In a pre-lesson conversation, Molly McNinch shares with colleague Jim Karditzas her strategies for monitoring students’ work during the lesson. Molly knows that in prior lessons, her students may have “had a good idea, or a good argument, but then some had their argument and then were not able to justify it, or made calculations that were not supported by their argument.”
To address this issue, she plans to prompt her students to adjust the measures in their objects (the slant height, for example) and evaluate the results. The students will use relevant tools, including a computer simulation of rolling objects. Molly will challenge them to create a status poster to share their current thinking and justifications.
This class is an Enriched Geometry class. So it's a slightly more rigorous class, and the students who are in Enriched Geometry are the upper level of Geometry students. The curriculum in both regular and Enriched Geometry is the same; we use the same textbook. The difference is with Enriched, we go slightly further in the concepts and slightly deeper. And so that's why some of these students will get caught in a particular detail, or a particular idea, and will get caught in that piece and unable to bring in the other elements. Because these are “advanced” students they understand how to use formulas and “do the math,” but they really struggle with understanding the definitions and reasoning abstractly about concepts. Proofs are a huge struggle, since there is no set recipe. So they are given little direction, and the freedom is difficult for some students. So when you ask them to think outside of what's being asked of them, it's not always the easiest. They can do it, but it takes a push.