More than Steepness: Introducing Slope Quantitatively with Interactive Dynamic Representations

We report on a long-term collaboration with ninth-grade mathematics teachers at a linguistically diverse high school in which we examined the intersection between mathematics and language, and how language and mathematical thinking can be developed together in a multilingual setting. We co-designed lessons that promoted conceptual understanding, increased students’ access to grade level mathematics and created opportunities for students who are classified as English learners to participate in discussions. Our content focus was linear and exponential rates of change. In this article, we focus on linear rate of change and its connection to slope. After identifying three distinct meanings for and uses of slope in a ninth-grade mathematics textbook: (a) slope as steepness, (b) slope as rate of change, and (c) slope as a property of collinearity (presented in this order) and observing student interactions around slope concepts, we considered whether it may be more beneficial for students, particularly emergent multilingual students, to develop a robust quantitative understanding of slope first, then introduce the other two meanings of slope as an application of rate of change. To achieve this, we created a series of lessons incorporating dynamic interactive technology and mathematical language routines. We share three of these lessons in this article and include a classroom vignette illustrating the classroom interactions that were achieved through using our first Desmos activity.