Knowledge for Teaching Mathematics to Latino English Language Learners: An Instrument Development Study
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The purpose of this study was to identify the domains, as well as specific aspects of, knowledge for teaching mathematics to Latino English Language Learners (KT-MELL) and to develop a valid and reliable measure of this knowledge. Latino ELLs are rapidly becoming one of the most populous of student groups in schools--in urban cities especially, but across the nation increasingly. Furthermore, there is evidence that many mathematics teachers of these Latino ELLs may not have encountered or been given the opportunity to learn how to teach these students. A central element of preparation of teachers is the knowledge needed by effective teachers. While there exist studies of the knowledge needed to be effective in teaching mathematics, there is only limited, if any, study of what mathematics teachers of ELLs need to know in order to effectively teach these students. As an initial step toward filling this gap in research, this study sought to identify domains of knowledge needed thought to be important for to teaching math to ELLs. Based upon rigorous review of the research and practitioner literature, and upon many hours of mathematics classroom observations, this study defined a framework for the pedagogical content knowledge needed by mathematics teachers of Latino ELLs. Three domains of knowledge were proposed: KDIFF-knowledge of the difficulties that Latino ELLs may encounter in learning mathematics, KCAP-knowledge of the special capacities for learning mathematics that Latino ELLs may possess based upon their particular cultural, linguistic and learning backgrounds, and KSTRAT-knowledge of strategies for teaching mathematics to Latino ELLs. This framework is closely aligned with existing frameworks of mathematical knowledge for teaching. Using this framework and classroom observational data, a survey instrument was developed and field-tested among both pre-service and in-service teachers from diverse regions of the state of Texas. Based upon the results of data analysis methods central to both classical test theory (CTT) and item response theory (IRT), the underlying factor structure of the instrument was identified to be bi-dimensional; KDIFF and KCAP formed a single scale and KSTRAT a separate scale. Furthermore, precise psychometric properties of the items were uncovered, which demonstrated that the measurements obtained had an acceptable degree of reliability within specific ranges of ability of the respondents. Additionally, a number of interesting response patterns were observed along with several important evidences of construct validity.