The Process of Learning Mathematics
The Process of Learning Mathematics

Author: L. R. Chapman

Publisher: Elsevier

Published: 2013-10-22

Total Pages: 407

ISBN-13: 1483147584

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The Process of Learning Mathematics describes the process of learning mathematics and covers topics ranging from the nature of mathematics to the role of intuition and logic in mathematics; the thought processes involved in the teaching of mathematics; reflective intelligence and the use of symbols; and discovery as a way of learning mathematics. Computer-assisted instruction in mathematics is also considered. This book is comprised of 19 chapters and begins with a reflection on the nature of mathematics, followed by a discussion on the importance of intuition and logic in mathematics. The ideas of generalization, structure, approximations, and the evolution of some particular aspect of applied mathematics are then examined from the viewpoint of a teacher. Subsequent chapters deal with schematic learning; motivation and emotional and interpersonal factors; uses of programmed material in British schools and colleges; and structural apparatuses used in teaching mathematics. The Midlands Mathematical Experiment and the Nuffield Foundation Mathematics Teaching Project in Britain are also described. This monograph will be of interest to teachers and students of mathematics.

The Process of Learning Mathematics
The Process of Learning Mathematics

Author: L. R. Chapman

Publisher: Elsevier

Published: 2016-06-06

Total Pages: 409

ISBN-13: 1483140016

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The Process of Learning Mathematics is a collection of essays from a two-term course of intercollegiate lectures for students of B.Ed. degree. This collection starts with two different views on the nature of mathematics. One essay discusses the role of intuition in understanding mathematics, while another paper expounds on the role of logic. This book then discusses the generalization, structure, and approximations used in teaching mathematics, and emphasizes the problems of applied mathematics and technology pertaining to equations of motion, mathematical representation of physical phenomena, or in relations such as conservation of matter. One paper reviews Piaget's studies on the development of children's thinking process, noting that teachers should consider the level of thinking the pupil uses when designing his teaching material. Another essay deals with how the existing knowledge in a student can affect new kinds of learning through assimilation and accommodation. This book then describes the use of symbols and "reflective intelligence," addressing reflective activities, communication, and the contribution of symbols. This text then discusses computer-assisted education and several mathematical teaching or learning experiments. This compendium can prove useful for mathematics majors, educators, school administrators, and math teachers.

Visible Learning for Mathematics, Grades K-12
Visible Learning for Mathematics, Grades K-12

Author: John Hattie

Publisher: Corwin Press

Published: 2016-09-15

Total Pages: 209

ISBN-13: 1506362958

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Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.

Strengths-Based Teaching and Learning in Mathematics
Strengths-Based Teaching and Learning in Mathematics

Author: Beth McCord Kobett

Publisher: Corwin Press

Published: 2020-02-27

Total Pages: 189

ISBN-13: 1544374925

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"This book is a game changer! Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K- 6 goes beyond simply providing information by sharing a pathway for changing practice. . . Focusing on our students’ strengths should be routine and can be lost in the day-to-day teaching demands. A teacher using these approaches can change the trajectory of students’ lives forever. All teachers need this resource! Connie S. Schrock Emporia State University National Council of Supervisors of Mathematics President, 2017-2019 NEW COVID RESOURCES ADDED: A Parent’s Toolkit to Strengths-Based Learning in Math is now available on the book’s companion website to support families engaged in math learning at home. This toolkit provides a variety of home-based activities and games for families to engage in together. Your game plan for unlocking mathematics by focusing on students’ strengths. We often evaluate student thinking and their work from a deficit point of view, particularly in mathematics, where many teachers have been taught that their role is to diagnose and eradicate students’ misconceptions. But what if instead of focusing on what students don’t know or haven’t mastered, we identify their mathematical strengths and build next instructional steps on students’ points of power? Beth McCord Kobett and Karen S. Karp answer this question and others by highlighting five key teaching turnarounds for improving students’ mathematics learning: identify teaching strengths, discover and leverage students’ strengths, design instruction from a strengths-based perspective, help students identify their points of power, and promote strengths in the school community and at home. Each chapter provides opportunities to stop and consider current practice, reflect, and transfer practice while also sharing · Downloadable resources, activities, and tools · Examples of student work within Grades K–6 · Real teachers’ notes and reflections for discussion It’s time to turn around our approach to mathematics instruction, end deficit thinking, and nurture each student’s mathematical strengths by emphasizing what makes them each unique and powerful.

Reading and Writing to Learn Mathematics
Reading and Writing to Learn Mathematics

Author: Joseph G. R. Martinez

Publisher: Allyn & Bacon

Published: 2001

Total Pages: 260

ISBN-13:

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Shows K-6 teachers how to teach math using writing and reading lessons and activities in accordance with NCTM standard #2, math-as-communication. Includes classroom examples, lessons, activities, and stories for teachers to show how everyday language skills can transfer to math learning. Illustrates how to make writing a meaningful part of cognitive as well as affective development, how to use reading and writing in assessment of math sills, and how to make reading-math assignments more meaningful.

Helping Children Learn Mathematics
Helping Children Learn Mathematics

Author: National Research Council

Publisher: National Academies Press

Published: 2002-07-31

Total Pages: 53

ISBN-13: 0309131987

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Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.

Building Thinking Classrooms in Mathematics, Grades K-12
Building Thinking Classrooms in Mathematics, Grades K-12

Author: Peter Liljedahl

Publisher: Corwin Press

Published: 2020-09-28

Total Pages: 454

ISBN-13: 1544374844

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A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.