Browsing by Subject "Mathematical knowledge for teaching"
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Item An exploratory study of teachers’ use of mathematical knowledge for teaching to support mathematical argumentation in middle-grades classrooms(2011-12) Kim, Hee-Joon; Empson, Susan B.; Shechtman, Nicole; Michalchik, Vera; Treisman, Uri; Stroup, WalterMathematical argumentation is fundamental to doing mathematics and developing new knowledge. Working from the view that mathematical argumentation is also integral to teaching and learning mathematics, this study investigated teachers’ use of mathematical knowledge for teaching (MKT) to support student participation in mathematical argumentation. Classroom observations were made of three case-study teachers’ implementation of a three-day curriculum unit on mathematical argumentation and supplemented with paper and pencil assessments of teachers’ MKT. Teaching moves, or teachers’ actions directed toward supporting argumentation, were identified as a unit of discourse in which MKT-in-action appeared. Teachers’ MKT showed up in three types of teaching moves including: Revoicing by Reformulation, Responding to Student Difficulties, and Pressing for Generalization in Defining. MKT that was evident in these moves included knowledge of core information in argument, heuristic methods, and vii formulation of mathematical definition through and in argumentation. Findings highlight that supporting mathematical argumentation requires teachers to have a sophisticated understanding of the subject matter as well as how concepts develop through argumentation. Findings have limitations in understanding complex teaching practices by considering MKT as a single factor. The study has implications on teacher learning and MKT assessments.Item Prospective and Practicing Middle School Teachers' Knowledge of Curriculum for Teaching Simple Algebraic Equations(2012-11-28) Ma, TingtingKnowledge of curriculum is a significant component of mathematical knowledge for teaching. However, clearly understanding knowledge of curriculum requires further refinement and substantial research. This study consists of three papers that aim to explore prospective and practicing middle school teachers? Knowledge of Curriculum for Teaching Simple Algebraic Equations (KCTE). The first paper reviews trends in and the evolution of standards and policies and synthesizes significant findings of research on mathematics curriculum and Knowledge of Curriculum for Mathematics Teaching (KCMT). Through this synthesis, the paper examines policy changes and research relevant to mathematics curriculum and KCMT and anticipates future research approaches and topics that show promise. Building on the context provided by the first paper, the following two papers investigate KCTE from the perspectives of prospective and practicing middle school mathematics teachers. For the second paper, data was collected from a convenience sample of 58 prospective middle school mathematics teachers and a subsample of six participants. The findings of this study identify patterns of key mathematical topics in the teaching sequence of simple algebraic equations, compare the participants? sequences with experts?, reveal participants? orientations toward KCTE, draw connections between participants? KCTE and their knowledge of content and teaching, and establish relationships between participants? KCTE and their knowledge of content and students. Four middle school mathematics teachers participated in the third study. The results indicate that state-level intended curriculum is the most prevailing component of participants? KCTE. Furthermore, from a vertical view of curriculum, participants? awareness of their students? lack of basic mathematical knowledge impacted their KCTE. The paper also identifies the role of the state-level intended curriculum in participants? KCTE, alternative approaches to curriculum implementation that participants used to respond to the multiple intelligences of their students, and the participants? lack of lateral curriculum knowledge in KCTE. Together, these three papers offer a closer look at KCMT with a focus on simple algebraic equations. This research broadens our understanding of prospective and practicing middle school teachers? KCMT and discusses implications for professional development.