Teaching Mathematics in Secondary and Middle School: An Interactive Approach (3rd Edition)

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9780130950185: Teaching Mathematics in Secondary and Middle School: An Interactive Approach (3rd Edition)

Interactive in its approach, this book focuses on all the complex aspects of teaching mathematics in today's classroom and the most current NCTM standards. It illustrates how to creatively incorporate the standards into teaching along with inquiry-based instructional strategies. The book illustrates how to lead pupils toward meaningful mathematics and strategies for developing mathematics skills. Includes an abundance of illustrative examples, mini case studies, one expansive case study that follows a mathematics teacher through his first year in the profession, cooperative learning activities, field-based activities, and transitional activities. Reviews applying for faculty positions as a mathematics teacher, teaching math from a historical perspective, communication with math, working with students as individuals, working with ESL/EFL and integrating math with other content areas. Includes updated information with respect to the research literature, the publication of PSSM, and advances in technology. For educators teaching mathematics in secondary and middle school.

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From the Publisher:

Focused on all the complex aspects of teaching mathematics in today's classroom -- and the most current NCTM recommendations and standards -- this text shows students how to creatively incorporate the Standards into their teaching -- along with inquiry instructional strategies (for leading pupils to do meaningful mathematics) and direct strategies (for developing mathematical skills). Interactive in approach, it includes an abundance of illustrative examples, numerous cases, one expansive case study that follows a mathematics teacher through his first year in the profession, cooperative learning activities, field-based activities, and transitional activities.

Excerpt. © Reprinted by permission. All rights reserved.:

Contrary to popular belief, mathematics is an everyday human endeavor by which ordinary people construct concepts, discover relationships, invent algorithms and models, organize and communicate their thoughts in the language of mathematics, execute algorithms, and address their real-world problems. Likewise, by capitalizing on the use of common and personally relevant mathematics problems, mathematics teachers can help students learn and creatively apply mathematics to their everyday lives. Using research-based strategies, effective mathematics teachers guide students to invent and discover new mathematics perspectives and in so doing help students acquire confident attitudes and abilities in mathematics. Case studies in this text, the third edition of Teaching Mathematics an Secondary and Muddle School, demonstrate how.

According to consistent findings in research studies cited throughout this book, students develop confident attitudes and abilities in mathematics by engaging in:

  • inquiry lessons that lead them to reason inductively to construct mathematical concepts and discover mathematical relationships
  • direct-instructional lessons that lead them to gain knowledge of conventions and develop algorithmic skills
  • comprehension-and-communication lessons that lead them to take advantage of the special features of mathematical language
  • inquiry lessons that lead them to reason deductively to devise solutions to real-life problems

However, most students do not have these experiences. Rather, they acquire a considerably different view of mathematics, perceiving it as a boring string of terms, symbols, facts, and algorithms—truly understood only by rare geniuses. Too many students are asked only to memorize mathematical content without ever discovering, inventing, or creatively applying it. The unhealthy attitudes and inabilities to extend mathematics beyond what is memorized are perpetuated by the most dominant method of teaching mathematics in our schools. Many teachers' lessons follow a tiresome sequence—lessons void of experiences whereby meaningful mathematics is discovered, invented, or applied: Students are told about a fact or the steps in an algorithm, walked through textbook examples, assigned exercises from the textbook, and given feedback on their work with the exercises.

For over a century, mathematics education specialists have encouraged teachers to deviate from common practice by applying research-based strategies. Promise for bringing typically practiced mathematics teaching in line with research-based strategies springs from the widespread dissemination and support for the National Council of Teachers of Mathematics' (NCTM) plan for school mathematics curriculum reform as articulated in Principles and Standards for School Mathematics (PSSM) (NCTM, 2000b).

Teaching Mathematics in Secondary and Middle School: An Interactive Approach is designed to lead you to develop your talent for teaching in accordance with PSSM so that your students eagerly construct mathematical concepts for themselves, discover mathematical relationships, develop and maintain algorithmic skills, communicate in the language of mathematics, and use mathematics to devise solutions to real-life problems.

WHERE ARE RESEARCH-BASED STRATEGIES INTEGRATED INTO THIS TEXT?

Introducing topics in a spiral fashion, this book actively involves you in researched-based learning activities throughout its 11 chapters.

Chapter 1, "Beginning a Career as a Professional Mathematics Teacher," will lead you to vicariously experience the professional activities of Casey Rudd, a beginning mathematics teacher, and expose you to some preliminary ideas for developing mathematics curricula and engaging students in meaningful lessons—ideas that you will further develop in depth as you work with chapters 2-11.

Chapter 2, "Gaining Students' Cooperation in an Environment Conducive to Doing Mathematics," will help you develop strategies that lead students to cooperate in the business of learning mathematics. From your work with other chapters you will learn how to design courses, plan lessons, conduct learning activities, and monitor students' progress toward meaningful mathematical goals. However, the success of even the best designed curricula depends on how well you establish a classroom environment in which students willingly work on-task and engage in the business of learning—an environment in which students feel free to experiment, make mistakes, raise questions, interact with you and one another, contribute ideas, and expose their thought processes without fear that they are risking embarrassment, harassment, or judgment of their self-worth.

Chapter 3, "Motivating Students to Engage in Mathematical Learning Activities," is an extension of chapter 2 that focuses on using problem-based lessons to motivate students to do mathematics, strategies for responding to students' questions, and strategies for keeping students engaged in the following types of learning activities: large-group presentations, question-discussion sessions, cooperative-learning, independent-work sessions, and homework.

Chapter 4, "Developing Mathematics Curricula," will familiarize you with PSSM. You will understand why PSSM-based curricula lead students to do meaningful mathematics whereas typical textbook-driven curricula lead students to perceive mathematics as a linear sequence of meaningless definitions, symbols, rules, and algorithms. From your work with chapter 4, you will develop an advanced organizer for designing courses that are consistent with PSSM-based curricula-an advanced organizer that interrelates the work you will be doing with chapters 5-11.

Chapter 5, "Leading Students to Construct Concepts and Discover Relationships," explains and illustrates how to design and conduct inquiry lessons that lead students to construct mathematical concepts and discover mathematical relationships. You will also develop strategies for conducting miniexperiments to monitor students' progress during these types of lessons and assess how well the objectives were achieved.

Chapter 6, "Leading Students to Develop Knowledge and Algorithmic Skills," is organized similarly to chapter 5, but the focus is on using direct-instructional strategies for lessons designed to lead students to acquire and remember mathematical information and develop algorithmic skills. The mini-experiments you will design for this learning level will emphasize the identification and correction of error patterns in students' execution of algorithms.

Chapter 7, "Leading Students to Communicate With Mathematics," is organized similarly to chapters 5 and 6, but the focus is on using a combination of inquiry and direct-instructional strategies for lessons designed to lead students to use mathematics for organizing and communicating ideas and to comprehend the language of mathematics. You will learn how to incorporate conversation, speaking, listening, writing, and reading in your lessons so that students do meaningful mathematics.

Chapter 8, "Leading Students to Creatively Use Mathematics," is organized similarly to chapters 5-7, but the focus is on inquiry lessons that lead students to apply mathematics to real-life situations, foster their creativity with mathematics, and develop an appreciation for and willingness to do mathematics. As with chapters 5-7, you will engage in activities that prompt you to design and field-test lessons and miniexperiments. Such activities provide critical experiences upon which you build your teaching talents. You will also collect artifacts (e.g., lesson plans) for the professional portfolio you will have organized from your work with chapter 1.

Chapter 9, "Assessing and Reporting Students' Progress With Mathematics," will lead you to (a) develop an efficient system for monitoring and evaluating students' progress and (b) apply authentic assessment strategies to make and communicate summative evaluations of your students' mathematical achievements. Furthermore, you will learn about some of the misuses of high-stakes testing and how to interpret the results of standardized and core-curriculum tests.

Chapter 10, "Technology and Resources for Teaching and Learning Mathematics," will direct you to a wide variety of (a) resources for stimulating ideas on teaching mathematics, learning mathematics, and doing mathematics and (b) technologies and mathematics curriculum materials typically available for use in middle, junior high, and high schools. You will critique curriculum materials (e.g., textbooks) and sample Internet-based resources.

Chapter 11, "Analyzing Examples of Mathematics Curricula and Instructional Practice," will lead you to further develop your talent for designing mathematics courses and conducting lessons for students by prompting you to analyze cases in which teachers implement strategies you learned from your work with chapters 1-10. With an emphasis on integrating mathematics curricula with those of other subject-content areas (e.g., biology, physical education, and social studies), you will be immersed in the thoughts and practices of teachers as they design and conduct a variety of middle, junior high, and high school mathematics courses.

HOW DOES THIS TEXT DEMONSTRATE RESEARCH-BASED TEACHING PRINCIPLES?

Teaching Mathematics in Secondary and Middle School: An Interactive Approach is an extremely unusual book. Not only does it present research-based principles for teaching mathematics, it also demonstrates each by contrasting actual classroom examples in which the principle is applied with actual examples that violate the principle. Throughout, topics (e.g., defining learning goals, designing lessons, motivating students' cooperation, and assessing learning) are integrated by the book's 189 actual classroom cases that follow teachers' thoughts, actions, reactions, and interactions as they engage in work of professional mathematics teachers. The book's pedagogy employs the same research-based teaching strategies it suggests you use with your students:

  • You are stimulated to reason inductively to construct concepts and discover relationships as you interact with carefully selected examples and nonexamples.
  • Direct instructional strategies are used to present you with information, conventions (e.g., word meanings), and processes.
  • A combination of inquiry and direct-instructional strategies are employed throughout to lead you to comprehend and communicate ideas related to teaching mathematics.
  • You are stimulated to reason deductively to apply concepts, relationships, and processes to your own teaching situations.

To incorporate these research-based teaching strategies, the organization of the book is much more complex than for a typical mathematics teaching methods textbook that simply presents information about teaching and examples of learning activities for teachers to use with their students. The non-linear, spiral structure of Teaching Mathematics in Secondary and Middle School: An Interactive Approach is not conducive to reading chapters out of order. Another consequence is that you will occasionally be prompted to visit cases and exhibits from chapters other than the one you are studying. This inconvenience benefits you by continually interconnecting chapters and building on what you are learning or on what you have already learned.

Each chapter begins with a goal defined by a set of objectives and ends with a set of synthesis activities and a transitional activity. The synthesis activities are designed to help you bring together the chapter's content, reinforce and extend what you learned, and assess what you gained from the chapter so that you can identify your areas of proficiency and the topics you need to review. Each chapter's transitional activity sets the stage for your work with the next chapter. There are also activities in which you will engage as you work with the main body of each chapter. These learning activities are designed to stimulate your ideas, lead you to clarify or expand upon what you have just read, prepare you to work with the next section of the chapter, address a problem, collaborate with colleagues, or design and use a product (e.g., a lesson plan). The numerous cases generate a considerable number of exhibits for you to analyze and model as you generate your own curriculum materials. Consequently, this book contains an unusually high number of exhibits (i.e., figures, tables, and illustrations): 256.

WHAT IS NEW ABOUT THIS EDITION?

This third edition of Teaching Mathematics in Secondary and Middle School: An Interactive Approach is considerably different from the second edition:

  • The organization and writing are thoroughly reworked. The content is expanded, but the book's length is not appreciably increased because the writing is much crisper.
  • This third edition addresses the following topics in much greater depth than they were addressed in the second edition: applying for faculty positions as a mathematics teacher, interacting with students (e.g., the use of naturalistic conversations), teaching mathematics from a historical perspective, communicating with mathematics, working with students as individuals, application of multicultural education strategies, working with students for whom English is not a first language, integrating mathematics curricula with those of other subject-content areas, differences among mathematics courses and age levels of students, Internet-based learning activities and resources, and high-stakes testing.
  • This third edition reflects considerable updating with respect to the research literature, the publication of PSSM, and advances in technology.
  • The third edition prompts you to organize your work in a professional teaching portfolio.
  • Chapters have been reworked and reorganized with increased attention to mathematical modeling and mathematics as communication.
  • Chapter 10 reflects new advances in technology and Web-based resources and activities.
  • The text now includes a glossary of technical terms introduced in the book.

The instructor's manual for this third edition provides suggestions for designing mathematical teaching methods courses. It includes a course syllabus, a sequence of course activities, and exams with detailed scoring rubrics. It is available upon request from Merrill/Prentice Hall to course instructors.

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