IDR2eAM Goals and Origins
The research goals of this project are to investigate how to differentiate mathematics instruction for cognitively diverse middle school students and to understand how students’ rational number knowledge and algebraic reasoning are related. In years 3-5 of the project we will also be investigating how classroom teachers learn to differentiate instruction.
The educational goals of this project are to enhance the abilities of prospective and practicing teachers to teach cognitively diverse students, to improve doctoral students’ understanding of relationships between students’ learning and teachers’ practice, and to form a community of mathematics teachers committed to on-going professional learning about how to effectively differentiate instruction.
Amy taught middle school and high school students for 9 years prior to doctoral work in mathematics education. The origins of this project come from Amy’s desires to communicate better with more students in the same classroom. As Amy came to better understand students’ cognitive diversity in her doctoral studies, her desires to differentiate instruction only grew.
Three broad, interrelated reasons underlie the project.
- First, classrooms are becoming more cognitively diverse, particularly as more students with learning disabilities spend the majority of their time in mainstream classrooms (U.S. Department of Education, National Center of Educational Statistics, 2011), and as funding for gifted programs decreases (Tomlinson et al., 2003). Differentiating instruction is a tool for managing this diversity. Yet very little research has been conducted on how to differentiate instruction in mathematics classrooms. Indeed, secondary mathematics classrooms are places where differentiation is least likely to occur (Gamoran & Weinstein, 1998). Thus, research is needed to learn how to differentiate instruction in secondary mathematics classrooms, starting with middle schools.
- Second, broadly speaking, students enter middle school at three different levels of reasoning that have significant implications for how they build mathematical knowledge in middle school, including their rational number knowledge (e.g., Hackenberg, 2007, 2010; Hackenberg & Tillema, 2009; Steffe & Olive, 2010) and their algebraic reasoning (Hackenberg, 2013; Hackenberg & Lee, under review a; Olive & Caglayan, 2008).
- Third, students continue to struggle to learn algebra (ACT, 2010; National Mathematics Advisory Panel [NMAP], 2008), which is now a middle school course for many students (Chazan et al., 2007). Although rational number knowledge is implicated in many aspects of students’ algebraic reasoning, little is known about how students’ rational number knowledge can support students’ algebraic reasoning—and vice versa.