Refining The Mathematics Knowledge Base

Author : Bindu Elizabeth Pothen
Publisher : Stanford University
ISBN 13 :
Total Pages : 253 pages
Book Rating : 4.92/5 ( download)

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Download or read book Refining the Mathematics Knowledge Base written by Bindu Elizabeth Pothen and published by Stanford University. This book was released on 2011 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the knowledge that teachers must bring to their classrooms is critical to the advancement of the field of teacher education. Understanding how teacher knowledge impacts various aspects of teacher practice is also critical. Understanding the interplay between teacher knowledge and practice, and consequently the result that this relationship has on student learning is most important. This dissertation attempts to advance our collective understanding of the complex relationship between teacher knowledge, teacher practice, and student learning in the field of elementary mathematics. Four third-grade teachers were followed as they taught a subset of lessons in a unit on fractions. The study first investigates the types of knowledge that the teachers brought to their classrooms. Then, an examination is conducted of the way in which these types of knowledge impacted their teaching practice. Finally, the student learning that resulted over the course of these lessons is discussed. This study supports the widespread belief that teacher knowledge is important to instruction. The descriptions of the case study teachers highlight that their varying levels of knowledge resulted in unique aspects of practice being emphasized in their classrooms. This dissertation documents the differences in teaching practice and the trade-offs that produce differences in student learning. Interesting student learning patterns emerged, based on qualitative student interviews. Medium students from classrooms in which teachers focused for more sustained periods on mathematical concepts seemed to demonstrate greater procedural fluency and deeper conceptual understanding than their peers in the other classrooms. Low students in classrooms where fluency was the focus seemed to show slightly greater procedural fluency, though less conceptual understanding, than their peers in the classrooms that spent more time on concepts. High students showed no appreciable difference across all classrooms. This study adds to the field by introducing a new construct, the conceptual threshold, to offer an explanation of these student learning trends.

Author : Bindu Elizabeth Pothen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.75/5 ( download)

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Download or read book Refining the Mathematics Knowledge Base written by Bindu Elizabeth Pothen and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the knowledge that teachers must bring to their classrooms is critical to the advancement of the field of teacher education. Understanding how teacher knowledge impacts various aspects of teacher practice is also critical. Understanding the interplay between teacher knowledge and practice, and consequently the result that this relationship has on student learning is most important. This dissertation attempts to advance our collective understanding of the complex relationship between teacher knowledge, teacher practice, and student learning in the field of elementary mathematics. Four third-grade teachers were followed as they taught a subset of lessons in a unit on fractions. The study first investigates the types of knowledge that the teachers brought to their classrooms. Then, an examination is conducted of the way in which these types of knowledge impacted their teaching practice. Finally, the student learning that resulted over the course of these lessons is discussed. This study supports the widespread belief that teacher knowledge is important to instruction. The descriptions of the case study teachers highlight that their varying levels of knowledge resulted in unique aspects of practice being emphasized in their classrooms. This dissertation documents the differences in teaching practice and the trade-offs that produce differences in student learning. Interesting student learning patterns emerged, based on qualitative student interviews. Medium students from classrooms in which teachers focused for more sustained periods on mathematical concepts seemed to demonstrate greater procedural fluency and deeper conceptual understanding than their peers in the other classrooms. Low students in classrooms where fluency was the focus seemed to show slightly greater procedural fluency, though less conceptual understanding, than their peers in the classrooms that spent more time on concepts. High students showed no appreciable difference across all classrooms. This study adds to the field by introducing a new construct, the conceptual threshold, to offer an explanation of these student learning trends.

Author : Allen Ginsberg
Publisher : Pitman Publishing
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.41/5 ( download)

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Download or read book Automatic Refinement of Expert System Knowledge Bases written by Allen Ginsberg and published by Pitman Publishing. This book was released on 1988 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Maggie B. McGatha
Publisher : IAP
ISBN 13 : 1681238241
Total Pages : 253 pages
Book Rating : 4.41/5 ( download)

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Download or read book Elementary Mathematics Specialists written by Maggie B. McGatha and published by IAP. This book was released on 2017-02-01 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary mathematics specialists are teacher leaders who are responsible for supporting effective PK–6 mathematics instruction and student learning. The Association of Mathematics Teacher Educators (AMTE), the Association of State Supervisors of Mathematics, the National Council of Supervisors of Mathematics, and the National Council of Teachers of Mathematics, in a 2010 joint position paper on Elementary Mathematics Specialists (EMSs), all advocate for the use of EMSs to support the teaching and learning of mathematics. The specific roles and expectations of EMSs will vary according to the needs of each setting, “but their expertise and successful experience at the elementary level is critical” (p 1). Elementary Mathematics Specialists: Developing, Refining, and Examining Programs that Support Mathematics Teaching and Learning is AMTE’s latest resource supporting the important work of EMSs. It has five sections related to the preparation and professional development of EMSs: (a) Overview and Current State of Affairs; (b) Models of EMS Program Development & Delivery; (c) Supporting EMSs in the Field; (d) The Mathematics Specialist Research; and (e) Future Directions. The book provides support to EMS practitioners, program providers/developers, and researchers seeking to answer important questions about how to prepare Mathematics Specialists, support them in the field, and research their effectiveness.

Author : Tonya Gau Bartell
Publisher : Springer
ISBN 13 : 3030210170
Total Pages : 181 pages
Book Rating : 4.75/5 ( download)

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Download or read book Transforming Mathematics Teacher Education written by Tonya Gau Bartell and published by Springer. This book was released on 2019-08-01 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book builds on the Teachers Empowered to Advance Change in Mathematics (TEACH Math) project, which was an initiative that sought to develop a new generation of preK-8 mathematics teachers to connect mathematics, children’s mathematical thinking, and community and family knowledge in mathematics instruction – or what we have come to call children’s multiple mathematical knowledge bases in mathematics instruction, with an explicit focus on equity. Much of the work involved in the TEACH Math project included the development of three instructional modules for preK-8 mathematics methods courses to support the project’s goals. These activities were used and refined over eight semesters, and in Fall 2014 shared at a dissemination conference with other mathematics teacher educators from a variety of universities across the United States. Chapter contributions represent diverse program and geographical contexts and teach prospective and practicing teachers from a variety of socioeconomic and ethnic backgrounds, in particular providing accounts of supports, challenges, and tensions in implementing equity-based mathematics teacher education. The chapters supply rich evidence and illustrative examples of how other mathematics teacher educators and professional developers might make the modules work for their unique practices, courses, workshops, and prospective teachers/teachers. It promises to be an important resource for offering guidance and examples to those working with prospective teachers of mathematics who want to create positive, culturally responsive, and equity-based mathematics experiences for our nation’s youth.

Author : Michael Kohlhase
Publisher : Springer
ISBN 13 : 3540314318
Total Pages : 414 pages
Book Rating : 4.18/5 ( download)

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Download or read book Mathematical Knowledge Management written by Michael Kohlhase and published by Springer. This book was released on 2006-01-20 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 4th International Conference on Mathematical Knowledge Management. The 26 revised full papers presented were carefully selected during two rounds of reviewing and improvement from 38 submissions. The papers cover mathematical knowledge management. Topics range from foundations and the representational and document-structure aspects of mathematical knowledge, over process questions like authoring, migration, and consistency management by automated theorem proving to applications in e-learning and case studies.

Author : Agida Manizade
Publisher : Springer Nature
ISBN 13 : 3031311930
Total Pages : 380 pages
Book Rating : 4.32/5 ( download)

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Download or read book The Evolution of Research on Teaching Mathematics written by Agida Manizade and published by Springer Nature. This book was released on 2023-09-11 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book investigates current issues related to the evolution of research on teaching mathematics and examines up to thirty years of presage-process-product research (PPPR) in mathematics with respect to conceptualization, instrumentation, and design. The book discusses the theoretical and methodological challenges associated with PPPR, critically reviews current research, and explores the likely direction of further developments to identify future paths for research on high-quality mathematics teaching in the digital era. Subjects that are covered in this work focus on the relationships between 1) student learning outcomes measured upon completion of the mathematics teaching; 2) student learning activities in the classroom; 3) interactive mathematics teacher activities, and best practices in mathematics classrooms conducted in the presence of students; 4) pre-post-active mathematics teacher activities such as planning, assessment, and other teaching-related activities outside of the classroom; 5) mathematics teachers’ competencies, knowledge, and skills; and 6) mathematics teachers’ characteristics, including beliefs, attitudes, and motivation. This book discusses the evolution of such research in mathematics teaching and teacher education in the digital era and is of interest to researchers exploring the field of mathematics teaching and mathematics teacher education as well as educators.

Author : Fernando Hitt
Publisher : American Mathematical Soc.
ISBN 13 : 0821849964
Total Pages : 277 pages
Book Rating : 4.65/5 ( download)

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Download or read book Research in Collegiate Mathematics Education VII written by Fernando Hitt and published by American Mathematical Soc.. This book was released on 2010-03-05 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume of Research in Collegiate Mathematics Education, like previous volumes in this series, reflects the importance of research in mathematics education at the collegiate level. The editors in this series encourage communication between mathematicians and mathematics educators, and as pointed out by the International Commission of Mathematics Instruction (ICMI), much more work is needed in concert with these two groups. Indeed, editors of RCME are aware of this need and the articles published in this series are in line with that goal. Nine papers constitute this volume. The first two examine problems students experience when converting a representation from one particular system of representations to another. The next three papers investigate students learning about proofs. In the next two papers, the focus is instructor knowledge for teaching calculus. The final two papers in the volume address the nature of ``conception'' in mathematics. Whether they are specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas that they can use.

Author : Andrea Asperti
Publisher : Springer Science & Business Media
ISBN 13 : 3540364692
Total Pages : 230 pages
Book Rating : 4.96/5 ( download)

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Download or read book Mathematical Knowledge Management written by Andrea Asperti and published by Springer Science & Business Media. This book was released on 2007-10-28 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Mathematical Knowledge Management, MKM 2003, held in Betinoro, Italy, in February 2003. The 16 revised full papers presented together with an invited paper were carefully reviewed and selected for presentation. Among the topics addressed are digitization, representation, formalization, proof assistants, distributed libraries of mathematics, NAG library, LaTeX, MathML, mathematics markup, theorem description, query languages for mathematical metadata, mathematical information retrieval, XML-based mathematical knowledge processing, semantic Web, mathematical content management, formalized mathematics repositories, theorem proving, and proof theory.

Author : Tim Rowland
Publisher : Springer Science & Business Media
ISBN 13 : 904819766X
Total Pages : 300 pages
Book Rating : 4.68/5 ( download)

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Download or read book Mathematical Knowledge in Teaching written by Tim Rowland and published by Springer Science & Business Media. This book was released on 2011-01-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quality of primary and secondary school mathematics teaching is generally agreed to depend crucially on the subject-related knowledge of the teacher. However, there is increasing recognition that effective teaching calls for distinctive forms of subject-related knowledge and thinking. Thus, established ways of conceptualizing, developing and assessing mathematical knowledge for teaching may be less than adequate. These are important issues for policy and practice because of longstanding difficulties in recruiting teachers who are confident and conventionally well-qualified in mathematics, and because of rising concern that teaching of the subject has not adapted sufficiently. The issues to be examined in Mathematical Knowledge in Teaching are of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing more effective approaches to characterizing, assessing and developing mathematical knowledge for teaching.