Knowing mathematics for teaching: a case study of teacher responses to students' errors and difficulties in teaching equivalent fractions

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Title: Knowing mathematics for teaching: a case study of teacher responses to students' errors and difficulties in teaching equivalent fractions
Author: Ding, Meixia
Abstract: The goal of this study is to align teachers ? Mathematical Knowledge for Teaching (MKT ) with their classroom instruction . To reduce the classroom complexity while keeping the connection between teaching and learning , I focused on Teacher Responses to Student Errors and Difficulties (TRED ) in teaching equivalent fractions with an eye on students ? cognitive gains as the assessment of teaching effects . This research used a qualitative paradigm . Classroom videos concerning equivalent fractions from six teachers were observed and triangulated with tests of teacher knowledge and personal interviews . The data collection and analysis went through a naturalistic inquiry process . The results indicated that great differences about TRED existed in different classrooms around six themes : two learning difficulties regarding critical prior knowledge ; two common errors related to the learning goal , and two emergent topics concerning basic mathematical ideas . Each of these themes affected students ? cognitive gains . Teachers ? knowledge as reflected by teacher interviews , however , was not necessarily consistent with their classroom instruction . Among these six teachers , other than one teacher whose knowledge obviously lagged behind , the other five teachers demonstrated similar good understanding of equivalent fractions . With respect to the basic mathematical ideas , their knowledge and sensitivity showed differences . The teachers who understood equivalent fractions and also the basic mathematical ideas were able to teach for understanding . Based on these six teachers ? practitioner knowledge , a Mathematical Knowledge Package for Teaching (MKPT ) concerning equivalent fractions was provided as a professional knowledge base . In addition , this study argued that only when teachers had knowledge bases with strong connections to mathematical foundations could they flexibly activate and transfer their knowledge (CCK and PCK ) to their use of knowledge (SCK ) in the teaching contexts . Therefore , further attention is called for in collaboratively cultivating teachers ? mathematical sensitivity .
URI: http : / /hdl .handle .net /1969 .1 /ETD -TAMU -1481
Date: 2009-05-15

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Knowing mathematics for teaching: a case study of teacher responses to students' errors and difficulties in teaching equivalent fractions. Available electronically from http : / /hdl .handle .net /1969 .1 /ETD -TAMU -1481 .

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