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Problem Solving: A statistician's guide, Second edition (Chapman & Hall/CRC Texts in Statistical Science)
by Chris ChatfieldThis book illuminates the complex process of problem solving, including formulating the problem, collecting and analyzing data, and presenting the conclusions.
Problem-solving 3-4
by Hyacinth Dorleon Karen Morrison Rodney JulienWe live in an increasingly technological and information-rich world. Education is focusingmore on enquiry and skills-based approaches. Students, even at the early levels ofschooling, are expected to develop a range of skills, including problem solving skills.Creative thinking, using information appropriately and problem solving are important for students in the school curriculum and in daily life. This book will help students learn how to apply mathematical skills in different contexts and explain how they got to their solutions.This book is easy for parents and teachers to use, and teaches multiple strategies forsolving problems, using challenging but supportive contexts. The approach is underpinnedby the Five E's approach to learning.The course will help student to:· Engage with problems meaningfully· Explore different options for approaching and solving problems· Explain how they are thinking· Elaborate on their working and processes and see connections between different areasof mathematics· Evaluate what worked and what didn't, learning from mistakes as well as successes
Problem-solving 5-6
by Hyacinth Dorleon Karen Morrison Rodney JulienWe live in an increasingly technological and information-rich world. Education is focusingmore on enquiry and skills-based approaches. Students, even at the early levels ofschooling, are expected to develop a range of skills, including problem solving skills.Creative thinking, using information appropriately and problem solving are important for students in the school curriculum and in daily life. This book will help students learn how to apply mathematical skills in different contexts and explain how they got to their solutions.This book is easy for parents and teachers to use, and teaches multiple strategies forsolving problems, using challenging but supportive contexts. The approach is underpinnedby the Five E's approach to learning.The course will help student to:· Engage with problems meaningfully· Explore different options for approaching and solving problems· Explain their thought processes · Elaborate on their working and processes and see connections between different areasof mathematics· Evaluate what worked and what didn't, learning from mistakes as well as successes
Problem Solving and Data Analysis Using Minitab: A Clear and Easy Guide to Six Sigma Methodology
by Rehman M. KhanSix Sigma statistical methodology using Minitab Problem Solving and Data Analysis using Minitab presents example-based learning to aid readers in understanding how to use MINITAB 16 for statistical analysis and problem solving. Each example and exercise is broken down into the exact steps that must be followed in order to take the reader through key learning points and work through complex analyses. Exercises are featured at the end of each example so that the reader can be assured that they have understood the key learning points. Key features: Provides readers with a step by step guide to problem solving and statistical analysis using Minitab 16 which is also compatible with version 15. Includes fully worked examples with graphics showing menu selections and Minitab outputs. Uses example based learning that the reader can work through at their pace. Contains hundreds of screenshots to aid the reader, along with explanations of the statistics being performed and interpretation of results. Presents the core statistical techniques used by Six Sigma Black Belts. Contains examples, exercises and solutions throughout, and is supported by an accompanying website featuring the numerous example data sets. Making Six Sigma statistical methodology accessible to beginners, this book is aimed at numerical professionals, students or academics who wish to learn and apply statistical techniques for problem solving, process improvement or data analysis whilst keeping mathematical theory to a minimum.
Problem-Solving and Selected Topics in Euclidean Geometry
by Michael Th. Rassias Sotirios E. Louridas"Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution. Applications of the basic geometrical methods which include analysis, synthesis, construction and proof are given. Selected problems which have been given in mathematical olympiads or proposed in short lists in IMO's are discussed. In addition, a number of problems proposed by leading mathematicians in the subject are included here. The book also contains new problems with their solutions. The scope of the publication of the present book is to teach mathematical thinking through Geometry and to provide inspiration for both students and teachers to formulate "positive" conjectures and provide solutions.
A Problem Solving Approach to Mathematics for Elementary School Teachers
by Rick Billstein Barbara Boschmans Shlomo Libeskind Johnny W. LottA Problem Solving Approach to Mathematics for Elementary School Teachers not only helps students learn the math - it provides an invaluable reference to future teachers by including professional development features and discussions of today's standards. <p><p> Revised throughout to prepare students more effectively for their own classrooms, the 13th Edition gives instructors a variety of approaches to teaching, and encourages discussion and collaboration among students and with their instructors. The MyLab(TM) Math course for this revision is updated extensively with new resources and features.
A Problem Solving Approach To Mathematics For Elementary School Teachers
by Rick Billstein Shlomo Libeskind Johnny LottA Problem Solving Approach to Mathematics for Elementary School Teachers
A Problem Solving Approach to Mathematics for Elementary School Teachers
by Shlomo Libeskind Rick Billstein Johnny LottMore than 350,000 students have prepared for teaching mathematics with A Problem Solving Approach to Mathematics for Elementary School Teachers since its first edition, and it remains the gold standard today. This text not only helps students learn the material by promoting active learning and developing skills and concepts--it also provides an invaluable reference to future teachers by including professional development features and discussions of today's standards. The Eleventh Edition is streamlined to keep students focused on what is most important. The Common Core State Standards (CCSS) have been integrated into the book to keep current with educational developments.
Problem Solving in Mathematics Education
by Peter Liljedahl Manuel Santos-Trigo Uldarico Malaspina Regina BruderThis survey book reviews four interrelated areas: (i) the relevance of heuristics in problem-solving approaches why they are important and what research tells us about their use; (ii) the need to characterize and foster creative problem-solving approaches what type of heuristics helps learners devise and practice creative solutions; (iii) the importance that learners formulate and pursue their own problems; and iv) the role played by the use of both multiple-purpose and ad hoc mathematical action types of technologies in problem-solving contexts what ways of reasoning learners construct when they rely on the use of digital technologies, and how technology and technology approaches can be reconciled. "
Problem Solving in Mathematics, Grades 3-6: Powerful Strategies to Deepen Understanding
by Alfred S. Posamentier Stephen KrulikWith sample problems and solutions, this book demonstrates how teachers can incorporate nine problem solving strategies into any mathematics curriculum to help students succeed.
Problem Solving in Mathematics Instruction and Teacher Professional Development (Research in Mathematics Education)
by Peter Liljedahl Patricio Felmer Boris KoichuRecent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the role of teachers in problem-solving classrooms and their professional development, moving onto—secondly—the role of students when solving problems, with particular consideration of factors like group work, discussion, role of students in discussions and the effect of students’ engagement on their self-perception and their view of mathematics. Finally, the book considers the question of problem solving in mathematics instruction as it overlaps with problem design, problem-solving situations, and actual classroom implementation. The volume brings together diverse contributors from a variety of countries and with wide and varied experiences, combining the voices of leading and developing researchers. The book will be of interest to any reader keeping on the frontiers of research in problem solving, more specifically researchers and graduate students in mathematics education, researchers in problem solving, as well as teachers and practitioners.
Problem Solving In Operation Management
by Patricia Esperanza Balderas-Cañas Gabriel de las Nieves Sánchez-GuerreroThis volume examines problem solving and applied systems aimed at improving performance and management of organizations. The book’s eight chapters are integrated into two parts: methodologies and techniques that discuss complex dynamic analysis of the organizations, participative processes for building trend scenarios, consultancy as a systemic intervention process, processes to promote innovative goals in organizations, and analytical processes and solid mathematical representation systems. The authors also include a model to urban parks location, an analytic model to urban services location, and a system to forecast demand with fussy sets.Describes methodologies to analyze processes in complex dynamic organizations, including as participative, interventional, innovative, and analytical approaches;Clarifies a strategies for providing structure to complex organizations and applying analytical methods to decision making;Illustrates problem holistic solving strategies;Explains how to approach several problems from a holistic point of view and how analyze the subjacent processes to make decisions.
Problem Solving in Primary Mathematics: Learning to Investigate!
by Christine Edwards-Leis Debbie RobinsonProblem Solving in Primary Mathematics is an essential text designed to support new and experienced teachers in guiding pupils through mathematical investigations and problem solving, offering a framework that children themselves can begin to adopt as they progress to greater metacognitive awareness. Underpinned by the latest international research and theory, it examines how individual pupils think and act differently and offers guidance on how to promote independence and autonomy in the classroom. It examines key topics such as: Preparing for mathematical learning Designing learning material Assessing and evaluating learning Identifying key points for intervention What to do when learning is stalled Critical numeracy for real-world problem solving Mental Model Theory and the Mental Model Mode Different approaches to problem solving and investigating Aimed at new and experienced educators, particularly those with a maths specialism, and illustrated with investigations and activities, Problem Solving in Primary Mathematics demonstrates how frameworks can be used in key mathematical areas and assists students in progressing towards more meaningful problem solving.
Problem-solving K-2
by Hyacinth Dorleon Karen Morrison Rodney JulienWe live in an increasingly technological and information-rich world. Education is focusing more on enquiry and skills-based approaches. Students, even at the early levels of schooling, are expected to develop a range of skills, including problem solving skills. Creative thinking and problem solving are not only important elements in the curriculum but they are also crucial in daily life. Students need to learn basic mathematical skills, but they also have to be able to apply these in unfamiliar contexts, communicate their thinking and explain how they got to their solutions. This book is easy for parents and teachers to use, and teaches multiple strategies for solving problems, using challenging but supportive contexts. The approach is underpinned by the Five E's approach to learning. The course will help student to: · Engage with problems meaningfully · Explore different options for approaching and solving problems· Explain how they are thinking· Elaborate on their working and processes and see connections between different areas of mathematics· Evaluate what worked and what didn't, learning from mistakes as well as successes.
Problem-Solving Methods in Combinatorics
by Pablo SoberónEvery year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests. It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book. The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.
Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12: A Resource for the Mathematics Teacher
by Alfred S. Posamentier Stephen KrulikThis updated edition presents ten strategies for solving a wide range of mathematics problems, plus new sample problems.
Problem Solving Through Recreational Mathematics
by Bonnie Averbach Orin CheinHistorically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact, using recreational mathematics -- problems, puzzles and games -- to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving them. Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire games and puzzles, and much more. Sample problems (solved in the text) whet readers' appetites and motivate discussions; practice problems solidify their grasp of mathematical ideas; and exercises challenge them, fostering problem-solving ability. Appendixes contain information on basic algebraic techniques and mathematical inductions, and other helpful addenda include hints and solutions, plus answers to selected problems. An extensive appendix on probability is new to this Dover edition.
The Problem with Math Is English: A Language-Focused Approach to Helping All Students Develop a Deeper Understanding of Mathematics
by Concepcion MolinaTeaching K-12 math becomes an easier task when everyone understands the language, symbolism, and representation of math concepts Published in partnership with SEDL, The Problem with Math Is English illustrates how students often understand fundamental mathematical concepts at a superficial level. <P><P>Written to inspire ?aha? moments, this book enables teachers to help students identify and comprehend the nuances and true meaning of math concepts by exploring them through the lenses of language and symbolism, delving into such essential topics as multiplication, division, fractions, place value, proportional reasoning, graphs, slope, order of operations, and the distributive property. Offers a new way to approach teaching math content in a way that will improve how all students, and especially English language learners, understand math Emphasizes major attributes of conceptual understanding in mathematics, including simple yet deep definitions of key terms, connections among key topics, and insightful interpretation This important new book fills a gap in math education by illustrating how a deeper knowledge of math concepts can be developed in all students through a focus on language and symbolism.
Problembasiertes Lernen im Mathematikunterricht der Grundschule: Entwicklung und Evaluation des Unterrichtskonzepts ELIF (Hildesheimer Studien zur Mathematikdidaktik)
by Sandra Strunk Julia WichersELIF (Eigenständige Lernzielentwicklung und Inhaltserschließung am Fall) ist eine Unterrichtskonzeption, die ausgehend vom Problembasierten Lernen theoriebasiert entwickelt und mithilfe mehrerer Design-Based Research-Zyklen an die Anforderungen der Praxis angepasst wurde. Die Schüler entwickeln auf Grundlage eines Falls inhaltliche Lernziele in Form von Lernfragen, die sie sich selbstständig in individuellen und kooperativen Arbeitsphasen erarbeiten. Damit soll insbesondere die Fähigkeit zur selbstständigen Lebensbewältigung durch eine stärkere Anwendungs- und Schülerorientierung des Unterrichts gefördert werden.
Probleme der Statistik und Prozessanalyse mit Excel lösen: Ein praktischer Ratgeber zum Buch "Methoden der Statistik und Prozessanalyse"
by Yuri A.W. Shardt Carsten GatermannDieser praktische Ratgeber zum Buch „Methoden der Statistik und Prozessanalyse – Eine anwendungsorientierte Einführung“ gibt einen kompakten Überblick über die Nutzung von Excel zur Lösung typischer statistischer Fragestellungen. Neben kurzen Theorieteilen liegt der Fokus des Buchs auf detailliert dargestellten Excel Beispiele zur Lösung der Aufgaben. Weiterhin werden typische Abläufe für Standardaufgaben in Excel vorgestellt und erklärt. Kontrollfragen am Ende jedes Kapitels ermöglichen dem Lesenden, das erworbene Wissen selbstständig zu testen.
Problemlösen: Begriff – Strategien – Einflussgrößen – Unterricht – (häusliche) Förderung
by Ulrike KipmanProblemlösen gilt als eine der Schlüsselqualifikationen des 21. Jahrhunderts. Es geht beim Problemlösen nicht nur darum, Informationen sinnvoll zu vernetzen, dynamisch in Beziehung zu setzen, Wahrscheinlichkeiten zu berechnen und eine Kette richtiger Entscheidungen zu treffen, sondern auch vielfach darum, eine Vielzahl an Außenkriterien zu berücksichtigen und ein entsprechendes „Weltwissen“ an den Tag zu legen. Dieses Buch soll die Frage beantworten, wie man zu einem guten Problemlöser / einer guten Problemlöserin werden kann bzw. warum bestimmte Personen bei der Lösung von Problemen erfolgreicher sind als andere. Nach einer umfassenden Zusammenstellung der Literatur zu diesem Thema werden Einflussgrößen auf das Problemlösen analysiert und miteinander abgeglichen und Ideen für den Unterricht in der Primarstufe und Sekundarstufe I präsentiert. Zudem werden verschiedene Arten des Unterrichts im Hinblick auf die Wirksamkeit für unterschiedliche Personengruppen diskutiert, dies vor dem Hintergrund, dass nicht nur Problemstellungen stark variieren sondern auch die Problemlöser/innen. Eine Handreichung mit Brettspielen, die die Kriterien des Problemlösens erfüllen, ist ebenfalls Teil dieses Buches. Letztendlich wird ein Modell vorgeschlagen, welches erfolgreiches Problemlösen vielschichtig zu erklären versucht.
Problemlösen: Begriff – Strategien – Einflussgrößen – Unterricht – (häusliche) Förderung
by Ulrike KipmanProblemlösen gilt als eine der Schlüsselqualifikationen des 21. Jahrhunderts. Es geht beim Problemlösen nicht nur darum, Informationen sinnvoll zu vernetzen, dynamisch in Beziehung zu setzen, Wahrscheinlichkeiten zu berechnen und eine Kette richtiger Entscheidungen zu treffen, sondern auch vielfach darum, eine Vielzahl an Außenkriterien zu berücksichtigen und ein entsprechendes „Weltwissen“ an den Tag zu legen. Dieses Buch soll die Frage beantworten, wie man zu einem guten Problemlöser / einer guten Problemlöserin werden kann bzw. warum bestimmte Personen bei der Lösung von Problemen erfolgreicher sind als andere. Nach einer umfassenden Zusammenstellung der Literatur zu diesem Thema werden Einflussgrößen auf das Problemlösen analysiert und miteinander abgeglichen und Ideen für den Unterricht in der Primarstufe und Sekundarstufe I präsentiert. Zudem werden verschiedene Arten des Unterrichts im Hinblick auf die Wirksamkeit für unterschiedliche Personengruppen diskutiert, dies vor dem Hintergrund, dass nicht nur Problemstellungen stark variieren sondern auch die Problemlöser/innen. Eine Handreichung mit Brettspielen, die die Kriterien des Problemlösens erfüllen, ist ebenfalls Teil dieses Buches. Letztendlich wird ein Modell vorgeschlagen, welches erfolgreiches Problemlösen vielschichtig zu erklären versucht. In der 2. Auflage wurden alle Kapitel überarbeitet und an den neuesten Kenntnisstand zum Thema Problemlösen angepasst. Die Kapitel zur schulischen und häuslichen Förderung der Problemlösekompetenz wurden stark erweitert und es werden nun eine Vielzahl an neuen Aufgaben und Spielen präsentiert, die beim Fördern von Problemlösen eine wertvolle Unterstützung leisten können. Das Kapitel zur Kombinatorik wurde nach der Rückmeldung von Studierenden und Kollegen komplett umstrukturiert und ist nun verständlicher und übersichtlicher aufgebaut.
Problemlösen in der Mathematik: Ein heuristischer Werkzeugkasten
by Wolfgang SchwarzErinnern Sie sich an eine Alltagssituation, in der es Ihnen gelungen ist, aus einem Problem eine Aufgabe zu machen, die Sie erfolgreich bewältigen konnten? Und haben Sie dabei vom Einsatz geeigneter Werkzeuge profitiert? Solche Szenarien prägen den beruflichen Alltag aller Studierenden mathematischer Fachrichtungen. Man sieht sich permanent mit mathematischen Problemen konfrontiert, zu deren Lösung es einer guten Idee bedarf; oft findet man diese aber nicht, weil man sich der Werkzeuge nicht bewusst ist, mit denen man die Lösungsidee freilegen kann. Dieses Buch soll hier Abhilfe schaffen. Anhand von ca. 70 Beispielen aus der Diskreten Mathematik, der Arithmetik, der Zahlentheorie, der Stochastik, der Geometrie, der Linearen Algebra, der reellen Analysis, der Funktionentheorie, der Kombinatorik und der Mathematikgeschichte wird eine umfangreiche Auswahl heuristischer Vorgehensweisen erläutert, denen die Rolle des Werkzeugs in Problemlöseprozessen zufällt. Die heuristischen Strategien des Problemlösens werden strukturell systematisiert und nach Möglichkeit prozessual den verschiedenen Phasen des Problemlöseprozesses nach Pólya zugeordnet; dadurch entsteht nicht nur Ordnung im heuristischen Werkzeugkasten, sondern auch eine Verfeinerung des Pólya'schen Phasenmodells des Problemlösens.
Problemlösen mit Strategieschlüsseln: Eine explorative Studie zur Unterstützung von Problembearbeitungsprozessen bei Dritt- und Viertklässlern (Essener Beiträge zur Mathematikdidaktik)
by Raja Herold-BlasiusLernhilfen in Form von Hilfe- oder auch Tippkarten werden als Material zur Differenzierung im Unterricht eingesetzt. Ob diese Lernenden tatsächlich helfen, ist bisher unzureichend geklärt. Für die vorliegende Untersuchung dienen sog. Strategieschlüssel als Interventionsinstrument. Theoretisch ist zu vermuten, dass die Schlüssel den Einsatz von Strategien triggern und die Selbstregulation im Bearbeitungsprozess anregen. Im Kontext des mathematischen Problemlösens wird untersucht, auf welche Art und Weise die Strategieschlüssel den Problembearbeitungsprozess von Dritt- bis Viertklässlern beeinflussen. Die quantitativen Analysen ergeben einen statistisch hoch signifikanten Zusammenhang zwischen der Interaktion mit den Strategieschlüsseln, dem Heurismeneinsatz und dem Wechsel zwischen Episoden im Problembearbeitungsprozess. Die qualitativen Analysen zeigen, dass die Strategieschlüssel auf neun verschiedene Weisen genutzt werden, der Einsatz von Heurismen durch sie getriggert wird und dass selbstregulatorische Tätigkeiten angeregt werden. Bei der Verwendung der Strategieschlüssel werden neun Muster identifiziert.
Problems and Examples in Differential Equations
by Piotr Biler Tadeusz NadziejaThis book presents original problems from graduate courses in pure and applied mathematics and even small research topics, significant theorems and information on recent results. It is helpful for specialists working in differential equations.