This book addresses the cognitive, social, and psychological dimensions that shape students’ mathematics experience to help students become more capable, cooperative, and confident in the process of engaging mathematics. In these ways they can have a more valuable and enjoyable mathematics experience, and become more valued participants in society. The book focuses on the mathematics classroom for students grades six to twelve and how students can become more successful mathematical thinkers, in addition to how the curriculum could be presented so as to provide a more engaging mathematics experience.
Research-based strategies to reach English learners – now aligned with the Common Core! Instead of just watching your English learners struggle, ensure that they develop high-level math skills and gain greater fluency in English. Debra Coggins’ bestselling book has helped many teachers achieve these intertwined goals by offering strategies that support mathematics learning along with language acquisition for English Learners. Now in its second edition, English Learners in the Mathematics Classroom addresses Common Core requirements, enabling your students to build 21st century skills that will serve them well into the future. Through this trusted resource, you’ll develop specialized teaching strategies that can be adapted across grade levels for students at all stages of English language acquisition. You’ll discover Mathematics lesson scenarios in every chapter, directly connected to the Common Core Standards and the Standards for Mathematical Practice Instructional approaches that promote participation, hands-on learning, and true comprehension of mathematics concepts that benefit all students Sample lessons, visuals, and essential vocabulary that connect mathematical concepts with language development Whether you are rediscovering this book or picking it up for the first time, you’ll find standards-based strategies that will enable your English learners to enjoy and master mathematics. "The ideas and strategies in this book, supported by research and field experiences, will benefit ALL students because they are addressing learning challenges that are common for many learners." Trudy Mitchell, Middle School Math Consultant San Diego, CA "This is by far the best book on designing mathematics instruction for English learners. The short but thorough research reviewed in each chapter gives background for why the teaching tips are so important in developing mathematically literate students." Dan Battey, Associate Professor Rutgers University
by Leibniz-Institut für die Pädagogik der Naturwissenschaften und Mathematik an der Universität Kiel
Technology-enabled Mathematics Education explores how teachers of mathematics are using digital technologies to enhance student engagement in classrooms, from the early years through to the senior years of school. The research underpinning this book is grounded in real classrooms. The chapters offer ten rich case studies of mathematics teachers who have become exemplary users of technology. Each case study includes the voices of leaders, teachers and their students, providing insights into their practices, beliefs and perceptions of mathematics and technology-enabled teaching. These insights inform an exciting new theoretical model, the Technology Integration Pyramid, for guiding teachers and researchers as they endeavour to understand the complexities involved in planning for effective teaching with technology. This book is a unique resource for educational researchers and students studying primary and secondary mathematics teaching, as well as practising mathematics teachers.
Issues of language in mathematics learning and teaching are important for both practical and theoretical reasons. Addressing issues of language is crucial for improving mathematics learning and teaching for students who are bilingual, multilingual, or learning English. These issues are also relevant to theory: studies that make language visible provide a complex perspective of the role of language in reasoning and learning mathematics. What is the relevant knowledge base to consider when designing research studies that address issues of language in the learning and teaching of mathematics? What scholarly literature is relevant and can contribute to research? In order to address issues of language in mathematics education, researchers need to use theoretical perspectives that integrate current views of mathematics learning and teaching with current views on language, discourse, bilingualism, and second language acquisition. This volume contributes to the development of such integrated approaches to research on language issues in mathematics education by describing theoretical perspectives for framing the study of language issues and methodological issues to consider when designing research studies. The volume provides interdisciplinary reviews of the research literature from four very different perspectives: mathematics education (Moschkovich), Cultural-Historical-Activity Theory (Gutiérrez, Sengupta-Irving, & Dieckmann), systemic functional linguistics (Schleppegrell), and assessment (Solano-Flores). This volume offers graduate students and researchers new to the study of language in mathematics education an introduction to resources for conceptualizing, framing, and designing research studies. For those already involved in examining language issues, the volume provides useful and critical reviews of the literature as well as recommendations for moving forward in designing research. Lastly, the volume provides a basis for dialogue across multiple research communities engaged in collaborative work to address these pressing issues.
At a time when political interest in mathematics education is at its highest, this book demonstrates that the issues are far from straightforward. A wide range of international contributors address such questions as: What is mathematics, and what is it for? What skills does mathematics education need to provide as technology advances? What are the implications for teacher education? What can we learn from past attempts to change the mathematics curriculum? Rethinking the Mathematics Curriculum offers stimulating discussions, showing much is to be learnt from the differences in culture, national expectations, and political restraints revealed in the book. This accessible book will be of particular interest to policy makers, curriculum developers, educators, researchers and employers as well as the general reader.
This volume deals with a wealth of issues related to self, from the overarching theoretical perspective of Bandura and his careful and thorough analysis of the agentic self, highlighting the complexities of our multiple selves acting in an integrated, holistic, and dynamic fashion, to the engaging and novel treatment of self concept as a rope by John Hattie. From many of the chapters we see the utility value of the social cognitive theory and self-determination theory frameworks for interpreting self-processes and how these processes might drive engagement in learning. In particular we see how autonomy support, self-regulation, self-efficacy, and self-regulation are part and parcel of self-processes intimately involved as individuals work out their futures and possible selves. Entwined with these processes are the development of identity, resilience, and a sense of well-being. The BFLPE and bullying chapters provide two examples of self-processes in operation in the school context. What can we take from this? Self-processes are complex, differentiated,and yet coordinated. By focusing on the agentic self we consider the whole person-picture as a rich, integrated, and dynamic tapestry and by focusing on differentiated self elements such as self-regulation, self-determination, self-concept, and self-efficacy, we are able to examine, in more detail, some of the individual threads of the tapestry and the roles they play in the integrated self. Overall, we learn that self-processes are dynamic and are fundamental to enabling human potential.
Developed by an experienced educator and classroom tested for more than a decade, the "I Love Math" program presents a complete elementary math curriculum! Each volume provides an entire year's worth of challenging exercises focused on standardsbased topics. Using engaging color graphics and easytofollow practical lessons, the program is perfect for students of various learning styles and skill levels. The unique learning approach featured in the program furnishes a funfilled means of motivating students to think more deeply, investigate, explain, and understand problemsolving strategies. Each workbook provides completed coverage of the following concepts: whole numbers, patterns & algebra, mass, addition & subtraction, data, time, multiplication & division, length, threedimensional space, chance, volume & capacity, and position. Concepts are divided into two sections one per semester. Each section is two or three pages in length and is followed by an assessment which allows for immediate and continuous feedback. Lesson extensions and suggestions for going forward are also included with each activity. The handson activities can be performed using a variety of commonly available classroom materials.
Making Mathematics Meaningful For Students in the Intermediate Grades is an invaluable resource for anyone interested in helping students reach the key learning outcomes of any mathematics curriculum. Developed through live and videotaped classroom observation and through diagnostic and achievement interviews with students, Making Mathematics Meaningful is a research-based guide to mathematics education that eschews outdated models based primarily and memorization and repetition in favor of a more holistic approach that encourages students to develop their mathematical reasoning skills through problem solving. This approach not only teaches students to become critical thinkers, but also contributes to language development, reading comprehension, and evaluative skills. Author Werner W. Liedtke offers advice on developing questioning strategies and creating practice tasks to ensure that students encounter the critical components of a mathematics program. For each topic, he provides assessment strategies and identifies key prerequisite skills and ideas that can be used for pre-tests, diagnostic purposes, or introductory teaching/learning settings. Making Mathematics Meaningful teaches students to * improve written and oral communication; * connect ideas to previous learning and to settings outside the classroom; * discover strategies for personal estimation and mental mathematics; * learn through problem solving; * develop curiosity, perseverance, and confidence.
"This book, aimed at precollege teachers, shows how the role of simulation modeling in investigation dynamic processes is now extending beyond research and university environments to the precollege world. Computer modeling has the potential to significantly improve the quality of secondary science and mathematics education. This book introduces teachers and students to many different perspectives of and approaches to scientific inquiry. Each of the chapters and associated software applications integrates mathematics, science, and technology in an authentic manner. The contributors discuss the issues raised by classroom-based modeling projects and provide most of the software applications described."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved
A comprehensive handbook for mathematics teachers with practical advice on all aspects of the maths curriculum including developing an effective classroom culture, assessment and progressing mathematical concept development.
In a range of professions, professional practice today is under threat. It is endangered, for example, by pressures of bureaucratic control, commodification, marketization, and the standardisation of practice in some professions. In these times, there is a need for deeper understandings of professional practice and how it develops through professional careers. Enabling Praxis: Challenges for education explores these questions in the context of initial and continuing professional education of teachers.
Mathematics is becoming increasingly collaborative, but software does not sufficiently support that: Social Web applications do not currently make mathematical knowledge accessible to automated agents that have a deeper understanding of mathematical structures. Such agents exist but focus on individual research tasks, such as authoring, publishing, peer-review, or verification, instead of complex collaboration workflows. This work effectively enables their integration by bridging the document-oriented perspective of mathematical authoring and publishing, and the network perspective of threaded discussions and Web information retrieval. This is achieved by giving existing representations of mathematical and relevant related knowledge about applications, projects and people a common Semantic Web foundation. Service integration is addressed from the two perspectives of enriching published documents by embedding assistive services, and translating between different knowledge representations inside knowledge bases. A usability evaluation of a semantic wiki that coherently integrates knowledge production and consumption services points out the remaining challenges in making such heterogeneously integrated environments support realistic workflows. The results of this thesis will soon also enable collaborative acquisition of new mathematical knowledge, as well as the contributions of existing knowledge collections of the Web of Data.
It is commonly agreed that learning with understanding is more desirable than learning by rote. Understanding is described in terms of the way information is represented and structured in the memory. A mathematical idea or procedure or fact is understood if it is a part of an internal network, and the degree of understanding is determined by the number and the strength of the connections between ideas. When a student learns a piece of mathematical knowledge without making connections with items in his or her existing networks of internal knowledge, he or she is learning without understanding. Learning with understanding has progressively been elevated to one of the most important goals for all learners in all subjects. However, the realisation of this goal has been problematic, especially in the domain of mathematics where there are marked difficulties in learning and understanding. The experience of working with learners who do not do well in mathematics suggests that much of the problem is that learners are required to spend so much time in mathematics lessons engaged in tasks which seek to give them competence in mathematical procedures. This leaves inadequate time for gaining understanding or seeking how the procedures can be applied in life. Much of the satisfaction inherent in learning is that of understanding: making connections, relating the symbols of mathematics to real situations, seeing how things fit together, and articulating the patterns and relationships which are fundamental to our number system and number operations. Other factors include attitudes towards mathematics, working memory capacity, extent of field dependency, curriculum approaches, the classroom climate and assessment. In this study, attitudes, working memory capacity and extent of field dependency will be considered. The work will be underpinned by an information processing model for learning. A mathematics curriculum framework released by the US National Council of Teachers of Mathematics (NCTM, 2000) offers a research-based description of what is involved for students to learn mathematics with understanding. The approach is based on?how learners learn, not on?how to teach?, and it should enable mathematics teachers to see mathematics from the standpoint of the learner as he progresses through the various stages of cognitive development. The focus in the present study is to try to find out what aspects of the process of teaching and learning seem to be important in enabling students to grow, develop and achieve. The attention here is on the learner and the nature of the learning process. What is known about learning and memory is reviewed while the literature on specific areas of difficulty in learning mathematics is summarised. Some likely explanations for these difficulties are discussed. Attitudes and how they are measured are then discussed and there is a brief section of learner characteristics, with special emphasis on field dependency as this characteristic seems to be of importance in learning mathematics. The study is set in schools in Nigeria and England but the aim is not to make comparisons. Several types of measurement are made with students: working memory capacity and extent of field dependency are measured using well-established tests (digit span backward test and the hidden figure test). Performance in mathematics is obtained from tests and examinations used in the various schools, standardised as appropriate. Surveys and interviews are also used to probe perceptions, attitudes and aspects of difficulties. Throughout, large samples were employed in the data collection with the overall aim of obtaining a clear picture about the nature and the influence of attitudes, working memory capacity and extent of field dependency in relation to learning, and to see how this was related to mathematics achievement as measured by formal examination. The study starts by focussing on gaining an overview of the nature of the problems and relating these to student perception and attitudes as well as working memory capacity. At that stage, the focus moves more towards extent of field dependency, seen as one way by which the fixed and limited working memory capacity can be used more efficiently. Data analysis was in form of comparison and correlation although there are also much descriptive data. Some very clear patterns and trends were observable. Students are consistently positive towards the more cognitive elements of attitude to mathematics (mathematics is important; lessons are essential). However, they are more negative towards the more affective elements like enjoyment, satisfaction and interest. Thus, they are very realistic about the value of mathematics but find their experiences of learning it much more daunting. Attitudes towards the learning of mathematics change with age. As students grow older, the belief that mathematics is interesting and relevant to them is weakened, although many still think positively about the importance of mathematics. Loss of interest in mathematics may well be related to an inability to grasp what is required and the oft-stated problem that it is difficult trying to take in too much information and selecting what is important. These and other features probably relate to working memory overload, with field dependency skills area being important. The study identified clearly the topics which were perceived as most difficult at various ages. These topics involved ideas and concepts where many things had to be handled cognitively at the same time, thus placing high demands on the limited working memory capacity. As expected, working memory capacity and mathematics achievement relate strongly while extent of field dependency also relates strongly to performance. Performance in mathematics is best for those who are more field-independent. It was found that extent of field dependency grew with age. Thus, as students grow older (at least between 12 and about 17), they tend to become more field-independent. It was also found that girls tend to be more field-independent than boys, perhaps reflecting maturity or their greater commitment and attention to details to undertake their work with care during the years of adolescence. The outcomes of the findings are interpreted in terms of an information processing model. It is argued that curriculum design, teaching approaches and assessment which are consistent with the known limitations of the working memory must be considered during the learning process. There is also discussion of the importance of learning for understanding and the problem of seeking to achieve this while gaining mastery in procedural skills in the light of limited working memory capacity. It is also argued that positive attitudes towards the learning in mathematics must not only be related to the problem of limited working memory capacity but also to ways to develop increased field independence as well as seeing mathematics as a subject to be understood and capable of being applied usefully.
Contains directories of federal agencies that promote mathematics and science education at elementary and secondary levels; organized in sections by agency name, national program name, and state highlights by region.
Maximize your mathematics curriculum to challenge all students This collection of lessons from experienced teachers provides multifaceted examples of rigorous learning opportunities for mathematics students in Grades 6–12. The four sample units focus on fractions, linear programming, geometry, and quadratic relationships. The authors provide user-friendly methods for instruction and demonstrate how to differentiate the lessons for the benefit of all students. Included are standards-based strategies that guide students through: Understanding secondary mathematics concepts Discovering connections between mathematics and other subjects Developing critical thinking skills Connecting mathematics learning to society through the study of real-world data, proportional reasoning, and problem solving
Teachers are looking for a text that will guide them in the selection of appropriate educational software and help them make decisions about the myriad of available Internet sites. They want to know how all this material can help their students learn better. This text integrates both theory and practice with assessment to make learning outcomes possible.
Mobile Learning and Mathematics provides an overview of current research on how mobile devices are supporting mathematics educators in classrooms across the globe. Through nine case studies, chapter authors investigate the use of mobile technologies over a range of grade levels and mathematical topics, while connecting chapters provide a strong foundational background in mobile learning theories, instructional design, and learner support. For current educators, Mobile Learning and Mathematics provides concrete ideas and strategies for integrating mobile learning into their mathematics instruction—for example, by sharing resources that will help implement Common Core State Standards, or by streamlining the process of selecting from the competing and often confusing technology options currently available. A cutting edge research volume, this collection also provides a springboard for educational researchers to conduct further study.
This book provides examples of the ways in which 9-12 grade mathematics teachers from across North America are engaging in research. It offers a glimpse of the questions that capture the attention of teachers, the methodologies that they use to gather data, and the ways in which they make sense of what they find. The focus of these teachers’ investigations into mathematics classrooms ranges from students’ understanding of content to pedagogical changes to social issues. Underlying the chapters is the common goal of enabling students to develop a deep understanding of the mathematics they learn in their classrooms.