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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 ' mathemat ..."
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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
Teaching With The Web: Challenges In A Complex Information Space
"... this paper. 3/1/99 Wallace Proposal Page 28 http://wwwpersonal.umich.edu/~ravenmw/wallaceproposal.pdf ..."
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this paper. 3/1/99 Wallace Proposal Page 28 http://wwwpersonal.umich.edu/~ravenmw/wallaceproposal.pdf
Content or Process as Approaches to Technology Curriculum: Does It Matter Come Monday Morning?
"... Process approaches and their justification are next examined and critiqued. A discussion follows in which the competing rationales, arguments, and counterarguments are reflected upon. Whether the tensions here are of any significance come Monday morning in the typical technology education classroom ..."
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Process approaches and their justification are next examined and critiqued. A discussion follows in which the competing rationales, arguments, and counterarguments are reflected upon. Whether the tensions here are of any significance come Monday morning in the typical technology education classroom or laboratory provides the basis for concluding comment. ____________________________ Theodore Lewis (lewis007@maroon.tc.umn.edu) is a Professor in Industrial Education, College of Education and Human Development, University of Minnesota, St. Paul. 46 The Perennial Search for Conceptual Structure The recent publication of the curriculum document Technology for All Americans, in which a rationale and structure for the study of technology is set forth (International Technology Education Association, 1996), is evidence that the subject matter and conceptual structure of technology education still remains an unsettled issue and a preoccupation of leaders of the field in the United States.
National Education Association
"... July 2006The views presented in this publication should not be construed as representing the policy or position of the National Education Association. The publication expresses the views of its authors and is intended to facilitate informed discussion by educators, policymakers, and others intereste ..."
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July 2006The views presented in this publication should not be construed as representing the policy or position of the National Education Association. The publication expresses the views of its authors and is intended to facilitate informed discussion by educators, policymakers, and others interested in educational reform. A limited supply of complimentary copies of this publication is available from NEA Research for NEA state and local associations, and UniServ staff. Additional copies may be purchased from
WHAT IS THE PHILOSOPHY OF MATHEMATICS EDUCATION?
"... This question (what is the philosophy of mathematics education?) provokes a number of reactions, even before one tries to answer it. Is it a philosophy of mathematics education, or is it the philosophy of mathematics education? Use of the preposition ‘a ’ suggests that what is being offered is one o ..."
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This question (what is the philosophy of mathematics education?) provokes a number of reactions, even before one tries to answer it. Is it a philosophy of mathematics education, or is it the philosophy of mathematics education? Use of the preposition ‘a ’ suggests that what is being offered is one of several such perspectives, practices or areas of study. Use of the definite article ‘the ’ suggests to some the arrogation of definitiveness to the account given. 1 In other words, it is the dominant or otherwise unique account of philosophy of mathematics education. However, an alternative reading is that ‘the ’ refers to a definite area of enquiry, a specific domain, within which one account is offered. So the philosophy of mathematics education need not be a dominant interpretation so much as an area of study, an area of investigation, and hence something with this title can be an exploratory assay into this area. This is what I intend here. Moving beyond the first word, there is the more substantive question of the reference of the term ‘philosophy of mathematics education’. There is a narrow sense that can be applied in interpreting the words ‘philosophy ’ and ‘mathematics education’. The philosophy of some area or activity can be understood as its aims or rationale. Mathematics education understood
AT
"... This thesis explores the knowledge needed for teaching statistics through investigations at the primary (elementary) school level. Statistics has a relatively short history in the primary school curriculum, compared with mathematics. Recent research in statistics education has prompted a worldwide m ..."
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This thesis explores the knowledge needed for teaching statistics through investigations at the primary (elementary) school level. Statistics has a relatively short history in the primary school curriculum, compared with mathematics. Recent research in statistics education has prompted a worldwide move away from the teaching of statistical skills, towards a broader underpinning of statistical thinking and reasoning. New Zealand’s nationally mandated curriculum reflects this move. Consequently, little is known about the types of knowledge needed to teach statistics effectively. Ideas from two contemporary areas of research, namely teacher content knowledge in relation to mathematics, and statistical thinking, are incorporated into a new framework, for exploring knowledge for teaching statistics. The study’s methodological approach is based on Popper’s philosophy of realism, and the associated logic of learning approach for classroom research. Four primary teachers (in their second year of teaching) planned and taught a sequence of four or five lessons, which were videotaped. Following each lesson, a stimulated recall
Moving Toward More Authentic Proof Practices in Geometry
"... Various stakeholders in mathematics education have called for increasing the role of reasoning and proving in the school mathematics curriculum. There is some evidence that these recommendations have been taken seriously by mathematics educators and textbook developers. However, if we are truly to r ..."
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Various stakeholders in mathematics education have called for increasing the role of reasoning and proving in the school mathematics curriculum. There is some evidence that these recommendations have been taken seriously by mathematics educators and textbook developers. However, if we are truly to realize this goal, we must pose problems to students that allow them to play a greater role in proving. We offer nine such problems and discuss how using multiple proof representations moves us toward more authentic proof practices in geometry. Over the past few decades, proof has been given increased attention in many countries around the world (see, e.g., Knipping, 2004). This is primarily because proof is considered the basis of mathematical understanding and is essential for developing, establishing, and communicating mathematical
Integrating a Disciplinary View of Mathematics Into the Classroom
"... To know something in mathematics is not simply to be able to regurgitate facts or fluently perform a procedure. At the heart of the discipline is the notion that there is some underlying logic tying together all of these facts or skills and that, fundamentally, everything in mathematics should make ..."
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To know something in mathematics is not simply to be able to regurgitate facts or fluently perform a procedure. At the heart of the discipline is the notion that there is some underlying logic tying together all of these facts or skills and that, fundamentally, everything in mathematics should make sense. In particular, it should be possible to justify all of one's arguments and conclusions. This ability to justify is one of the essential components of knowing something in mathematics, and its importance is reflected in the expectation of absolute proof: A classical mathematical proof... begin[s] with a series of axioms … Then by arguing logically, stepbystep, it is possible to arrive at a conclusion. If the axioms are correct and the logic is flawless, then the conclusion will be undeniable. (Singh, 1997, p. 21) This is the desired standard of proof so that the conclusions may serve as the foundation for generating more knowledge. In particular, once a claim has been established as fact by way of proof, it is possible to use it to motivate and answer additional questions thereby advancing one's knowledge further. Thus, it is essential that the foundational claims be verified by sound logic. Intuition Although the desired final product is sound logical justification, that is not always the