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TopIntroduction
The exploration of pre-service candidates and their journey in education has been a longstanding pursuit. Over the years, much of the research in this area of education has revolved around two concepts: knowledge and practice (Oliveira & Henriques, 2021; Charalambous et al., 2020; Da Ponte & Chapman, 2015; Ball et al., 2008; Ma, 1999; Even, 1990; Shulman, 1986). What has been learned is that candidates need to be engaged in activities that enhance their understanding of what and how to teach mathematics. Stylianides and Stylianides (2006) define teacher-related mathematical tasks (TRMT) as encompassing this dual role through a series of activities that focus on a primary goal. Engaging in activities, such as TRMT is seen as crucial for candidates, as they strive to cultivate their knowledge and skills for effective teaching (Oliveira & Henriques, 2021; Akar, 2015; Da Ponte & Chapman, 2015; Ball, et al., 2008; Stylianides & Stylianides, 2006).
This investigation of pre-service candidate teachers' knowledge of similar figures was part of a larger study that investigated candidate knowledge of what and how to teach proportional reasoning concepts, while engaged in TRMT. The TRMT involved a combination of teaching and research methods. The research was based on standards from the National Council of Teachers of Mathematics' (NCTM) which provide a vision for the teaching of mathematics (NCTM, 2000; NCTM, 2007). During the explorations of TRMT, researchers focused on understanding candidates’ initial images of similar figures, and with this focus, formulated the following research question:
When given opportunities to discuss and plan a lesson, what are candidates’ images of what and how to teach similar figures?
Therefore, this study has the potential to enhance the body of research concerning candidates’ images of similar figures while engaged in TRMT. It accomplishes this through a conceptual framework that supports candidates’ subject matter knowledge (SMK) and pedagogical content knowledge (PCK). While the primary focus is on a group of initial licensure candidates, this research also provides insights into a teacher education course that implements TRMT.
TopConceptual Framework
Stylianides and Stylianides (2006) define TRMT as having a dual purpose. They are mathematics tasks that are connected to teaching, which also support the learning of mathematics and what is important to teach and help teachers to see how the mathematics relate to teaching. A “task” is described as a series of related activities focusing on ideas and aims promoting a goal (Stylianides & Stylianides, 2006). Lappan and Even (1989) state that to support students’ mathematical empowerment, “teachers themselves need to know mathematics and experience learning in ways that build a deep and flexible understanding of what mathematics is and what it means to do mathematics” (p.22). TRMT can be seen as a hybrid of two types of teaching experiments: classroom experiments (Borba & Confrey, 1993; Cobb & Steffe, 1983; Steffe, 1991) and candidate teacher development (Simon, 1995).