Problems Encountered in the Teaching of Algebra to Secondary School Pupils PDF Download
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Author: A. P. Rhodes
Publisher:
ISBN:
Category :
Languages : en
Pages : 114
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Book Description
Author: A. P. Rhodes
Publisher:
ISBN:
Category :
Languages : en
Pages : 114
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Book Description
Author: Steve Rhine
Publisher: IAP
ISBN: 1641134135
Category : Education
Languages : en
Pages : 351
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Book Description
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: Sherry Parrish
Publisher: Math Solutions
ISBN: 1935099116
Category : Education
Languages : en
Pages : 434
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Book Description
"A multimedia professional learning resource"--Cover.
Author: Sinan Kanbir
Publisher: Springer
ISBN: 3319592041
Category : Education
Languages : en
Pages : 339
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Book Description
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: 1135434212
Category : Education
Languages : en
Pages : 286
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Book Description
First Published in 1989. Routledge is an imprint of Taylor & Francis, an informa company.
Author: Sigrid Wagner
Publisher: Routledge
ISBN:
Category : Education
Languages : en
Pages : 318
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Book Description
First Published in 1989. Routledge is an imprint of Taylor & Francis, an informa company.
Author: Alfred S. Posamentier
Publisher: ASCD
ISBN: 1416605967
Category : Education
Languages : en
Pages : 242
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Book Description
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: Carol Ann Tomlinson
Publisher: ASCD
ISBN: 141660376X
Category : Education
Languages : en
Pages : 209
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Book Description
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: Stephen Mubanga
Publisher: GRIN Verlag
ISBN: 3346508676
Category : Education
Languages : en
Pages : 138
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Book Description
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: Sue Johnston-Wilder
Publisher: Routledge
ISBN: 1317704428
Category : Education
Languages : en
Pages : 348
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Book Description
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.
