2013 NCTM Conference (4/18/13 - 2:30 pm - Tim Pope):
Tim Pope is the curriculum manager at Kendall Hunt Publishing Company. While this made his session a little more of an advertising campaign, he had some good ideas to share as well.
One statement Tim made really stuck with me, perhaps more than any other at the conference. He said, "If we can remind students of a story that kids can remember, we'll always have something to build on." He elaborated on this idea further, suggesting that if we make math real to students and get them involved in the classroom, they'll remember it much better than they would if they memorized a bunch of formulas. They'll remember even better if a teacher makes math fun as well, or allows students to get up and move around, physically participating as well as mentally participating.
Tim got the audience to participate in an activity identical to one he would use with students. We calculated the amount of time it takes for a specified number of people to complete the "wave", and plotted this data in a scatterplot. We then used this data to create a line of best fit and discussed the properties of this line.
Tim advocated the Van Heile structure for building an understanding of mathematical concepts, and gave an example of each.
Level 0: Visual - students are able to visually identify shapes, patterns, etc., but can't explain why. "It is a rectangle because it looks like a door."
Level 1: Descriptive - students are able to describe the properties of shapes and patterns, but are unfamiliar with the ways different properties interact with each other. "It is a rectangle because it is a quadrilateral with four right angles."
Level 2: Abstract - students can more fully describe the ways the properties of shapes and patterns interact with each other and understand what makes each individual group unique. "I know it’s a rectangle if it’s a parallelogram with four right angles."
Level 3: Proof - students can prove why the properties of shapes and patterns are true. "I can prove it is a rectangle if it’s a parallelogram with one right angle."
Level 4: Rigor - students understand a concept so fully they don't need to consider the basic properties of the concept. "I know that is a rectangle - what would happen if I tried to put it on a sphere?"
Tim suggested that we should challenge students to wrestle with higher-level mathematical questions, that they may gain a fuller understanding of the mathematical concepts involved.