Knowing and Teaching Elementary Mathematics

Knowing and Teaching Elementary Mathematics

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  • Author: Liping Ma
  • Publisher: Routledge
  • ISBN: 1135149496
  • Category : Education
  • Languages : en
  • Pages : 290

Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.


Knowing Mathematics

Knowing Mathematics

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  • Author: Liping Ma
  • Publisher:
  • ISBN: 9780618105274
  • Category : Mathematics
  • Languages : en
  • Pages : 0


Mathematics for Machine Learning

Mathematics for Machine Learning

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  • Author: Marc Peter Deisenroth
  • Publisher: Cambridge University Press
  • ISBN: 1108569323
  • Category : Computers
  • Languages : en
  • Pages : 392

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.


Knowing and Learning Mathematics for Teaching

Knowing and Learning Mathematics for Teaching

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  • Author: National Research Council
  • Publisher: National Academies Press
  • ISBN: 0309072522
  • Category : Education
  • Languages : en
  • Pages : 233

There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions: What is the mathematical knowledge teachers need to know in order to teach well? How can teachers develop the mathematical knowledge they need to teach well? The Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, Knowing and Learning Mathematics for Teaching, is a collection of the papers presented, the activities, and plenary sessions that took place.


Visible Learning for Mathematics, Grades K-12

Visible Learning for Mathematics, Grades K-12

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  • Author: John Hattie
  • Publisher: Corwin Press
  • ISBN: 1506362958
  • Category : Education
  • Languages : en
  • Pages : 209

Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.


Challenging Ways Of Knowing

Challenging Ways Of Knowing

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  • Author: Dave Baker
  • Publisher: Routledge
  • ISBN: 1136366474
  • Category : Education
  • Languages : en
  • Pages : 217

This work provides an analysis of how knowledge is constructed and defined by teachers and lecturers in schools and universities/colleges. It considers how everyday uses of reading, writing, numeracy and science are cast aside in favour of academic language and academic discourse, arguing that such discourses are alien to learners' daily experiences and are, therefore, difficult to acquire and adopt.; Chapters examine literacies of English, mathematics and science as practised in and outside schools and colleges. The book is interdisciplinary and multicultural, adopting perspectives from the UK, USA, South Africa, India, Brazil and Kenya. It should be of interest to a wide market of educationalists, including those involved in educational policy making, teacher education, cultural/multicultural studies, development studies, anthropology, and adult and continuing education.


Teaching Mathematics in the Visible Learning Classroom, Grades 6-8

Teaching Mathematics in the Visible Learning Classroom, Grades 6-8

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  • Author: John Almarode
  • Publisher: Corwin Press
  • ISBN: 154433317X
  • Category : Education
  • Languages : en
  • Pages : 154

Select the right task, at the right time, for the right phase of learning It could happen in the morning during homework review. Or perhaps it happens when listening to students as they struggle through a challenging problem. Or maybe even after class, when planning a lesson. At some point, the question arises: How do I influence students′ learning—what’s going to generate that light bulb "aha" moment of understanding? In this sequel to the megawatt best seller Visible Learning for Mathematics, John Almarode, Douglas Fisher, Nancy Frey, John Hattie, and Kateri Thunder help you answer that question by showing how Visible Learning strategies look in action in the mathematics classroom. Walk in the shoes of middle school teachers as they engage in the 200 micro-decisions-per-minute needed to balance the strategies, tasks, and assessments seminal to high-impact mathematics instruction. Using grade-leveled examples and a decision-making matrix, you’ll learn to Articulate clear learning intentions and success criteria at surface, deep, and transfer levels Employ evidence to guide students along the path of becoming metacognitive and self-directed mathematics achievers Use formative assessments to track what students understand, what they don’t, and why Select the right task for the conceptual, procedural, or application emphasis you want, ensuring the task is for the right phase of learning Adjust the difficulty and complexity of any task to meet the needs of all learners It’s not only what works, but when. Exemplary lessons, video clips, and online resources help you leverage the most effective teaching practices at the most effective time to meet the surface, deep, and transfer learning needs of every student.


The Singapore Model Method for Learning Mathematics

The Singapore Model Method for Learning Mathematics

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  • Author: Houghton Mifflin Harcourt
  • Publisher: Houghton Mifflin School
  • ISBN: 9789812806604
  • Category : Education
  • Languages : en
  • Pages : 136

This monograph serves as a resource book on the Model Method. The main purpose is to make explicit how the Model Method is used to develop students' understanding of fundamental mathematics concepts and proficiency in solving basic mathematics word problems. Through the construction of a pictorial model to represent the known and unknown quantities and their relationships in a problem, students gain better understanding of the problem and develop their abilities in mathematical thinking and problem solving. This would provide a strong foundation for the learning of matheatics from the primary to secondary levels and beyond. This monograph also features the Mathematics Framework of the Singapore mathematics curriculum, and discusses the changes that it has undergone over the past two decades. These changes reflected the changing emphases, needs and challenges in the mathematics curriculum as we entered the 21s century.


Knowing and Teaching Elementary Mathematics

Knowing and Teaching Elementary Mathematics

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  • Author: Liping Ma
  • Publisher: Routledge
  • ISBN: 1000023087
  • Category : Education
  • Languages : en
  • Pages : 220

The 20th anniversary edition of this groundbreaking and bestselling volume offers powerful examples of the mathematics that can develop the thinking of elementary school children. Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. Along with the original studies of U.S. and Chinese teachers’ mathematical understanding, this 20th anniversary edition includes a new preface and a 2013 journal article by Ma, "A Critique of the Structure of U.S. Elementary School Mathematics" that describe differences in U.S. and Chinese elementary mathematics. These are augmented by a new series editor’s introduction and two key journal articles that frame and contextualize this seminal work.


Understanding Emotions in Mathematical Thinking and Learning

Understanding Emotions in Mathematical Thinking and Learning

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  • Author: Ulises Xolocotzin
  • Publisher: Academic Press
  • ISBN: 0128024895
  • Category : Psychology
  • Languages : en
  • Pages : 476

Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally, it covers social and affective issues such as identity and attitudes toward mathematics. Covers methodologies in studying emotion in mathematical knowledge Reflects the diverse and innovative nature of the methodological approaches and theoretical frameworks proposed by current investigations of emotions and mathematical cognition Includes perspectives from cognitive experimental psychology, neuroscience, and from sociocultural, semiotic, and discursive approaches Explores the role of anxiety in mathematical learning Synthesizes unifies the work of multiple sub-disciplines in one place