New math unit tomorrow: algebra, following the approach explained to us by Ruth Beatty ( http://ijcscl.org/?go=contents&article=21 ) at a recent math PD workshop. All of these processes are new to me. Because I have a moderately good facility with number patterns I can often solve balanced equations “by inspection,” – at least at the Grade 7/8 level. But I have no background knowledge to draw on. The whole concept of slope for example is new to me. I was always just seeing the “math,” or the calculations, in isolation from the meaning.
Back in the days of the old Grade 13, I took two English, two history and two French. No math, and Grade 12 math was not a memorable or very successful experience, despite a great teacher.
So I like the approach put forward by Beatty, which starts with using manipulatives to extend patterns and segues into actually building bar graphs and then onward to tables of values and drawing line graphs. Eventually we get to a version of y=mx+b. A month ago I could not have told you what that meant, or explained the curriculum requirement that the students understand the role of the m and the b. I know I didn’t, and the textbook that we use has exactly two pages on this entire topic.
For me the big breakthrough occurred while poring over Ruth’s PPT pages, and finally noticing that if the graph went up by two lines, or five, that this corresponded to the value of the m. And then the slope was either more or less steep. Well, duh, I said to myself. Oh well.
I now “get” enough of Beatty’s presentation to plan out the lessons that will make up the unit, and to feel that I can discuss these concepts with the students as I lead them, hopefully, to some of the same discoveries.