Download or read book The Teaching and Learning of Algorithms in School Mathematics written by Lorna J. Morrow and published by . This book was released on 1998 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1998 yearbook aims to stimulate and answer questions that all educators of mathematics need to consider to adapt school mathematics for the 21st century. The papers included in this book cover a wide variety of topics, including student-invented algorithms, the assessment of such algorithms, algorithms from history and other cultures, ways that algorithms grow and change, and the importance of algorithms in a technological world. Chapters include: (1) "Whither Algorithms? Mathematics Educators Express Their Views" (Lorna J. Morrow); (2) "Paper-and-Pencil Algorithms in a Calculator-and-Computer Age" (Zalman Usiskin); (3) "What Is an Algorithm? What Is an Answer?" (Stephen B. Maurer); (4) "Algorithmic and Recursive Thinking: Current Beliefs and Their Implications for the Future" (Tabitha T.Y. Mingus and Richard M. Grassl); (5) "Teaching Mental Algorithms Constructively" (Alistair McIntosh); (6) "What Criteria for Student-Invented Algorithms?" (Patricia F. Campbell, Thomas E. Rowan, and Anna R. Suarez); (7) "The Importance of Algorithms in Performance-Based Assessments" (Dominic Peressini and Eric Knuth); (8) "A Brief History of Algorithms in Mathematics" (Janet Heine Barnett); (9) "Understanding Algorithms from Their History" (Barnabas Hughes); (10) "An Exploration of the Russian Peasant Method of Multiplication" (Laura Sgroi); (11) "Hammurabi's Calculator" (Clifford Wagner); (12) "Capsule Lessons in Alternative Algorithms for the Classroom" (Diane E. Mason); (13) "Historical Algorithms: Sources for Student Projects" (Rheta N. Rubenstein); (14)"Alternative Algorithms for Whole-Number Operations" (William M. Carroll and Denise Porter); (15) "My Family Taught Me This Way" (Pilar Ron); (16) "Calculators in Primary Mathematics: Exploring Number Before Teaching Algorithms" (Susie Groves and Kaye Stacey); (17) "The Harmful Effects of Algorithms in Grades 1-4" (Constance Kamii and Ann Dominick); (18) "A Contextual Investigation of Three-Digit Addition and Subtraction" (Kay McClain, Paul Cobb, and Janet Bowers); (19) "Children's Invented Algorithms for Multidigit Multiplication Problems" (Jae-Meen Baek); (20) "The 'Write' Way To Mathematical Understanding" (David J. Whitin and Phyllis E. Whitin); (21) "Letting Fraction Algorithms Emerge through Problem Solving" (DeAnn Huinker); (22) "Developing Algorithms for Adding and Subtracting Fractions" (Glenda Lappan and Mary K. Bouck); (23) "A Constructed Algorithm for the Division of Fractions" (Janet Sharp); (24) "Dividing Fractions by Using the Ratio Table" (Jonathan L. Brendefur and Ruth C. Pitingoro); (25) "Teaching Statistics: What's Average?" (Susan N. Friel); (26) "Algorithms for Solving Nonroutine Mathematical Problems" (Jinfa Cai and Connie Laughlin); (27) "Algebra and Technology" (Ann Bruner, Kathy Coskey, and Sharon K. Sheehan); (28) "A New Look at an Old Algorithm: The Semiaverage Line" (Michael McNamara); (29) "Random-Number Generators: A Mysterious Use of Algorithms" (Stephanie O. Robinson and Donald J. Dessart); (30) "Algorithmic Problem Solving in Discrete Mathematics" (Eric W. Hart); (31) "The Traveling Salesperson: Some Algorithms Are Different" (Lowell Leake); and (32) "Using Algorithms To Generate Objects of Mathematical Interest" (Elaine Simmt). (ASK)
Download or read book Figuring Out Fluency in Mathematics Teaching and Learning Grades K 8 written by Jennifer M. Bay-Williams and published by Corwin. This book was released on 2021-03-02 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.
Download or read book Teaching and Learning Discrete Mathematics Worldwide Curriculum and Research written by Eric W. Hart and published by Springer. This book was released on 2017-12-09 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses examples of discrete mathematics in school curricula, including in the areas of graph theory, recursion and discrete dynamical systems, combinatorics, logic, game theory, and the mathematics of fairness. In addition, it describes current discrete mathematics curriculum initiatives in several countries, and presents ongoing research, especially in the areas of combinatorial reasoning and the affective dimension of learning discrete mathematics. Discrete mathematics is the math of our time.' So declared the immediate past president of the National Council of Teachers of Mathematics, John Dossey, in 1991. Nearly 30 years later that statement is still true, although the news has not yet fully reached school mathematics curricula. Nevertheless, much valuable work has been done, and continues to be done. This volume reports on some of that work. It provides a glimpse of the state of the art in learning and teaching discrete mathematics around the world, and it makes the case once again that discrete mathematics is indeed mathematics for our time, even more so today in our digital age, and it should be included in the core curricula of all countries for all students.
Download or read book The Mathematical Education of Teachers written by Conference Board of the Mathematical Sciences and published by American Mathematical Soc.. This book was released on 2001 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now is a time of great interest in mathematics education. Student performance, curriculum, and teacher education are the subjects of much scrutiny and debate. Studies on the mathematical knowledge of prospective and practicing U. S. teachers suggest ways to improve their mathematical educations. It is often assumed that because the topics covered in K-12 mathematics are so basic, they should be easy to teach. However, research in mathematics education has shown that to teach well,substantial mathematical understanding is necessary--even to teach whole-number arithmetic. Prospective teachers need a solid understanding of mathematics so that they can teach it as a coherent, reasoned activity and communicate its elegance and power. This volume gathers and reports current thinkingon curriculum and policy issues affecting the mathematical education of teachers. It considers two general themes: (1) the intellectual substance in school mathematics; and (2) the special nature of the mathematical knowledge needed for teaching. The underlying study was funded by a grant from the U.S. Department of Education. The mathematical knowledge needed for teaching is quite different from that required by students pursuing other mathematics-related professions. Material here is gearedtoward stimulating efforts on individual campuses to improve programs for prospective teachers. This report contains general recommendations for all grades and extensive discussions of the specific mathematical knowledge required for teaching elementary, middle, and high-school grades, respectively.It is also designed to marshal efforts in the mathematical sciences community to back important national initiatives to improve mathematics education and to expand professional development opportunities. The book will be an important resource for mathematics faculty and other parties involved in the mathematical education of teachers. Information for our distributors: This series is published in cooperation with the Mathematical Association of America.
Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
Download or read book Teaching and Learning About Whole Numbers in Primary School written by Terezinha Nunes and published by Springer. This book was released on 2016-08-29 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished – the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible to compare different approaches to making numbers meaningful in the classroom and contrast the outcomes of these diverse aspects of teaching. The book identifies themes and trends in empirical research on the teaching and learning of whole numbers since the launch of the major journals in mathematics education research in the 1970s. It documents a shift in focus in the teaching of arithmetic from research about teaching written algorithms to teaching arithmetic in ways that result in flexible approaches to calculation. The analysis of studies on quantitative reasoning reveals classifications of problem types that are related to different cognitive demands and rates of success in both additive and multiplicative reasoning. Three different approaches to quantitative reasoning education illustrate current thinking on teaching problem solving: teaching reasoning before arithmetic, schema-based instruction, and the use of pre-designed diagrams. The book also includes a summary of contemporary approaches to the description of the knowledge of numbers and arithmetic that teachers need to be effective teachers of these aspects of mathematics in primary school. The concluding section includes a brief summary of the major themes addressed and the challenges for the future. The new theoretical framework presented offers researchers in mathematics education novel insights into the differences between empirical studies in this domain. At the same time the description of the two meanings of numbers helps teachers distinguish between the different aims of teaching about numbers supported by diverse methods used in primary school. The framework is a valuable tool for comparing the different methods and identifying the various assumptions about teaching and learning.
Download or read book Integrating Differentiated Instruction and Understanding by Design written by Carol Ann Tomlinson and published by ASCD. This book was released on 2006-01-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teachers struggle every day to bring quality instruction to their students. Beset by lists of content standards and accompanying "high-stakes" accountability tests, many educators sense that both teaching and learning have been redirected in ways that are potentially impoverishing for those who teach and those who learn. Educators need a model that acknowledges the centrality of standards but also ensures that students truly understand content and can apply it in meaningful ways. For many educators, Understanding by Design addresses that need. Simultaneously, teachers find it increasingly difficult to ignore the diversity of the learners who populate their classrooms. Few teachers find their work effective or satisfying when they simply "serve up" a curriculum—even an elegant one—to students with no regard for their varied learning needs. For many educators, Differentiated Instruction offers a framework for addressing learner variance as a critical component of instructional planning. In this book the two models converge, providing readers fresh perspectives on two of the greatest contemporary challenges for educators: crafting powerful curriculum in a standards-dominated era and ensuring academic success for the full spectrum of learners. Each model strengthens the other. Understanding by Design is predominantly a curriculum design model that focuses on what we teach. Differentiated Instruction focuses on whom we teach, where we teach, and how we teach. Carol Ann Tomlinson and Jay McTighe show you how to use the principles of backward design and differentiation together to craft lesson plans that will teach essential knowledge and skills for the full spectrum of learners. Connecting content and kids in meaningful ways is what teachers strive to do every day. In tandem, UbD and DI help educators meet that goal by providing structures, tools, and guidance for developing curriculum and instruction that bring to students the best of what we know about effective teaching and learning.
Download or read book The Math We Need to Know and Do in Grades PreK 5 written by Pearl Gold Solomon and published by Corwin Press. This book was released on 2006-06-14 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers elementary math teachers a step-by-step approach to planning standards-based curriculum, instruction, and assessment, with sample activities, problems, and assessments and expert advice for every stage of the process.
Download or read book The Teaching and Assessing of Mathematical Problem Solving written by National Council of Teachers of Mathematics and published by Routledge. This book was released on 1988 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-08-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
Download or read book Teaching Mathematics written by Michelle Selinger and published by Routledge. This book was released on 2013-10-31 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this reader, maths teachers in the early years of their careers will find a concise yet comprehensive guide to developments in mathematics teaching in secondary schools and the controversies which currently surround it. After a brief summary of the historical context, a series of short articles provides a range of perspectives on various issues of current debate which will help new teachers in the development of their own teaching styles. These include the impact of computers and calculators in maths teaching, the various arguments about the use of published schemes and for more investigational approaches to the curriculum, and the way in which social and cultural factors can be approached through the teaching of various topics in mathematics. The final section looks at how teachers might continue their professional development through action research in their own classrooms.
Download or read book Teaching Computational Thinking written by Maureen D. Neumann and published by MIT Press. This book was released on 2021-12-21 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide for educators to incorporate computational thinking—a set of cognitive skills applied to problem solving—into a broad range of subjects. Computational thinking—a set of mental and cognitive tools applied to problem solving—is a fundamental skill that all of us (and not just computer scientists) draw on. Educators have found that computational thinking enhances learning across a range of subjects and reinforces students’ abilities in reading, writing, and arithmetic. This book offers a guide for incorporating computational thinking into middle school and high school classrooms, presenting a series of activities, projects, and tasks that employ a range of pedagogical practices and cross a variety of content areas. As students problem solve, communicate, persevere, work as a team, and learn from mistakes, they develop a concrete understanding of the abstract principles used in computer science to create code and other digital artifacts. The book guides students and teachers to integrate computer programming with visual art and geometry, generating abstract expressionist–style images; construct topological graphs that represent the relationships between characters in such literary works as Harry Potter and the Sorcerer’s Stone and Romeo and Juliet; apply Newtonian physics to the creation of computer games; and locate, analyze, and present empirical data relevant to social and political issues. Finally, the book lists a variety of classroom resources, including the programming languages Scratch (free to all) and Codesters (free to teachers). An accompanying website contains the executable programs used in the book’s activities.
Download or read book Children Learn Mathematics written by and published by BRILL. This book was released on 2008-01-01 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Improving the quality of education is an important endeavor of educational policy and TAL aims to contribute to this. TAL is a project initiated by the Dutch Ministry of Education, Culture and Sciences, and carried out by the Freudenthal Institute (FI) of Utrecht University and the Dutch National Institute for Curriculum Development (SLO), in collaboration with the Rotterdam Center for Educational Services (CED). The quality of education can be improved in many ways. TAL proposes to do this by providing insights into the broad outline of the learning-teaching process and its internal coherence. It aims to be a support for teachers alongside mathematics textbook series. Furthermore, TAL can provide extra support for teachers if it is incorporated into a circle of implementation.
Download or read book What We Know About Mathematics Teaching and Learning written by McREL and published by Solution Tree Press. This book was released on 2011-09-20 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book supports mathematics education reform and brings the rich world of education research and practice to pre-K–12 educators. Designed for accessibility, each chapter is broken down into important questions. For each question, the authors provide background information from a research perspective, offer implications for improving classroom instruction, and list resources for further reading.
Download or read book What s Math Got to Do with It written by Jo Boaler and published by Penguin. This book was released on 2008 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses how to make mathematics for children enjoyable and why it is important for American children to succeed in mathematics and choose math-based career paths in the future.
Download or read book Beyond Classical Pedagogy written by Terry Wood and published by Routledge. This book was released on 2014-04-04 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of the National Council of Teachers of Mathematics Standards in 1989 sparked a sea change in thinking about the nature and quality of mathematics instruction in U.S. schools. Much is known about transmission forms of mathematics teaching and the influence of this teaching on students' learning, but there is still little knowledge about the alternative forms of instruction that have evolved from the recent widespread efforts to reform mathematics education. Beyond Classical Pedagogy: Teaching Elementary School Mathematics reports on the current state of knowledge about these new instructional practices, which differ in significant ways from the traditional pedagogy that has permeated mathematics education in the past. This book provides a research-based view of the nature of facilitative teaching in its relatively mature form, along with opposing views and critique of this form of pedagogy. The focus is on elementary school mathematics classrooms, where the majority of the reform-based efforts have occurred, and on the micro level of teaching (classroom interaction) as a source for revealing the complexity involved in teaching, teachers' learning, and the impact of both on children's learning. The work in elementary mathematics teaching is situated in the larger context of research on teaching. Research and insights from three disciplinary perspectives are presented: the psychological perspective centers on facilitative teaching as a process of teachers' learning; the mathematical perspective focuses on the nature of the mathematical knowledge teachers need in order to engage in this form of teaching; the sociological perspective attends to the interactive process of meaning construction as teachers and students create intellectual communities in their classrooms. The multidisciplinary perspectives presented provide the editors with the necessary triangulation to provide confirming evidence and rich detail about the nature of facilitative teaching. Audiences for this book include scholars in mathematics education and teacher education, teacher educators, staff developers, and classroom teachers. It is also appropriate as a text for graduate courses in mathematics education, teacher education, elementary mathematics teaching methods, and methods of research in mathematics education.
Download or read book Yearbook written by National Council of Teachers of Mathematics and published by . This book was released on 1972 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:
