In-service Teachers' Reasoning about Scenarios of Teaching Mathematics to English Language Learners

IntroductionAs the student population in U.S. classrooms becomes increasingly diverse, it is critical that all teachers develop the knowledge and skills to support English language learners (ELLs) in mainstream classrooms at every grade level. However, the majority of teachers are not adequately prepared to teach academic content to ELLs (Lucas & Villegas, 2011). Mathematics may be especially challenging for ELLs (Martiniello, 2008). The National Assessment of Education Progress (NAEP) mathematics test results in 2013 (United States Department of Education, 2015) showed that the achievement gap between non-ELL and ELL students both at the 4th and 8th grades did not significantly differ from the achievement gaps reported in previous years in 2011, 2009, 2000, or 1996. Challenges in learning mathematics might preclude access to mathematical and scientific fields, which raises a critical issue of equity (Moschkovich, 2002; Oakes, 1990; Secada, 1992). Teachers play a key role in leveling the playing field for ELLs in mathematics (Moschkovich, 1999; Secada, 1998). However, there is a clear gap between the demands of teaching ELLs and the supply of mainstream mathematics teachers who are adequately prepared to teach (Ballantyne, Sanderman, & Levy, 2008). As the ELL population has increased up to 10% of public school students (National Clearinghouse for English Language Acquisition, 2011), the demand for trained mathematics teachers has as well; many, if not most, teachers need to develop the knowledge and skills needed to teach in classrooms with increasingly diverse populations of students.Despite the need, little is known about the knowledge base needed to teach mathematics to ELLs. Recent conceptualizations of the teacher knowledge base (Ball, Thames, & Phelps, 2008) have not addressed how manifestations of it change depending on who the students in the classroom are and what they bring to the learning experience. To inform research on the teacher knowledge base, most of the existing scholarship on educational linguistics (de Oliveira & Cheng, 2011; Fang, 2006; Lucas, Villegas, & Freedson-Gonzalez, 2008; Schleppegrell, 2001) suggests that language is central to teaching mathematics and that mathematics teachers, even at the secondary level, should know how to identify the linguistic demands in the mathematical content and model mathematics-specific language use. This line of work suggests that language serves as a medium to understanding and communicating the content in mathematics, which in turn is central to the work of teaching mathematics to ELLs.However, our understandings as to what this knowledge base entails and how it gets or should get enacted in mathematics classrooms are limited. To better understand the knowledge base and reasoning involved in teaching mathematics to ELLs, eliciting teachers' reasoning around particular scenarios formatted in an assessment environment might help. As research (Ball & Hill, 2008; Jacobson, Remillard, Hoover, & Aaron, in press) suggests, there needs to be a reciprocal interplay between conceptualizations of teacher knowledge base and measurement in that the development of teacher knowledge assessments needs to be informed by conceptual work in the domain of effective and equitable teaching of mathematics. To facilitate this interplay, new lines of research also show that authentic classroom scenarios formatted into the assessment environment could serve as powerful tools for eliciting teacher reasoning as well as reflective teacher learning (Lai & Howell, 2014). Further, emerging research shows that instructional scenarios help to situate explorations about pre-service and in-service teachers' reasoning about teaching (Grossman et al., 2009; Masingila & Doerr, 2002). This study was therefore based on the premise that the instructional scenarios might be instrumental in explorations of the knowledge base needed to teach mathematics to ELLs. …