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Using and Applying Mathematics at Key Stage 2: A Guide to Teaching Problem Solving and Thinking Skills
by Sue Lowndes Elaine SellarsAll pupils - able children included - need to be taught strategies to enable their thinking skills to progress. They also need help with developing different approaches to problem solving. A sustained piece of work that requires perseverance, logical strategies, and refinement of method and extension of the original task is not the same as a straightforward quick-fix type problem. Both types of problem solving need to be taught. This book presents a series of activities that can be used with whole classes to provide a curriculum for the teaching of problem solving and the development of thinking skills. Each tried and tested investigation is clearly explained with ideas on how to introduce the task to a class, full solutions and resource sheets. Activities include prisoners: a fun way of generating square numbers; handshakes: exploring arithmetic progressions; T-shape: an activity to lead pupils from numerical calculations to algebraic generalizations; frogs: encouraging systematic working and listing; and opposite corners: an advanced piece of work for independent learners.
Using and Interpreting Statistics
by Eric W. CortyEric Corty's engaging textbook is exceptionally well suited for behavioral science students studying statistical practice in their field for the first time. An award-winning master teacher, Corty speaks to students in their language, with an approachable voice that conveys the basics of collecting and understanding statistical data step by step. Examples come from the behavioral and social sciences, as well as from recognizable aspects of everyday life to help students see the relevance of what they are studying.
Using and Understanding Mathematics: A Quantitative Reasoning Approach
by Jeffrey Bennett William BriggsUsing and Understanding Mathematics: A Quantitative Reasoning Approach prepares students for the mathematics they will encounter in college courses, their future career, and life in general. Its quantitative reasoning approach helps students to build the skills needed to understand major issues in everyday life, and compels students to acquire the problem-solving tools that they will need to think critically about quantitative issues in contemporary society.
Using And Understanding Mathematics: A Quantitative Reasoning Approach
by Jeffrey O. Bennett William L. BriggsThe standard in quantitative reasoning instruction – by authorities in the field <P><P> The 7th Edition of Using & Understanding Mathematics by Jeff Bennett and Bill Briggs aims to prepare students for the mathematics they will encounter in other college courses, future careers, and life. <P><P> The authors' goal is to develop students’ ability to reason with quantitative information in a way that will help achieve success in their careers, and to give students the critical-thinking and quantitative reasoning skills needed to understand major life issues. Through new resources in MyLab™ Math and updated content within the text, the Bennett/Briggs team continues to set the standard in quantitative reasoning instruction.
Using and Understanding Mathematics: A Quantitative Reasoning Approach (5th Edition)
by Jeffrey O. Bennett William L. BriggsUsing and Understanding Mathematics: A Quantitative Reasoning Approach, Fifth Edition increases readers' mathematical literacy so that they better understand the mathematics used in their daily lives, and can use math effectively to make better decisions every day. Contents are organized with that in mind, with engaging coverage in sections like Taking Control of Your Finances, Dividing the Political Pie, and a full chapter about Mathematics and the Arts. Prologue: Literacy for the Modern World. Logic and Problem Solving:Thinking Critically; Approaches to Problem Solving. Quantitative Information in Everyday Life:Numbers in the Real World; Managing Your Money. Probability and Statistics:Statistical Reasoning; Putting Statistics to Work; Probability: Living with the Odds. Modeling:Exponential Astonishment; Modeling Our World; Modeling with Geometry. Further Applications:Mathematics and the Arts; Mathematics and Politics; Mathematics and Business. For all readers interested in a quantitative reasoning approach to using and understanding mathematics.
Using Assessment To Reshape Mathematics Teaching: A Casebook for Teachers and Teacher Educators, Curriculum and Staff Development Specialists (Studies in Mathematical Thinking and Learning Series)
by Sandra K. Wilcox Perry E. LanierThis casebook is intended to support professionals who are working in a variety of contexts to use classroom-based assessment more effectively to support teacher learning and teaching change, and to enhance the opportunities for all students to develop mathematical power. It grows out of a collaboration of mathematics teachers and teacher educators, and mathematicians, to better understand the role of assessment as an ongoing activity to help teachers reshape their own teaching practices. At the heart of each case is using assessment to make sense of what students understand and what they are confused about, deciding what counts as evidence of that understanding, and using the analysis to consider what the teacher's next instructional moves might be. All of the cases in this volume are built around actual episodes from mathematics classrooms. Intended as decision-making exercises, they present the raw data of classroom events in a straightforward way and are designed to stimulate analysis and reflection; provoke various and sometimes conflicting interpretations of an event; bring to the fore deeply held beliefs of beginning and experienced teachers so they can be reconsidered; and engage professionals in pedagogical problem solving in the context of complex classroom settings. This volume reflects the growing interest in cases as a pedagogical tool in teacher professional development. The cases are organized to take up key themes of the NCTM Professional Teaching Standards in ways that will assist and support teachers, teacher educators, and curriculum and staff development specialists in learning to assess and in linking assessment with curriculum, teaching, and learning. Although each case contains many ideas for linking assessment with curriculum and instruction, the most powerful use of these materials resides in their design intended to foster conversations among groups of professional colleagues. The editors' field-testing of the cases--in initial teacher certification courses and in in-service workshops--has shown that they prompt engaging and demanding analysis through a variety of analytic lenses. A videotape containing vignettes for four of the cases in the Casebook is available with this book. Transcriptions of the video vignettes are printed in the case materials in the book. Course instructors and professional development facilitators will need both the Casebook and the videotape and should order the Casebook/Video set. The video can also be ordered separately.
Using Basic Statistics in the Behavioral and Social Sciences
by Annabel Ness EvansUsing Basic Statistics in the Behavioral and Social Sciences, Fifth Edition, by Annabel Ness Evans, presents introductory statistics in a practical, conceptual, and humorous way, reducing the anxiety that many students experience in introductory courses. Avoiding complex notation and derivation, the book focuses on helping readers develop an understanding of the underlying logic of statistics. Practical Focus on Research boxes engage students with realistic applications of statistics, and end-of-chapter exercises ensure student comprehension. This exciting new edition includes a greater number of realistic and engaging global examples within the social and behavioral sciences, making it ideal for use within many departments or in interdisciplinary settings.
Using Children's Literature to Teach Problem Solving in Math: Addressing the Standards for Mathematical Practice in K–5
by Jeanne WhiteLearn how children’s literature can help K–5 students see the real-life applications of mathematical concepts. This user-friendly book shows how to use stories to engage students in building critical reasoning, abstract thinking, and communication skills, all while helping students understand the relevance of math in their everyday lives. Each chapter is dedicated to one of the eight Standards for Mathematical Practice, and offers examples of children’s literature that can be used to help students develop that practice. You’ll find out how to: Encourage students to persevere in solving mathematical problems and use multiple approaches to find the answer; Help students reason abstractly with the aid of concrete objects and visuals; Guide students in constructing arguments to explain their reasoning and engage in critical discussion with their peers; Teach students to recognize mathematical patterns and use them to solve problems efficiently; And more! The book offers activities for beginners as well as for more advanced problem solvers. Each chapter also provides guidance for ELLs and students with special needs, so no matter your classroom environment, you’ll be able to use these strategies to make math class more dynamic, engaging, and fun.
Using Data to Improve Student Learning: Theory, Research and Practice (The Enabling Power of Assessment #9)
by Graham S. MaxwellThis book offers a coherent research-based overview and analysis of theories and practices in using data to improve student learning. It clarifies what 'use of data' means and differentiates the different levels of decision-making in education (relating to the system, district, school, classroom, or individual student). The relationship between data and decision-making is considered and various movements in the use of data to improve student learning are analysed, especially from the perspective of their assumptions and effects. This leads to a focus on effective educational decision-making as a social process requiring collaboration among all relevant participants. It also requires a clear understanding of educational aims, and these are seen to transcend what can be assessed by standardised tests. The consequences of this analysis for decision processes are explored and conclusions are drawn about what principles might best guide educational practice as well as what ambiguities remain. Throughout, the focus is on what existing research says about each of the issues explored.
Using Design Research and History to Tackle a Fundamental Problem with School Algebra
by Sinan Kanbir M. A. Ken Clements Nerida F. EllertonIn this well-illustrated book the authors, Sinan Kanbir, Ken Clements, and Nerida Ellerton, tackle a persistent, and universal, problem in school mathematics--why do so many middle-school and secondary-school students find it difficult to learn algebra well? What makes the book important are the unique features which comprise the design-research approach that the authors adopted in seeking a solution to the problem. The first unique feature is that the authors offer an overview of the history of school algebra. Despite the fact that algebra has been an important component of secondary-school mathematics for more than three centuries, there has never been a comprehensive historical analysis of factors influencing the teaching and learning of that component. The authors identify, through historical analysis, six purposes of school algebra: (a) algebra as a body of knowledge essential to higher mathematical and scientific studies, (b) algebra as generalized arithmetic, (c) algebra as a prerequisite for entry to higher studies, (d) algebra as offering a language and set of procedures for modeling real-life problems, (e) algebra as an aid to describing structural properties in elementary mathematics, and (f) algebra as a study of variables. They also raise the question whether school algebra represents a unidimensional trait. Kanbir, Clements and Ellerton offer an unusual hybrid theoretical framework for their intervention study (by which seventh-grade students signifi cantly improved their elementary algebra knowledge and skills). Their theoretical frame combined Charles Sanders Peirce's triadic signifier-interpretant-signified theory, which is in the realm of semiotics, with Johann Friedrich Herbart's theory of apperception, and Ken Clements' and Gina Del Campo's theory relating to the need to expand modes of communications in mathematics classrooms so that students engage in receptive and expressive modes. Practicing classroom teachers formed part of the research team. This book appears in Springer's series on the "History of Mathematics Education. " Not only does it include an important analysis of the history of school algebra, but it also adopts a theoretical frame which relies more on "theories from the past," than on contemporary theories in the field of mathematics education. The results of the well-designed classroom intervention are sufficiently impressive that the study might have created and illuminated a pathway for future researchers to take.
Using Event-B for Critical Device Software Systems
by Neeraj Kumar SinghDefining a new development life-cycle methodology, together with a set of associated techniques and tools to develop highly critical systems using formal techniques, this book adopts a rigorous safety assessment approach explored via several layers (from requirements analysis to automatic source code generation). This is assessed and evaluated via a standard case study: the cardiac pacemaker. Additionally a formalisation of an Electrocardiogram (ECG) is used to identify anomalies in order to improve existing medical protocols. This allows the key issue - that formal methods are not currently integrated into established critical systems development processes - to be discussed in a highly effective and informative way. Using Event-B for Critical Device Software Systems serves as a valuable resource for researchers and students of formal methods. The assessment of critical systems development is applicable to all industries, but engineers and physicians from the health domain will find the cardiac pacemaker case study of particular value.
Using Excel to Solve Statistical Problems: A Practical Guide to the Book “Statistics for Chemical and Process Engineers”
by Yuri A.W. ShardtThis book provides a complete overview of how to use Excel to solve typical statistical problems in engineering. In addition to short sections on the required theory, the focus of the book is on detailed Excel examples for solving specific problems. Furthermore, solutions are provided for standard problems that can then be re-used and modified as necessary. End-of-chapter questions allow the reader to independently test the knowledge acquired.
Using Formative Assessment to Differentiate Mathematics Instruction, Grades 4–10: Seven Practices to Maximize Learning
by Leslie E. LaudSeven easy steps to differentiating math instruction for busy teachers Staff development expert Leslie Laud provides a clear roadmap for using formative assessment to differentiate mathematics instruction for students in Grades 4–10. She presents a comprehensive framework of seven research-based practices that show teachers how to: Get started and establish norms Implement formative assessment Create tiered lessons Manage a multitasking classroom effectively Tested, reviewed, and enhanced by experienced math teachers, the book includes practical examples, reproducibles, and student activities that are easy for busy teachers to implement immediately.
Using Formative Assessment to Drive Mathematics Instruction in Grades 3-5
by Jennifer Taylor-Cox Christine OberdorfProvide targeted mathematics instruction for every child. These books combine formative assessment with practical activities to differentiate the elementary classroom. The formative assessments include student work samples at varying levels. The authors... Illustrate the distinction between a "traditional" assessment and an "enhanced" assessment. Describe specific differentiated activities so each student may consistently receive instruction geared to specific need. Provide teachers with "Questions to Assess" to determine what each child understands about the math concept. Show how to move students to higher-level mathematics thinking and to apply math concepts. Include extension activities to offer challenging work for children who have achieved skill mastery level. Each activity states a goal, the materials needed, a description of the activity, as well as specific questions to ask students. The assessments and activities are aligned with the Common Core State Standards for Mathematics and the expectations described by the National Council of Teachers of Mathematics.This resource will help teachers, principals, and curriculum directors identify students' levels of understanding about mathematics and provide concrete resources for remediation, instruction, and enrichment. These books are also an excellent resource for use during workshops and in-class observations.
Using Fundamental Analysis and an Ensemble of Classifier Models Along with a Risk-Off Filter to Select Outperforming Companies (Synthesis Lectures on Technology Management & Entrepreneurship)
by Rui Neves Manuel MouraThis book develops a quantitative stock market investment methodology using financial indicators that beats the benchmark of S&P500 index. To achieve this goal, an ensemble of machine learning models is meticulously constructed, incorporating four distinct algorithms: support vector machine, k-nearest neighbors, random forest, and logistic regression. These models all make use of financial ratios extracted from company financial statements for the purposes of predictive forecasting. The ensemble classifier is subject to a strict testing of precision which compares it to the performance of its constituent models separately. Rolling window and cross-validation tests are used in this evaluation in order to provide a comprehensive assessment framework. A risk-off filter is developed to limit risk during uncertain market periods, and consequently to improve the Sharpe ratio of the model. The risk adjusted performance of the final model, supported by the risk-off filter, achieves a Sharpe ratio of 1.63 which surpasses both the model’s performance without the filter that delivers Sharpe ratio of 1.41 and the one from the S&P500 index of 0.80. The substantial increase in risk-adjusted returns is accomplished by reducing the model’s volatility from an annual standard of deviation of 15.75% to 11.22%, which represents an almost 30% decrease in volatility.
Using Game Theory to Improve Safety within Chemical Industrial Parks
by Genserik Reniers Yulia PavlovaThough the game-theoretic approach has been vastly studied and utilized in relation to economics of industrial organizations, it has hardly been used to tackle safety management in multi-plant chemical industrial settings. Using Game Theory for Improving Safety within Chemical Industrial Parks presents an in-depth discussion of game-theoretic modeling which may be applied to improve cross-company prevention and -safety management in a chemical industrial park. By systematically analyzing game-theoretic models and approaches in relation to managing safety in chemical industrial parks, Using Game Theory for Improving Safety within Chemical Industrial Parks explores the ways game theory can predict the outcome of complex strategic investment decision making processes involving several adjacent chemical plants. A number of game-theoretic decision models are discussed to provide strategic tools for decision-making situations. Offering clear and straightforward explanations of methodologies, Using Game Theory for Improving Safety within Chemical Industrial Parks provides managers and management teams with approaches to asses situations and to improve strategic safety- and prevention arrangements.
Using IBM® SPSS® Statistics: An Interactive Hands-On Approach
by James O. AldrichUsing IBM® SPSS® Statistics: An Interactive Hands-On Approach, Third Edition gives readers an accessible and comprehensive guide to walking through SPSS®, providing them with step-by-step knowledge for effectively analyzing their data. From entering data to working with existing databases, and working with the help menu through performing factor analysis, Using IBM® SPSS® Statistics covers every aspect of SPSS® from introductory through intermediate statistics. The book is divided into parts that focus on mastering SPSS® basics, dealing with univariate statistics and graphing, inferential statistics, relational statistics, and more. Written using IBM® SPSS® version 25 and 24, and compatible with the earlier releases, this book is one of the most comprehensive SPSS® guides available.
Using IBM® SPSS® Statistics: An Interactive Hands-On Approach
by James O. AldrichUsing IBM® SPSS® Statistics: An Interactive Hands-On Approach, Third Edition gives readers an accessible and comprehensive guide to walking through SPSS®, providing them with step-by-step knowledge for effectively analyzing their data. From entering data to working with existing databases, and working with the help menu through performing factor analysis, Using IBM® SPSS® Statistics covers every aspect of SPSS® from introductory through intermediate statistics. The book is divided into parts that focus on mastering SPSS® basics, dealing with univariate statistics and graphing, inferential statistics, relational statistics, and more. Written using IBM® SPSS® version 25 and 24, and compatible with the earlier releases, this book is one of the most comprehensive SPSS® guides available.
Using IBM® SPSS® Statistics for Research Methods and Social Science Statistics
by Dr William E. WagnerReliable and student-friendly, Using IBM® SPSS® Statistics for Research Methods and Social Science Statistics by William E. Wagner, III is known for its effectiveness in helping readers learn to use SPSS software for simple data management. Now reflecting SPSS Version 23.0, the Sixth Edition includes updated examples, screenshots, and tables based on current GSS (General Social Survey) data. This manual is an excellent companion to any undergraduate social statistics and research methods text and is ideal as a stand-alone guide for those learning to use SPSS software for the first time.
Using IBM® SPSS® Statistics for Research Methods and Social Science Statistics
by Dr William E. WagnerReliable and student-friendly, Using IBM® SPSS® Statistics for Research Methods and Social Science Statistics by William E. Wagner, III is known for its effectiveness in helping readers learn to use SPSS software for simple data management. Now reflecting SPSS Version 23.0, the Sixth Edition includes updated examples, screenshots, and tables based on current GSS (General Social Survey) data. This manual is an excellent companion to any undergraduate social statistics and research methods text and is ideal as a stand-alone guide for those learning to use SPSS software for the first time.
Using IBM® SPSS® Statistics for Research Methods and Social Science Statistics
by Dr. William E. WagnerUsing IBM SPSS for Social Statistics and Research Methods supports the use of SPSS for social statistics and research methods classes and is an excellent companion to any undergraduate statistics or research methods textbook. The book covers a wide range of data analysis topics to help students working on papers, research projects, and proposals. Using examples, tables, and actual SPSS screen captures, along with current data sets from the General Social Survey, it guides users through several different kinds of SPSS files including data files, output files, and syntax files.
Using IBM® SPSS® Statistics for Research Methods and Social Science Statistics
by Dr. William E. WagnerUsing IBM SPSS for Social Statistics and Research Methods supports the use of SPSS for social statistics and research methods classes and is an excellent companion to any undergraduate statistics or research methods textbook. The book covers a wide range of data analysis topics to help students working on papers, research projects, and proposals. Using examples, tables, and actual SPSS screen captures, along with current data sets from the General Social Survey, it guides users through several different kinds of SPSS files including data files, output files, and syntax files.
Using Information Technology in Mathematics Education
by James Tooke Norma HendersonComputers have changed the ways that mathematics are taught and learned. Is your institution taking advantage of what today's technology offers?With contributions from researchers and practitioners alike, Using Information Technology in Mathematics Education explores the impact of the computer on the curriculum, the teaching and learning of mathematics, and the professional development of teachers, both pre-service and in-service.As editor James Tooke states: “The connection between mathematics and the computer is obvious. Elementary notions of mathematics gave rise to the computer; advanced notions gave it a more powerful state. As the computer advanced, it expanded mathematics, allowing the creation of further branches of the field; for instance, fractal geometry had no reality until the advent of high-speed computers.”In its look at the relationship between mathematics, the computer, and mathematics education, Using Information Technology in Mathematics Education: addresses the computer as a vehicle for teaching calculus at Texas A&M includes reports from several programs that have utilized the computer when teaching mathematics at lower levels of content than calculus such as intermediate algebra and geometry examines the computer's role in student learning probability discusses the use of computers in the professional development of teachers explores ways to use computers to reduce mathematics anxietyUsing Information Technology in Mathematics Education examines the history and impact of computers in mathematics and mathematics education--from the early, crude computer-assisted instruction efforts through LOGO software for elementary schools, through MAPLE for the university, to the Web-based calculus courses now being offered by outstanding universities. Use it to facilitate learning and teacher growth in your institution!
Using & Interpreting Statistics: A Practical Text for the Behavioral, Social, and Health Sciences,2nd Edition
by Eric W. CortyEric Corty’s engaging, easy-to-understand textbook focuses on the needs of behavioral science students encountering statistical practices for the first time. An award-winning master teacher, Corty speaks to students in their language, with an approachable voice that conveys the basics of statistics step-by-step. Examples come from the behavioral and social sciences, as well as from recognizable aspects of everyday life to help students see the relevance of statistics.
Using Mathematica for Quantum Mechanics: A Student’s Manual
by Roman SchmiedThis book revisits many of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding and visualizing analytical and numerical solutions. It subsequently uses these implementations as building blocks to solve more complex problems, such as coherent laser-driven dynamics in the Rubidium hyperfine structure or the Rashba interaction of an electron moving in 2D. The simulations are highlighted using the programming language Mathematica. No prior knowledge of Mathematica is needed; alternatives, such as Matlab, Python, or Maple, can also be used.