Abstract
This chapter describes the design of integrated learning spaces (ILS) for prospective teachers (PSTs) to support PSTs' learning about reform-based teaching by helping them experience, think about, understand, and position mathematical argumentation in their future classrooms. Drawing on a longitudinal research program that explored PSTs' learning about argumentation in elementary and middle school mathematics, the authors discuss the design of ILS in the context of mathematics and pedagogy with field experience courses in a teacher education program. The authors also share the visions of mathematical argumentation as a teaching-learning practice that PSTs developed in the ILS context. Finally, this chapter poses questions for future research that might explore design principles for creating effective ILS in teacher education programs and examine how PSTs' learning in the ILS context supports their content and pedagogical knowledge development. This chapter also poses questions about ongoing support that future teachers might need to implement and sustain instructional reform.
TopIntroduction
In recent years, the preparation of mathematics teachers has become an increasingly important area of interest to mathematics educators and policymakers in the United States. They agree that reforming teacher preparation in postsecondary institutions is a central factor in enhancing the capacity to improve mathematics education for all students (e.g., the Association of Mathematics Teacher Educators [AMTE], 2017; Conference Board of Mathematical Sciences [CBMS], 2001; National Research Council [NRC], 1996). Teachers play a critical role in implementing ambitious reform-oriented teaching (e.g., Kinser-Traut & Turner, 2020; Schoen et al., 2003). Thus, mathematics teacher educators, researchers, and policymakers recognize that improving mathematics education for all students needs to begin in teacher preparation (e.g., NRC, 2000; Schmidt, Cogan, & Houang, 2011; Schmidt, Blömeke, et al., 2011). To prepare teachers for implementing the reformed vision of mathematics education, they need to experience reform-based learning and teaching in their teacher preparation programs and professional development. To do so, mathematics teacher educators need to identify the approaches and tasks that facilitate prospective teachers’ (PSTs’) learning, support their content and pedagogical knowledge development, and help them develop productive beliefs about reform-based instruction in mathematics (Chapman, 2012; Philipp, 2007).
Preparing mathematics teachers for implementing reform-based curricula and instructional approaches raises many questions. Central to this chapter are dispositions that PSTs should develop in teacher preparation programs to position themselves for facilitating reform-oriented instruction upon entering the teaching profession. Research shows that teachers’ beliefs about mathematics and student learning greatly influence how they implement the curriculum and what opportunities for student learning they provide in their instruction (e.g., Akinsola, 2009; Richardson, 2003). Many PSTs in the United States enter teacher education programs with conceptions of mathematics teaching and learning based on their K-12 experiences with mathematics, often limited to traditional mathematics instruction (e.g., Handal & Herrington, 2003; Maasepp & Bobis, 2015; Valentine & Bolyard, 2019). PSTs with limited experiences in learning mathematics from a reform-based perspective need to experience and develop visions of reform-oriented mathematics classrooms as they transition in teacher education programs from being students to teachers.
In this chapter, we draw on studies conducted as part of a longitudinal research project that explored prospective K–8 teachers’ learning about argumentation in elementary and middle school mathematics (Magiera, 2020; Magiera & Zambak, 2020, 2021; Park & Magiera, 2019, 2020; Zambak & Magiera, 2020). We focus our discussion on creating Integrated Learning Spaces (ILS) in teacher education programs to illustrate coherent efforts of supporting PSTs in developing visions of mathematics teaching and learning consistent with reform-oriented pedagogies. We discuss PSTs’ experiences and the visions of mathematical argumentation as a teaching-learning practice PSTs developed in the context of their mathematics and pedagogy with field experience courses that formed the ILS.
Key Terms in this Chapter
Visions of Mathematics Teaching and Learning: One’s views and beliefs that provide frameworks through which an individual interprets mathematics teaching and learning.
Mathematical Argumentation: A sociomathematical practice that gives foundation to much of mathematics and mathematical development. Using definitions and previously established results to develop conjectures, explore, verify the truth, or refute.
Reform-Based Instruction: Instruction that positions students to be active participants in their learning and helps them develop complex cognitive skills by shifting focus from generating answers to revealing students’ intuitive and informal ways of mathematical reasoning.
Mathematical Argument: A line of reasoning that shows or explains why a mathematical result is true and shows how one arrived at a given conclusion.
Integrated Learning Space in a Teacher Education Program: Curricular experiences that facilitate making significant connections to increase PSTs’ understanding and their thinking about learning and teaching school mathematics.