Pacing (part 1)

I really struggled with what topic to start the blog with. There are so many relevant things I want to share with you all, but my classes on Friday pretty much decided for me!! I think one of the most stressful things for teachers when they first start using Carnegie’s curriculum is pacing. When I first started using the curriculum, we had gotten a grant for the textbooks and software and I didn’t even get started with it until mid-September. Already over a month behind, I stressed every day about how long each lesson was taking. As much as I knew that this new way of thinking about and discovering mathematics was right for my students I was still completely overwhelmed with covering the content. By Christmas break we hadn’t even gotten through Chapter 3! We were STILL solving equations in January...I was petrified.

Despite my apprehensions, I pressed on. And as I did I started to notice something interesting…the farther we got in the content, the quicker the students figured out the deeper things and the deeper they connected with them.

This week we have been developing the concept of slope as well as “discovering” slope-intercept form. On Thursday, my students (in groups) were each given a different scenario (similar to one they had seen in the lab) to write an equation, make a table of data, graph the data, find the x and y intercepts and use their data to find the slope. The next day the groups made posters of their scenario and we ended up with ten different posters with a wide variety of slopes and y-intercepts. After that, they did a gallery walk recording the equation, the x and y intercepts and the slopes of each different scenario. Before I could even ask them questions they were already figuring out that the slope was always the number before x and the y-intercept was always the “extra” number.

The discussion following the gallery walk about WHY that was always true was so valuable!! The students themselves talked about how slope is just the “rate” in the problem and it makes sense that that’s why they are multiplying it by the variable. They talked about how the y-intercept was always their starting point and they came up with a “formula” for writing almost all equations; b + mx = y. I think it’s cute that they write it “backwards”….I learned it y = mx + b, but their way is so much more practical; the starting value (b) + (or –) the rate, multiplied by your independent variable will give you your dependent variable. Duh!! Or at least it was duh to them at that point!!

Never, in my years of teaching before Carnegie (and even in my years of learning in high school and college) did I ever understand slope-intercept form that deeply!! I realized quickly as I kept pressing on that first year of Carnegie that my students weren’t behind in the curriculum. They were getting ALL of the curriculum ALL of the time and when it was time to develop a concept, they understood it at such a deeper level that just “here’s a formula and here’s how you use it.” What more could a teacher ask for?!?!!