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Research in Collegiate Mathematics Education V
This fifth volume of ""Research in Collegiate Mathematics Education"" (RCME) presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level.The articles in RCME are peer-reviewed for two major features: advancing our understanding of collegiate mathematics education, and readability by a wide audience of practicing mathematicians interested in issues affecting their own students.This is not a collection of scholarly arcana, but a compilation of useful and informative research regarding the ways our students think about and learn mathematics.The volume begins with a study from Mexico of the cross-cutting concept of variable followed by two studies dealing with aspects of calculus reform.The next study frames its discussion of students' conceptions of infinite sets using the psychological work of Efraim Fischbein on (mathematical) intuition.This is followed by two papers concerned with APOS theory and other frameworks regarding mathematical understanding.The final study provides some preliminary results on student learning using technology when lessons are delivered via the Internet.Whether specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas they can use.
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Mathematics in Early Years Education
This fourth edition of the bestselling Mathematics in Early Years Education provides an accessible introduction to the teaching of mathematics in the early years.Covering all areas of mathematics – number and counting, calculation, pattern, shape, measures and data handling – it provides a wide range of practical activities and guidance on how to support young children’s mathematical development.There is also guidance on managing the transition to KS1 and a strong emphasis throughout on creating home links and working in partnership with parents.This new edition has been fully updated to incorporate the latest research and thinking in this area and includes: why mathematics is important as a way of making sense of the world how attitudes to mathematics can influence teaching and learning how children learn mathematics and what they are capable of learning how technology can support maths teaching maths phobia and the impact society has on maths teaching material on sorting, matching and handling data the importance of educating about finance in today’s world ideas for observation and questioning to assess children’s understanding examples of planned activities suggestions for language development assessment criteria.This textbook is ideal for those training to be teachers through an undergraduate or PGCE route, those training for Early Years Professional Status and those studying early childhood on foundation or honours degrees, as well as parents looking to explore how their young children learn mathematics.This will be an essential text for any early years practitioner looking to make mathematics interesting, exciting and engaging in their classroom.
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The Philosophy of Mathematics Education
This survey provides a brief and selective overview of research in the philosophy of mathematics education.It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics.A case study is provided of an emerging research tradition in one country.This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil.This illustrates one orientation towards research inquiry in the philosophy of mathematics education.It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education.An extensive bibliography is also included.
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Multilingualism in Mathematics Education in Africa
This book brings together the first book collection of African research in mathematics education in multilingual societies and chronicles current research in different linguistic contexts across the African continent, (including Algeria, Namibia, Malawi, Morocco, Rwanda, South Africa) on issues of multilingualism in mathematics education, but more importantly, it foregrounds pertinent issues for future research.With many of the authors building on earlier path-breaking African research, the book is a unique contribution of careful thinking through how linguistic diversity and multilingualism manifest in ways that differ from one geopolitical context to another.This volume is an important contribution to the growing recognition of multilingualism as the global ‘linguistic dispensation’ in mathematics education.It is an invitation to how we might (as an international community where more and more multilingualism is the norm rather than an exception) pay more attention to the multilingual agency and capabilities of both students and teachers in order to better harness the epistemic potential of multiple languages in contexts of language diversity in mathematics education.
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Which education requires little mathematics?
Some examples of education that requires little mathematics include liberal arts, social sciences, humanities, and some vocational or technical programs. These fields typically focus more on critical thinking, analysis, and communication skills rather than mathematical proficiency. However, it's important to note that even in these fields, some level of mathematical understanding may still be necessary, depending on the specific courses or career paths within the field.
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What is the mathematics research paper about?
The mathematics research paper explores the application of differential equations in modeling real-world phenomena. It discusses the use of differential equations to describe various physical, biological, and social systems, and how these equations can be solved and analyzed to gain insights into the behavior of these systems. The paper also delves into the development of new mathematical techniques for solving complex differential equations and their implications for understanding and predicting the dynamics of natural and human-made systems.
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What does systematization mean in mathematics education?
Systematization in mathematics education refers to the process of organizing mathematical concepts, skills, and procedures in a logical and coherent manner. It involves structuring the curriculum in a way that helps students see the connections between different topics and understand how they build upon each other. By systematizing mathematical content, educators can help students develop a deeper understanding of the subject and improve their problem-solving abilities. This approach also helps students retain information better and apply their knowledge to new situations.
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How is mathematics education divided in Japan?
In Japan, mathematics education is divided into two main stages: elementary school and junior high school. In elementary school, students are taught basic arithmetic, geometry, and measurement. They also learn problem-solving skills and logical thinking. In junior high school, the focus shifts to more advanced topics such as algebra, geometry, and statistics. The curriculum is designed to build a strong foundation in mathematical concepts and skills, preparing students for higher-level mathematics in high school and beyond.
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A Focus on Addition and Subtraction : Bringing Mathematics Education Research to the Classroom
This innovative text offers a unique approach to making mathematics education research on addition, subtraction, and number concepts readily accessible and understandable to pre-service and in-service teachers of grades K–3. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of teachers’ experiences, this book provides educators with the knowledge and tools needed to modify their lessons and improve student learning of additive reasoning in the primary grades.Based on research gathered in the Ongoing Assessment Project (OGAP), this engaging, easy-to-use resource features practical resources such as: A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess, and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding; A focus on the OGAP Addition, Subtraction, and Base Ten Number Progressions, based on research conducted with hundreds of teachers and thousands of pieces of student work; In-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education research; End-of-chapter questions to allow teachers to analyze student thinking and consider instructional strategies for their own students; Instructional links to help teachers relate concepts from each chapter to their own instructional materials and programs; An accompanying eResource, available online, offers an answer key to Looking Back questions, as well as a copy of the OGAP Additive Framework and the OGAP Number Line Continuum. A Focus on Addition and Subtraction marks the fourth installment of the popular A Focus on… collection, designed to aid the professional development of pre-service and in-service mathematics teachers.Following from previous volumes on ratios and proportions, multiplication and division, and fractions, this newest addition is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.
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A Focus on Multiplication and Division : Bringing Mathematics Education Research to the Classroom
The second edition of this book offers a unique approach to making mathematics education research on the teaching and learning of multiplication and division concepts readily accessible and understandable to preservice and in-service K-6 mathematics teachers. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers’ experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction, and ultimately improve student learning.Based on research gathered in the Ongoing Assessment Project (OGAP) and updated throughout, this engaging and easy-to-use resource also features the following:New chapters on the OGAP Multiplicative Reasoning Framework and Learning Progressions and Using the OGAP Multiplicative Progression to inform instruction and support student learningIn-chapter sections on how Common Core State Standards for Math are supported by math education research Case Studies focusing on a core mathematical idea and different types of instructional responses to illustrate how teachers can elicit evidence of student thinking and use that information to inform instruction Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division Looking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own students Instructional Links to help teachers relate concepts from each chapter to their own instructional materials and programsAccompanying online Support Material that includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and Progression A Focus on Multiplication and Division is part of the popular A Focus on . . . collection, designed to aid the professional development of preservice and in-service mathematics teachers.As with the other volumes on addition and subtraction, ratios and proportions, and fractions, this updated new edition bridges the gap between what math education researchers know and what teachers need to know to better understand evidence in student work and make effective instructional decisions.
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STEM in Early Childhood Education : How Science, Technology, Engineering, and Mathematics Strengthen Learning
Bringing together a diverse cohort of experts, STEM in Early Childhood Education explores the ways STEM can be integrated into early childhood curricula, highlighting recent research and innovations in the field, and implications for both practice and policy. Based on the argument that high-quality STEM education needs to start early, this book emphasizes that early childhood education must include science, technology, engineering, and mathematics in developmentally appropriate ways based on the latest research and theories.Experienced chapter authors address the theoretical underpinnings of teaching STEM in the early years, while contextualizing these ideas for the real world using illustrative examples from the classroom.This cutting-edge collection also looks beyond the classroom to how STEM learning can be facilitated in museums, nature-based learning outdoors, and after-school programs.STEM in Early Childhood Education is an excellent resource for aspiring and veteran educators alike, exploring the latest research, providing inspiration, and advancing best practices for teaching STEM in the early years.
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A Mathematics Course for Political and Social Research
Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a "math camp" or a semester-long or yearlong course to acquire the necessary skills.Available textbooks are written for mathematics or economics majors, and fail to convey to students of political science and sociology the reasons for learning often-abstract mathematical concepts.A Mathematics Course for Political and Social Research fills this gap, providing both a primer for math novices in the social sciences and a handy reference for seasoned researchers.The book begins with the fundamental building blocks of mathematics and basic algebra, then goes on to cover essential subjects such as calculus in one and more than one variable, including optimization, constrained optimization, and implicit functions; linear algebra, including Markov chains and eigenvectors; and probability.It describes the intermediate steps most other textbooks leave out, features numerous exercises throughout, and grounds all concepts by illustrating their use and importance in political science and sociology. * Uniquely designed and ideal for students and researchers in political science and sociology * Uses practical examples from political science and sociology * Features "Why Do I Care?" sections that explain why concepts are useful * Includes numerous exercises * Complete online solutions manual (available only to professors, email david.siegel at duke.edu, subject line "Solution Set") * Selected solutions available online to students
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How is mathematics applied in physical education?
Mathematics is applied in physical education in various ways. For example, students can use mathematical concepts such as measurement, angles, and geometry to understand and improve their performance in sports. They can calculate their speed, distance, and time during activities like running or swimming. Additionally, students can use statistics and data analysis to track their progress and performance in different physical activities. Overall, mathematics plays a crucial role in helping students understand and improve their physical abilities in physical education.
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How much mathematics is included in business education?
Mathematics is a crucial component of business education, as it is used in various aspects of business such as accounting, finance, economics, and statistics. Students in business programs are typically required to take courses in areas such as calculus, algebra, and statistics to develop the quantitative skills necessary for analyzing data, making financial decisions, and understanding economic principles. Additionally, mathematical concepts are often integrated into business courses to help students understand and apply quantitative methods in real-world business scenarios. Overall, a strong foundation in mathematics is essential for success in business education and the business world.
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Business mathematics or pure mathematics?
It ultimately depends on your career goals and interests. Business mathematics focuses on practical applications in business and finance, such as accounting, economics, and statistics. Pure mathematics, on the other hand, delves into theoretical concepts and abstract reasoning, with applications in fields like physics, engineering, and computer science. If you are interested in pursuing a career in business or finance, business mathematics may be more relevant. However, if you are passionate about theoretical concepts and problem-solving, pure mathematics may be a better fit for you.
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Does market research hinder innovation in business administration?
Market research does not necessarily hinder innovation in business administration. In fact, it can provide valuable insights into consumer needs and preferences, helping businesses to develop innovative products and services that meet market demands. By understanding market trends and customer behavior, businesses can identify opportunities for innovation and stay ahead of competitors. However, relying too heavily on market research without allowing room for creativity and risk-taking can limit the potential for groundbreaking innovations. It is important for businesses to strike a balance between leveraging market research and fostering a culture of innovation to drive success in business administration.
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