Source: Journal of Mathematics Teacher Education, Volume 18 issue 6, p. 577–601 (2015)
(Reviewed by the Portal Team)
This study examines how preservice teachers (PTs) engage in a mathematics simulation focused on iconic interpretation.
Methods
Eight PTs were enrolled in a methods course and were participating in this simulation as a non-evaluative course requirement. There were six female students and two male students.
The authors used two sets of documents—a Teacher Interaction Protocol and a Standardized Individual Protocol to foster a live simulation.
The authors begin by examining who holds responsibility, what content or instructional strategies were considered, and when and how instructional decisions should be implemented.
First, they consider who holds responsibility in a one-to-one learning environment. This clinical simulation is designed to closely approximate an interaction that a novice mathematics teacher would have with a high school student. Thus, they discuss the instructional and learning roles that these PTs hold in simulation as a representation of the same roles each would maintain within a high school classroom environment. The data suggest that the PTs recognized their instructional responsibility. Closer inspection of the data, though, indicate nuanced instructional styles and perspectives on responsibility. For example, they see two PTs who are comfortable with and versed in providing instructional directives. They not only saw themselves as the instructional authority, but also felt comfortable exercising that authority through appropriate instructional directives.
Second, the authors briefly discuss what strategies and content were selected and how they were implemented within—and reflected on after—the clinical simulation. Each PT used visualization prompts to either support the student’s understanding of the homework, or as a suggestion she might use when working with graphs in the future. The manner in which visualizations were implemented showed through the use of manipulatives and representations.
As an additional example of what strategies were selected and how they were implemented, these data suggest PTs’ considerations of the types of questions they posed. Each PT worked to scaffold the student’s understanding of the homework problems through questions, but there is emerging cognizance of how questions should be structured to help this student engage more actively.
Additionally, the degree to which PTs operated within or extended beyond the student’s mathematical contexts also represents a point of discussion. For the first homework problem, some PTs operated within the ‘basketball three-pointer’ context that the student presented, while others started their explanations there, and later extended or qualified those contexts.
The data reported herein show how a clinical simulation illuminates PTs’ mathematical knowledge, instructional abilities, and practices in need of refinement. Simulations allow the authors to see PTs practicing, making mistakes, and using data to build from within and from each other. For educators vested in the development of future educators, the simulation concept and resulting data sets are extending our views of ‘clinical preparation.’