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The six articles in this issue tackle topics that relate to the role and function of numeracy in adult life. "Reading Comprehension in Written Mathematics Problems" (Sue Wareham) examines the levels of reading ability required of numeracy students and offers strategies to help students with limited reading skills. "Can Ordinary People Do Real Maths?" (Joan O'Hagan) tackles the issue of "real" math through a review of historical, philosophical, and cultural perspectives on the nature of mathematics and considers the consequences for tutors and students. "Numeracy: A Core Skill or Not?" (George Barr) reviews the place of numeracy within recently established core skills frameworks. "Sorting Out Statistics: Confessions of a Numeracy Tutor" (Sarah Oliver) considers the place of statistics in life and in the curriculum. "Learning Contracts in Higher Education: Towards Confidence in Developing Numeracy Skills" (Ian Beveridge, Gordon Weller) describes the development of numeracy support for Access (a program which attracts a lot of single parent mothers, housewives with older children, and non-mainstream groups) and higher education students at Luton College, England. "Effective Provision of Literacy and Numeracy Instruction for Long-Term Unemployed Persons" (Joy Cumming), an article that reviews the provision of employment-related courses in Australia, evaluates the features of good practice in both literacy and numeracy, and considers the most effective approaches in developing numeracy skills. (YLB)

This special issue of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques (CMESG/GCEDM) Proceedings looks at CMESG/GCEDM's collective history, reflects on where the group has been, and who the members have become as an organization. Through a selection of excerpts from past proceedings, the editors have stitched together a partial history of CMESG/GCEDM's time as an organization. This serves not only as a summary of the collective history, but also serves as an introduction to the activities of CMESG/GCEDM through the first 40 years. The pieces selected for inclusion in this special issue stand as signposts along CMESG/GCEDM's history--as exemplifications of what CMESG/GCEDM is as an organization as well as the activities of CMESG/GCEDM at annual meetings. Crafted introductions to each piece articulate the ways in which that piece exemplifies the valued aspects of CMESG/GCEDM. Following an introduction to the special issue (Peter Liljedahl) [Written in English and French], a foreword (Peter Taylor) [Written in English and French], a Preface to the 1977 CMESG Proceedings (Albert Coleman, Bill Higginson, and David Wheeler), and The Origins and Activities of CMESG (David Wheeler), this issue contains the following papers: (1) Mathematics Education Research in Canada: A Prospective View (Tom Kieren); (2) Innovations in Teacher Education Programmes (Claude Gaulin); (3) The Objectives of Mathematics Education (Albert Coleman); (4) Confessions of an Accidental Theorist (Alan Schoenfeld); (5) The Role of Epistemology in the Analysis of Teaching/Learning Relationships In Mathematics Education (Michèle Artigue); (6) Alive Mathematical Reasoning (David Henderson); (7) Toward a Practice-Based Theory of Mathematical Knowledge for Teaching (Deborah Loewenberg Ball and Hyman Bass); (8) Mathematics as Medicine (Edward Doolittle); (9) Old and New Mathematical Ideas from Africa: Challenges for Reflection (Paulus Gerdes); (10) The Role of Proof in Post-Secondary Education (William Byers and Harvey Gerber); (11) From Theory To Observational Data (And Back Again) (Carolyn Kieran and Jo Towers); (12) Where Is The Mathematics? (John Mason and Eric Muller); (13) The Arithmetic/Algebra Interface: Implications For Primary And Secondary Mathematics = Articulation Arithmétique/Algèbre: implications pour l'enseignement des mathématiques au primaire et au secondaire (Nadine Bednarz and Lesley) [Written in English and French]; (14) Images Of Undergraduate Mathematics (Miroslav Lovric and David Poole); (15) A Mathematics Curriculum Manifesto (Walter Whiteley and Brent Davis); (16) Learner Generated Examples (Nathalie Sinclair, Anne Watson, and Rina Zazkis); (17) Étude des pratiques d'enseignement (Jamie Pyper, Hassane Squalli, and Laurent Theis) [Written in English and French]; (18) Mathematics of Planet Earth 2013: Education and Communication = Mathématiques de la planète terre 2013: formation et communication (Doug Franks, Kathleen Pineau, and Walter Whiteley); (19) Indigenous Ways of Knowing in Mathematics (Lisa Lunney Borden and Florence Glanfield); (20) The Commonsense of Teaching (David Wheeler); (21) A Historical Perspective on Mathematics Education Research in Canada: The Emergence of a Community (Carolyn Kieran); (22) Lessons from the Past, Questions for the Future: Méditation sur thème impose (Roberta Mura) [Written in French]; (23) Building Thinking Classrooms: Conditions for Problem Solving (Peter Liljedahl); (24) Where Do I Want Students' Attention? And What Can I Do to Affect Their Attention? (David Hewitt); and (25) Measuring the Impact of a Mentor Program (A. J. Dawson). Individual papers contain references.

This book presents case studies of classroom research into the teaching and learning of English, mathematics, and sciences, drawing on the experiences of teacher researchers who, in partnership with their local education agencies and local universities, set out to intervene in key areas of the primary curriculum. After "Introduction: Inviting Research" (Olwen McNamara and Bill Rogers), there are 12 papers in three parts. Part 1, "Emerging Issues in Teacher Research," includes (1) Evidence-Based Practice through Practice-Based Evidence" (Olwen McNamara); (2) "Research and the Professional Self" (Anne Campbell); and (3) "Using Videos to Investigate Speaking and Listening" (Liz Jones). Part 2, "Insights into Teacher Research," includes (4) "Happily Ever After: Plotting Effective Narrative Writing with 10-Year-Old Children" (Gudrun Heatley and Ian Stronach); (5) "Helping Weak Readers Up the Reading Ladder" (Sue Jennings); (6) "One Mouth, Two Ears: Seeking Ways to Make Children and Teachers Effective Speakers and Listeners" (Sarah Brealey and Claire Van-Es); (7) "'Not Only, but Also...': 'Hard' and 'Soft' Research Stories" (Mandy Walsh and Dave Hustler); (8) "Temple Goes Mental: Researching the Learning and Teaching of Mental Arithmetic" (Gary Gornell and Rob Halsall); (9) 'Homing in' on Mathematics" (Brian Corbin and Sandy Holt); (10) "Balancing the Forces: Researching Primary Science in the Classroom" (Dave Heywood and Ann-Marie Roberts); and (11) "Streaming Reviewed: Some Reflections from an Inner-City, Multi-Ethnic Primary School" (Mike Berry, Helen White, and Peter Foster). Part 3, "Reflections upon Collaborative Research," includes (12) "Working Together: The Long Spoons and Short Straws of Collaboration" (Ian Stronach and Olwen McNamara). (Papers contain references.) (SM)

This book contains 16 papers on the theory, research, and practice of adult numeracy development. The following papers are included: "The Numeracy Challenge" (Iddo Gal); "Numeracy, Mathematics, and Adult Learning" (Diane Coben); "Building a Problem-Solving Environment for Teaching Mathematics" (Peter Kloosterman, Bin Hassan Mohamad-Ali, Lynda R. Wiest); "Preparing Adult Students to Be Better Decision Makers" (Robert Clemen, Robin Gregory); "Instructional Strategies for Adult Numeracy Education" (Lynda Ginsburg, Iddo Gal); "Characteristics of Adult Learners of Mathematics" (James Steele Foerch); "Adult Numeracy at the Elementary Level: Addition and Subtraction Up to 100" (Wim Matthijsse); "Technology and the Development of Mathematical Skills in Adult Learners" (Betty Hurley Lawrence); "Teaching Mathematics to Adults with Specific Learning Difficulties" (Martha Sacks, Dorothy M. Cebula); "Writing about Life: Creating Original Math Projects with Adults" (Kare Hicks McCormick, Elizabeth Wadlington); "Learning to Learn: Mathematics as Problem Solving" (Leslie Arriola); "Journey into Journal Jottings: Mathematics as Communication" (Donna Curry); "The Challenge of Diversity in Adult Numeracy Instruction" (Harriet Hartman); "Mathematics and the Traditional Work of Women" (Mary Harris); "Assessment in Adult Numeracy Education: Issues and Principles for Good Practice" (Joy Cumming, Iddo Gal); and "Assessment of Adult Students' Mathematical Strategies" (Mieke van Groenestijn). Many papers contain substantial bibliographies. An author index and a subject index are included. (MN)

By studying and practicing metacognition, teachers and parents are instilling positive attitudes toward learning by teaching how-to-learn skills that prepare children for assessing their own thinking about learning as they become more and more developmentally prepared. This book stresses the strategies for thinking in mathematical terms without paper and pencil. It contains a series of mentally manipulative card games for children age three to seven. Many games have been modified to allow teachers to use them in self-directed centers within classrooms. Sixty games and 10 activities are included. These games are aimed at improving number sense, arithmetic, comparison, counting, and other important skills for elementary mathematics students. (ASK)

Although the name of the person who prepared this seven-page manuscript, and of the place where it was prepared, are unknown, the last owner indicated that the manuscript was purchased from a very long-established family in Maine, New England. Importantly, the paper is clearly watermarked, and the watermark indicates the paper was made in 1666 or 1667. We have assumed that the paper was brought from Europe to New England during the second half of the 1660s, and that the writing in the manuscript was done in New England. If that was indeed the case then this is easily the oldest of known extant North American cyphering books and, in that sense, is extraordinary. A second notable feature of the manuscript is that the mathematics and spelling are at a very low level. Two other interesting features of the manuscript are: (a) the person who prepared it seemed to want to be able to claim that he or she had cyphered to the rule of three because, all of a sudden, that rule is mentioned on the last page; and (b) one of the topics mentioned was ˵halving,″ which was not a normal part of the abbaco curriculum sequence for arithmetic, but was part of the Sacrobosco curriculum sequence for arithmetic. [ABSTRACT FROM AUTHOR]

This book contributes to a growing body of research relevant to efforts to make algebra an integral part of early mathematics instruction, an area of studies that has come to be known as Early Algebra. It provides both a rationale for promoting algebraic reasoning in the elementary school curriculum and empirical data to support it. The authors regard Early Algebra not as accelerated instruction but as an approach to existing topics in the early mathematics curriculum that highlights their algebraic character. Each chapter shows young learners engaged in mathematics tasks where there has been a shift away from computations on specific amounts toward thinking about relations and functional dependencies. The authors show how young learners attempt to work with mathematical generalizations before they have learned formal algebraic notation. The book, suitable as a text in undergraduate or graduate mathematics education courses, includes a CD-ROM with additional text and video footage on how students reason about addition and subtraction as functions; on how students understand multiplication when it is presented as a function; and on how children use notations in algebraic problems involving fractions. These three video papers (written text with embedded video footage) present relevant discussions that help identify students' mathematical reasoning. The printed text in the book includes transcriptions of the video episodes in the CD-ROM. "Bringing Out the Algebraic Character of Arithmetic" is aimed at researchers, practitioners, curriculum developers, policy makers and graduate students across the mathematics education community who wish to understand how young learners deal with algebra before they have learned about algebraic notation. Following a preface, Rethinking Early Mathematics Education: Interpreting Research about Learning Algebra, this book in divided into two parts. Part I, Interview Studies, presents the first two chapters of the book: (1) Young Children's Understanding of Equivalences; and (2) Can Young Students Solve Equations? Part II, Classroom Studies, then presents chapters: (3) Addition Operations as Functions; (4) From Quantities to Ratio, Functions, and Algebraic Notation; (5) On Children's Written Notation to Solve Problems; and (6) Discussion.

This collection of papers was solicited from a variety of educators in an effort to provide direction to teachers, curriculum developers and textbook publishers on topics in mathematics education that are consistently mentioned in recent national reports and study groups. The consensus of reports sponsored by various professional associations suggests the topics addressed in this document. It contains papers on: (1) mathematics content; (2) geometry at the middle school level; (3) probability and statistics at the middle school level; (4) the inclusion of number theory in the mathematics curriculum; (5) estimation and mental computation; (6) problem solving; (7) mental images and visual thinking; (8) the role of technology in mathematics education; and (9) the development of teachers' conceptualization of mathematics. Because many of the professional groups addressing these topics have had difficulty in establishing definitions and directions for teachers, this document is an effort to address each topic as it would (should or could) appear in textbooks for students moving from arithmetic to algebra. (TW)

Arithmetic is the major focus of elementary mathematics instruction. This book offers lessons for developing children's numerical understanding and skills. The lessons help children learn to estimate, understand numerical relationships, develop number sense, compute mentally and with paper and pencil, and use arithmetic as a tool to solve problems. Practical and child-centered, the lessons show teachers how to use regular classroom routines, children's literature, manipulative materials, and real-world problems. (KHR)

This book contains a collection of multiplication lessons that support curriculum and instruction. The goals of the lessons are to give all students the chance to learn how to mentally multiply by 10, powers of 10, and multiples of 10; use the distributive property to calculate products; use paper and pencil to record thinking when solving problems involving multi-digit multiplication; identify factors, multiples, products, primes, and compositions; and explain how multiplication relates to addition and division. In order to help teachers with planning and teaching the lessons, each lesson is organized into sections that include an overview, materials, time, teaching directions, teaching notes, a vignette describing the actual lesson, follow-up suggestions, and questions and discussion. (KHR)

The goal of this book is to help students make sense of mathematics and become confident in their ability to do so. Section 1: "Foundations of Teaching Mathematics," includes chapters entitled: (1) "Teaching Mathematics: Reflections and Directions"; (2) "Exploring What It Means to Do Mathematics"; (3) "Developing Understanding in Mathematics"; (4) "Teaching through Problem Solving"; and (5) "Building Assessment into Instruction." Section 2: "Development of Mathematical Concepts and Procedures"; (6) "Developing Number Concepts and Number Sense"; (7) "Developing Meanings for the Operations"; (8) "Helping Children Master the Basic Facts"; (9) "Whole-Number Place-Value Development"; (10) "Mental Computation and Estimation"; (11) "Pencil-and-Paper Computation with Whole Numbers"; (12)"Developing Fraction Concepts"; (13) "Computation with Fractions"; (14) "Decimal and Percent Concepts and Decimal Computation"; (15) "Developing Concepts of Ratio and Proportion"; (16) "Developing Measurement Concepts"; (17) "Geometric Thinking and Geometric Concepts"; (18) "Logical Reasoning: Attribute and Pattern Activities"; (19) "Exploring Concepts of Probability and Statistics"; (20) "Preparing for Algebra"; and (21) "Functions and Variables." Section 3 includes chapters entitled (22) "Planning for Effective Instruction"; (23) "Teaching All Children Mathematics"; and (24) "Technology and School Mathematics." Includes Appendix A: Curriculum and Evaluation Standards for School Mathematics, Appendix B: Professional Standards for Teaching Mathematics. (Contains 426 references, an index and Blackline Masters and Materials Construction Tips.) (LH)

The fundamentals of algebra and algebraic thinking should be a part of the background of all citizens in society. The vast increase in the use of technology requires that school mathematics ensure the teaching of algebraic thinking as well as its use at both the elementary and secondary school levels. Algebra is a universal theme that runs through all of mathematics, and it is a tool required by nearly all aspects of the economy. Many businesses and industries are requiring higher levels of thinking of their employees. This book is a set of essays, each pertaining to a specific aspect of the need to teach the fundamentals of algebra to the entire population. The following papers are included: (1) "The Problem, The Issues That Speak to Change" (Dene R. Lawson); (2) "Prior Experiences" (Hilde Howden); (3) "The Transition from Arithmetic to Algebra" (Richard Lodholz); (4) "Enhancing the Maintenance of Skills" (David J. Glatzer and Glenda Lappan); (5) "Teacher Expectations of Students Enrolled in an Algebra Course" (Ross Taylor); (6) "Instructional Strategies and Delivery Systems" (Franklin D. Demana and Bert K. Waits); and (7) "Communicating the Importance of Algebra to Students" (Paul Christmas and James T. Fey). An annotated listing of resources includes the topics of expectations, equity, learning styles, cooperative learning, practices and programs, funding sources, instructional materials, manipulatives, and computer software. (CW)

As we look back to the philosophy of the period from 1914 to 1945, we tend to think of this as a time when ‘analytic philosophy’ flourished, though of course many other types of philosophy also flourished at this time (idealism, phenomenology, pragmatism, etc.). But what was this ‘analytic philosophy’ of which John Wisdom wrote when he opened his book Problems of Mind and Matter (1934) by saying ‘It is to analytic philosophy that this book is intended to be introduction’ (1934: 1)? Wisdom makes a start at answering this question by contrasting analytic philosophy with ‘speculative’ philosophy: the contrast is that speculative philosophy aims to provide new information (for example, by proving the existence of God), whereas analytic philosophy aims only to provide clearer knowledge of facts already known. Much the same contrast is to be found in the ‘statement of policy’ which opens the first issue of the journal Analysis in 1933: papers to be published will be concerned ‘with the elucidation or explanation of facts…the general nature of which is, by common consent, already known; rather than with attempts to establish new kinds of fact about the world’ (Vol. I: 1). As we shall see, the thesis that philosophy does not aim to provide new knowledge is indeed a central theme of many ‘analytic’ philosophers of this period. But first we need to investigate the relevant conception of analysis – ‘philosophical’ analysis. [ABSTRACT FROM AUTHOR]

The 3D Set Partitioning In Hierarchical Trees (SPIHT) is a video coding algorithm extended from the SPIHT algorithm, which is initially introduced by A. Said and W. Pearlman for image coding. Previous works have show that the performance of 3D SPIHT with Arithmetic Coding (AC) is comparable to H.263 and MPEG-2. Moreover, the 3D SPIHT algorithm also supports progressive video transmission with controllable bit rates. This paper presents a new configuration of adaptive arithmetic model (also known as adaptive model) which can enhance the coding efficiency of AC, and achieves better performance in terms of Peak Signal-to-Noise Ratio (PSNR). The adaptive model is a very important module in AC, which is used to store the probability distribution of all the symbols that appear in a system. In the new configuration, each type of output bits in 3D SPIHT is assigned with a separate set of adaptive models. This new configuration takes into account the different probability patterns which exist in each type of output bits. On the other hand, the maximum frequency used to reset the adaptive model is also presented. This is a parameter that determines the adaptation rate of the AC. The simulation results show that the new configuration can improve the mean PSNR by 0.2 to 1.66 dB for various video test sequences in QCIF and SIF formats. [ABSTRACT FROM AUTHOR]

This paper describes the implementation of an advanced multiplication algorithm on quantum-dot cellular automata (QCA) nanotechnology, promising molecular density circuits with extreme operating frequencies, using a single homogeneous layer of the basic cells. The multiplier layout is verified with time-dependent quantum mechanical simulation, to ensure stable ground state computation under the fine-grained pipelining constraints of the technology. The novel design utilizes radix-4 modified Booth recoding and ultra-fast carry-save addition, resulting in stall-free pipeline operation, with twice the throughput of the previous sequential structure and minimized active circuit area. [ABSTRACT FROM AUTHOR]

Quantum-dot cellular automata nanotechnology promises molecular digital circuits with ultra-high clock frequencies, to replace the traditional approaches reaching their physical limits. Although large scale utilization requires still several breakthroughs, there has been serious effort in digital design on this sunrise technology. This review describes the basic concepts of the nanotechnology and the most important existing designs, providing new research directions for the digital community. [ABSTRACT FROM AUTHOR]

Normal basis in finite fields has proved to be very useful for fast arithmetic computations. The elements in a normal basis are exactly the roots of a normal polynomial. Hence a normal polynomial is just another way of describing a normal basis. In this paper, we give some computational results of normal polynomial up to degree n = 19 according to the fast algorithm from Chang et al. [1]. [ABSTRACT FROM AUTHOR]

The article features math lessons/activities using the calculator. One activity involves making up calculator messages by translating some numbers into letters. Another activity is a multiplication trick, which uses a scientific or graphic calculator for speed. A calculator trick is also presented to help double-check large sums of numbers.

Chapter 1 of the book "Stop Faking It! Finally Understanding Science So You Can Teach It" is presented. It demonstrates the difference between the memorization of rules and the comprehension of various processes used in mathematics. It likewise discusses the application of arithmetic operations, including addition, subtraction, multiplication and division, for numbers under the base 10 number system.

Chapter XXX of the book "Villette," by Charlotte Bronte is presented. It focuses on the behavior of Emanuel towards his co-teachers especially Snowe and how he works hard to recommend Snowe for the position left by Madame Panache. It highlights how Emanuel guided and assisted Snowe upon learning that she has an educational deficiency in arithmetic.