Reflections on some great Math PD

Another PD Day, another blog post to consolidate everything!

This afternoon I attended and helped run the OCDSB Math PD Day. Man, do I love a good workshop! And today, I experienced 5 of them. 

Marian Small - Building Number Sense

Marian presented a lot of good questions we can ask students in order to improve their understanding of  algebra. Some of my favourite examples were: 

1. Look at y = 3x - 9. Is y big or little when x is big? When is y basically the same as 3x?

I really like this question because it students get the opportunity to talk about "bigness" of numbers, and what it means to be big or small. Does is matter if the number is negative or positive? Is it the magnitude of the number that makes it small or big? I think there could be some great discussion there -- and it would be great for grade nine students, who are just beginning to relate algebra and graphs, as well as even grade 12 students working on things like asymptotes and end behaviours. I think that this type of question could be a great idea for looking at various equations in physics, as well. There is already a practical connection there, and they can "make sense" of the various equations. 

2. Instead of saying "three x plus 5" say, "five more than triple some number".

This is important especially for younger students. I think that by grade 12 students have some understanding of what "x" means, but I know that many of my younger students think its some nebulous thing. I do use this language when I am creating equations with students. I'll often say things like, "x, which is just some number", but I think I need to be more conscientious about using language like that, and finding those teachable moments to discuss the meaning of variables. This, combined with   writing out things like "3 times a number plus 2 times a different number is 20" and having students come up with an equation, could eliminate some of the issues created when students face "the dreaded word problem". Incorporating this language can scaffold this process a bit. 

The Power of Self-Assessment

A teacher in the school board presented on how he is saving time, as well as giving students better feedback, by getting students to assess their own tests. I have used self-assessment on students' quizzes in summer school with great success, so I was interested to see what this was all about. I really like the idea of using a bit of class time for students to take up their own tests.

Why do I like it? Not because it saves me a lot of time marking -- but because the students are giving themselves meaningful, timely, feedback which they are going to learn from. They are forced to actually go through their tests, and give themselves comments and reminders about what to do better next time. It also gives them a chance to go through their tests without already knowing their marks. A good point that he made was that students brains usually turn off once they see a mark, and they don't really look at all of the good, descriptive feedback that we are trying to give.

Here are some key points of the self-assessment plan that I wanted to remember:
- hand out a pile of green pens to mark the tests
- you can photocopy tests before the kids mark them, if you are worried about people cheating
- higher achieving students can have their solutions put up on the projector as an example for other students (gives them something to strive for)

I think I'd try a version of this if I teach summer school again this year. Thinking about self-assessment also reminds me to do the same thing with the students I see at the hospital. I know that I am always strapped for time, but I should be reviewing tests with students more thoroughly after I send them off. I think in the interest of time spent reviewing tests in class, I'll look at the tests first, and then pick a key question or two to go through with them. I think it would be worth it!

Letting Go of Units

I caught the middle of this presentation by a teacher I know from the Math Subject Council. He uses a "spiral method" to teach his math courses, teaching all strands at once by using more of a problem-based approach. He said he typically cycles through material three to four times in the course. I'm interested in knowing more about this method of teaching. It reminds me of a course I took in university, where we just did interesting math problems. I think one of the key things for this type of course is to have multiple entry points for the activities/problems so that students aren't lost or bored. When I teach in the "regular" classroom in the summer, I like using problem-based activities. I really want to look into this more. The more students see a topic, the better. It also gives you more freedom to look at more interesting or topical things.

Cup Stacking

I was intrigued by this presentation, because I like doing things "hands-on", and I try my best -- somehow not as much as I'd like -- to do this kind of thing. The activity was a really interesting question which was, "how many red plastic cups does it take to make a tower as tall as your teacher?" There's lots of cool math involved, including measurement, geometry, using tables of values, creating equations... sky's the limit really. It would make a great summative -- or at least part of one -- for a few different math classes.

Math 1D Summative

This was similar to the red cup idea, but instead used a tooth pick video from Dan Meyer as a jump off point for a summative. Students watched a video, and then worked in groups with toothpicks to show off as much grade nine math as possible. They consolidated all of the ideas at the end of the day, and then the next day worked on more directed questions, with their firs day sheet of paper in hand. The teacher had used open ended tasks like this throughout her course, so I can see why her students did well on this activity. I was also happy to be reminded about Dan Meyer's site. I've used some of his stuff for physics.