This page contains more detailed information about the TEACH Math project, including the rationale and conceptual framework, goals and purposes, and research design.
Goals and Purposes
The primary goal of TEACH MATH is to study ways to support prospective and early career teachers in developing the knowledge, beliefs, dispositions, and practices needed to effectively plan, adapt and implement mathematics instruction in culturally, linguistically, and socio-economically diverse schools. More specifically, we aim to:
- Document and enhance prospective and early career teachers’ understandings of children’s mathematical thinking, and of children’s linguistic, cultural, and community-based funds of knowledge relevant to their mathematics learning.
- Develop a detailed learning trajectory describing how prospective and early career teachers develop and enact instructional practices that build upon and integrate children’s mathematical thinking and their linguistic, cultural, and community-based funds of knowledge.
- Investigate relationships between teachers’ knowledge, beliefs, dispositions and practices that integrate children’s multiple mathematical funds of knowledge and preK-8 students’ learning and mathematical dispositions.
Products and Outcomes
- Increased knowledge and understanding of how to prepare and support prospective and early career teachers to effectively teach mathematics to all students.
- The refinement and widespread dissemination of a series of instructional modules to help preK-8 prospective teachers learn to integrate children’s mathematical thinking and their cultural, linguistic, and community-based funds of knowledge in mathematics instruction. These modules are organized around key practices of teaching elementary mathematics – including developing mathematical tasks, lesson and curriculum analysis, and assessment of children’s thinking.
- The development and dissemination of professional development materials, including on-line resources, aimed at supporting teachers’ capacity to extend understandings gained in methods courses to their student teaching and early teaching experiences.
- The refinement of a set of research instruments to measure teachers’ knowledge, beliefs, dispositions and practices related to integrating children’s multiple mathematical funds of knowledge in mathematics instruction. Instruments include pre and post surveys, interview protocols, and classroom observation protocols.
Each of these products has been made available to other mathematics teacher educators and researchers for use in designing, enacting, and assessing their work with prospective teachers and early-career teachers.
Rationale and Conceptual Framework
The central aim of the TEACH MATH project is to transform preK-8 mathematics teacher preparation so that new generations of teachers will be equipped with powerful tools and strategies to increase student learning and achievement in mathematics in our nation’s increasingly diverse public schools. We intend to accomplish this by studying a) the iterative refinement of instructional modules for preK-8 mathematics methods courses that explicitly develop teacher competencies related to mathematics, children’s mathematical thinking and community/cultural funds of knowledge, b) the development of an innovative model of structured support and mentoring for new teachers and c) the creation of on-line networks to facilitate ongoing teacher and teacher educator collaboration. The project combines design research in university elementary mathematics methods courses with a longitudinal study that uses a staggered cohort model, leveraging understandings gained from initial cohorts to inform work with subsequent groups. Six university sites that represent a diverse range of teaching contexts from primarily urban (CUNY, University of Washington at Tacoma), to a mixture of urban, suburban, and rural (Iowa State University, Washington State University Tri-Cities), to suburban (University of Delaware), to borderlands (University of Arizona), will participate. The diversity of sites will inform our understanding of how local instructor, course, program, university, and school contexts impact the implementation of the instructional modules and professional development materials, thereby supporting the successful widespread dissemination of these products. The design and scope of the TEACH MATH project have been informed by four identified needs outlined below.
First, the field of mathematics education lacks a deep understanding of how mathematics instruction might integrate children’s mathematical thinking with the cultural, linguistic, and community-based knowledge that children bring to classrooms in ways that support student learning. On one hand, there is a vast body of research documenting the effectiveness of instruction that centers on children’s mathematical thinking (e.g., Cognitively Guided Instruction (CGI), Carpenter, Fennema, Peterson, Chiang & Loef, 1989; Carpenter, Franke, Jacobs & Fennema, 1998; Fennema, Carpenter, Franke, Levi, Jacobs & Empson, 1996). This research has linked teachers’ knowledge of children’s mathematical thinking to productive changes in teachers’ knowledge and beliefs, classroom practices, and student learning (Fennema, Carpenter, Franke, Levi, Jacobs, & Empson, 1996). For example, children in CGI classrooms perform better on problem solving tasks and equally well on computation, when compared to students of non-CGI teachers (Carpenter et al., 1989, 1996, 1998; Fennema et al., 1996).
Other research documents that historically underrepresented groups benefit from instruction that draws upon their cultural, linguistic and community-based knowledge (Ladson-Billings, 1994; Lee, 2007; Silver & Stein, 1996; Turner, Celedón-Pattichis & Marshall, 2008). This research has argued that teachers need to understand how students’ home and community-based funds of knowledge – the knowledge, skills and experiences found in students’ homes and communities – can support their mathematical learning (Civil, 2002; González, Andrade, Civil, & Moll, 2001; González, Moll & Amanti, 2005; Moll, Amanti, Neff & Gonzalez, 1992). We contend that experiences that help preK-8 teachers understand the mathematical knowledge and practices of students’ communities can enhance teachers’ ability to provide effective mathematics instruction for diverse learners (see also Gay, 2009; Ladson-Billings, 1994, 2001; Nieto, 2004; Rodriguez & Kitchen, 2005; Villegas & Lucas, 2002). However, research on how pre-service teacher (PST) preparation and early career professional development might integrate these multiple knowledge bases is limited (e.g., Aguirre, 2009; Leonard, 2007). The TEACH MATH project proposes to expand our understandings by integrating these two bodies of research in teacher preparation and development.
Second, persistent gaps in opportunities and achievement between historically underrepresented students and their middle-class white counterparts are cause for concern. On major assessments of mathematics achievement (e.g., National Assessment of Educational Progress), low-income, African American, Latino/a and Native American students score below their middle-class white counterparts, and these gaps have remained fairly stable over time (NCES, 2003; NCES, 2007; see also Gutierrez, 2008; Lubienski, 2008). Significant gaps also exist in students’ access to high-quality mathematics instruction. Low-income and minority students are less likely to have qualified teachers and well-resourced schools (Hill & Lubienski, 2007; Oakes, 2005; Peske & Haycock, 2006), and more likely to experience school mathematics, and often school in general, as disconnected from their out-of-school experiences (Civil, 2007; Ladson-Billings, 1995, 1997; Nasir, Hand & Taylor, 2008; Tate, 1995). We argue that addressing these gaps requires teachers to understand mathematics as a set of ideas, practices, and tools that are part of, and relevant to, students’ lives and communities. The TEACH MATH project directly addresses this key challenge.
Third, teachers are underprepared to teach mathematics effectively in diverse classrooms. This is an issue of both a general lack of preparation to teach mathematics in ways that build on children’s mathematical thinking, as well as a more specific lack of preparation to teach mathematics to an increasingly ethnically, linguistically and socio-economically diverse student population. For example, almost 20 percent of current students speak a language other than English at home and, within three years, this will increase to 30 percent (NCES, 2007). Furthermore, racial and ethnic minority students make up 43 percent of public school enrollment and this percentage is increasing (NCES, 2007). At the same time, teachers – largely white, female, monolingual and middle class – are typically under-prepared to address such diversity (Hollins & Guzman, 2005; Howard, 1999; Nieto, 2004; Sleeter, 2001). While there is significant research related to preparing teachers to work in diverse classrooms, little of it addresses the specific challenges and resources of learning to teach mathematics to diverse learners. The TEACH MATH project is designed to address teachers’ increased need to understand not only how to access and build on children’s multiple ways of understanding mathematics and solving mathematical problems, but also how to capitalize on students’ diverse cultural, linguistic, and community knowledge in ways that support students’ mathematics learning.
Fourth, we know very little about how PSTs transfer their new understandings into early teaching experiences, or about the resulting impact on their preK-8 students’ mathematics learning. In a review of research on teacher preparation for diverse populations, Hollins and Guzman (2005) note that, “we need research that examines the links among teacher preparation for diversity, what teacher candidates learn from this preparation, how this affects their professional practices in schools, and what the impact is on their pupils’ learning” (p. 512). A central aim of the TEACH MATH project is to contribute these much-needed understandings to the field of mathematics teacher education.
Research and Development Design
By studying preK-8 mathematics methods courses and early career professional development that explicitly integrate children’s mathematical thinking with children’s cultural, linguistic and community-based funds of knowledge, the TEACH MATH project will contribute to understandings of prospective and early career teacher learning and inform revisions to teacher preparation programs and induction programs for new teachers. These dual and iterative outcomes of building theory and improving practice are core elements of design research (Brown, 1992; Collins, Joseph, & Bielaczyc, 2004; Grossman, 2005). An iterative design research cycle supports developing and refining effective instructional modules and engaging in longitudinal, cross-site research to evaluate the interventions and their effects. At all stages of the cycle, our work informs and is informed by a developing theory of prospective and early-career teacher learning. In particular, our project seeks to understand how prospective teachers engage in and learn from the instructional modules, how they apply their knowledge and skills as early career teachers in diverse schools, and, ultimately, the relationship of the early career teachers’ knowledge, beliefs, dispositions, and practices to preK-8 students’ mathematics learning and dispositions.
The TEACH MATH project addresses the following research questions:
- How do pre-service teachers’ knowledge, beliefs, dispositions, and practices related to integrating children’s mathematical thinking and children’s cultural, linguistic, and community-based funds of knowledge in mathematics instruction change as a result of a series of instructional modules for mathematics methods courses?
- How do local instructor, course, program, university, and community contexts mediate the implementation of these modules?
- What supports and challenges do pre-service and early career teachers face in implementing instructional practices in their preK-8 classrooms that integrate children’s mathematical thinking and children’s cultural, linguistic, and community-based funds of knowledge, and how do they negotiate these challenges?
- What are the relationships between early career teachers’ knowledge, beliefs, dispositions and instructional practices and their preK-8 students’ mathematics learning and dispositions?
Our research design includes both an ongoing cross-sectional study of preK-8 mathematics methods courses at the six university sites and a longitudinal study using a staggered cohort model. The longitudinal component maximizes opportunities to refine theory related to preparing teachers to teach mathematics to diverse learners by assuring a steady stream of data from cohorts at different points in their career trajectories (see table). The longitudinal nature of the project will allow us to follow participants in all cohorts from their final year(s) in the preparation program (methods and student teaching) through their first two years of teaching. In addition, to enhance the trustworthiness and naturalistic generalizations of our findings (Erlandson, Harris, Skipper & Allen, 1993), we will conduct the research in multiple, diverse settings and investigate the different ways that contexts (i.e., university teacher education program, student teaching, and first teaching placements) shape experiences and outcomes.
|Component I:Ongoing Cross-Sectional Methods Course Research(n=30 per year per site, 540 total)||Component II:Longitudinal Research using a Staggered Cohorts Model(n=6 case study participants per site, or 36 total)
|ALL SITES||Cohort 1Site ASite B||Cohort 2Site CSite D
|Cohort 3Site F|
|Year 1||Each site will implement instructional modules and collect data with at least 30 methods students per year||Methods Students|
|Year 2||Student Teaching||Methods Students|
|Summer Workshop||Summer Workshop|
|Year 3||Year 1 Teachers||Year 1 Teachers||Methods Students|
|Academic Year Teacher Study Group||Academic Year Teacher Study Group||Student Teaching|
|Summer Workshop||Summer Workshop||Summer Workshop|
|Year 4||Year 2 Teachers||Year 2 Teachers||Year 1 Teachers|
|Academic Year Teacher Study Group||Academic Year Teacher Study Group||Academic Year Teacher Study Group|
|Summer Workshop||Summer Workshop||Summer Workshop|
|Year 5||Year 2 Teachers|
|Academic Year Teacher Study Group|
|Summer Workshop||Summer Workshop||Summer Worksho|
We draw upon both qualitative and quantitative data analysis methods to gain a more complete understanding of how prospective and early career teachers learn to integrate children’s multiple knowledge bases to teach mathematics more effectively and how teacher educators support this learning. See research publications for more details about the specific analysis methods used.