Does being able to "do" mathematics mean being competent at techniques and understanding how ideas and techniques fit together? By being given appropriate tasks, learners develop their powers to think mathematically and learn to appreciate how ideas fit together. (Education/Teaching)
Does being able to "do" mathematics mean being competent at techniques and understanding how ideas and techniques fit together?
Author: John Mason
Publisher: Tarquin Publications
'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 elseor all of these? This book addresses these questions through a definition of learning as transformation in the way that learners perceive or think. Learners increase their choice of actions and develop their powers to think mathematically and their competence and fluency in using specific techniques and language and their appreciation of how ideas fit together.
'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: Professor John Mason
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.
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
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.
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
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. ).
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,
Ministry of ...
Combining research-based theory with fresh, practical guidance for the classroom, The Essential Guide to Secondary Mathematics is a stimulating new resource for all student and practising teachers looking for new ideas and inspiration. With an emphasis on exciting your mathematical and pedagogical passions, it focuses on the dynamics of the classroom and the process of designing and using rich mathematical tasks. Written by a highly experienced mathematics teacher who understands the realities of the secondary classroom, this book combines insights from the latest research into mathematical learning with useful strategies and ideas for engaging teaching. The text is punctuated by frequent tasks, some mathematical and others more reflective, which are designed to encourage independent thinking. Key topics covered include: Preparing yourself: thinking about mathematics and pedagogy, taking care of your health and dealing with stress Different styles of learning and teaching mathematics Ideas for lessons: what does it take to turn an idea into a lesson? Tasks, timings and resources Equality and dealing positively with difference Mathematical starters, fillers and finishers: achieving variety The mathematical classroom community: seating layouts, displays and practical considerations Assessment: effective strategies for responding to learners‘ mathematics and writing reports. The Essential Guide to Secondary Mathematics will be a valuable resource both for beginning teachers interested in developing their understanding, and for experienced teachers looking to re-evaluate their practice. Aiming to develop all aspects of your mathematics teaching, this book will help you to devise, adapt and implement ideas for successful and enjoyable teaching and learning.
Aiming to develop all aspects of your mathematics teaching, this book will help you to devise, adapt and implement ideas for successful and enjoyable teaching and learning.
Author: Colin Foster
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
Washington, DC: NCES. Kaur, B., & Lee, N. H. (2017). Empowering mathematics
learners. Singapore: World Scientific. Mason, J., & Johnston-Wilder, S. (2006).
Designing and using mathematical tasks. United Kingdom: Tarquin Publications.
Author: Toh Pee Choon
Publisher: World Scientific
This volume brings together recent research and commentary in secondary school mathematics from a breadth of contemporary Canadian and International researchers and educators. It is both representative of mathematics education generally, as well as unique to the particular geography and culture of Canada. The chapters address topics of broad applicability such as technology in learning mathematics, recent interest in social justice contexts in the learning of mathematics, as well as Indigenous education. The voices of classroom practitioners, the group ultimately responsible for implementing this new vision of mathematics teaching and learning, are not forgotten. Each section includes a chapter written by a classroom teacher, making this volume unique in its approach. We have much to learn from one another, and this volume takes the stance that the development of a united vision, supported by both research and professional dialog, provides the first step.
A task is what to do to in order to solve the problem, or, in other words, the
question to investigate. ... Using. Contexts. to. Design. Mathematical. Tasks.
Designing a mathematical task involves identifying the mathematical knowledge
to be ...
Author: Ann Kajander
This 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.
This book is the product of ICMI Study 22 Task Design in Mathematics Education.
Author: Anne Watson
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.
This was expected and the choice of the student work in Figure 4.2 was intended
to provoke further mathematical work on the task by engaging them in a proof
about the task they had not produced on their own but which used an important ...
Author: Ian Thompson
The tasks with which students engage in their mathematics courses determine, for a large part, what students learn. Therefore, it is essential that teachers are able to design tasks that are worthwhile for developing mathematical understanding. Since practicing teachers seldom incorporate worthwhile mathematical tasks in their lessons, we would expect that they did not become proficient at designing worthwhile tasks while in their teacher education programs. This thesis describes a study that investigated what preservice secondary teachers attend to as they attempt to design worthwhile mathematical tasks. Three participants were selected from a course at a large private university where preservice teachers are taught and practice the skill of task design. This "Task Design" course was observed, and the three participants were interviewed to determine what they attend to while designing tasks. There were seven main characteristics that the main participants in the study attended to the most often and thought were the most important: sound and significant mathematics, reasoning, appropriateness, clarity, communication, engagement, and openness. How the participants attended to these characteristics is described. Some implications for teacher education, such as requiring preservice teachers to explain how their tasks embody certain characteristics, are given based on the results.
The tasks with which students engage in their mathematics courses determine, for a large part, what students learn.
Author: Elizabeth K. Zwahlen
CliffsNotes TExES Math 4-8 (115) and Math 7-12 (235) is the perfect way to study for Texas’ middle school and high school math teacher certification tests. Becoming a certified middle school math teacher and high school math teacher in Texas means first passing the TExES Math 4-8 (115) teacher certification test for middle school teachers or the TExES Math 7-12 (235) teacher certification test for high school teachers. This professional teacher certification test is required for all teachers who want to teach math in a Texas middle or high school. Covering each test’s six domains and individual competencies with in-depth subject reviews, this test-prep book also includes two model practice tests with answers and explanations for the Math 4-8 and two model practice tests with answers and explanations for the Math 7-12. Answer explanations detail why correct answers are correct, as well as what makes incorrect answer choices incorrect.
Tasks should be based on sound and significant mathematics and should be
designed to provide opportunities for students to cognitively engage with
important mathematical ideas. By being aware of the thinking that goes on when
Author: Sandra Luna McCune
Publisher: Houghton Mifflin Harcourt
Category: Study Aids
This volume collects most recent work on the role of technology in mathematics education. It offers fresh insight and understanding of the many ways in which technological resources can improve the teaching and learning of mathematics. The first section of the volume focuses on the question how a proposed mathematical task in a technological environment can influence the acquisition of knowledge and what elements are important to retain in the design of mathematical tasks in computing environments. The use of white smart boards, platforms as Moodle, tablets and smartphones have transformed the way we communicate both inside and outside the mathematics classroom. Therefore the second section discussed how to make efficient use of these resources in the classroom and beyond. The third section addresses how technology modifies the way information is transmitted and how mathematical education has to take into account the new ways of learning through connected networks as well as new ways of teaching. The last section is on the training of teachers in the digital era. The editors of this volume have selected papers from the proceedings of the 65th, 66th and 67th CIEAEM conference, and invited the correspondent authors to contribute to this volume by discussing one of the four important topics. The book continues a series of sourcebooks edited by CIEAEM, the Commission Internationale pour l’Étude et l’Amélioration de l’Enseignement des Mathématiques / International Commission for the Study and Improvement of Mathematics Education.
This volume collects most recent work on the role of technology in mathematics education. It offers fresh insight and understanding of the many ways in which technological resources can improve the teaching and learning of mathematics.
Author: Gilles Aldon
The work took place in two sections : mathematical problems of experiment
design and the use of the active experiment in chemical and physicochemical
research . Seventy - nine reports and communications were heard and discussed
Category: Chemistry, Analytic
A crucial step towards improving the conceptual use of digital technology (DT) in the mathematics classroom is to increase teacher involvement in the development of tasks. Hence, this research considers some teacher factors that might influence DT algebra task development and implementation in secondary schools. We observed and assisted one group of three teachers as they designed and implemented DT tasks. Our preliminary analysis examines the richness of the two tasks produced by one group and seeks to explain the difference between them. The results suggest the intervention provided with respect to task design led to improved Pedagogical Technology Knowledge for the teachers, and hence a richer task. The delivery of the intervention could be of assistance in focusing professional development programs so they may better facilitate the training of teachers in the use of digital technology in teaching mathematics.
A crucial step towards improving the conceptual use of digital technology (DT) in the mathematics classroom is to increase teacher involvement in the development of tasks.
Author: Iresha Ratnayake
Chapter III DESIGN OF THE STUDY Chapter I defined the problem and identified
the specific questions and null hypotheses ... Will fourth - grade students with low
cognitive restruc. turing ability learn the set of mathematics objectives requiring ...
Author: Kathleen Ann Cramer
This book contributes towards literature in the field of mathematics education, specifically on mathematics instruction and the design of mathematical tasks and activities."--Publisher's website.
Author: Pee Choon Toh
Teaching is a complex, ongoing endeavor that involves a myriad of decisions. NCTM's sixty-sixth yearbook is organised around three aspects of teaching: foundations for teaching, the enactment of teaching and the support of teaching nurtured in preservice education and strengthened throughout a teacher's career. The accompanying professional development guidebook, edited by George W. Bright, contains activities that illustrate and extend some of the ideas in the yearbook in order to further teachers' growth and development in understanding and implementing effective mathematics instruction.
Thus , students ' understanding of mathematics , their ability to use it to solve
problems , their confidence in , and disposition ... The learning tool we designed
is a task - sorting activity , and we based our design in work done by the
Author: Rheta Norma Rubenstein
Publisher: National Council of Teachers of
This brief presents the results of a study on the development of the mobile app-supported math trail program for learning mathematics. This study is a part of the MathCityMap-Project, a project of the MATIS I Team from IDMI Goethe-Universität Frankfurt, Germany, that comprises math trails around the city that are supported by the use of GPS-enabled mobile phone technology. The project offers an activity that is designed to support students in constructing their own mathematical knowledge by solving the prepared mathematical tasks on the math trail and interacting with the environment, including the digital environment. The brief focuses specifically on the development of a model for a mobile app-supported math trail programme and the implementation of this programme in Indonesia. It offers both an empirical exploration of its implementation as well as critical assessment of students’ motivation in mathematics, their own performance, as well as teachers’ mathematics beliefs. It concludes with a future-forward perspective by recommending strategies for implementation in schools, among the general public of the existing math trails (including its supporting tool). It also discusses strategies for developing and designing new trails and suggests further research in other geographical regions and contexts for continued project development and implementation. Learning Mathematics in a Mobile App-Supported Math Trail Environment articulates an innovative and exciting future for integrating real mathematical tasks and geographic and digital environment into effective mathematics education.
Learning Mathematics in a Mobile App-Supported Math Trail Environment articulates an innovative and exciting future for integrating real mathematical tasks and geographic and digital environment into effective mathematics education.
Author: Adi Nur Cahyono
This book is an edited volume addressing specific issues of significance for individuals involved with the undergraduate mathematics content preparation of prospective elementary teachers (PSTs). Teaching mathematics content courses to this group of students presents unique challenges. While some PSTs enter their teacher preparation with weak mathematical skills and knowledge, many also hold negative attitudes, anxiety, and misguided beliefs about mathematics. This book is designed to support instructors who teach these students in mathematics content for elementary teachers courses. Elementary teachers need a richly developed understanding of the mathematics they are teaching in order to teach it effectively. Providing them with the needed preparation is difficult, but can be eased with a solid understanding of the mathematical concerns and limitations PSTs bring to the learning of mathematics and a familiarity with the standards and curricula topics PSTs will be expected to teach. Chapter One makes the argument that elementary mathematics is not trivial. This is followed by an analysis of four central issues related to the mathematical preparation of elementary teachers, specifically: (1) selecting/creating/modifying and implementing mathematical tasks (2) noticing/understanding children’s ways of thinking as a foundation for learning mathematics, (3) developing mathematical habits of mind in PSTs, and (4) understanding the role affect plays in the mathematical learning of PSTs. The final chapter presents three international examples of programs that currently consider these factors in the implementation of their courses.
This book is an edited volume addressing specific issues of significance for individuals involved with the undergraduate mathematics content preparation of prospective elementary teachers (PSTs).
Author: Lynn C. Hart