Although many factors beyond the classroom clearly impact students’ opportunities to learn, empirical research has established that the quality of instruction is directly related to teachers’ knowledge and skill and that it makes a difference for students’ learning (Darling-Hammond, 1999; Ingersoll, 2002; Whitehurst, 2002).

In the study described in this presentation, I investigate how attention to issues of equity may implicate particular mathematical skill and insight by studying classroom practice.  Leveraging the framework and methods used for developing the theory of Mathematical Knowledge for Teaching (Ball, Thames, & Phelps, 2008), the work described in this paper extends this theory to consider how attention to issues of equity may shape the nature and use of mathematical knowledge for teaching and considers what kinds of opportunities might be designed for teachers to develop such skill.

Theoretical Frameworks:  Cultural Modeling and Mathematical Knowledge for Teaching

 Researchers over the last several years have argued that one of the most important resources for improving student learning is improving teachers’ knowledge (Cohen, Raudenbush, & Ball, 2003).  Teacher knowledge, particular content knowledge, plays a critical role in high quality instruction (Ball, Hill, & Bass, 2005; Hill, Rowan, & Ball, 2005).  In this study, I argue that equitable teaching requires providing equitable access to mathematics content for each student.  I also argue that providing equitable access requires a cultural perspective about who the students are and recognizes the experiences, resources, and perspectives they bring to learning.  Thus, to provide equitable instruction, teachers must rely both on a solid knowledge of the subject matter as well as knowledge of their students’ cultural lived experiences, and bring sensibilities and awareness of issues related to equity.  In this way, the theoretical frameworks of Cultural Modeling and Mathematical Knowledge for Teaching provide the foundation for this study.

Cultural Modeling.  Cultural Modeling (Lee, 2007) offers a unique framework for considering the dimensions and teaching practices of equitable mathematics instruction. The Cultural Modeling framework contributes to the analyses in this study by articulating a dimension of cultural knowledge that (1) makes teaching relevant to students’ life experiences and (2) builds connections with the required content to be learned.  Moreover, this framework is based on the premise that students bring to the classroom a rich array of knowledge that is useful for learning.  Lee’s work begins to illustrate the relationship between pedagogical content knowledge and deliberate attention to issues of equity.

Mathematical Knowledge for Teaching.  This study is designed to explore what constitutes equitable mathematics instruction and to unpack ideas about what it might take to teach in these ways, and as such, must carefully consider the role of teacher knowledge for designing and carrying out mathematically skillful instruction that focuses on students’ learning. Based on empirical analyses of the work of teaching, researchers at the University of Michigan developed taxonomy of tasks that teachers carry out routinely that seemed to be mathematical in nature (e.g., posing questions, analyzing students’ errors, choosing representations) and then analyzed the kind of mathematical skill, knowledge and sensibilities required to carry out these tasks effectively. In this way, mathematical knowledge for teaching (MKT) is defined as the mathematical knowledge demanded by the actual work of teaching (Ball & Bass, 2003; Ball, Thames & Phelps, 2008).

Cultural Modeling helps to explain how and why teachers need to know and use students’ cultural perspectives, experiences and practices for teaching.  Mathematical knowledge for teaching (MKT) helps to articulate the categories or domains of mathematical knowledge that are demanded by the actual work of teaching.  These theoretical perspectives are grounded in the work that teachers have to do and they have illuminated how this work places demands on teachers’ capacities. Therefore, the complementary frameworks of MKT and Cultural Modeling provide tools for studying the resources needed to produce equitable teaching in mathematics classrooms. The two central questions for this study are: What constitutes equitable mathematics instruction? What types of opportunities can be designed for practicing elementary and middle school mathematics teachers to learn to design and enact equitable instruction?

Data Sources and Tools

In previous work codes were developed to serve as indicators of equitable teaching practices in mathematics classrooms for an observational instrument.  This observational instrument, Mathematical Quality and Equity (MQE) video codes measure mathematical quality and attention to equity (Author, 2010; Learning Mathematics for Teaching Project, 2010).  For this study, the MQE codes were used as the guiding framework for designing features of the above-mentioned “Issues” course.  In particular, strands of the course were designed to reflect the teaching practices advocated in the MQE tool and to help teachers develop a lens for both designing equitable mathematics instruction and for practicing teaching in these ways.

The main sources of data used in this study are drawn from work produced in a mathematics education graduate course. Sixteen elementary and middle school mathematics teachers were enrolled in a course offered in the spring semester entitled “Issues (of Equity and Diversity) in Mathematics Education”.  Detailed course lesson plans from the University instructor (i.e. how were MQE codes used to design the course) as well as student work products (including video data of their teaching and written reflections) from this course are the primary data for this study.

Results/ Preliminary Findings/ Scholarly Significance

Preliminary findings indicate that codes of the MQE tool serve as a useful framework for designing a graduate course for mathematics teachers.  Analyses of student work indicate that their understanding of developing equitable practices increased dramatically over the course of the semester.  In particular, analyses of student work from the Studying Practice strand show that carefully designed sequences of work can enable teachers to design and enact equitable mathematics teaching such as ‘explicitly using mathematical language’ and ‘teacher encourages a diverse array of mathematical competence’.  Implications of this work can re-shape teacher education efforts to deliberately intervene on patterns of inequity in mathematics education and work towards equitable instruction for all students.