Mathematics activity in an after-school robotics program: An investigation of mathematics use in a semiformal learning environment

This study contributes to both educational practice and theory through examining the mathematics used by urban youth in an after-school robotics program and the environment in which that activity occurred. The work has several audiences, including mathematics education practitioners, mathematics education researchers, out-of-schooltime educational practitioners, and learning theorists. The research builds on our knowledge of how youth use mathematics outside of the classroom as well as how various sociocultural learning theories can be used to understand the affordances and constraints of an afterschool STEM development program located, like most of these programs, between what are considered formal and informal learning environments. This project is a continuation of a larger three-year participant-observation study across three sites. This qualitative study included participant observation with youth through a cycle of the program. Observational data was triangulated with experience interviews and clinical task-based interviews, the latter being designed to investigate the participants‘ use of mathematics in more depth. The mathematics use of the youth matched much of the previous research on how people use mathematics outside of school time, with some notable differences. Specifically, in the robotics program the youth drew on a varied set of mathematics learned and used in school, out of school, and during robotics. Youth drawing on mathematics from across different spaces contrasts with the research literature, which has shown that people tend to silo mathematics use. I argue that the setting, made up of a combination of in-school and out-of-school structures and supports, helped to facilitate this phenomenon, as did the program that had been designed to support youth autonomy in design, building, and problem-solving decisions. Two new ideas are presented: semiformal learning environment to capture a setting that shares features of formal and informal contexts and the math use framework to conceptualize the different mathematics resources people bring to a given setting.