Thursday, June 26, 2014

France Thibault

 Sometimes in our life we cross paths with someone who makes a difference in our lives. I have been teaching Math for 24 years, in three different schools, led by 8 different principals. All the principals that I have worked with are amazing. My current principal, France Thibault, has engaged in my teaching in a way that I am not used to. Let me be clear - in a good way. Here is a youtube video from a few years back that indicates a little of what she is like. I am sure she would have much to add to this now as she is a life long learner.

The number one role that I see her engaging in, as the principal of our school, is as an instructional leader. Here are some of her behaviours that I see from her as the instructional leader in our school. I am sure there are more that I am overlooking. Here are my fav five. Or around that many.

1. She walks the talk. She leads by example. She wants everyone in the building to change for the better. I think she strives to do this as well. On her journey she is willing to make mistakes and learn from them.

2. She engages in our lessons. France participates in lesson study at our school at all levels, in departments that are not her expertise, in cross curricular professional learning teams, as part of her evaluation of teachers (TPA). I know she has also participated in lesson study at other schools to help them get started. You can read about her thoughts on lesson study here.

3. She shares / buys resources. I have watched her give out books about teaching to the masses. I have received more books about teaching from France in the last two years than I did in the first 22 years of my career. Maybe she is trying to tell me something!

4. She increases her zone of influence. France has found a way to influence all in the building towards our personal journey of change as educators. It is like we are all changing at the same time. Of course some more rapidly than others but change none the less. She also is helping other principals to create change in their buildings.

5. She encourages risk taking. France has opened the door for people to take risks. It is OK to try something different - successful or not. Learn from it.

6. She provides time. France will find $$$$ for release to participate in lesson study, to co-plan  courses, to present PD to others, among other things. She also takes the time for herself to do these things.

7. ..........

May she have continued success in the role of instructional leader because I think it is working. At least it is working for me as a teacher in the trenches. And I have turned into one of the old ones.....how did that happen?

Tuesday, June 17, 2014

Area = Length * Width

In grade 10 Applied Math in Ontario our students need to learn about quadratic relations. One of the overall expectations in the quadratic strand is that students will be able to manipulate algebraic expressions as needed to understand quadratic relations.

Instead of calling it factoring and expanding, I like to refer to the two different equations the students are responsible for as this.

y = ax^2 + bx + c as y intercept form or area form.

y = a (x-p) (x-q) as x intercept form or length width form

The curriculum requires that students can work with these equations when a=1

To get at changing from area form to length width form or vice versa, I use rectangles and algebra tiles.

The first thing I like to do is to give the students an equation in area form. They are already familiar with it as we have modelled quadratics with the graphing calculator.

So here is an example. y = x^2 + 4x +3. I will use this example for the rest of the blog post.

Then I ask them to get three different colored piles of cube a links. One for the x^2 term, one for the x term, and one for the number term.

Once the students have the three piles I ask them to create a pile of the correct number of tiles for stage 1 (when x=1), stage 2 (when x=2), stage 3 (when x=3) and stage 4 (when x=4). Here are what the piles look like for our example.

Then we create a stack for each stage. Numbers on the bottom, then the x cubes in the middle followed by the x^2 cubes on the top. Nice discussion at this point about the graph of y = 3, y = 4x + 3 and y = x^2 + 4x + 3. Here is what it looks like.

Students then deconstruct their towers and I ask them to create a rectangle for each stage. x^2 blocks need to be in a square and the ones blocks touch the x^2 blocks at a corner. We also create the rectangles with algebra tiles. I particularly like doing this as students can see x increase (be variable). Eventually students will get to this.

And a little poster action demonstrating some algebra and some key characteristics of quadratics.