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What Is So Difficult About the Preparation of Mathematics Teachers?
, 2001
"... this article, I consulted a related one by Al Cuoco ([Cuoco]) and was surprised that, while his views on preservice professional development are consistent with mine, the two articles have almost no overlap ..."
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this article, I consulted a related one by Al Cuoco ([Cuoco]) and was surprised that, while his views on preservice professional development are consistent with mine, the two articles have almost no overlap
Preservice secondary mathematics teachers’ beliefs about the nature of technology in the classroom
 Canadian Journal of Science, Mathematics, and Technology Education
, 2007
"... This study investigated preservice secondary mathematics teachers ’ (PSTs) beliefs about teaching mathematics with technology, the experiences in which those beliefs were grounded, and how those beliefs were held. Beliefs were defined as dispositions to act. Coherentism and the metaphor of a belief ..."
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This study investigated preservice secondary mathematics teachers ’ (PSTs) beliefs about teaching mathematics with technology, the experiences in which those beliefs were grounded, and how those beliefs were held. Beliefs were defined as dispositions to act. Coherentism and the metaphor of a belief system provided a conceptual framework through which the PSTs ’ beliefs were seen as sensible systems. Coherentism was posited as an alternative way of interpreting apparent inconsistencies between teacher’s beliefs and their practice. Through the qualitative research methodology called ground theory, four PSTs were purposefully selected and studied. Data stories were written that demonstrated the organization and structure of the PSTs ’ belief systems. From an analysis of the PSTs ’ experiences with technology, a theory was posited that focused on the PSTs ’ ownership of learning mathematics with technology. Experience, knowledge, and confidence were the primary factors that constituted ownership. The primary dimensions of the PSTs ’ core beliefs with respect to technology, referred to as their beliefs about the nature of technology in the classroom, were the availability of
Pedagogical Content Knowledge for Teaching Primary Mathematics: A Case Study of Two Teachers
"... This paper explores the usefulness of a framework for investigating teachers ’ Pedagogical Content Knowledge (PCK). Two primary mathematics teachers completed a questionnaire about mathematics and mathematics teaching, and were interviewed about their responses. These responses were then analysed us ..."
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This paper explores the usefulness of a framework for investigating teachers ’ Pedagogical Content Knowledge (PCK). Two primary mathematics teachers completed a questionnaire about mathematics and mathematics teaching, and were interviewed about their responses. These responses were then analysed using the PCK framework. The PCK held by the two teachers was found to differ in many ways, including the connectedness of their knowledge, and the specificity with which they discussed the mathematics involved. Teacher knowledge has long been the subject of intense research, and the range of knowledge that teachers draw upon every day is vast — knowledge of content, of students, of curriculum, of pedagogy, of psychology. To examine one aspect of a teacher’s knowledge in isolation is not only unrealistic, it is difficult. Nevertheless, in order to examine teachers ’ particular knowledge for teaching mathematics, it is also necessary. Examining Pedagogical Content Knowledge Shulman (1987) defined pedagogical content knowledge (PCK) as the blending of content and pedagogy into an understanding of how particular topics, problems, or issues are organized, represented, and adapted to the diverse interests and abilities of learners, and
Investigation of Effective Mathematics Teaching and Learning in Australian Schools
 Attitudes, Intentions and Participation. (LSAY Research Report No. 41). Camberwell
, 2004
"... This report has been prepared for the Australian Government Department of Education, Science and Training by ..."
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This report has been prepared for the Australian Government Department of Education, Science and Training by
ASPECTS OF MATHEMATICAL KNOWLEDGE FOR TEACHING FRACTION MULTIPLICATION
"... I report on mathematical knowledge that two U.S. 6thgrade teachers used while teaching fraction multiplication for the first time with lengths and rectangular areas. Both teachers were using versions of the Bits and Pieces II unit from Connected Mathematics. Data came from videotaped lessons, teach ..."
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I report on mathematical knowledge that two U.S. 6thgrade teachers used while teaching fraction multiplication for the first time with lengths and rectangular areas. Both teachers were using versions of the Bits and Pieces II unit from Connected Mathematics. Data came from videotaped lessons, teacher interviews, and student interviews. To explain where each teacher did, and did not, adapt to her students ’ explanations and drawn representations, I examined the unit structures that each teacher evidenced and the purposes for which they used drawn representations. The results highlight the importance for teachers of reasoning flexibly with three levels of units when responding to students ’ representations of fractional quantities. Context and Objectives Research on teachers ’ knowledge has expanded from studies of subject matter knowledge of various content areas to the organization of knowledge for teaching particular topics (e.g., Ball,
Preservice teachers' problem solving processes
 Mathematics Education Research Journal
, 1998
"... The purpose of the study reported in this paper is to explore some of the common difficulties with mathematical word problems experienced by preservice primary teachers. It examines weaknesses in students ' content and procedural knowledge, with a particular focus on how they apply these aspect ..."
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The purpose of the study reported in this paper is to explore some of the common difficulties with mathematical word problems experienced by preservice primary teachers. It examines weaknesses in students ' content and procedural knowledge, with a particular focus on how they apply these aspects of knowledge to solving closed word problems " The SOLO Taxonomy (Biggs & Collis, 1982, 1991) is used to classify the processes used by students who attempted to solve a group of word problems of varying difficulty. Other characteristics of the students ' processes that are analysed include the way they used the cues provided in the problem, the way they brought in additional concepts or processes, and the types of errors they made. It has long been acknowledged that one of the responsibilities of a p~eservice mathematics education program is to ensure that student teachers develop adequate knowledge about mathematics (Cockcroft, 1982; Department of Employment, Education and Training [DEETt 1989; National Council of Teachers of Mathematics [NCTMt 1991). Such documents have recommended that action should be taken within teacher education institutions to ensure that graduating
PROSPECTIVE TEACHERS ’ UNDERSTANDINGS: FUNCTION AND COMPOSITE FUNCTION
"... The current education reform efforts have placed greater emphasis on conceptual understanding and have focused attention on teacher preparation especially on the adequacy of teachers ' mathematical knowledge of the material they will be engaged in teaching. This paper discussed the responses of ..."
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The current education reform efforts have placed greater emphasis on conceptual understanding and have focused attention on teacher preparation especially on the adequacy of teachers ' mathematical knowledge of the material they will be engaged in teaching. This paper discussed the responses of 29 prospective elementary and special education mathematics specialists to questions focused on conceptualization of the function concept as well as facility with composite functions. The results point to the conclusion that many of the prospective teachers held historical definitions tied to formulaic rules and this negatively affected their ability to solve composite function problems. Over the past decade, many researchers have turned their attention from studying students' understanding of elementary school content knowledge to examining the content and pedagogical understandings held by inservice and prospective teachers. In particular, this shift resulted from the growing disfavor over quantifying the mathematical content knowledge of teachers by the number of courses taken or scores attained on standardized tests (Ball, 1991). Researchers felt that such information does not reflect the teachers ' understandings of the material that they will be teaching nor how they will transmit those understandings. This study investigated the content knowledge of prospective teachers by examining their responses to a cognitivelyguided instrument designed to answer the following questions: (1) What are the definitions of functions that these prospective teachers would be willing to accept and what definition would they consider the best? and (2) How do prospective teachers interpret the composition of functions and how does this reflect on the understanding of the function concept? These two questions arose from analyzing the previous research both on prospective teachers' understandings of the function concept (Even, 1993; Ebert, 1993; Wilson, 1993) and typical student misconceptions associated with the function concept. The next section discusses the various conceptions of the function definition held by mathematics students and teachers.
Developing Mathematical Content Knowledge for Teaching Elementary School Mathematics. IUMPST: The Journal. Vol 1 (Content Knowledge
, 2010
"... In this paper the authors present three design principles they use to develop preservice teachers ' mathematical content knowledge for teaching in their mathematics content and/or methods courses: (1) building on currently held conceptions, (2) modeling teaching for understanding, (3) focusing ..."
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In this paper the authors present three design principles they use to develop preservice teachers ' mathematical content knowledge for teaching in their mathematics content and/or methods courses: (1) building on currently held conceptions, (2) modeling teaching for understanding, (3) focusing on connections between content knowledge and other types of knowledge. The authors share results of individual research projects and teaching approaches focusing on helping preservice elementary teachers develop such knowledge. Specific examples from different content areas (whole number, fractions,
1Integration of didactical knowledge and mathematical content knowledge in preservice teacher training
"... We suggest some ideas about how content knowledge and didactical knowledge could be integrated in preservice secondary mathematics teachers ’ training. We identify the activities we expect a teacher to perform when planning a lesson and determine the didactical knowledge that she has to put into pl ..."
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We suggest some ideas about how content knowledge and didactical knowledge could be integrated in preservice secondary mathematics teachers ’ training. We identify the activities we expect a teacher to perform when planning a lesson and determine the didactical knowledge that she has to put into play in order to do so. We then show the relationship between that didactical knowledge and the corresponding content knowledge.
Interpreting Teachers ’ Movement toward Reform in Mathematics 1
"... American classrooms are notoriously dominated by the teachercentered activities of explaining and lecturing (Goodlad, 1984, p. 105) which often leads to learning by imitation. Recent calls for reform such as those advocated by the Mathematical Sciences Education Board [MSEB] (1989) and the National ..."
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American classrooms are notoriously dominated by the teachercentered activities of explaining and lecturing (Goodlad, 1984, p. 105) which often leads to learning by imitation. Recent calls for reform such as those advocated by the Mathematical Sciences Education Board [MSEB] (1989) and the National Council of