RUME 26
2024
Omaha, Nebraska
Exploring Graphical Reasoning From Revised Responses to Function Composition Tasks
Page: 170
Students learn about function composition, (𝑔 ∘ 𝑓)(𝑥), in secondary school. From two given equations, one might identify the composite function algebraically via substitution, 𝑔(𝑓(𝑥)). But what about when functions are given as graphs? This study aims to explore how students reasoned graphically with their revised responses to function composition tasks. We previously identified common types of resultant graphs participants generated in trying to sketch – in a short time period – the composition of various graphically-depicted functions. This paper specifically examines the ways in which students revised their graphs, when given more time to do so and after having engaged in trying to compose functions in a wider variety of contexts, and the reasoning that they provided for these changes. As such, we extend prior work by exploring how students reason about function composition when provided unlimited time constraints on their activity.