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Research on teaching mathematics: Making subject matter knowledge part of the equation
 in Advances in Research in Teaching, Volume 2
, 1991
"... Subject matter understanding and its role in teaching mathematics are the focus of this paper. Although few would disagree with the assertion that, in order to teach mathematics effectively, teachers must understand mathematics themselves, past efforts to show the relationship of teachers ' mat ..."
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Cited by 80 (1 self)
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Subject matter understanding and its role in teaching mathematics are the focus of this paper. Although few would disagree with the assertion that, in order to teach mathematics effectively, teachers must understand mathematics themselves, past efforts to show the relationship of teachers ' mathematical knowledge to their teaching of mathematics have been largely unsuccessful. How can this be? My
Guidelines for authors
 Educational and Psychological Measurement
, 1994
"... ∙The author has no financial conflicts of interest. After glioma pathogenesisrelated protein 1 (GLIPR1/Glipr1) was identified, the expression of GLIPR1 was shown to be downregulated in human prostate cancer, owing in part to methylation in the regulatory region of this gene in prostate cancer cell ..."
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Cited by 70 (6 self)
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∙The author has no financial conflicts of interest. After glioma pathogenesisrelated protein 1 (GLIPR1/Glipr1) was identified, the expression of GLIPR1 was shown to be downregulated in human prostate cancer, owing in part to methylation in the regulatory region of this gene in prostate cancer cells. Additional studies showed that GLIPR1/Glipr1 expression is induced by DNAdamaging agents independent of p53. Functional analysis of GLIPR1 using in vitro and in vivo genetransfer approaches revealed both growth suppression and proapoptotic activities for mouse Glipr1 and human GLIPR1 in multiple cancer cell lines. The proapoptotic activities were dependent on production of reactive oxygen species and sustained cJunNH2 kinase signaling. It was interesting that adenoviral vectormediated Glipr1 (AdGlipr1) transduction into prostate cancer tissues using an immunocompetent orthotopic mouse model revealed additional biologic activities consistent with tumorsuppressor functions. Significantly reduced tumorassociated angiogenesis and direct suppression of endothelialcell sprouting
KNOWLEDGE AND REASONING IN MATHEMATICAL PEDAGOGY: EXAMINING WHAT PROSPECTIVE TEACHERS BRING TO TEACHER EDUCATION
, 1988
"... This study focuses on the knowledge and beliefs about mathematics and the teaching of mathematics held by prospective teachers when they enter teacher education. It offers frameworks for thinking about the role and relationship of different kinds of knowledge in teaching mathematics. Grounded in a v ..."
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Cited by 60 (11 self)
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This study focuses on the knowledge and beliefs about mathematics and the teaching of mathematics held by prospective teachers when they enter teacher education. It offers frameworks for thinking about the role and relationship of different kinds of knowledge in teaching mathematics. Grounded in a vision of a particular mathematical pedagogy, these frameworks are constructed around teacher knowledge, beliefs, and dispositions in the domains of subject matter, teaching and learning, students, and context. A twopart interview was designed to explore prospective teachers ' ideas and thinking about mathematics and the teaching and learning of mathematics. Nineteen prospective teachers were interviewed. The study's results include description and appraisal of the participants ' understandings and ways of thinking about the subject matter, teaching and learning, the teacher's role, and students. These results suggest categories useful for examining what prospective teachers bring with them to their professional preparation to teach mathematics. Focal subject matter knowledge categories included the explicitness and connectedness of substantive understandings, as well as ideas about the justification and nature of mathematical knowledge and activity. With respect to teaching and learning, central
An investigation of teachers' beliefs of students' algebra development
 Cognition and Instruction
, 2000
"... Elementary, middle, and high school mathematics teachers (N = 105) ranked a set of mathematics problems based on expectations of their relative problemsolving difficulty. Teachers also rated their levels of agreement to a variety of reformbased statements on teaching and learning mathematics. Anal ..."
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Elementary, middle, and high school mathematics teachers (N = 105) ranked a set of mathematics problems based on expectations of their relative problemsolving difficulty. Teachers also rated their levels of agreement to a variety of reformbased statements on teaching and learning mathematics. Analyses suggest that teachers hold a symbolprecedence view of student mathematical development, wherein arithmetic reasoning strictly precedes algebraic reasoning, and symbolic problemsolving develops prior to verbal reasoning. High school teachers were most likely to hold the symbolprecedence view and made the poorest predictions of students ’ performances, whereas middle school teachers ’ predictions were most accurate. The discord between teachers ’ reformbased beliefs and their instructional decisions appears to be influenced by textbook organization, which institutionalizes the symbolprecedence view. Because of their extensive content training, high school teachers may be particularly susceptible to an expert blindspot, whereby they overestimate the accessibility of symbolbased representations and procedures for students ’ learning introductory algebra. The study of people engaged in cognitively demanding tasks must consider the relation between people’s judgments and actions and the beliefs they hold. Several aspects of people’s decision making are well established. People do not strictly follow the laws of logic and probability when weighing information or following im
Calculational and conceptual orientations in teaching mathematics
 In D. B. Aichele & A. F. Coxford (Eds.), Professional Development for Teachers of Mathematics: 1994 Yearbook. Reston, VA: National Council of Teachers of Mathematics
, 1994
"... and do not necessarily reflect official positions of NSF or Apple Computer. ..."
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and do not necessarily reflect official positions of NSF or Apple Computer.
Examining values and beliefs about teaching diverse students: Understanding the challenges for teacher education. Educational Evaluation and Policy Analysis
, 1996
"... The online version of this article can be found at: Published on behalf of ..."
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Cited by 34 (3 self)
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The online version of this article can be found at: Published on behalf of
Examining the relationship between beliefs and goals in teacher practice
 Journal of mathematical behavior
, 1999
"... This article presents a detailed analysis of how teacher beliefs interact with goals and influence the momenttomoment actions of teaching. The beliefs, goals and instructional practice of two secondary mathematics teachers were examined as each conducted an algebra lesson. We discuss how specific ..."
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Cited by 30 (2 self)
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This article presents a detailed analysis of how teacher beliefs interact with goals and influence the momenttomoment actions of teaching. The beliefs, goals and instructional practice of two secondary mathematics teachers were examined as each conducted an algebra lesson. We discuss how specific beliefs organized to influence the selection and prioritization of goals that then influenced the actions of each teacher. Finegrained analysis of classroom video and teacher interviews revealed that particular collections of beliefs become apparent when there is a shift in the teacher’s goals. Exploring the relationship between teacher beliefs and goals at this level of detail allows for the investigation of the mechanisms of the teaching process. Implications of this research for teacher education and professional development are also discussed.
Education reform and subject matter knowledge
 Journal of Research in Science Teaching
, 1998
"... with an eye toward defining what good teaching practice consists of. It then examines a wide range of literature to delineate the varieties of knowledge that have been associated with this kind of teaching. While the focus is on subject matter knowledge, the article addressed the character of that k ..."
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Cited by 24 (0 self)
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with an eye toward defining what good teaching practice consists of. It then examines a wide range of literature to delineate the varieties of knowledge that have been associated with this kind of teaching. While the focus is on subject matter knowledge, the article addressed the character of that knowledge rather than the content of that knowledge. Types of knowledge identified in the literature include conceptual understanding of the subject, pedagogical content knowledge, beliefs about the nature of work in science and mathematics, attitudes toward these subjects, and actual teaching practices with students. The literature is incomplete with respect to which of these is relatively more or relatively less important. © 1998 John Wiley & Sons, Inc. J Res Sci Teach 35: 249263, 1998. Although the United States does not have a national curriculum, many organizations are working together to achieve an agreedupon set of goals for science and mathematics teaching and learning. Contemporary education leaders in general, and science and mathematics leaders in particular, have distinct ideas about the best directions for K12 science and mathematics education, and distinct ideas about teachers and teacher education that follow from these goals. This article examines these proposals and outlines the kinds of subject matter knowledge that teachers need to learn during their higher education in science and mathematics. For the analysis
Mathematics teachers belief and curriculum reform
 Mathematics Education Research Journal
, 2003
"... This paper discusses the role of mathematics teachers ’ beliefs and their impact on curriculum reform. It is argued that teachers ’ beliefs about the teaching and learning mathematics are critical in determining the pace of curriculum reform. Educational change is a complex process in which teachers ..."
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This paper discusses the role of mathematics teachers ’ beliefs and their impact on curriculum reform. It is argued that teachers ’ beliefs about the teaching and learning mathematics are critical in determining the pace of curriculum reform. Educational change is a complex process in which teachers hold strong beliefs about the quality and the process of innovation. Curriculum implementation may only occur through sufferance as many teachers are suspicious of reform in mathematics education given its equivocal success over the past decades. It is not surprising then that many teachers, when they come to enact the curriculum in their classes, rely more on their own beliefs than on current trends in pedagogy. These beliefs, conservative as they might be, have their own rationality in the practical and daily nature of the teaching profession, and in the compelling influence of educational systems from which these teachers are paradoxically the social product. The literature indicates that many of these teachers hold behaviourist beliefs, a fact that has strong implications for the success of constructivistoriented curriculum reform. In general, studies of teachers’
Elementary teachers' mathematics subject knowledge: The Knowledge Quartet and the case of Naomi
 JOURNAL OF MATHEMATICS TEACHER EDUCATION
, 2005
"... This paper draws on videotapes of mathematics lessons prepared and conducted by preservice elementary teachers towards the end of their initial training at one university. The aim was to locate ways in which they drew on their knowledge of mathematics and mathematics pedagogy in their teaching. A ..."
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This paper draws on videotapes of mathematics lessons prepared and conducted by preservice elementary teachers towards the end of their initial training at one university. The aim was to locate ways in which they drew on their knowledge of mathematics and mathematics pedagogy in their teaching. A grounded approach to data analysis led to the identification of a ‘knowledge quartet’, with four broad dimensions, or ‘units’, through which mathematicsrelated knowledge of these beginning teachers could be observed in practice. We term the four units: foundation, transformation, connection and contingency. This paper describes how each of these units is characterised and analyses one of the videotaped lessons, showing how each dimension of the quartet can be identified in the lesson. We claim that the quartet can be used as a framework for lesson observation and for mathematics teaching development.