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Author : A. P. Rhodes
Publisher :
ISBN 13 :
Total Pages : 114 pages
Book Rating : 4.F/5 ( download)
Download or read book Problems Encountered in the Teaching of Algebra to Secondary School Pupils written by A. P. Rhodes and published by . This book was released on 1922 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Steve Rhine
Publisher : IAP
ISBN 13 : 1641134135
Total Pages : 351 pages
Book Rating : 4.6/5 (411 download)
Download or read book How Students Think When Doing Algebra written by Steve Rhine and published by IAP. This book was released on 2018-11-01 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra is the gateway to college and careers, yet it functions as the eye of the needle because of low pass rates for the middle school/high school course and students’ struggles to understand. We have forty years of research that discusses the ways students think and their cognitive challenges as they engage with algebra. This book is a response to the National Council of Teachers of Mathematics’ (NCTM) call to better link research and practice by capturing what we have learned about students’ algebraic thinking in a way that is usable by teachers as they prepare lessons or reflect on their experiences in the classroom. Through a Fund for the Improvement of Post-Secondary Education (FIPSE) grant, 17 teachers and mathematics educators read through the past 40 years of research on students’ algebraic thinking to capture what might be useful information for teachers to know—over 1000 articles altogether. The resulting five domains addressed in the book (Variables & Expressions, Algebraic Relations, Analysis of Change, Patterns & Functions, and Modeling & Word Problems) are closely tied to CCSS topics. Over time, veteran math teachers develop extensive knowledge of how students engage with algebraic concepts—their misconceptions, ways of thinking, and when and how they are challenged to understand—and use that knowledge to anticipate students’ struggles with particular lessons and plan accordingly. Veteran teachers learn to evaluate whether an incorrect response is a simple error or the symptom of a faulty or naïve understanding of a concept. Novice teachers, on the other hand, lack the experience to anticipate important moments in the learning of their students. They often struggle to make sense of what students say in the classroom and determine whether the response is useful or can further discussion (Leatham, Stockero, Peterson, & Van Zoest 2011; Peterson & Leatham, 2009). The purpose of this book is to accelerate early career teachers’ “experience” with how students think when doing algebra in middle or high school as well as to supplement veteran teachers’ knowledge of content and students. The research that this book is based upon can provide teachers with insight into the nature of a student’s struggles with particular algebraic ideas—to help teachers identify patterns that imply underlying thinking. Our book, How Students Think When Doing Algebra, is not intended to be a “how to” book for teachers. Instead, it is intended to orient new teachers to the ways students think and be a book that teachers at all points in their career continually pull of the shelf when they wonder, “how might my students struggle with this algebraic concept I am about to teach?” The primary audience for this book is early career mathematics teachers who don’t have extensive experience working with students engaged in mathematics. However, the book can also be useful to veteran teachers to supplement their knowledge and is an ideal resource for mathematics educators who are preparing preservice teachers.
Author : Sinan Kanbir
Publisher : Springer
ISBN 13 : 3319592041
Total Pages : 339 pages
Book Rating : 4.3/5 (195 download)
Download or read book Using Design Research and History to Tackle a Fundamental Problem with School Algebra written by Sinan Kanbir and published by Springer. This book was released on 2017-10-28 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this well-illustrated book the authors, Sinan Kanbir, Ken Clements, and Nerida Ellerton, tackle a persistent, and universal, problem in school mathematics—why do so many middle-school and secondary-school students find it difficult to learn algebra well? What makes the book important are the unique features which comprise the design-research approach that the authors adopted in seeking a solution to the problem. The first unique feature is that the authors offer an overview of the history of school algebra. Despite the fact that algebra has been an important component of secondary-school mathematics for more than three centuries, there has never been a comprehensive historical analysis of factors influencing the teaching and learning of that component. The authors identify, through historical analysis, six purposes of school algebra: (a) algebra as a body of knowledge essential to higher mathematical and scientific studies, (b) algebra as generalized arithmetic, (c) algebra as a prerequisite for entry to higher studies, (d) algebra as offering a language and set of procedures for modeling real-life problems, (e) algebra as an aid to describing structural properties in elementary mathematics, and (f) algebra as a study of variables. They also raise the question whether school algebra represents a unidimensional trait. Kanbir, Clements and Ellerton offer an unusual hybrid theoretical framework for their intervention study (by which seventh-grade students significantly improved their elementary algebra knowledge and skills). Their theoretical frame combined Charles Sanders Peirce’s triadic signifier-interpretant-signified theory, which is in the realm of semiotics, with Johann Friedrich Herbart’s theory of apperception, and Ken Clements’ and Gina Del Campo’s theory relating to the need to expand modes of communications in mathematics classrooms so that students engage in receptive and expressive modes. Practicing classroom teachers formed part of the research team. This book appears in Springer’s series on the “History of Mathematics Education.” Not only does it include an important analysis of the history of school algebra, but it also adopts a theoretical frame which relies more on “theories from the past,” than on contemporary theories in the field of mathematics education. The results of the well-designed classroom intervention are sufficiently impressive that the study might havecreated and illuminated a pathway for future researchers to take.
Author : Sigrid Wagner
Publisher : Routledge
ISBN 13 : 1135434212
Total Pages : 307 pages
Book Rating : 4.1/5 (354 download)
Download or read book Research Issues in the Learning and Teaching of Algebra written by Sigrid Wagner and published by Routledge. This book was released on 2018-12-07 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 1989. Routledge is an imprint of Taylor & Francis, an informa company.
Author : Sigrid Wagner
Publisher : Routledge
ISBN 13 :
Total Pages : 318 pages
Book Rating : 4.F/5 ( download)
Download or read book Research Issues in the Learning and Teaching of Algebra written by Sigrid Wagner and published by Routledge. This book was released on 1989 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 1989. Routledge is an imprint of Taylor & Francis, an informa company.
Author : Sherry Parrish
Publisher : Math Solutions
ISBN 13 : 1935099116
Total Pages : 434 pages
Book Rating : 4.9/5 (35 download)
Download or read book Number Talks written by Sherry Parrish and published by Math Solutions. This book was released on 2010 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A multimedia professional learning resource"--Cover.
Author : Alfred S. Posamentier
Publisher : ASCD
ISBN 13 : 1416605967
Total Pages : 242 pages
Book Rating : 4.4/5 (166 download)
Download or read book Exemplary Practices for Secondary Math Teachers written by Alfred S. Posamentier and published by ASCD. This book was released on 2007-03-15 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every year new secondary mathematics teachers take up positions in middle and high schools. The luckiest novices receive assistance from a coach or mentor: a master mathematics teacher who makes constructive comments, models effective approaches, and illuminates other practical aspects of teaching secondary math. But many new teachers don't have this advantage and must further their development on their own. If you are one of these teachers, this is the book you need. In these pages, veteran mathematics educators Alfred S. Posamentier, Daniel Jaye, and Stephen Krulik present a treasure chest of ideas to guide new secondary math teachers through the challenging first few months and also provide more experienced teachers with interesting alternatives to familiar methods. The topics covered include * The most effective instructional practices * The best uses of the textbook * Designing successful lessons * Creating homework that promotes learning * Incorporating challenge * Teaching reasoning and problem solving * Strategies for assessment and grading * Specific innovative ideas for teaching key concepts * Options for extracurricular activities * Long-term professional enrichment and growth. It's during the first few years of a teacher's experience that he or she develops the habits, methods, procedures, and techniques that tend to define a career. Exemplary Practices for Secondary Math Teachers provides both a foundation for excellence and a touchstone for years to come. Note: This product listing is for the Adobe Acrobat (PDF) version of the book.
Author : Sue Johnston-Wilder
Publisher : Routledge
ISBN 13 : 1317704428
Total Pages : 348 pages
Book Rating : 4.3/5 (177 download)
Download or read book Learning to Teach Mathematics in the Secondary School written by Sue Johnston-Wilder and published by Routledge. This book was released on 2010-09-13 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the role of mathematics in the secondary classroom? What is expected of a would-be maths teacher? How is mathematics best taught and learnt? Learning to Teach Mathematics in the Secondary School combines theory and practice to present a broad introduction to the opportunities and challenges of teaching mathematics in the modern secondary school classroom. Written specifically with the new and student teacher in mind, the book covers a wide range of issues related to the teaching of mathematics, including: The role of ICT Assessment for Learning NEW Using mathematics in context NEW Communicating mathematically Planning mathematics lessons Including special-needs pupils Teaching mathematics post-16 Professional Development Already a major text for many university teaching courses, this fully revised third edition takes into account new developments in the National Curriculum as well as recent changes to the standards for Qualified Teacher Status. Featuring two brand new chapters, a glossary of useful terms, addresses for resources and organisations, and tasks designed to prompt critical reflection and support thinking and writing at Masters level, this book will help you make the most of school experience, during your training and beyond. Designed for use as a core textbook, this new edition of Learning to Teach Mathematics in the Secondary School provides essential guidance and advice for all trainee and practising teachers of secondary mathematics.
Author : Great Britain. Committee of Inquiry into the Teaching of Mathematics in Schools
Publisher : Stationery Office Books (TSO)
ISBN 13 :
Total Pages : 332 pages
Book Rating : 4.:/5 (31 download)
Download or read book Mathematics Counts written by Great Britain. Committee of Inquiry into the Teaching of Mathematics in Schools and published by Stationery Office Books (TSO). This book was released on 1982 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: SUMMARY: Recommendations on the teaching of mathematics in primary & secondary schools in England & Wales, with particular regard to the mathematics required in further & higher education, employment & adult life generally.
Author : Stephen Mubanga
Publisher : GRIN Verlag
ISBN 13 : 3346508676
Total Pages : 138 pages
Book Rating : 4.3/5 (465 download)
Download or read book Teachers' classroom practices in addressing learners' errors in algebraic word problems written by Stephen Mubanga and published by GRIN Verlag. This book was released on 2021-10-08 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master's Thesis from the year 2020 in the subject Pedagogy - School Pedagogics, University of Zambia (Postgraduate studies), course: Master of Mathematics Education, language: English, abstract: The study explored teachers’ classroom practices in addressing learners’ errors regarding how they engaged grade eight learners in reading; how they probed learners’ understanding; and what they did to enhance learners’ process skills and encoding abilities in algebraic word problems. Five teachers and twenty five learners (in five focus groups discussions of five members each), at three secondary schools in Isoka district of Muchinga province, Zambia were purposively sampled to participate in the study. The study used a qualitative approach which followed a descriptive case study design. Data collection was done using lesson observations, semi-structured interviews, document analysis and focus group discussions. To capture observations and interviews in totality, video and audio recordings were used respectively. Thematic analysis was used to analyse data. The five performance strategies of solving word problems by Newman namely; reading ability, comprehension ability, transformation ability, process skills and encoding ability guided the analysis of data. The study was guided by the following research questions: How do teachers engage learners in reading algebraic word problems? How do teachers probe learners’ understanding of algebraic word problems? What do teachers do to enhance learners’ process skills and encoding abilities in algebraic word problems?
Author : Daniel Chazan
Publisher : Teachers College Press
ISBN 13 : 9780807739181
Total Pages : 222 pages
Book Rating : 4.7/5 (391 download)
Download or read book Beyond Formulas in Mathematics and Teaching written by Daniel Chazan and published by Teachers College Press. This book was released on 2000-01-01 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the author’s experience as a researcher and teacher of lower-track students, Beyond Formulas in Mathematics and Teaching illuminates the complex dynamics of the algebra classroom. From within this setting, Daniel Chazan thoughtfully explores topics that concern all dedicated educators, how to really know one’s students, how to find engaging material, and how to inspire meaningful classroom conversations. Throughout, he addresses the predicaments that are central to the lives of teachers who work in standard educational settings. By highlighting teaching dilemmas, Chazan prompts readers to consider what their own responses would be in similar situations. With an eye to ways of restructuring roles and relationships, Beyond Formulas in Mathematics and Teaching is essential reading for educators seeking to enhance their teaching practices and understanding of students who may be estranged from school.
Author : Juergen Maasz
Publisher : Springer Science & Business Media
ISBN 13 : 9460915434
Total Pages : 283 pages
Book Rating : 4.4/5 (69 download)
Download or read book Real-World Problems for Secondary School Mathematics Students written by Juergen Maasz and published by Springer Science & Business Media. This book was released on 2011-10-30 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book full of ideas for introducing real world problems into mathematics classrooms and assisting teachers and students to benefit from the experience. Taken as a whole these contributions provide a rich resource for mathematics teachers and their students that is readily available in a single volume. Nowadays there is a universal emphasis on teaching for understanding, motivating students to learn mathematics and using real world problems to improve the mathematics experience of school students. However, using real world problems in mathematics classrooms places extra demands on teachers in terms of extra-mathematical knowledge e.g. knowledge of the area of applications, and pedagogical knowledge. Care must also be taken to avoid overly complex situations and applications. Papers in this collection offer a practical perspective on these issues, and more. While many papers offer specific well worked out lesson type ideas, others concentrate on the teacher knowledge needed to introduce real world applications of mathematics into the classroom. We are confident that mathematics teachers who read the book will find a myriad of ways to introduce the material into their classrooms whether in ways suggested by the contributing authors or in their own ways, perhaps through mini-projects or extended projects or practical sessions or enquiry based learning. We are happy if they do! This book is written for mathematics classroom teachers and their students, mathematics teacher educators, and mathematics teachers in training at pre-service and in-service phases of their careers.
Author : Bradley S. Witzel
Publisher : Council For Exceptional Children
ISBN 13 : 0865865086
Total Pages : 200 pages
Book Rating : 4.8/5 (658 download)
Download or read book Bridging the Gap Between Arithmetic & Algebra written by Bradley S. Witzel and published by Council For Exceptional Children. This book was released on 2015-11-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although two federal panels have concluded that all students can learn mathematics and most can succeed through Algebra 2, the abstractness of algebra and missing precursor understandings may be overwhelming to many students … and their teachers. Bridging the Gap Between Arithmetic & Algebra responds to this need for instruction and interventions that go beyond typical math lesson plans. Providing a review of evidence-based practices, the book is an essential reference for mathematics teachers and special education teachers when teaching mathematics to students who struggle with the critical concepts and skills necessary for success in algebra. Audiences: General education (mathematics) teachers, special education teachers, administrators, teacher educators.
Author : Carol Ann Tomlinson
Publisher : ASCD
ISBN 13 : 141660376X
Total Pages : 209 pages
Book Rating : 4.4/5 (166 download)
Download or read book Integrating Differentiated Instruction and Understanding by Design written by Carol Ann Tomlinson and published by ASCD. This book was released on 2006-01-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teachers struggle every day to bring quality instruction to their students. Beset by lists of content standards and accompanying "high-stakes" accountability tests, many educators sense that both teaching and learning have been redirected in ways that are potentially impoverishing for those who teach and those who learn. Educators need a model that acknowledges the centrality of standards but also ensures that students truly understand content and can apply it in meaningful ways. For many educators, Understanding by Design addresses that need. Simultaneously, teachers find it increasingly difficult to ignore the diversity of the learners who populate their classrooms. Few teachers find their work effective or satisfying when they simply "serve up" a curriculum—even an elegant one—to students with no regard for their varied learning needs. For many educators, Differentiated Instruction offers a framework for addressing learner variance as a critical component of instructional planning. In this book the two models converge, providing readers fresh perspectives on two of the greatest contemporary challenges for educators: crafting powerful curriculum in a standards-dominated era and ensuring academic success for the full spectrum of learners. Each model strengthens the other. Understanding by Design is predominantly a curriculum design model that focuses on what we teach. Differentiated Instruction focuses on whom we teach, where we teach, and how we teach. Carol Ann Tomlinson and Jay McTighe show you how to use the principles of backward design and differentiation together to craft lesson plans that will teach essential knowledge and skills for the full spectrum of learners. Connecting content and kids in meaningful ways is what teachers strive to do every day. In tandem, UbD and DI help educators meet that goal by providing structures, tools, and guidance for developing curriculum and instruction that bring to students the best of what we know about effective teaching and learning.
Author : Jo Boaler
Publisher :
ISBN 13 :
Total Pages : 180 pages
Book Rating : 4.F/5 ( download)
Download or read book Experiencing School Mathematics written by Jo Boaler and published by . This book was released on 1997 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book of its kind to provide direct evidence for the effectiveness of traditional and progressive teaching methods. It reports on careful and extensive case studies of two schools which taught mathematics in totally different ways. Three hundred students were followed over three years and the interviews that are reproduced in the book give compelling insights into what it meant to be a student in the classrooms of the two schools. The different school approaches are compared and analyzed using student interviews, lesson observations, questionnaires given to students and staff and a range of different assessments, including GCSE examinations. Questions are raised about the effectiveness of different teaching methods in preparing students for the demands of the 'real world' and the 21st century, the impact of setted and mixed ability teaching upon student attitude and achievement, and gender and learning styles. New evidence is provided for each of these issues. The book draws some radical new conclusions about the ways that traditional teaching methods lead to limited forms of knowledge that are ineffective in non-school settings. The book will be essential reading for math teachers, parents, and policy makers in education.
Author : Alexander Karp
Publisher : IAP
ISBN 13 : 1623968143
Total Pages : 456 pages
Book Rating : 4.6/5 (239 download)
Download or read book Mathematics in Middle and Secondary School written by Alexander Karp and published by IAP. This book was released on 2014-11-01 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The experience and knowledge acquired in teacher education courses should build important fundamentals for the future teaching of mathematics. In particular, experience in mathematical problem solving, and in planning lessons devoted to problem solving, is an essential component of teacher preparation. This book develops a problem solving approach and is intended to be a text used in mathematics education courses (or professional development) for pre-service or in-service middle and secondary school teachers. It can be used both in graduate and undergraduate courses, in accordance with the focus of teacher preparation programs. The content of the book is suited especially for those students who are further along in their mathematics education preparation, as the text is more involved with mathematical ideas and problem solving, and discusses some of the intricate pedagogical considerations that arise in teaching. The text is written not as an introduction to mathematics education (a first course), but rather as a second, or probably, third course. The book deals both with general methodology issues in mathematics education incorporating a problem solving approach (Chapters 1-6) and with more concrete applications within the context of specific topics – algebra, geometry, and discrete mathematics (Chapters 7-13). The book provides opportunities for teachers to engage in authentic mathematical thinking. The mathematical ideas under consideration build on specific middle and secondary school content while simultaneously pushing the teacher to consider more advanced topics, as well as various connections across mathematical domains. The book strives to preserve the spirit of discussion, and at times even argument, typical of collaborative work on a lesson plan. Based on the accumulated experience of work with future and current teachers, the book assumes that students have some background in lesson planning, and extends their thinking further. Specifically, this book aims to provide a discussion of how a lesson plan is constructed, including the ways in which problems are selected or invented, rather than the compilation of prepared lesson plans. This approach reflects the authors’ view that the process of searching for an answer is often more important than the formal result.
Author : Paul Drijvers
Publisher : Springer Science & Business Media
ISBN 13 : 9460913342
Total Pages : 229 pages
Book Rating : 4.4/5 (69 download)
Download or read book Secondary Algebra Education: Revisiting Topics and Themes and Exploring the Unknown written by Paul Drijvers and published by Springer Science & Business Media. This book was released on 2011-10-19 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays, algebra education is subject to worldwide scrutiny. Different opinions on its goals, approaches and achievements are at the heart of debates among teachers, educators, researchers and decision makers. What should the teaching of algebra in secondary school mathematics look like? Should it focus on procedural skills or on algebraic insight? Should it stress practice or integrate technology? Do we require formal proofs and notations, or do informal representations suffice? Is algebra in school an abstract subject, or does it take its relevance from application in (daily life) contexts? What should secondary school algebra education that prepares for higher education and professional practice in the twenty-first century look like? This book addresses these questions, and aims to inform in-service and future teachers, mathematics educators and researchers on recent insights in the domain, and on specific topics and themes such as the historical development of algebra, the role of productive practice, and algebra in science and engineering in particular. The authors, all affiliated with the Freudenthal Institute for Science and Mathematics Education in the Netherlands, share a common philosophy, which acts as a ? sometimes nearly invisible ? backbone for the overall view on algebra education: the theory of realistic mathematics education. From this point of departure, different perspectives are chosen to describe the opportunities and pitfalls of today’s and tomorrow’s algebra education. Inspiring examples and reflections illustrate current practice and explore the unknown future of algebra education to appropriately meet students’ needs.
