## Friday, September 26, 2014

### Another Advantage of my Vertical Classroom

I recently wrote on my blog about Vertical Non-Permanent Surfaces and Visible Random Groupings.

I teach a grade 10 math course in Ontario called Applied Math. The students in this course are year after year beaten down by mathematics. My job is to undo that. Not easy.

This year I have been spiraling the course. Basically no more units and teaching through activities only. I have been spiraling this course for years. With the help of my good colleague Bruce McLaurin @BDMclaurin we have been able to spread this idea around Ontario. Mary Bourassa did a blog post about it recently.

blah, blah, blah

Anyhow this year I am trying to do VNPS and VRG (acronyms for the opening line). As Nathan Craft so elegantly put it.
Here is the link to his thoughts.

With my grade ten applied class I like to do an activity with them that I call introductory activities for Quadratics. The questions we did will follow in this post. In the past I have just photocopied the tasks and students have worked on it in class. Typically two to three periods. I would wander around the room helping students move forward with their thinking.

This year I used VNPS and VRG. What a difference! All students were able to do some questions. As a class we accomplished more. What used to take 2-3 periods was done in 1 period. There was no hiding. All students were engaged. Information passed around the room. It was something about me taking a picture of their work. It was awesome!

Here is the first two problems and sample student solutions.

For the first one.

For the second question.

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Then I posed the third question. And a few sample solutions.

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Sample student solutions.

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## Tuesday, September 9, 2014

### Finding Time for the Mathematical Processes

As this new school year starts and I embark on my journey as a life long learner in my profession, I am focusing this year on two things:
2) the mathematical processes more and more and more and more. If you get my drift.

In Ontario there are 7 mathematical processes that you can read about here. In a nutshell they are:
Problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing and communication.

Finding the time to focus on these process expectations versus the curriculum expectations in our courses is challenging but I would say the processes should be our priority.

I recently huddled my class in the centre of the room and told them at noon the hour hand and the minute hand were at the same place. I then asked them to find all the times over the next 12 hours that the hands would be at the same place.

Students were put in random groups of three (10 groups in total) and were given a vertical 4 ft by 8 ft sheet of white board to write up their solution. I asked them to write it out so someone could come along and read it and understand it. Groups were given about 50 minutes. After the time was up they paired with another group. Each group read the other groups solutions and asked them clarifying questions and then revised or added to the solution in a different colour.

I am going to group photos of student work by type of solution. This is a sample of the work from two classes of 30 students.

Solution 1 Happens 11 times over the 12 hours so.....12/11 hours in between each time.

Solution 2 Using the intersection of the two trigonometric graphs. No groups actually finished this idea.

Solution 3 Splitting the twelve hours up 11 times like solution one. Realizing it is not perfect and taking the missing time and dividing it up 11 times and adding that part in along the way. In other words using our error or mistake and adjusting the answers. The first group divided the missing 25 seconds by twelve instead of eleven.

Unfortunately this group erased their original times which was out by 25 seconds. They then used this to adjust the times.

Solution 4

Solution 5

Solution 6 Using some equations to show where the hands are and equating them.

Solution 7 Plotting degrees versus minutes for both hands and using the intersection of two lines.

This was well worth it. From my perspective we hit the following process expectations:
Problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing and communication. HMMM I think that was all of them.

Now if I could just do this everyday..........

On a personal note I was thrilled with some of the approaches.