On August 16 and 17 we held a two-day collaborative meeting at the Center for Research in Mathematics and Science Education. In attendance where three teachers and our reteach team. Our goal was to summarize early insights from our work in academic year 2016-17 and to prepare for our work in 2017-18. The meeting was also an opportunity for us to say thank you and goodbye to students who were wrapping up their work on the project, and to welcome new student assistants.
During the workshop one thing we discussed was the use of metaphors to introduce the concept of slope. In our observations during academic year 2016-17 we noticed that Integrated Math 1 textbook used three different conceptualizations for slope: 1) Steepness, 2) Rate of Change, and 3) Invariant Property of Collinear Points.
For each of these conceptualizations the book then used multiple real life and metaphorical examples to illustrate the conceptualization. For example, for steepness the book presented an image of four different roofs and asked students to discuss which roof was steepest, and how they know. We discussed in our meeting how the use of multiple real-life examples (e.g. roof pitch for steepness) and metaphors (e.g. an image of ducks in a row for collinearity) might afford ELs access to the conceptualization of slope, or might constrain ELs’ opportunity to engage with content due to unfamiliar contexts. This year we plan to propose reducing the use of unnecessary contexts, and to focus the unit by choosing one main real life example or metaphor per conceptualization about slope. Keep posted as we translate these plans into reality.