Designing and Using Mathematical Tasks

Designing and Using Mathematical Tasks

'Beginning and established teachers of mathematics as well as teacher educators will all find this book a rich resource when focusing on the crucial issue of designing and using tasks to provoke real learning in mathematics.

Author: John Mason

Publisher: Tarquin Publications

ISBN: UOM:39015074052948

Category: Education

Page: 156

View: 721

'Beginning and established teachers of mathematics as well as teacher educators will all find this book a rich resource when focusing on the crucial issue of designing and using tasks to provoke real learning in mathematics. It has become a central feature of our PGCE course in mathematics'. David Wright, Tutor in mathematics education, University of Newcastle Mathematics seems, on the face of it, a cut and dried subject. But does being able to 'do' mathematics mean being competent at techniques? Understanding how ideas and techniques fit together? Using basic principles in problem-solving? Something else.or all of these? Designing and Using Mathematical Tasks addresses these questions by thinking about learning as transformation in the way that learners perceive or think. By being given appropriate tasks, learners increase their choice of actions and develop their powers to think mathematically. They also develop their competence and fluency in using specific techniques and language and their appreciation of how ideas fit together. Contents include: . Introduction: learning, teaching and behaviour: theory and practice . Mathematical topics . Mathematical tasks . Mathematical activity . Interaction . Progression in mathematics This book forms part of the Open University course ME825
Categories: Education

Mathematical Tasks

Mathematical Tasks

This is a book for classroom teachers. Chris McGrane offers a range of practical examples for nurturing deep learning in mathematics that can be adapted and embedded in one's own classroom practice.

Author: Chris McGrane

Publisher: John Catt Educational

ISBN: 9781913808341

Category: Electronic books

Page: 306

View: 185

If we want our pupils to develop fluency, understanding and the ability to solve complex problems, then it is vital that teachers develop the ability to select, adapt and design appropriate mathematical tasks. In 'Mathematical Tasks: The Bridge Between Teaching and Learning', Chris McGrane and Mark McCourt a range of practical approaches, strategies and principles behind the design and effective use of tasks in the mathematics classroom that lead to all pupils becoming successful learners. First-hand interviews with world class mathematics education experts and practicing teachers bring to life the ideas behind how tasks can act as a bridge between what the teacher wants the pupil to make sense of and what the pupil actually does makes sense of; tasks are how we enable pupils to enact mathematics - it is only by being mathematical that pupils can truly make connections across mathematical ideas and understand the bigger picture. This is a book for classroom teachers. Chris McGrane offers a range of practical examples for nurturing deep learning in mathematics that can be adapted and embedded in one's own classroom practice. This is also a book for those who are interested in the theory behind tasks. Chris and his interviewees examine the key role tasks play in shaping learning, teaching, curriculum and assessment. Suitable for teachers at all stages in their careers and teachers are encouraged to return to the book from time to time over the years to notice how their use of tasks in the classroom changes as they themselves develop.
Categories: Electronic books

Digital Technologies in Designing Mathematics Education Tasks

Digital Technologies in Designing Mathematics Education Tasks

This book is about the role and potential of using digital technology in designing teaching and learning tasks in the mathematics classroom.

Author: Allen Leung

Publisher: Springer

ISBN: 9783319434230

Category: Education

Page: 352

View: 280

This book is about the role and potential of using digital technology in designing teaching and learning tasks in the mathematics classroom. Digital technology has opened up different new educational spaces for the mathematics classroom in the past few decades and, as technology is constantly evolving, novel ideas and approaches are brewing to enrich these spaces with diverse didactical flavors. A key issue is always how technology can, or cannot, play epistemic and pedagogic roles in the mathematics classroom. The main purpose of this book is to explore mathematics task design when digital technology is part of the teaching and learning environment. What features of the technology used can be capitalized upon to design tasks that transform learners’ experiential knowledge, gained from using the technology, into conceptual mathematical knowledge? When do digital environments actually bring an essential (educationally, speaking) new dimension to classroom activities? What are some pragmatic and semiotic values of the technology used? These are some of the concerns addressed in the book by expert scholars in this area of research in mathematics education. This volume is the first devoted entirely to issues on designing mathematical tasks in digital teaching and learning environments, outlining different current research scenarios.
Categories: Education

Mathematical Tasks

Mathematical Tasks

Suitable for teachers at all stages in their careers and teachers are encouraged to return to the book from time to time over the years to notice how their use of tasks in the classroom changes as they themselves develop.

Author: Chris McGrane

Publisher: John Catt Educational

ISBN: 1913622061

Category:

Page: 317

View: 900

If we want our pupils to develop fluency, understanding and the ability to solve complex problems, then it is vital that teachers develop the ability to select, adapt and design appropriate mathematical tasks. In 'Mathematical Tasks: The Bridge Between Teaching and Learning', Chris McGrane and Mark McCourt explore a range of practical approaches, strategies and principles behind the design and effective use of tasks in the mathematics classroom that lead to all pupils becoming successful learners. First-hand interviews with world-class mathematics education experts and practicing teachers bring to life the ideas behind how tasks can act as a bridge between what the teacher wants the pupil to make sense of and what the pupil actually does makes sense of; tasks are how we enable pupils to enact mathematics - it is only by being mathematical that pupils can truly make connections across mathematical ideas and understand the bigger picture. Suitable for teachers at all stages in their careers and teachers are encouraged to return to the book from time to time over the years to notice how their use of tasks in the classroom changes as they themselves develop.
Categories:

Mathematics as the Science of Patterns

Mathematics as the Science of Patterns

Importantly, teaching mathematics requires an understanding, on the part of teacher, of mathematical-task knowledge and how mathematical tasks are designed and used to increase student learning by supporting students' conceptual ...

Author: Patrick M. Jenlink

Publisher: IAP

ISBN: 9781648027468

Category: Education

Page: 265

View: 505

Mathematics as the Science of Patterns: Making the Invisible Visible to Students through Teaching introduces the reader to a collection of thoughtful, research-based works by authors that represent current thinking about mathematics, mathematics education, and the preparation of mathematics teachers. Each chapter focuses on mathematics teaching and the preparation of teachers who will enter classrooms to instruct the next generation of students in mathematics. The value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond. Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep-seated cognitive patterns that both teachers and students bring to the classroom require change. Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Po lya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers’ patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students’ learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov’s Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching.
Categories: Education

Mathematical Tasks in Classrooms Around the World

Mathematical Tasks in Classrooms Around the World

Designing and using mathematical tasks. St Albans, UK: Tarquin Publications. Ministry of Education. (2006). A guide to teaching & learning of 'O' level mathematics 2007. Singapore: Curriculum Planning and Development Division, ...

Author:

Publisher: BRILL

ISBN: 9789460911507

Category: Education

Page:

View: 840

This book presents an international perspective on environmental educational and specifically the influence that context has on this aspect of curriculum. The focus is on environmental education both formal and non formal and the factors that impact upon its effectiveness, particularly in non-Western and non-English-speaking contexts (i.e., outside the UK, USA, Australia, NZ, etc. ).
Categories: Education

Designing Tasks in Secondary Education

Designing Tasks in Secondary Education

In our planning and teaching of these sessions, we take account of their background knowledge and experiences in the design and sequencing of tasks. In our university-based work with prospective secondary mathematics teachers we use ...

Author: Ian Thompson

Publisher: Routledge

ISBN: 9781317627166

Category: Education

Page: 226

View: 540

Engaging students in learning about their subject is a central concern for all teachers and teacher educators. How teachers view and use the pedagogic potential of different tasks to engage pupils with knowledge in different subjects, is central to this endeavour. Designing Tasks in Secondary Education explores models for effective task design, helping you translate the curriculum into the tasks and activities that you ask your students to do in order to facilitate developmental or higher-level understanding of curriculum content. Written by experts in the field of education from a range of subjects and including a foreword written by renowned author Professor Walter Doyle, this book spans an international context and offers a refreshing alternative of how to plan and design tasks that will not only intellectually stimulate but improve teaching quality. Key topics explored include: Designing tasks which engage learners with knowledge Policy perspectives on task design Designing cognitively demanding classroom tasks Task design issues in the secondary subjects Designing Tasks in Secondary Education offers essential insight into task design and its importance for enhancing subject understanding and student engagement. It will challenge and support all education professionals concerned with issues of curriculum design, subject knowledge, classroom organisation, agency in the learning process and teaching quality.
Categories: Education

Mathematics Instruction Goals Tasks And Activities Yearbook 2018 Association Of Mathematics Educators

Mathematics Instruction  Goals  Tasks And Activities   Yearbook 2018  Association Of Mathematics Educators

Empowering mathematics learners. Singapore: World Scientific. Mason, J., & Johnston-Wilder, S. (2006). Designing and using mathematical tasks. United Kingdom: Tarquin Publications. Shimizu, Y., Kaur, B., Huang, R., & Clarke, D. (2010).

Author: Toh Pee Choon

Publisher: World Scientific

ISBN: 9789813271685

Category: Mathematics

Page: 288

View: 122

The book, the tenth volume in the series of yearbooks by the Association of Mathematics Educators in Singapore, comprises 14 chapters written by renowned researchers in mathematics education. The chapters offer mathematics teachers a cache of teaching ideas and resources for classroom instruction. Readers will find various task design principles, examples of mathematical tasks used in classrooms and teaching approaches to implement the tasks. Through these discussions, readers are invited to reflect and rethink their beliefs about mathematics teaching and learning in the 21st century, and reexamine the tasks and activities that they use in the classroom, in order to bring about positive impact on students' learning of mathematics. This book contributes towards literature in the field of mathematics education, specifically on mathematics instruction and the design of mathematical tasks and activities. Contents: Tasks and Activities in the Mathematics Classroom (Boon Liang CHUA and Pee Choon TOH) From Task to Activity: Noticing Affordances, Design, and Orchestration (CHOY Ban Heng) Affordances of Typical Problems (Jaguthsing DINDYAL) Mathematical Tasks Enacted by Two Competent Teachers to Facilitate the Learning of Vectors by Grade Ten Students (Berinderjeet KAUR, Lai Fong WONG and Chong Kiat CHEW) Use of Comics and Its Adaptation in the Mathematics Classroom (TOH Tin Lam, CHAN Chun Ming Eric, CHENG Lu Pien, LIM Kam Ming and LIM Lee Hean) Designing and Implementing Scientific Calculator Tasks and Activities (Barry KISSANE) Engaging the Hearts of Mathematics Learners (Joseph B W YEO) Developing Interaction Toward the Goal of the Lesson in a Primary Mathematics Classroom (Keiko HINO) Designing and Implementing Activities in the Flipped Classroom in the Singapore Primary Mathematics Classroom (CHENG Lu Pien, NG Swee Fong, TAN Bee Kian Jasmine Susie and NG Ee Noch) Designing Mathematical Modelling Activities for the Primary Mathematics Classroom (Chun Ming Eric CHAN, Rashidah VAPUMARICAN and Huanjia Tracy LIU) Extending d104book Exercises into Short Open-Ended Tasks for Primary Mathematics Classroom Instruction (YEO Kai Kow Joseph) Integrating Problem Posing into Mathematical Problem Solving: An Experimental Study (JIANG Chunlian and CHUA Boon Liang) A Vicennial Walk Through 'A' Level Mathematics in Singapore: Reflecting on the Curriculum Leadership Role of the JC Mathematics Teacher (Weng Kin HO and Christina RATNAM-LIM) Probability: Theory and Teaching (YAP Von Bing) Readership: Graduate students, researchers, practitioners and teachers in mathematics. Keywords: Mathematics;Instruction;Task Design;Singapore;Teachers;InstructionReview: Key Features: Firstly it has a focused theme: Mathematics instruction and task design, which is of prime concern to mathematics educators Secondly it is written by university scholars who work closely with classroom mathematics teachers thereby drawing on their research knowledge and classroom experiences Lastly, the book is rich resource, of tried and tested practical know-how of approaches that promote mathematics learning, for mathematics educators in Singapore schools and elsewhere
Categories: Mathematics

Posing and Solving Mathematical Problems

Posing and Solving Mathematical Problems

Task and activity. In B. Christiansen, G. Howson, & M. Otte (Eds.), Perspectives in mathematics education (pp. 243–307). Dordrecht: Reidel. ... Designing and using mathematical tasks, Open University, Milton Keynes.

Author: Patricio Felmer

Publisher: Springer

ISBN: 9783319280233

Category: Education

Page: 402

View: 266

This book collects recent research on posing and solving mathematical problems. Rather than treating these two crucial aspects of school mathematics as separate areas of study, the authors approach them as a unit where both areas are measured on equal grounds in relation to each other. The contributors are from a vast variety of countries and with a wide range of experience; it includes the work from many of the leading researchers in the area and an important number of young researchers. The book is divided in three parts, one directed to new research perspectives and the other two directed to teachers and students, respectively.
Categories: Education

Task Design In Mathematics Education

Task Design In Mathematics Education

Emergent task design can build flexibly and effectively on student responses to support their engagement with mathematical thinking, but makes considerable demands on the teacher's ability to act “in the moment”. It is, of course, ...

Author: Anne Watson

Publisher: Springer

ISBN: 9783319096292

Category: Education

Page: 339

View: 571

*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* This open access book is the product of ICMI Study 22 Task Design in Mathematics Education. The study offers a state-of-the-art summary of relevant research and goes beyond that to develop new insights and new areas of knowledge and study about task design. The authors represent a wide range of countries and cultures and are leading researchers, teachers and designers. In particular, the authors develop explicit understandings of the opportunities and difficulties involved in designing and implementing tasks and of the interfaces between the teaching, researching and designing roles – recognising that these might be undertaken by the same person or by completely separate teams. Tasks generate the activity through which learners meet mathematical concepts, ideas, strategies and learn to use and develop mathematical thinking and modes of enquiry. Teaching includes the selection, modification, design, sequencing, installation, observation and evaluation of tasks. The book illustrates how task design is core to effective teaching, whether the task is a complex, extended, investigation or a small part of a lesson; whether it is part of a curriculum system, such as a textbook, or promotes free standing activity; whether the task comes from published source or is devised by the teacher or the student.
Categories: Education