Developing A Student Heuristic For The Use And Selection Of Mathematics Instructional Videos Using the Didactic Contract and Responsibilities

Abstract

This study investigated the ways in which college algebra students watch mathematics instructional videos with the goal of answering the following research questions: (1) How are student responsibility frames similar or different among students within a particular video? (2) How do the various video design principles support or constrain the uses of particular responsibility frames? This research was guided by the cognitive theory of multimedia design and the theory of didactic situations. The cognitive theory of multimedia design outlined principles for video creation and design that could impact student learning from video watching. The theory of didactic situations defined implicit teacher and student responsibilities within the context of the face-to-face mathematics classroom and was applied in this study to students watching mathematics instructional videos. Participants were recruited from five college algebra classes at a university in the northeastern United States and were asked to attend two semi-structured interviews. During the first interview, participants were pretested to determine their prior knowledge about how to solve quadratic functions and to measure their mathematics-related beliefs. During the second interview, participants watched three different videos about solving quadratic equations by completing the square and were asked questions about the mathematics that they viewed in the videos. Transcriptions of audio recordings of these interviews were coded thematically using categories previously identified by the didactic contract for the face-to-face classroom and expanding the types of student responsibilities identified specifically for video watching as needed. This study found that participants, regardless of overall prior knowledge or mathematics-related beliefs, but who had prior knowledge of completing the square, held a responsibility to use the specific set of steps they were taught by their teacher to solve problems. Additionally, participants at some levels of prior knowledge expressed a responsibility to not watch videos that showed a visual representation of the mathematics. Findings also suggested a student heuristic for the selection and use of mathematics instructional videos that may be useful to both mathematics teachers and video creators.