Teaching Mathematical Thinking

2017
Teaching Mathematical Thinking

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  • Author: Marian Small
  • Publisher: Teachers College Press
  • ISBN: 0807775886
  • Category : Education
  • Languages : en
  • Pages : 129

This new resource by math education expert Marian Small helps schools and districts to refine their teaching of standards-based mathematical practices. Small devotes a chapter to each of the eight standards of practice and includes a discussion of what each standard looks like in grades K–2, 3–5, and 6–8. Specific attention is given to helping students make sense of problems and persevere in solving them (Standard 1) and to encouraging students to create viable mathematical arguments and to effectively and respectfully critique the reasoning of others (Standard 3). The author also discusses how to formatively assess student performance for each practice standard. To provide additional support to U.S. teachers in their instructional planning, this resource includes attention to the Canadian math processes of visualization and mental math and estimation. “Whether you are a new teacher or a seasoned educator, this book will enrich your abilities to develop your students' mathematical thinking.” —From the Foreword by Linda Dacey, professor emerita, Mathematics, Lesley University “One of the best ways to prepare students for their futures is to teach mathematical thinking. Marian Small shows us the way with powerful tasks, probing questions, and incredible student work samples. This is the book I have been looking for and is definitely a must-have for every teacher.” —Ruth Harbin Miles, Mary Baldwin University

The Nature of Mathematical Thinking

1996
The Nature of Mathematical Thinking

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  • Author: Robert J. Sternberg
  • Publisher: Psychology Press
  • ISBN: 9780805817997
  • Category : Education
  • Languages : en
  • Pages : 356

First Published in 1996. Routledge is an imprint of Taylor & Francis, an informa company.

Mathematical Thinking

2012
Mathematical Thinking

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  • Author: Masami Isoda
  • Publisher: World Scientific
  • ISBN: 9814350850
  • Category : Mathematics
  • Languages : en
  • Pages : 318

Developing mathematical thinking is one of major aims of mathematics education. In mathematics education research, there are a number of researches which describe what it is and how we can observe in experimental research. However, teachers have difficulties developing it in the classrooms. This book is the result of lesson studies over the past 50 years. It describes three perspectives of mathematical thinking: Mathematical Attitude (Minds set), Mathematical Methods in General and Mathematical Ideas with Content and explains how to develop them in the classroom with illuminating examples.

Developing Mathematical Thinking

2014-07-07
Developing Mathematical Thinking

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  • Author: Jonathan D. Katz
  • Publisher: Rowman & Littlefield
  • ISBN: 147581058X
  • Category : Education
  • Languages : en
  • Pages : 145

In this country we have done a poor job of helping students come to see the wonder, beauty and power of mathematics. Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.

Teaching Mathematics in Elementary and Middle School

2007
Teaching Mathematics in Elementary and Middle School

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  • Author: Joseph G. R. Martinez
  • Publisher: Prentice Hall
  • ISBN:
  • Category : Education
  • Languages : en
  • Pages : 430

With an emphasis on inquiry and process, "Teaching Mathematics in Elementary and Middle School "embraces active mathematics instruction and the development of mathematical thinking through problem solving. The text challenges future teachers to prepare their K-8 students for a world that requires a higher level of mathematical literacy and enables them to compete in a global society.Teachers will develop their own mathematical abilities, allowing them to help students discover a rich combination of thinking processes and problem-solving strategies, raising the learning expectations for all. Unique text features "TIE-Thought, Investigation and Exploration "features ask pre-service teachers to develop their own thinking and learning abilities, preparing them to better challenge their students. "Mathematics in the Real World," "Idea Files," and "Teacher Profiles "model best practices and supply readers with concrete teaching tools and strategies. "Mathematical Thinking," "Mathematical Games" and "Mathematics and Technology" features detail activities to engage and develop students' mathematical thinking. Accompanying student artifacts illustrate the progression of students' conceptual understanding. [CD logo replaces bullet] "Math Activities CD-ROM" provides an outstanding text component containing more than 100 activities that use a three-step process-explore, invent, discover-to foster the development of mathematical thinking through guided inquiry. Aligned with the NCTM standards, each activity is integrated within the text and designed to help develop students' conceptual understanding of mathematics. "Mathematics in Literature" offers thoroughly developed ideas for using children's literature to create meaningful contexts for mathematics learning. An extensive bibliography that can be used for this purpose appears on the CD-Rom. "I think the text is an excellent resource for elementary and middle school methods courses. In particular, I like how the textbook handles the 'bigger issues' such as geometric reasoning rather than just 'geometry.' I also like the excellent foundation in educational research that the textbook provides, as well as some very careful attention and consistent referencing to the NCTM standards and principles. The incorporation of classroom vignettes, teacher illustrations, and samples of student work also all add to the excellent grounding of the text in real world classroom work." Dr. Neal Grandgenett, University of Nebraska at Omaha

Forms of Mathematical Knowledge

1999-11-30
Forms of Mathematical Knowledge

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  • Author: Dina Tirosh
  • Publisher: Springer Science & Business Media
  • ISBN: 9780792359951
  • Category : Education
  • Languages : en
  • Pages : 264

What mathematics is entailed in knowing to act in a moment? Is tacit, rhetorical knowledge significant in mathematics education? What is the role of intuitive models in understanding, learning and teaching mathematics? Are there differences between elementary and advanced mathematical thinking? Why can't students prove? What are the characteristics of teachers' ways of knowing? This book focuses on various types of knowledge that are significant for learning and teaching mathematics. The first part defines, discusses and contrasts psychological, philosophical and didactical issues related to various types of knowledge involved in the learning of mathematics. The second part describes ideas about forms of mathematical knowledge that are important for teachers to know and ways of implementing such ideas in preservice and in-service education. The chapters provide a wide overview of current thinking about mathematics learning and teaching which is of interest for researchers in mathematics education and mathematics educators. Topics covered include the role of intuition in mathematics learning and teaching, the growth from elementary to advanced mathematical thinking, the significance of genres and rhetoric for the learning of mathematics and the characterization of teachers' ways of knowing.

Mathematics Teacher Noticing

2011-02
Mathematics Teacher Noticing

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  • Author: Miriam Sherin
  • Publisher: Routledge
  • ISBN: 1136838260
  • Category : Education
  • Languages : en
  • Pages : 280

This is the first book to examine research on mathematics teacher noticing--how teachers pay attention to and make sense of what happens in the complexity of instructional situations

Teaching Numeracy

2011-03-23
Teaching Numeracy

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  • Author: Margie Pearse
  • Publisher: Corwin Press
  • ISBN: 1452224404
  • Category : Education
  • Languages : en
  • Pages : 241

Transform mathematics learning from “doing” to “thinking” American students are losing ground in the global mathematical environment. What many of them lack is numeracy—the ability to think through the math and apply it outside of the classroom. Referencing the new common core and NCTM standards, the authors outline nine critical thinking habits that foster numeracy and show you how to: Monitor and repair students’ understanding Guide students to recognize patterns Encourage questioning for understanding Develop students’ mathematics vocabulary Included are several numeracy-rich lesson plans, complete with clear directions and student handouts.

Children's Mathematical Thinking in Primary Years

2005-05-01
Children's Mathematical Thinking in Primary Years

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  • Author: Julia Anghileri
  • Publisher: Bloomsbury Publishing
  • ISBN: 1847144209
  • Category : Education
  • Languages : en
  • Pages : 193

This popular Continuum series, intended chiefly for teachers and trainee teachers, places strong emphasis on practice but at the same time incorporates the latest research in the field. The book demonstrates a strong belief in the ability of children to learn, and in the ability of teachers to increase children's learning potential. The series authors are distinguished practitioners in their fields who write with authority, but without jargon. With the increasingly popular constructivist framework for learning, teachers are coming to recognize the limitations of taught procedures and to find ways to encourage children to generate their own knowledge and understanding in mathematics. The challenge for teachers is to promote an environment that encourages mathematical thinking in which pupils of all abilities are able to achieve their full potential. This text brings together experiences of teachers and researchers who examine the ways children work mathematically, in order to provide an enhanced learning environment within the classroom. It also addresses key issues in current maths teaching.

Building Thinking Classrooms in Mathematics, Grades K-12

2020-09-28
Building Thinking Classrooms in Mathematics, Grades K-12

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  • Author: Peter Liljedahl
  • Publisher: Corwin Press
  • ISBN: 1544374844
  • Category : Education
  • Languages : en
  • Pages : 454

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.