ELL Policy and Mathematics Professional Development Colliding: Placing Teacher Experimentation within a Sociopolitical Context
by Daniel Battey, Silvia Llamas-Flores, Meg Burke, Paula Guerra, Hyun Jung Kang & Seong Hee Kim - 2013
Background/Context: A number of recent policies have specifically attacked immigrants and English Language Learners (ELLs), including Georgia’s HB 87 (2011), Arizona’s SB 1070 (2010), and Alabama’s HB 56 (2011), among others. The policy focus of this study is Arizona’s HB 2064 (2006), which added additional requirements that mandate tracking students by English language proficiency and separating English language instruction from subject matter for ELL students. Few scholars have considered how these broad social policies impact professional development (PD)-induced classroom change, especially in mathematics education. This sociopolitical context cannot help but affect teachers’ willingness to take on new practices in PD and thus affect educational opportunities for Latinos and English Language Learners. Yet, policies that target ELLs have not received much attention within mathematics education or PD. This exploratory study details teacher change produced by mathematics PD efforts before and after a new ELD policy was implemented in order to better understand this intersection.
Purpose/Objective/Research Question/Focus of Study: The teachers in this study participated in mathematics professional development focusing on Cognitively Guided Instruction (CGI). This exploratory research documents how teachers experimented in their classrooms before and after this policy was implemented and teachers’ views of HB 2064. Two research questions guided the study: 1) How did the mathematics PD affect change in teacher knowledge and classroom practice? and 2) How did the conflicting policy and PD efforts influence change in elementary mathematics instruction?
Setting: This research took place in the Monroe Elementary School District, an urban school district in Arizona. Three schools participated in mathematics professional development based on CGI principles. The student population was 95% Hispanic and 46% ELLs, and 89% of students received free or reduced lunch. Therefore, Arizona’s policies had the potential to greatly impact the student population in this school.
Population/Participants/Subjects: The professional development was implemented with three groups of K–3 teachers (n=44). Across the PD, just over one fourth of participating teachers were bilingual in Spanish and English.
Intervention/Program/Practice: The professional development focused on the principles of CGI, combining earlier work on student strategies and problem types (Carpenter, Fennema, Franke, Levi, & Empson, 1999) with more recent work on algebraic thinking (Carpenter, Franke, & Levi, 2003) and counting (Schwerdtfeger & Chan, 2007). This model of professional development focuses teachers on the development of student thinking, problem types for various mathematical operations, and building instruction from this knowledge base. The PD consisted of monthly on-site workgroup meetings and weekly on-site visits to support teachers in their classrooms.
Research Design: The research team conducted a mixed methods study of teacher change across the district. The study followed teachers for two years—one year before the policy was implemented and the year it was implemented—documenting the practices teachers maintained in their elementary mathematics classrooms. The study used a mixed methods design to respond to the two research questions (Creswell, 2003). A teacher knowledge assessment was used to see if teachers were gaining new knowledge as they implemented the principles of the PD. Observations allowed for the study to look at teacher experimentation in classrooms. Finally, an interview on the policy and its impact on their classroom practices was performed to add more understanding to why teachers did or did not implement more PD practices.
Findings/Results: Teacher knowledge change was minimal across the professional development. However, the data on change in practice suggest that more practices were adopted before the policy was implemented than during implementation. In contrast, teachers reported that the policy had minimal effect on their mathematics instruction. This conflict, between change in practice and the perceived lack of policy impact, seemed to be due to teachers’ view of mathematics and language as fundamentally separate. It seemed also to be due to an alignment between teacher beliefs and the views embedded in the policy.
Conclusions/Recommendations: The findings raise concerns about the conflict between PD and policy in generating teacher change. New questions emerge from this work about taking into consideration the sociopolitical context when researching PD efforts focused on intersections between policy and subject matter. Questions also emerge about the alignment of ideology in policy with teachers’ beliefs. The authors call for work in mathematics PD that takes on the intersections between policies and PD efforts and that targets particular student populations. Additionally, more research would be beneficial for understanding the impact of the sociopolitical context on teacher change efforts.
In educational institutions, professional development (PD) and policy are often intertwined. In order to align school practices with new educational policies, PD focusing on content, curriculum, assessment, and pedagogy is initiated to ensure teachers enact new policies with some degree of fidelity. An example of this alignment is the California Mathematics Professional Development Institutes (MPDIs). Initiated in 2000, this statewide program sought to improve the content knowledge of teachers. The mathematics PD alone that emerged from this policy served over 23,000 teachers during three years of implementation.
When professional development is implemented as a response to educational policy, it is assumed that there is a direct relationship between what is learned in the professional development and what then takes place in teachers practices. However, little is really known about whether or how teachers experiment in their classrooms as a result of policy-initiated PD efforts (Kazemi, 2008). Questions remain about which practices are taken up easily and which ones are more complex and therefore difficult to bring across the boundary of PD into classrooms, how practices are adapted or not taken up at all, and which practices are sustained over time and which left behind. For example, in a study of the MPDIs instituted in California, it was found that teachers attending more days of PD displayed greater content learning (Hill & Ball, 2004), but the study did not show how teachers did or did not change their practices in connection with this change in knowledge.
The translation of policy into practice through professional development is made even more complex by the fact that what teachers do in their classrooms is mediated by a range of organizational factors and arrangements (Fullan, 2000). Teachers do not have sole authority over curriculum and practice. Instead, district leadership, principals, and curricula also mediate change in classroom practice (Elmore, 1996). District personnel may exert control in the classroom in the form of a pacing plan. Similarly, a textbook dictates a daily blueprint for instruction for the teacher, and a principal may suggest changes to practice regardless of policy and professional development initiatives. Thus, educational policies can be buffered or intensified for teachers by educational institutions.
However, it is not only educational policy that gets interpreted through these institutional layers to impact classrooms. Broad laws on welfare and immigration, as well as other policies, also influence classroom teachers. That is, the sociopolitical context can enable or constrain reform efforts and the impact of professional development opportunities as well. Because teacher ideologies are connected to broader societal forces, those societal forces are critical to understand. Beyond the immediate social forces, historical, economic, and political influences can impact how teachers interpret reforms (Louis, 1990; Sarason, 1990). However, there is little work that examines the social, political, and historical context of reforms in relation to change in classroom practice. As Datnow and Castellano (2000, p. 778) state, Since teacher ideologies are rooted in their life experiences and interactions, teachers responses to reform can be deeply embedded within the larger societal context.
For instance, while Latinos have been the target of recent immigration laws, cuts to ethnic studies programs, and English-only programs, these efforts are embedded in particular ideologies and a sustained political battle. Since the Mexican-American war and the annexing of the southwest region of the current United States, prevalent beliefs held by whites have permeated the culture and signaled the onset of persistent discriminatory practices against people of Mexican origin living in the United States (San Miguel & Valencia, 1998). From fighting the segregation of Mexican-origin children to gaining access to educational resources and language support, countering these deficit beliefs is a constant struggle (Valencia, 2005).
A number of recent policies have specifically attacked immigrants and English Language Learners (ELLs). Georgias HB 87 (2011) and Arizonas SB 1070 (2010) target immigrants by requiring that they always carry identification and allowing law enforcement to check citizenship status at any time. Arizonas law in particular led to the creation of a copycat bill in Colorado, HB 1107, though it was defeated in the legislature. Alabamas HB 56 (2011) placed the responsibility for checking the immigration status of students on K-12 schools. Two voter propositions, Californias Proposition 227 (1998) and Arizonas Proposition 203 (2000), established English-only laws with the intent of replacing bilingual education with English immersion programs. Finally, Arizonas HB 2281 and the School Board of Education in Texas represent efforts to cut ethnic studies curricula and programs. Surrounding these laws, discourses have arisen that propagate notions that Latino immigrants are taking away jobs, that some children do not have the right to an education, that Spanish speakers are less legitimate students in schools, and that ethnic studies does not have space in the social studies curriculum.
Most educational researchers have not considered how the sociopolitical context impinges on the effects of professional development or how teachers interpret and enact what is learned in professional development opportunities. Few studies have looked at what happens to PD efforts when larger social change policies impact schooling. In this paper, we focus on how the broad sociopolitical context interacts with a PD effort, affecting teacher change and the quality of mathematics teaching. Specifically, we present findings from an exploratory study of a professional development initiative aimed at teaching mathematics for understanding, which was implemented at around the same time as Arizonas HB 2064 policy. Arizona Proposition 203 (2000) established English as the only language of instruction and issued a requirement that all children be English-language proficient in one year. Arizonas HB 2064 (2006) added additional requirements that mandated tracking students by English-language proficiency and separating English-language instruction from subject matter for ELL students.
This paper documents how teachers experimented in their classrooms before and after this policy was implemented and teachers views of HB 2064. This exploratory study was guided by two research questions: 1) How did the mathematics PD affect change in teacher knowledge and classroom practice? and 2) How did the conflicting policy and PD efforts influence change in elementary mathematics instruction? Before outlining the methodology and findings, we begin this paper with a review of literature.
REVIEW OF RELEVANT LITERATURE
The review begins with examining research on teachers responses to educational policy. The review then moves to what we know about effective PD for mathematics teachers. Finally, the section ends with a discussion of the intersection between policy and mathematics professional development, noting the absence of both detailed documentation of teacher change and of attention to change focused specifically on ELLs.
TEACHERS AND EDUCATIONAL POLICY
Gitlin and Margonis (1995) argue that researchers can gain insight into policy by attending to teachers reactions to reform. When mandated change is the impetus, teachers have been found to respond in varying ways, depending on the alignment between the policy and their beliefs about instruction. Imposed change can create a discrepancy between teachers aims and the goals of policies and schools (Sikes, 1992), and teachers can outright resist change that does not fit with their beliefs and practical experience (Bailey, 2000). Alternatively, some studies have found that mandated change can impose a culture of compliance: teachers want only to know the steps to implement in order to achieve compliance with the policy (Blackmore, 1998). These scholars speak to the difficulty of implementing change and aligning teachers ideologies and beliefs with those of change efforts. This research raises the issue of teachers autonomy to interpret, proceduralize, or resist policy.
Reforms that ascribe to rigid notions of fidelity often frame teachers interpretation of these change efforts negatively, but not all adaptations should be interpreted as resistant or contrary to the intent of policy. Certainly, policy goes through a process of translation as it moves across levels of the school system (Eisenhart, Cuthbert, Shrum, & Harding, 2001). For instance, teachers often tend to adapt policies according to their students needs and their particular classroom context (Helsby, 1999; McLaughlin & Talbert, 1993; Tyack & Cuban, 1995). Translation of reform can also occur because teachers have little knowledge or understanding of policy and how to implement it (Cuthbert, 1984). In that case, teacher translations can be problematic. However, when policy aligns with teacher beliefs and allows teachers to implement practices as professionals, research tells a different story. For example, in Heaths (1983) work, desegregation policies spurred teachers to implement practices more aligned with childrens home lives. Unfortunately, the policy changed and subsequently, teachers could no longer sustain the use of childrens families as resources in their teaching.
In research specific to mathematics teaching, a special issue of Educational Evaluation Policy Analysis (EEPA) focused on analyses of teachers responses to Californias new Mathematics Framework in 1985. This change in state policy imposed curricular and classroom changes supported by PD, making it particularly relevant to the current study. Through the various case studies, researchers found differing levels of compliance and resistance, including teachers who thought they were implementing the desired changes yet, in fact, were not (Ball, 1990; Cohen, 1990; Peterson, 1990; Wiemers, 1990; Wilson, 1990). Across the studies in this volume, we see that even when policy is aligned with PD and curricular change, effects can be quite varied. In the previously mentioned case studies, policy and PD were aligned, which might imply that if they were not aligned, little to no change would occur.
While much has been written about teachers responses to policy or lack thereof, the research base to date is less explicit about the ongoing work of implementing policy (Kazemi, 2008). For instance, researchers do not know which practices change first, which change last, how teachers implement and adapt new practices, and how or whether various practices are sustained over time. It is more complex than simple fidelity to a policy model, because taking on new practices as a teacher means brokering practices from a policy context and interpreting them for the classroom context (Kazemi & Hubbard, 2008). Therefore, the field needs a more detailed understanding of how and when teachers adapt practices in line with policy reform. As in the case of the EPAA special issue, many policies are accompanied by PD initiatives.
EFFECTIVE MATHEMATICS PD
One of the most common ways to facilitate teachers implementation of policy is to provide some kind of professional development or training around the policy. Many educational policies, however, have not been supported by high-quality professional development. Too often, teachers engage in one-day PD skill sessions despite evidence that these trainings produce little learning (Garet, Porter, Desimone, Birman, & Yoon, 2001; Little, 1989; Smylie, 1989).
Reviews of effective professional development have produced several principles of high-quality PD efforts, including supporting teacher inquiry within classrooms, engaging teachers collegially, sustaining learning opportunities for teachers, and balancing institutional and individual concerns (Abdal-Haqq, 1995; Darling-Hammond & McLaughlin, 1995; Little, 1993; Putnam & Borko, 1997; Wilson & Berne, 1999). The principles for effective PD from these reviews are consistent, in that teachers must engage in inquiry within their classrooms. This means that problems of practice should generate the content of PD, because this makes the learning relevant to teachers daily practice. However, this process cannot be undertaken individually. Instead, colleagues must engage in collective inquiry in a way that allows teachers to process intellectual, social, and emotional challenges. Additionally, these reviews find that this experience must be extended, not over days, but over years of mutual engagement so that teachers can continue to work and refine instructional practice. Finally, this collective inquiry must balance the individual and institutional parameters of change. This means sufficiently contextualizing teachers learning within the community and lives of the children they teach, while also respecting the core of the educational change being sought. Across this research base, effective PD must employ principles of professional inquiry, collective engagement with colleagues, extended learning opportunities, and engagement with problems of practice.
Over the last 25 years, a number of PD programs in mathematics education have used these principles to great success. While all of the efforts draw on principles of effective PD, they do so from three different approaches: focusing on mathematics, teaching practice, or student thinking. While these approaches certainly overlap, they provide a way to organize the primary focus of the different PD efforts. One example of focusing on mathematics is Teaching to the Big Ideas (TBI), a project focused on the development of elementary teachers mathematical understanding (Schifter, 1998; Schifter & Fostnot, 1993). A critical feature of the TBI approach is to place teachers as mathematics learners themselves. In this PD program, teachers explore content connections in mathematics, the learning of mathematics, and the implications for instruction. In a case study of two TBI teachers, Schifter (1998) shows how this focus on being a mathematics learner relates to teachers past mathematical experiences and produces learning that supports students in new ways. By engaging teachers in mathematical inquiry, teachers learn the social nature of engaging math and the importance of engaging students in mathematical inquiry. The study found that the PD supported teachers in developing new conceptions of the nature of mathematics, reflecting on their own learning, and listening to student thinking in new ways, which result in teaching mathematics for understanding.
Another approach in attending to effective PD principles is to foreground teaching practice. Video clubs have proved a useful forum for exploring and improving teachers mathematics practice (Sherin, 2003; Sherin & Han, 2004; Sherin & van Es, 2003). Using a school-based model, teachers met monthly to examine videotaped examples of one anothers teaching. At first teachers focused on issues extraneous to student learning; however, over time, their viewing shifted towards higher-level discussions of students mathematical conceptions (Sherin & Han, 2004). The use of video clubs engaged teachers in inquiry into their own teaching practice over the long term, consistent with the literature on effective PD. Another program, SummerMath for Teachers, focused on affecting teachers views of learning as a way to transform teacher decision-making (Schifter & Simon, 1992; Simon & Schifter, 1991). As teachers engaged in mathematics, the professional development placed them in student roles and supported their reflection on theories of learning mathematics. This, along with on-site support and follow-up sessions focused on designing sequenced lessons, increased student learning and instruction aligned with more constructivist goals. Researchers found a focus on developing a constructivist view of learning changed teachers beliefs and, in turn, their instructional decision-making (Schifter & Simon, 1992; Simon & Schifter, 1991).
Focusing on student thinking is a third approach to effective PD in mathematics. One of the best-researched PD programs in mathematics is the Cognitively Guided Instruction (CGI) project. This research program established a framework for using student thinking as a foundation for mathematics PD and teaching by providing teachers with information on the development of student solution strategies and word problem types across elementary operations (Carpenter, Fennema, & Franke, 1996). In providing teachers with a framework for understanding student thinking in mathematics that moves from concrete to abstract and with various problem types and their influence on student strategies, this PD focuses on designing instruction from the informal knowledge that students bring into schooling. In using teachers own student work to focus on problems of practice, the PD effort has linked changes in teachers knowledge and beliefs, classroom practices, and student learning in mathematics (Fennema et al., 1996). Teachers who had CGI training taught problem solving in their classes to a much greater extent than teachers in the same schools who had not received the training (Carpenter, Fennema, Peterson, Chiang, & Loef, 1989). The student achievement results indicated that children in the CGI classes performed equally well on tasks of standard computation when compared to non-CGI classes and that the children in CGI classes outscored the other children in problem-solving tasks (Carpenter et al., 1989). More recent work has studied CGI implementation in urban settings as well (Franke, Kazemi, Shih, Biagetti, & Battey, 2005; Kazemi & Franke, 2004). The teachers in this study developed detailed knowledge of their own students mathematical thinking and began to develop learning trajectories for their students and instructional trajectories to support their students work in mathematics (Kazemi & Franke, 2004). The school effects sustained themselves after the professional development ended, as teachers took on responsibility for their own learning (Franke et al., 2005). CGI has looked at change in teacher knowledge, classroom practice, and student learning, which makes it a well-researched form of PD (Wilson & Berne, 1999). CGI professional development also served as the basis for the PD used in this study.
These three approaches to mathematics professional development engage teachers in different ways to promote teacher inquiry within classrooms. Various records of practice have been used, from placing teachers in the role of students to observing classroom videos and analyzing student work. However, to date, the literature on effective models of professional development assumes that an intensive ongoing inquiry approach to PD will result in teachers taking up and trying out new educational policies and practices. However, what hasnt been researched across these PD efforts is their interaction with broader policies. What would happen if a policy were implemented consistent, or in conflict, with PD approaches aimed at shifting teachers approaches to mathematics instruction? Additionally, most of the focus on models of PD in mathematics education has focused on learning content rather than focusing on particular underserved student groups. This current study informs both of these gaps in the literature.
STUDIES OF MATHEMATICS PD AND ELL STUDENTS
The intersection of policy, mathematics PD, and ELLs has not been a focus of educational research. While this intersection is not attended to in the research literature, neither is the intersection of ELD instructional strategies and professional development. Despite this, a small but growing body of work does detail instruction that supports the mathematics learning of ELLs. Taken together, this literature finds that mathematics teachers must shift from a focus on vocabulary to one on meaning, value the cultural and linguistic resources of students, and allow students to generate the mathematics themselves.
With a focus on mathematics instruction for ELLs, teachers often overemphasize disconnected mathematical terms without also focusing on mathematical meaning. While acquiring vocabulary is important in learning to use the mathematical register, what is even more important is students ability to construct multiple meanings, negotiate meanings through interactions with peers and teachers, and participate in mathematical communication (Moschkovich, 2007, p. 89). Unfortunately, teachers often do not help ELLs construct the meaning of important mathematics vocabulary (Celedón-Pattichis, 1999). This is particularly important in mathematics, since many words hold different meanings in the mathematical register than in natural language (Khisty, 1995). In other words, mathematics is a language with a register of words, expressions, and meanings that differ from those of everyday language (Secada, 1991). If mathematics instruction merely stays at the level of vocabulary, it is not getting at more complex issues of mathematical understanding and its relationship to everyday language.
Moreover, by placing an emphasis on vocabulary without properly contextualizing the mathematical terms, teachers run the risk of perpetuating deficiency models, since focus is placed on what students cannot do rather than on what they can. As Moschkovich (2007) argues,
If all we see are students who dont speak English, mispronounce English words, or dont know vocabulary, instruction will focus on these deficiencies. If, instead, we learn to recognize the mathematical ideas these students express in spite of their accents, code switching, or missing vocabulary, then instruction can build on students competencies and resources (p. 90).
Along these same lines, research has found that using (Thomas & Collier, 1997) and valuing home language is critical (Khisty, 2001; Khisty, 2004). This practice has been found to be linked to higher achievement, especially in mathematics (Khisty, 2006).
Student generation of mathematical strategies is also critical if ELL students are to make meaning of the content. Moschkovich (1999) states that instruction for ELLs needs to provide numerous opportunities to engage in mathematical discussion: speaking, listening, reading, and writing the content. This is consistent with findings on mathematics instruction with ELLs, namely, that students must become producers of mathematical practice (González, Andrade, Civil, & Moll, 2001). Additionally, to support this form of instruction, teachers need to be able to change curricula to meet the needs of their students. Of course, use of these effective ELD instructional strategies is dependent on the policy that supports or constrains teachers instructional practices.
Policies that target ELLs have not received much attention within mathematics education. However, the literature just reviewed speaks to how ELL policy and quality math instruction can interact. Additionally, the present study aims to detail teacher change produced by a mathematics PD effort before and after a new ELD policy was implemented in order to understand this intersection. The authors now turn to frame the sociopolitical context surrounding the PD and new ELD policy.
CONTEXT FOR THE STUDY
As this research is situated within the sociopolitical landscape of educating ELLs in Arizona, we briefly review the political and legal context that led to the study. In 1992, Flores v. State of Arizona altered the shape of the political atmosphere with regards to educating ELL students. The major complaints of the suit, according to Mahoney et al. (2005), were that ELLs were taught by under-qualified teachers, that the state lacked adequate processes of identifying and monitoring ELLs, and lacked adequate funding for appropriate educational programs for these students (p. 32). In other words, by not providing adequate funding and educational resources for ELL students, the state was in direct violation of the Equal Educational Opportunities Act (EEOA). After 17 years, in 2009, the court ruled in favor of the schools, stating that the state of Arizona had since fulfilled their obligation to meet the needs of ELL students.
However, paralleling Flores v. State of Arizona was Proposition 203, the English for Children law passed on November 7, 2000, by Arizona voters. The basic tenets of this law were that (a) public schools have a moral obligation to teach English and (b) educational instruction would only be provided in English, restricting bilingual education and English as a Second Language (ESL) programs. In other words, the flexibility of school districts to select from a variety of programs for educating ELLs was replaced with a mandatory Structured English Immersion (SEI) model.
Another crucial stipulation of Proposition 203 was that students would become proficient in academic English, both in oral conversation and in written form, in one school year. The intent of the new legislation was to teach all Arizona public school students English as quickly and efficiently as possible (Arizona State Legislature, 2006). This stipulation in the law comes into conflict with research in the field of Second Language Acquisition (SLA), which has found that, on average, immigrant students with at least two years of schooling in their first language take between five and seven years to become proficient in English. A student without any formal schooling in his/her first language needs, on average, seven to ten years to reach proficiency, regardless of age (Collier, 1995; Hakuta, Butler, & Witt, 2000).
The passage of House Bill (HB) 2064 in 2006 signaled another language policy aimed at ELL students. This bill established a task force charged with creating research-based programs for the existing Structured English Immersion (SEI) model (Arizona Department of Education, 2008). The Task Force created a new model for SEI requiring a minimum of four hours a day of English Language Development (ELD), during which students receive instruction only in English and in isolation from other disciplines (Gándara et al., 2010). In addition,
Students are to be grouped with other students of the same proficiency level, and the Task Force has specified the number of minutes to be spent on each element of language and literacy instruction, with different time allotments at each level of proficiency. Thus, EL students in Arizona are segregated into classrooms with no exposure to English-dominant peers for 80% of the school day (4 hours), and the instruction they receive focuses on learning English over learning subject matter (e.g., math, science, social studies) (p. 27).
Proficiency in the English language is determined by the Arizona English Language Learner Assessment (AZELLA) test given to students at the start of each school year. If students do not perform at a high enough proficiency on the AZELLA after one year, students remain in the SEI program. The four-hour block is split into one hour of reading, one hour of grammar, 1445 minutes of conversation, 15 minutes of writing, and 60 minutes of vocabulary allotted for mathematics, science, and social studies.
Both the four-hour block and the one-year-to-proficiency expectation have important consequences for content instruction. Taken together, Arizona Proposition 203 and HB 2064 mean students are grouped by English language proficiency and, in turn, ELL students days are segregated by language levels. These segregating effects are not consistent with research that has found that in order for an ELL student to acquire English, he or she must have access to his or her English-dominant peers, who can model the language in formal and informal ways (Guerrero, 2004; Oller & Damico, 1991; Wong Fillmore, 1989).
HB 2064 further limits content instruction for ELLs. According to Kevin Clark (2009), the head of the Arizona Task Force,
The English language is the main content of SEI instruction. Academic content plays a supporting, but subordinate, role. The dominant focus is language itself: its rules, uses, forms, and application to daily school and non-school situations and topics. The operant principle is that students must have a strong understanding of the English language before they can be expected to learn grade-level content (p.44).
As a result of placement in the SEI program for multiple years with no regard to mathematics ability, student access to grade-level subject matter across disciplines is curtailed. In the district in which this study took place, these policies resulted in 40-45 minutes of mathematics instruction per day for students. Additionally, mathematics vocabulary was taught during language instruction, isolating mathematical vocabulary from mathematics concepts and meaning. While these policies focus on English-language acquisition, the four-hour block, one-year-to-fluency expectation, and the tracking of students by English language proficiency had critical implications for mathematics learning. These policies limited access to grade-level mathematics, reduced time allotted for math, and restricted pedagogy by isolating vocabulary from meaning. The implementation of HB 2064 occurred during the second year of a mathematics professional development initiative that sought to support teachers in shifting to teaching mathematics for understanding. It is to this PD initiative that this paper now turns.
THE PROFESSIONAL DEVELOPMENT INITIATIVE
The professional development focused on the principles of CGI, combining earlier work on student strategies and problem types (Carpenter et al., 1999) with more recent work on algebraic thinking (Carpenter, Franke, & Levi, 2003) and counting (Schwerdtfeger & Chan, 2007). This model of professional development focuses teachers on the development of student thinking, problem types for various mathematical operations, and building instruction from this knowledge base. Because of this, CGI places particular emphasis on mathematics communication, such as student sharing, justification, and problem solving. To achieve the aims of the PD and to ensure that the model of PD reflected the research base on effective teacher development efforts, the sessions focused on student work that teachers would bring back to the workgroup meetings. This centered conversations on teachers students and what was currently occurring in classrooms. The PD consisted of on-site monthly workgroup meetings and on-site weekly visits.
Monthly Workgroup Meetings
During year one, the first author met with the K1 teachers monthly after school. In year two, an experienced professional developer took over the meetings with K1 teachers, and the first author worked with second- and third-grade teachers. The meetings lasted 1.5 hours and were held at one of the participating schools. As the intent of the PD was to support teachers in gaining knowledge of mathematics and student thinking, we used the monthly meetings to discuss student work, examine videos, and discus how to build instruction on teaching for understanding. For example, the team would have teachers pose a problem to their students and bring the results back to the workgroup. In the next meeting, teachers would sort the student work based on the sophistication of student thinking, and the group would discuss the development of student mathematical understanding, how to pose problems for students, and instructional strategies to support students in their math learning.
On-Site Weekly Visits
In addition to the workgroup meetings, the research team spent one to two days each week on-site. Our goals were to support teachers, engage with them informally, and explicitly draw on teachers practices in future workgroup meetings. This allowed the PD to build on the problems of practice with which teachers were engaged, a critical feature of effective PD. Our visibility at the schools was also important for reminding teachers to experiment with new practices and build relationships with both students and teachers. During these visits, the team observed classes, discussed particular teaching practices and student thinking with teachers, and was available for informal conversation about anything the teachers wanted to talk about.
To understand how teachers responded to the PD, both before and after implementation of HB 2064, the research team conducted a mixed methods study to explore teacher change across one urban district. The study followed teachers for two years, one year before the policy was implemented and the year it was implemented, documenting the instructional practices teachers used to teach math and the influence of the policy on these practices. The study used a mixed methods design to respond to the two research questions (Creswell, 2003). The mixed methods design allowed for a quantitative comparison of the teachers in this PD to a national sample and allowed the authors to look for patterns across teachers on the project. Additionally, the design allowed for qualitative comparisons of the teachers, with reference to their classroom changes and their views on the ELD policy and its effects on their teaching. A teacher knowledge assessment was used to see if teachers were gaining new knowledge as they implemented the principles of the PD. Observations allowed for the study to look at teacher experimentation in classrooms. Finally, an interview on the policy and its impact on their classroom practices was performed to add more understanding to why teachers did or did not implement more PD practices.
PARTICIPANTS AND BACKGROUND
This research took place in the Monroe Elementary School District, an urban school district in Arizona comprised of four schools, of which three participated in the mathematics professional development based on CGI principles. The three schools served, on average, about 650 students across grades K8. The student population was 95% Hispanic and 46% ELLs, and 89% of students receive free or reduced lunch. These schools had been identified as having not met the Adequate Yearly Progress for No Child Left Behind. In the first year of the project (2009), 52% of third-grade students tested proficient in mathematics on Arizona's Instrument to Measure Standards, as opposed to 62% the year before (the state average was 72% for 2009). On the Terra Nova in 2009, 35% of third graders tested proficient in mathematics, compared to 40% a year prior (the national average was 50%). Third grade is the first time students take the standardized tests. Almost half (45.7%) of the teachers had been in the district for three years or fewer, although 34% of teachers held a masters degree.
The professional development was implemented over two years, and we worked with three groups of teachers and their students, as summarized in Table 1. In the first year of the project, the research team worked with a cohort of 21 kindergarten and first-grade teachers (Cohort 1, Year 1). Due to 7 K1 teachers leaving the district the following year, the project was left with 14 teachers (Cohort 1, Year 2). In year two of the project, the team began working with the second- and third-grade teachers (n=15) as well as the new K1 teachers (n=8). These new teachers to the project are grouped as Cohort 2, Year 1. Across the PD, just over one fourth of participating teachers were bilingual in Spanish and English.
Table 1: Number of Participating Teachers by Grade Level
As the studys aims were to document teacher change in relation to the professional development before and after the implementation of the policy, the project collected data on teacher change using two instruments: a measure of teacher-knowledge and observational field notes. Additionally, the research team conducted interviews to examine the impact of the ELD policy on the change, or the lack thereof, in relation to the PD effort. The sequence of data collection is provided in Table 2.
Table 2: Data Collected by Teacher Cohort
Teacher Knowledge Assessment
The teacher knowledge assessment consisted of a questionnaire of 12 items selected from Learning for Mathematics Teaching (LMT) (Ball, Hill, Rowan, & Schilling, 2002; Hill & Ball, 2004) and Developing Mathematical Ideas (DMI) (Bell, Wilson, Higgins, & McCoach, 2010; Higgins, Bell, Wilson, Oh, & McCoach, 2007; Schifter, Bastable, & Russell, 1999), with one additional item from the CGI work on algebraic thinking. The items consisted of a mix of multiple-choice and open-ended responses. The multiple-choice items were from LMT and focused on numbers and operations. The items were coded correct/incorrect and the content of the items served as an overlap and complement to the open-ended items. These items have been used with a national sample of teachers and relate to student achievement (Hill, Schilling, & Ball, 2004). The open-ended items for the assessments were adopted from DMI and asked teachers to generate possible student strategies, explain strategies, and assess the mathematical legitimacy of particular methods.1 These items have previously shown growth in knowledge due to high-quality mathematics PD (Bell et al., 2010). The content ranged from subtraction to multiplication, division, and fractions. The CGI item had teachers generate possible student answers and strategies for an open-ended number sentence on understanding the equal sign (8 + 4 = □ + 5).
To answer the research questions—whether teachers were using the math content from the PD in practice and how they were experimenting— we constructed observations of teachers’ practices. During the research team’s on-site visits, field notes were taken that focused on new practices the teachers were implementing and sustaining when teaching mathematics. The field notes were recorded as a running narrative describing the activities and practices that the teachers engaged in as well as the context of the classroom. These notes included any math problem posed to students, kinds of participation facilitated in the class, types of activities used, adaptations made by the teachers, and the resources that teachers drew on, such as manipulatives. The research team collected field notes every other week for all of the teachers, with each classroom observation lasting between 30 and 60 minutes.
Employing a semi-structured protocol, teachers were interviewed once at the end of the second year. Interviews focused on teachers views and experiences with the new ELD legislation. In these conversations, we sought to better understand how the newly structured four-hour SEI model and subsequent tracking played out in teachers mathematics instruction and their implementation of practices from the PD. The interview questions explored five main topics (Miles & Huberman, 1994): (1) knowledge of the ELD policy, (2) teachers orientation toward the policy, (3) parental involvement, (4) administrative support, and (5) the impact of the ELD policy on teachers mathematics practice and student learning. Grand tour questions (Spradly, 1979) were created for each of the five main themes. The interviewers were responsible for asking the grand tour questions and then asking follow up questions based on the responses of the teachers in order to gather more detail about their thinking.
The team interviewed a sample of seven Cohort 1, Year 2 teachers who participated in the project both years. The project only interviewed Cohort 1, Year 2 teachers, because they were the only teachers who had participated before and after the implementation of the policy and could speak to how the new legislation influenced their classroom experimentation. We purposefully selected the seven case teachers for variance in their adoption of practices from the PD. Teachers adopted from zero to seven practices. Additionally, this represented half of he teachers who remained in the project for the two year time period. Interviews lasted 3040 minutes and were audio recorded and transcribed verbatim.
We began data analysis by first looking at quantitative data and then delving into qualitative observations and interviews. These data sources were then brought together so that we could look at change before and after policy implementation. For instance, the teacher knowledge assessment and classroom observation were used to compare Cohort 1, Year 1 and Cohort 2, Year 1 teachers. This compared Year 1 cohorts that began under different policy contexts. The researchers next analyzed data to compare Cohort 1, Year 1 and Cohort 1, Year 2. This allowed for an analysis of the same teachers before and after the policy was implemented, to provide evidence on how it influenced their classroom change. Finally, the analysis of the teacher interviews provided a greater understanding of the sociopolitical context surrounding this change.
The LMT items were coded correct/incorrect. Z-scores were calculated for the LMT items to examine teachers mathematical knowledge in relation to the national sample used to develop the items (Hill et al., 2004). The LMT project requires report of their items in terms of z-scores so as not to disparage teachers on items that are designed to rank order teachers rather than reporting percentages. For the DMI items, we coded using the DMI rubric that looks at the depth of explanation and variety of students strategies teachers could provide. The CGI algebraic thinking item was coded on how many student strategies the teachers could anticipate, giving one point per distinct strategy. Across the open-ended items, the team calculated averages for each DMI stem (division, fractions, subtraction, and multiplication) and the algebraic thinking item. The scores were entered into a database for each teacher by test item.
Classroom Observation Coding
The field notes represented a window into classroom practices every other week across the entire year. Therefore, in analyzing each iteration, we looked across the year to see what change occurred and when. To begin analysis of the narrative field notes, the research team performed a careful reading of the observation data collected for half of the sample and noted the instructional practices that appeared repeatedly across classrooms. The team used this initial pass to come to categories of instructional practices that could be seen in the data. These categories were then used to examine the entire corpus of field notes. This meant that the original categories were contrasted again with the notes in order to confirm their validity, which resulted in some codes being refined and several new codes being added. A third pass was made based on these refined categories for final coding. Analyzing the field notes over three passes produced 10 categories: (i) use of word problems, (ii) journals, (iii) student sharing, (iv) counting, (v) breaking apart numbers, (vi) use of tools (e.g. manipulatives), (vii) attending to the details of student thinking (e.g. organizing activities around student strategies), (viii) adapting the textbook, (ix) designing their own problems, and (x) questioning student thinking. All of the practices coded were informed by research and represent mathematics teaching aimed at teaching for understanding.
The authors drew on the original CGI work in focusing on use of word problems, student sharing, tool use, teachers designing problems tailored to student thinking, and attending to the details of student thinking (Carpenter et al., 1996; Carpenter et al., 2003). In this same vein, using textbooks to meet the needs of particular students in the classrooms means monitoring curriculum use and selection (Franke & Grouws, 1997, pg. 334). In other words, there is no perfect curriculum, and teachers must adapt curricula to meet the specific needs of students. The PD also drew on more recent work on counting collections (Schwerdtfeger & Chan, 2007) and the algebraic thinking work that focuses on decomposing numbers (breaking apart numbers) while using the equal sign more flexibly (Carpenter et al., 2003). The researchers also looked at research examining the importance of teachers questioning student thinking (Franke et al., 2009; Webb et al., 2008). In the case of this paper, this merely means that teachers posed clarifying questions to students after a shared strategy. In this sense, it is a less detailed form of the kind of attendion to the details of student thinking mentioned earlier. Lastly, the analysis focused on journals as a way of recording student solution strategies. This is a way of making student thinking explicit for teachers (Kazemi & Franke, 2004). The ten codes served as a way to look at the micro-changes that occurred as teachers attempted to teach mathematics for understanding. They also provide a way to look for change in practice over time due to the PD.
From this coding, the researchers counted the frequency of these categories and recorded when a category became a regular part of the teachers classroom practice. If the field notes recorded a practice in one of our first two observations, we considered it to be occurring prior to the implementation of the PD. The practices were coded according to the semester in which they emerged and were only included in the analysis if the teachers maintained them in the classroom. In order to maintain the practices, teachers had to show use of them once a month in subsequent observations.
Teacher Interview Coding
Each interview was recorded and transcribed by the interviewer, who was also a member of the research team. After transcription, a researcher who had not transcribed the interview reviewed the audio recordings and transcripts to ensure accuracy. Any needed edits were made at this time. The research team constructed descriptions of each teacher based on the five themes from the interview protocol: (1) knowledge of the ELD policy, (2) teachers orientation toward the policy, (3) parental involvement, (4) administrative support, and (5) the impact of the ELD policy on teachers mathematics practice and student learning. These descriptions were then used to make assertions across the teachers, to look for common and differing understandings. In subsequent readings, the research team looked for confirming and disconfirming evidence consistent with Ericksons (1986) interpretive framework. The assertions were then revised and refined until the analysis described crosscutting ideas across the teachers.
Triangulation and Validation
The teacher knowledge assessments and field notes served as overlapping data sources. While the teacher knowledge assessment was at a greater distance from classroom change, it served as a way to measure knowledge change and to compare the teachers in the project to national samples of teachers. The field note analysis examined classroom change at a frequency that we often do not get to see in studies of professional development and policy. While the knowledge assessment looks for knowledge growth, the field note analysis looks for growth in teachers practices. Across both the teacher knowledge assessment and the field notes, the analysis was performed in two stages. First, Cohort 1, Year 1 and Cohort 2, Year 1 were compared to investigate potential differences for each group. This analysis allowed for the study to investigate changes in classroom practice across one year of the professional development. This layer of analysis adds evidence to inform Research Question 1, How did the mathematics PD affect change in teacher knowledge and classroom practice within mathematics? Additionally, comparing the Year 1 cohorts allowed for a contrast between teachers participating before and after the policy as a first step in informing Research Question 2, regarding the intersection of the PD and state ELL policy. Second, the researchers compared Cohort 1, Year 1 and Cohort 1, Year 2 to investigate growth in knowledge and classroom practices across two years of PD. This layer provided longer-term evidence for Question 1. This analysis also allowed the researchers to observe one teacher group for possible effects before and after the policy was implemented, which informed Question 2.
The teacher interview analysis responded specifically to Research Question 2, How did the conflicting policy and PD efforts intersect to influence change in elementary mathematics instruction? This analysis also served to validate previous analysis related to Question 2, about the impact of the ELD policy on change initiated by the PD. The resulting crosscutting themes served as another way of understanding teacher change in Year 2.
The results are broken into two sections that respond to the two research questions: PD Impact on Teacher Change and Policy Impact on Teacher Change. The first section begins by comparing Cohort 1, Year 1 to Cohort 2, Year 1 teachers in order to examine Year 1 cohorts before and after the policy implementation. It then compare Years 1 and 2 for Cohort 1 in order to look for change in knowledge and practicebefore and after the policyfor one teacher group. The second section of the findings examines Cohort 1, Year 2 teachers responses to the language policy.
PD IMPACT ON TEACHER CHANGE
Comparing Cohort 1, Year 1 and Cohort 2, Year 1
Using Cronbachs alpha, the study calculated the internal consistency of the teacher knowledge measure (both LMT and open-ended items) as .71, demonstrating sufficient reliability. Both cohorts looked similar in terms of MKT for both multiple-choice and open-ended items. The Z-scores for both cohorts on LMT items were similar, 0.15 of a standard deviation below the mean for Cohort 1, Year 1 and .04 below for Cohort 2, Year 1. Both groups were also comparable to the national sample. The DMI scores show teachers understanding of students mathematics thinking (see Table 3). Teachers understanding of student thinking and of mathematics were comparable in each group. The one exception was that Cohort 2 teachers could explain students methods in subtraction better than could Cohort 1 teachers. However, both cohorts scored similarly, showing comparable levels of MKT.
Table 3: Mean Score on Open-Ended Items by Teacher Group
Note. a n = 21, b n = 23
Observations of the Cohort 1, Year 1 teachers showed that they incorporated a number of instructional practices into their mathematics classrooms, suggesting that the PD had some impact.2 Cohort 1, Year 1 teachers incorporated supplemental activities (e.g. counting and breaking apart numbers) more than they probed student thinking and adapted the textbook. As can be seen in Table 4, Cohort 1, Year 1 teachers engaged in the practices of counting, use of tools, breaking apart numbers, and using word problems. Conversely, the least used practices were journaling, editing the textbook, designing their own problems, questioning student thinking, and attending to student thinking. It is important to note that the researchers only included practices that teachers maintained. If teachers tried the practice once or twice but did not continue it, it was not included in this analysis.
Table 4: Percentage of Teachers Engaging in New Instructional Practices
Note. a n= 19, b n = 23
Cohort 2, Year 1 teachers drew on practices focused on probing student thinking rather than on supplementary activities like counting or breaking apart numbers. Cohort 2, Year 1 teachers adopted questioning student thinking, student sharing, and attending to the details of student thinking at higher rates than other practices. The least-used practices by Cohort 2, Year 1 were word problems, editing the textbook, tool use, journaling, breaking apart numbers, counting, and designing word problems. For seven of the ten practices, fewer than 10% of the teachers used them in instruction.
The two cohorts were similar in taking on practices around student sharing, journaling, editing the textbook, and designing problems. Cohort 2, Year 1 teachers incorporated two instructional practices more than did Cohort 1, Year 1: questioning student thinking (17% more) and attending to student thinking (13%). Cohort 1, Year 1 adopted four more practices into instruction than did Cohort 2: counting (29% more), use of tools (28%), word problems (13%), and breaking apart numbers (13%).
Cohort 1, Year 1 teachers took on somewhat more practices than did Cohort 2, Year 1 teachers. This was true both in the number of new practices they adopted (1.89 vs. 1.24) and in the percentage of teachers who adopted various practices (see Table 5). Almost two thirds (63%) of Cohort 1 teachers adopted at least one practice in the first year of the PD, compared to 52% of Cohort 2 teachers. The data provide modest evidence that more Cohort 1, Year 1 teachers adopted PD practices and that they adopted these practices at somewhat higher rates.
Table 5: Percentage of Teachers Adopting Classroom Practices
Note. a n= 19, b n = 23
Comparing Cohort 1, Year 1 and Cohort 1, Year 2
The purpose of comparing Cohort 1, Year 1 and Cohort 1, Year 2 was to contrast changes before and after the ELD policy. The multiple-choice items did not show differences, but the open-ended items did. On the LMT items, the Cohort 1, Year 1 mean was located 0.10 of a standard deviation below the national mean, and the Cohort 1, Year 2 mean was 0.09 below. This indicates that Cohort 1, Year 2 teachers who participated in the project for two consecutive years performed at almost the exact same level as in year two as in year one. Year 2 teachers did show growth across the two years of the PD on two items (see Table 6). On the algebraic thinking item, 43% of Year 1 teachers provided one strategy, 14% two strategies, and 14% of teachers provided three or more strategies. For Year 2 teachers, 14% of teachers provided one strategy and 43% two, but 36% of teachers were able to provide three or more strategies. For the second DMI item on fractions, more teachers in Year 2 (34%) showed an understanding of students strategies than in Year 1 (20%). The difference in total score across these groups (8.43 for Year 1 and 10.93 for Year 2) was not statistically significant. However, one way of thinking about this difference meaningfully is that Year 2 teachers could explain and/or identify over two more student strategies across the five problems than could Year 1 teachers. This provides some evidence that knowledge change occurred.
Table 6: Mean Score on Open-Ended Items by Teacher Group
Note. n = 14
Little change was found in the use of new classroom practices by teachers who participated in the PD for two years. While Cohort 1, Year 1 teachers did not decrease their use of any practices in year two, they only increased their use in two categories. The two practices that more teachers took on were counting (9% increase) and questioning student thinking (9%). Only two teachers adopted new practices in year two. Most adoption of new practices took place in year one of the PD. Looking at how many new practices teachers took on in two years reveals a similar pattern (see Table 7). Forty two percent of teachers adopted at least three new practices.
Table 7: Percentage of Teachers Adopting Classroom Practices for Cohort 1 Across 2 Years
Note. a n=12
Teacher Knowledge and Classroom Change Summary
Cohort 1 teachers, who adopted more practices in their first year of participation, seemed to stop changing in year two. This was in spite of showing some growth in their knowledge of student thinking from year one to two. In year two of the study, the Cohort 2, Year 1 teachers began the PD, and results indicate that these teachers adopted fewer classroom practices. This pattern suggests that it might have been more difficult for teachers across cohorts to incorporate new practices in the second year of the project. However, the results should be interpreted cautiously, given that one school district was examined and given the limited differences between Cohorts 1 and 2. This emerging pattern, along with our informal conversations with teachers, led us to examine teachers responses to the new state language policy, which was implemented in the second year of the PD initiative.
POLICY IMPACT ON TEACHER CHANGE
The mathematics PD placed great importance on building instruction from student thinking, word problems, and mathematical representations. This PD placed heavy emphasis on language, in terms of explanation, student sharing, and a focus on the context of word problems rather than key words. However, in year two of the PD, the new law was implemented in all of Arizonas schools. As we began our second year in the district, we noticed that the language policy was causing stress and affecting teachers mathematics instruction. For example, teachers struggled with the limited time they now had to teach mathematics. While the policy split the 60 minutes for mathematics instruction into 15-20 minutes for subject matter vocabulary and 40 minutes for content instruction, teachers commented that they really only had 40 minutes for mathematics total. Additionally, teachers expressed frustration that the students were placed in their ELD levels weeks after the start of the year. When we interviewed the seven teachers from Cohort 1, Year 2 about the policy, we found that there were various perspectives on the state policy. One teacher strongly opposed it and one strongly supported it, while the other teachers held more moderate stances. A summary can be found in Table 8.
Table 8: Teacher Interview Summary by Teacher
Along with these various stances, four themes from the interviews spoke to issues of teacher change that resulted from the policy and PD. The first was the differing knowledge teachers had about the various components of the ELD policy. The second was the perceived impact that this policy had on mathematics instruction. A third theme was the distinction teachers made between language and mathematics. Finally, problematic views of students and parents were shared across teachers.
Knowledge of and stance towards the ELD policy
Two of the seven teachers were very knowledgeable about the newly implemented legislation. Mr. B, a 1st grade teacher, explained, the four-hour language block is explicitly language...you know, specific direction of sounds, letters, sentences, the actual grammar. He continued by adding more detailed language from the policy about the one-year-to-fluency expectation and the tracking of students by language proficiency. Mr. R, another 1st grade teacher, also provided explicit examples of the ELD block. Basically one hour of reading, about an hour of grammar, 30 minutes of conversation and ELD, which is basically speaking and talking. As far as math goes, theres an hour block of math; within that, we are supposed to spend 15 or 20 minutes specifically teaching specific vocabulary. This was just the beginning of what these two teachers knew about the policy. The other teachers were more mixed in the depth of their knowledge about the legislation.
These teachers spoke to one or two aspects of the policy, citing such issues as the four-hour block, language grouping, vocabulary, and academic language. For instance, Ms. H, a kindergarten teacher, focused on the four-hour block and the new curriculum: For our school, we have four hours of English Language Development a day for all classes with second-language learners. This is probably the main thing we are doing. Weve also adopted Avenues [a curriculum] as a means of improving their vocabulary. This represents a typical response, highlighting one aspect of the policy and the practical issues of new curricula which focuses instruction on vocabulary or language. This was critical to know, because a limited understanding of the policy might have shaped teachers' perspectives on how the policy shaped their daily instruction.
However, teachers views on the language legislation varied considerably. Mr. B described how he was fundamentally opposed to the ELD block. I think, um, I think its discrimination, ah, of a sort. I personally think it is approaching criminal. I think that strongly about it...The ELD block is just a shame, just a real shame. For Mr. B, the grouping called for ideas of inflexible tracking and segregation of kids, though we should note that we later present some comments by him that support ability grouping. In contrast, Mr. R was a supporter of the policy, stating, [the policy is] pretty routine and rigid, which I think is great because a lot of people need routine and structure and follow the system, so that kids can get in the habit of doing that. Beyond these two teachers, the other five teachers expressed varying levels of agreement with the policy. Ms. P expressed a level of support for the one-year-to-fluency expectation.
I guess maybe that one year is enough. I think its enough ifagain, I have the ones who scored highest to begin with. They werent proficient; they were intermediate or high basic, but they move several levels, so I think it is good to set the goal high, thats important. But if they dont meet that goal then they will, maybe in two years, hopefully. Its good to have that high goal, and I am surprised so many reached it.
While Ms. P supported the idea of the one-year requirement, she situated her support in terms of being a good goal for her intermediate or high basic students. For her, the policy was good for holding students to high expectations.
In comparison, another teacher said that the one-year expectation was unrealistic for various reasons. Ms. K explicitly stated, When the average takes seven years, you know, Id like to know a political person who set up that expectation [the 1-year limit] to tell me how to meet, you meet it! As educators, we are really struggling. I dont see how it can be done. It doesnt mean we dont try. We do, we certainly do. Ms. Ks comment is in line with the research literature on SLA. While the field knows from this research that social proficiency develops in two to four years, most ELLs continue to need help developing academic proficiency for approximately five to seven years (Collier, 1987; Cummins, 1994). Ms. K added that The goals that have been set for us as the educators, by the political realm, is really not realistic of the true classroom environment.
While four teachers spoke in favor of the policy, it is also possible that some were not comfortable explicitly speaking out against the legislation. However, two opposed the legislation explicitly, and another did not state a preference either way. It is also important to note that the two teachers with detailed knowledge of the policy were split, one for and one against the policy.
IMPACT OF POLICY ON MATHEMATICS INSTRUCTION
While teachers responded no when asked straightforwardly if this policy had changed their math instruction, some of their responses to follow-up questions in the interview suggest that the policy affected their instruction in two ways. First, teachers expressed that the policys limited impact was due to mathematics only intersecting language in terms of mathematical vocabulary. Second, teachers considered that class placement based on English proficiency resulted in an absence of English models in some mathematics classrooms.
When asked whether the policy had affected his mathematics instruction, Mr. B responded, No, not off hand. If I think of anything, Ill let you know, but no, none that I can think of. Ms. H expressed similar sentiments: No, I dont think so. No. We have always tried to accommodate. I think we have to go slowly at the beginning. We have to make the transition as smooth as possible into English&We still have to do vocabulary with them. We always did. While she noted that they still need to teach mathematics vocabulary, the important difference after the policy was that mathematics vocabulary was taught in a 15-20 minute window separate from the subject matter to be learned. Across teachers, when asked directly, the response was consistent; the ELD policy had not changed their mathematics instruction.
In trying to understand this response, we probed further. Two teachers believed that student learning was dependent upon good teaching practices. Mr. H stated, All students should become proficient with good teaching. Ms. P, while surprised at her students success at becoming proficient, attributed this success to her comfort level with teaching math to her intermediate or high-basic students. This belief is consistent with Mr. H and Ms. Ps earlier view that the policy did not have an effect on their mathematics teaching. Essentially, they said good math teaching is good math teaching, no matter who the learners are or the language practices used.
At other moments in the interview, some teachers shared that the policy had limited English-proficient models in the lower-proficiency classrooms. For example, Mr. B commented that not having English-proficient students as anchors to model academic language in his classroom limited the opportunities his students had in learning English:
And small groups allow usand CGI math, for example. Doesnt hurt to have a few kids in there that not only can do the math but can explain things in English, you know: how did you do that, why did you do that, just like we always do when questioning, tell me how you did that. Well, the kid might be a math wiz but doesnt have the language, sitting with four kids, five kids, you know, youre missing that anchor that can say, well, first I put the cubes together&
Mr. B notes that tracking by language proficiency (according to the policy) limits student explanation and models of solution strategies with peers and the teacher, a practice that was central to the PD and to effective practices with ELLs (Moschkovich, 2007). While Ms. S stated support for language tracking in general, she did note that having more English models would be beneficial: I mean, they get a lot of English exposure. I think [students] maybe need a little more English models in the room. But in my math, you know, we use a lot of speaking and English, with the sharing, so there is English in that. Both teachers note that lacking English models limits student sharing and explanation, but it seems less problematic for Ms. S. These are the rare moments when a comment pointed to the policy negatively impacting mathematics instruction, despite all teachers insistence that it had not. However, it could be that they conceived of this as a limitation on student models rather than to their own instruction.
Language and Mathematics
Whether teachers supported aspects of the policy or not, one theme that emerged was the limited intersection of language and mathematics. Five teachers saw them as separate entities. Three of these teachers conceptualized the intersection of mathematics and language as only focusing on vocabulary. In contrast, two teachers discussed the intersection with more complexity. For the most part, though, teachers made comments similar to Ms. Ps.
I just feel math is independent of language almost. I mean, when you are giving directions, of course, that matters that they understand the directions, but you can model it. But mathematical concepts 99% of the time can be modeled and use numbers and things. It doesnt matter if it is English or Spanish or Korean or Vietnamese, it doesnt matter. It is numbers and its groups, its stuff like that, so it has a little, small effect, but its not gonna hinder anyone too much, and it is not gonna be super beneficial outside of regular math teaching.
Ms. P drew a clear line between learning language and mathematics. Her description of what mathematics is was strictly limited to numeric notation, with no regard for communication, problem solving, and engaging in mathematical discourse. Mr. R stated a similar idea: Math is independent of language. It is it's own language, so you can use shapes and count, do all those things, and that's kind of universal. Here math is conceptualized as a universal language. Again, it is based on shapes, counting, and notation, but this universal definition does not seem to include the names of those shapes, number names, or reasoning about properties of numbers.
When probed deeper, three teachers implicitly referenced vocabulary as an intersection between mathematics and language. For instance, Mr. H felt that he had an advantage because he was teaching the English-proficient students: I feel its giving me an advantage, because I have so-called proficient kids that I do feel like come in with some more vocabulary. They already have a little bit more of a foundation. So, he believes that having students with greater English proficiency gives him an advantage in mathematics, but only in terms of vocabulary. Mr. R also noted that it was good for him to have knowledge of his students language level so that he could appropriately adjust his own use of mathematics vocabulary. The teachers viewed mathematics teaching and learning as separate tasks from teaching and learning English, with the exception of issues of vocabulary. In keeping with prior research, the separation of vocabulary and mathematics legislated in the policy was considered unproblematic by these teachers (Celedón-Pattichis, 1999). The danger in seeing language in math as limited to vocabulary, as Moschkovich (2007) has discussed, is that in placing an emphasis on vocabulary without contextualizing it, teachers may be aligning themselves with deficiency models by focusing on what students cannot do. Moreover, the exclusive focus on vocabulary misses building more complex mathematical skills, such as explanation, justification, and representation. Given this perspective on the lack of reciprocity between mathematics and language-learning and a strict focus on vocabulary and mathematical notation, it makes sense why these teachers believed that the language policy had not impacted their mathematics teaching.
Two teachers, as noted earlier, saw the lack of English models as an interaction between mathematics and language. Both Mr. B and Ms. S. discussed this issue. Only Mr. B, though, discussed this intersection in more depth: Yeah, math is full of language, and, uh, the word problems in particular, without the language they would be in a lot of trouble there. So, in addition to discussing English models and the need for anchors to express mathematics explanation, Mr. B presents mathematics as full of language, even beyond vocabulary. Mr. B was an exception: most teachers considered mathematics and language to be independent, while a few trivialized the intersection as only focusing on vocabulary. In light of their view of math and language as independent, it is perhaps not surprising that these teachers considered math instruction to be unaffected by the language policy.
Views of Students and Parents
In the process of asking about various facets of the policy, instruction, and parental involvement, a number of comments were shared that illuminated teachers views of students. As noted earlier, separating students by language proficiency was unproblematic for all but one of the teachers. In fact, the other teachers believed it to work better. Ms. P illustrates this point when she states, I think grouping them by language is okay, not by ability level, but by language is okay, because you know your whole class. Anytime you can teach one level of students instead of varying levels, it is easier. Most teachers saw grouping by language proficiency as a way of making instruction easier.
The teacher who earlier opposed the policy strongly opposed the process of grouping students outlined in the legislation. Mr. B stated,
Classes used to be grouped based on ability, but now theyre grouped on language, and for the life of me, there are just two sides, there is obviously some strong side that says this is the way it will be, and those are the powers that be, but I could not disagree with it more, because what we need in the room are anchors; we need kids who have some of the language so they can be role models and anchors...and, uh, that from conversations with teachers one of the most powerful influences on a childs ability to learn and willingness to learn is to see their peers.
While Mr. B supported the idea of having more English-proficient peers function as anchors in the classroom, he later contradicted himself when he expressed sentiments equating lower intelligence with lower language proficiency: But to take a normal, intelligent, you know, a kid with normal intelligence and dump him in a closet with a bunch of kids that dont speak the language, its unfair. In the earlier comment, he distinguishes language proficiency from ability, but here Mr. B equates the two. This comment seems to support the idea that ELLs have lower cognitive ability than their English-speaking peers. In addition, Mr. Bs view of the classroom as a closet or limited environment speaks to the detrimental effects of tracking in the policy.
Several teachers echoed Mr. Bs views that cognitive ability and language proficiency are equated. Mr. R felt that the one-year-to-fluency expectation was unattainable, not because of SLA research or practices, but because the students were incapable of retaining content knowledge over an extended period of time.
Knowing these kids and how much they retain and what I hear from other teachers, especially all of my first graders that are now second graders who completely forgot place value and so many different concepts that were taught in first grade, and theyre stuck in another intermediate class, I mean, they told us that, in our ELD training, that the intermediate group is the hardest group to move to proficient because theyre so close, but a lot of times they just didnt get the extra push or summer comes along, and they forget everything they learn in first grade and its retaining information.
While some teachers referred to the unrealistic expectations of learning academic language in one year, consistent with research, Mr. R explicitly tied this to an inability to retain information. As discussed earlier, the focus on decontextualized vocabulary may be focusing Mr. R on what students cannot retain or on vocabulary they do not recall, aligning him with a deficiency model.
As with deficit views of students cognitive ability, deficit views of culture and language proficiency surfaced in many of the interviews. Another teacher, Mr. H, attributed students inability to learn English in one year to parents lack of effort:
Knowing these kids and the fact that everything they learn is here. When they go home its like...ehhh! Its frustrating, because it feels like Im only doing the work. Like, I want the best for these kids. I try to give parents things to do at home with their kids and [there is] a lack of effort.
Ms. K, on the other hand, did not really address the issue of student learning. Instead, her emphasis was on enforcing the use of English only in the classroom to the point where she restricted students from speaking their first language. English only, and if the kids speak Spanish, then I ask them to speak in English. Mr. R expressed similar sentiments about teaching only in English by referring to English-only instruction as superior to bilingual education, which he viewed as a hindrance to students learning of English. This perspective is in contrast to ELL research in mathematics that makes the case for valuing students home languages (Khisty, 2001; Khisty, 2004).
Two of the teachers considered student learning to be hampered by institutional forces. Ms. S thought the policy created a situation where ELLs were automatically grouped with special education students. Consistent with the section on language ability grouping, this implies a link between language proficiency and cognitive ability (i.e., intelligence, ability, etc.) in the implementation of the policy. She found this problematic, though it should be noted that she is one of the teachers who supported the legislation.
I have the basic and intermediate; my students have to move from basic to intermediate throughout the year. So I have middle...low, middle, high, intermediate kids, more boys than girls. What else? At all levels, some are very low at math, some intermediate, some high. Although Ive seen a lot of them improve in math this year, a lot, I have, I dont know, I have five or six kids with speech issues, two IEPs. I have three that go to special therapies. So, you have to take all that into account while you are teaching some math and reading. So its been kind of a different class; its just the ELD component brought a lot of other issues as well.
In her comments, Ms. S shares the complexities of implementing a language tracking policy and demonstrates how this can conflate lower language-proficiency with speech issues and special needs. This raises concerns about the institutional and systemic problems that come with the application of such a broad policy to a local school context.
Overall, four major themes emerged across the teachers: varying knowledge and stances on the language policy, viewing the policy impact on math instruction as minimal, the independence of mathematics and language, and deficit views of language and culture. While knowledge and stances towards the language policy among teachers in this study varied considerably, all of the teachers, when asked directly, felt that the ELD policy did not affect their mathematics instruction. But in probing about various aspects of the policy, two teachers identified the lack of English models (which affects the quality of explanations) and the limits on content integration as issues that have limited their mathematics instruction. These were also the two teachers who saw an interaction between language and mathematics beyond vocabulary. For the other teachers, the lack of perceived impact of the policy on instruction might be due to the stark contrast they drew between mathematics and language. Contrary to the PD effortwhich focused teachers on student explanation, word problems, and representationsand literature on teaching math to ELLs, these teachers seemed to view math as a collection of symbols, limiting its intersection with language to vocabulary, and therefore limiting their view about the intersection between the policy and PD.
In fact, instead of noting the problems with the policy, when speaking of students attainment of knowledge, many teachers framed the students as deficient or placed blame on parents. Some of the deficit views were due to a confounding of cognitive ability and language proficiency by teachers. Teachers equated high English proficiency with greater intelligence and saw low proficiency and bilingualism as hindrances. One teacher also shared cultural deficit views about students families. In line with this, six of the seven teachers either implicitly or explicitly supported language grouping for students. Even in the instance where the teacher disagreed with this practice, he expressed agreement with ability grouping in general. Therefore, it seems that even when teachers disagreed with components of the policy, they sometimes agreed with the ideology underlying the policy. This also might explain why teachers felt that the policy did not impact their mathematics instruction, as many of them viewed their ELL students and bilingualism, in general, as problems.
While many studies examine teachers fidelity to reform or teachers beliefs around and responses to reform, studies that examine detailed change can show not only what teachers report but also how they respond within their classrooms. This study seeks to do this kind of documentation, and while the design does not measure change, the data collected over two years would suggest that the implementation of a new immigration policy in Arizona influenced what teachers took up from the PD and applied in their classrooms. Segregation by language proficiency, cutting time for mathematics instruction by one third, and restructuring that time so that one third of it focuses on vocabulary out of context does seem to have mediated the types of change teachers undertook in their mathematics instruction.
To be sure, this is a small exploratory study that is limited to one districts response to a specific type of mathematics professional development initiative within the immigration and ELL policy context of one state. Examining how multiple districts would have responded to the same PD within the same sociopolitical context would lend more support to the impact of the sociopolitical context on school reform efforts, as put forward in this paper. However, similar laws have been enacted in other states and the findings of this study would suggest that such policies aimed at populations of color, whether educational in intent or not, mediate school reform efforts. The findings of this study suggest .two tensions that can inform future professional development initiatives and research.
First, there is the tension between viewing mathematics as a non-linguistic body of knowledge and the necessity of meeting students language needs. Policymakers assume that language policy is independent of mathematics instruction. However, CGI is one example of the broader movement of reform mathematics, which emphasizes the employment of the experiential knowledge of students, student generation of strategies, making meaning of mathematics vocabulary and concepts, and the use of word problems. Accessing informal understandings sometimes requires accessing the home language of ELL students and using word problems sets the stage for negotiating mathematical meanings within a context that uses language. These practices view mathematics as a discourse as opposed to a set of symbols and procedures. Yet, the Arizona law separates subject matter vocabulary from the actual subject matter learning. The law also segregates more proficient language-models who can demonstrate mathematical strategies, explanations, and justification for their peers who are still developing mathematical literacy in English. It is perhaps not surprising, then, that many teachers in this study found it difficult to implement CGI principles in the second year of the study. Echoing the policy, teachers often viewed language and mathematics as separate aspects of human learning, citing mathematical vocabulary as the lone intersection of the two. The policys separation of vocabulary and content institutionally supported this perspective. This finding would suggest that those trying to bring mathematics reforms into schools must create strategies to help teachers understand mathematics as a discourse rather than as a symbolic discipline and to show teachers how this approach to math has implications for those with language learning needs. This may allow teachers to change classroom practices, see the need to design problems for students, and edit the textbook in a way that draws on students informal mathematical ideas and experiential knowledge, regardless of knowledge backgroundpractices that many teachers in the study did not employ. As the designers of the professional development initiative, recognizing this tension would have allowed us to speak to the intersection of the PD and policy and be more detailed in addressing the intersections of language and mathematics with participants.
A second, related issue is the influence of deficit views of ELL students, as embodied in the policy and reported by some teachers. The view that a lack of proficiency in English is evidence of a lesser intellectual capacity and a lack of educational support at home is deeply embedded in the history of policies for Latinos and ELL students. The fact that the Arizona policy required students to be segregated from their English-speaking peers and limited their access to content instruction until they became more proficient in English shows that the Arizona policy is consistent with the same deficit perspective. Unfortunately, this perspective aligned with some teachers views of students as well; ideas that it was appropriate to track ELL students and segregate them from English-speaking peers were consistent beliefs shared in the interviews. Some teachers in this study believed that students who were less proficient in English had less intellectual capacity and therefore would struggle to understand math. The belief that students have less intellectual ability may cause teachers to engage students in lower quality math, using rote instructional techniques believed to teach to their level, assuring that students will not be capable of more complex mathematical thinking, the type of thinking embodied in the CGI professional development initiative.
This issue speaks to the need for mathematics professional development to focus on particular student groups rather than focusing solely on the teaching of content as a one-size-fits-all approach. Not addressing teachers deficit views of ELL students meant the PD initiative was chipping away at the edges of practice rather than challenging teachers implicit theories about who is capable of doing substantive mathematical work; this prevented change. These issues are complex, but they are issues that PD efforts and research need to address. One way to do this would be to support teachers in gaining a deeper understanding of the linguistic and cultural needs of teaching ELL students across the disciplines as well as an understanding of the cognitive demands inherent in learning mathematics while simultaneously learning a second language. In a study of think-alouds used in mathematics classrooms, Celedón-Pattichis (1999) determined that ELLs needed to translate the problem to Spanish, read it at least twice, attribute meaning, translate it into mathematical symbols, and ignore irrelevant words. Celedón-Pattichiss research demonstrates the complexity of the cognitive activity that ELLs engage in when participating mathematically in classrooms. Many of the teachers in this study had a limited understanding of the complexity involved for ELL students in learning mathematics. The separation teachers spoke of between mathematics and language further limited teachers ability to students. For us, this means contextualizing teacher learning within the community and lives of the children they teach, while also respecting the core of the educational change being sought.
As this was an exploratory study of the interaction between the sociopolitical context and one mathematics PD initiative in one district, future research is needed to examine these complex relationships in more depth. To test the impact of sociopolitical forces on teacher change through PD and on the mathematics achievement of diverse student populations, a larger, more representative study is needed. This research would need to cut across states with similar policies, in addition to investigating how similar mathematics PD initiatives implemented in a range of districts are taken up and used in classroom practice. Some districts might align themselves more with policies and the ideologies embedded within them, making it critical to see how policies at the state level are interpreted and enacted within various professional development initiatives. The tracing of the relationships between policy, teacher beliefs, school context, professional development, and the mathematics achievement of ELL students is a complicated project but one that might better inform how to transform research-proven mathematics instruction into practice accessible to all students.
At the same time, more focused professional development studies that target teacher beliefs and understandings not only of mathematics but also of specific student populations are needed in order to identify strategies that help teachers understand how to engage all students in high-quality mathematics instruction. How districts, schools, and teachers do or do not align themselves with narrow framings of mathematics as separate from language or with the ideology embedded within policy are important considerations for PD efforts. In conclusion, while new models of professional development that aim to be teacher responsive and context specific are viewed as one means of improving mathematics teaching, the findings of this study would suggest that altering instruction is a far more complex task. The impact of professional development initiatives is mediated not only by teacher beliefs or school culture but also by various sociopolitical factors as well. Just as classroom instruction is situated within a broader cultural context, effective professional development needs to respond to the sociopolitical context in which it is situated. By not addressing the sociopolitical context, professional development initiatives will likely have little success in improving mathematics instruction for ELL students.
The authors would like to thank Jessica Hunsdon and Sharon Ryan for their extensive and thoughtful feedback on this paper. Additionally, they would like to recognize the research efforts of Brandon Helding, Jennifer Oloff-Lewis, Jim Middleton, and Barry Sloan who also supported this work.
1. It should also be noted that Susan Jo Russell, Virgina Bastable, and Deborah Schifter provided an earlier version of two assessments used while field testing DMI modules and that they contributed greatly to the content of the items used to develop this measure.
2. There were missing data on 2 teachers in the Cohort 1, Year 1 dataset due to health issues, so this analysis only includes 19 teachers.
3. The semi-structured nature of the interviews permitted deviation from the overarching interview questions. While the protocol provided room for teachers to express views of students, deficit or otherwise, without the need for probing or leading questions, there were times when we felt the teachers were primed for expressing deficit ideas by the interviewers. This was an issue in this section, in particular. In these cases, we did not include the data in the results.
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