 14, 2016

Exploring Polygon Relationships in Scratch

My grade nine class is currently investigating relationships between two variables. I wanted to find some interesting data to look at but also wanted it to be connected to other parts of the course. It occurred to me one day that the geometry portion of the course has students making connections between the number of sides in polygons and the sum of the interior and exterior angles of polygons. This seemed like a good relationship to look at.

I figured this would be a good opportunity to do some coding. I had students visit the Scratch website. A couple of students had used it before, but for most of them this was a new experience. We talked about how you might give somebody clear instructions to walk in a square then we coded those instructions in Scratch and before long everybody had a square. I then instructed students to create a regular triangle, pentagon, hexagon and heptagon. Upon completing each figure they completed the table on the handout.

After collecting the data they proceeded to investigate the relationship between the number of sides and the sum of the interior/exterior angles.

It was fun to watch them. Some started working by trial and error, others were able to make some connections right away. Many who found a solution quickly helped others make the same connections. This was a great way to integrate coding with the relationships and the geometry section of the course.

This activity had me thinking about how I might use a similar activity to have students draw triangles that were not equilateral. It seems like it could be a good application of the sine & cosine laws.

Here's the handout:

Sunday, October 16, 2016

When The Class Bombs A Test

Photo by Wendy Berry

Last Thursday I gave a test to my grade 12 Advanced Functions class. It was our first test of the year and the results were disastrous. My first hint that things may not go well came the day before the test.

Typically the day before a test students in this class keep me busy for what seems like every minute of the day. Some will come in before school and ask questions. Some will sit in my room during their spares and work so they can ask questions. There's usually a flurry of activity at lunch with students working in groups at their desks or at the board. My prep period becomes an impromptu tutorial for students lucky enough to have a spare at the same time. This year, I had a student or two at lunch time and one who stopped by for a few minutes during my prep period.

While students wrote the test I could tell things weren't going well. Some were taking the long way around for a lot of the questions, which meant they would need extra time (apologies to their period two teachers). Many of them seemed to be struggling. A number of them asked if I could drop this test mark or if we could do a rewrite as they handed the test in. Not a good sign.

I wasn't going to look at the tests that night, but I was curious to see what the results were actually like. My suspicions about the class as a whole doing poorly were confirmed. The marks were terrible. I spent a lot of time thinking about why they were so bad. How much of it was failure on my part? How much did they need to take ownership for? How could we rectify the poor result?

Without having enough time to come up with a solid plan of what to do next I decided that my number one priority had to be for students to master the content. The next day I put them in groups of three and gave each group a copy of the test. I had the groups work through the test at the boards. I was able to circulate, listen to the conversations and provide some leading questions when they were needed. There were some great discussions, problems solving and peer teaching going on. I think most students learned at least a little and some learned a lot.

The logical thing to do seems to be to have a retest. Past experience has shown me that the results from retests are generally not all that much better than the original test. Students have good intentions but then run out of time to prepare so their marks improve very little. I think that walking through the tests in groups helped but they won't be writing the test in groups. To help ensure every student who rewrites the test is well prepared I have decided that I will meet with each of them to go over their test. I will ask questions that will help identify what they know and what they need work on. Hopefully this gives them a list of topics that they should go over in preparation for the test.

It seems like a lot of work but I'm hopeful it will pay off. What strategies do you use when tests or other forms of assessment don't go the way you expected?

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.