Instructor Manual - Mathematics: Teaching Developmentally Tenth Edi...

Instructor Manual For Elementary and Middle School

Mathematics:

Teaching Developmentally Tenth Edition John A. Van de Walle Karen S. Karp Jennifer M. Bay-Williams Prepared by Elizabeth Todd Brown, Professor Emeritus 1 / 4

Copyright © 2019, 2016, 2013 Pearson Education, Inc. All rights reserved.iii

TABLE OF CONTENTS 


Introductory Thoughts .................................................................................................................................................. iv Course Designs and Options .......................................................................................................................................... v Introducing These Manual Notes .............................................................................................................................. xxiv Share Your Thoughts ................................................................................................................................................. xxv Chapter by Chapter Chapter 1: Teaching Mathematics in the 21st Century .............................................................................................. …1 Chapter 2: Exploring What It Means to Know and Do Mathematics ............................................................................ 4 Chapter 3: Teaching Through Problem Solving ............................................................................................................ 9 Chapter 4: Planning in the Problem-Based Classroom ................................................................................................ 12 Chapter 5: Creating Assessments for Learning ........................................................................................................... 15 Chapter 6: Teaching Mathematics Equitably to All Students ...................................................................................... 18 Chapter 7: Developing Early Number Concepts and Number Sense........................................................................... 21 Chapter 8: Developing Meanings for the Operation .................................................................................................... 23 Chapter 9 Developing Basic Fact Fluency................................................................................................................... 26 Chapter 10: Developing Whole-Number Place-Value Concepts ................................................................................. 29

Chapter 11: Developing Strategies for Addition and

Subtraction Computation ................................................................................................................ 32

Chapter 12: Developing Strategies for Multiplication and

Division Computation ..................................................................................................................... 37 Chapter 13: Algebraic Thinking, Equations, and Functions ........................................................................................ 39 Chapter 14: Developing Fraction Concepts ................................................................................................................. 42 Chapter 15: Developing Fraction Operations .............................................................................................................. 45 Chapter 16: Developing Decimal and Percent Concepts and Decimal Computation .................................................. 48 Chapter 17: Ratios, Proportions, and Proportional Reasoning .................................................................................... 53 Chapter 18: Developing Measurement Concepts ........................................................................................................ 57 Chapter 19: Geometric Thinking and Geometric Concepts ......................................................................................... 62 Chapter 20: Developing Concepts of Data and Statistics ............................................................................................ 66 Chapter 21: Exploring Concepts of Probability ........................................................................................................... 72

Chapter 22: Developing Concepts of Exponents, Integers, and

Real Numbers .................................................................................................................................. 75 2 / 4

Copyright © 2019, 2016, 2013 Pearson Education, Inc. All rights reserved.1

CHAPTER 1

TEACHING MATHEMATICS IN THE 21st C ENTURY

MAIN IDEAS/LEARNER OUTCOMES

The main purpose of this chapter is to introduce students to the changing world and ongoing revolution in school mathematics and their role in the continuation of this transformation. The four chapters that follow this one will create the foundational ideas for effective teaching in a problem-solving environment. Those chapters are to be seen in the context of the revolution that has been going on since 1989.For more than twenty-five years, mathematics has constantly undergone change. There are several significant factors in this transformation. Over the years, the pressures influencing school mathematics have become much more complex. The TIMSS data has caused much of the concern with the popular press pointing out that most industrialized countries significantly outperform U.S. students in mathematics and science. The National Assessment of Educational Progress (NAEP) offers ongoing indications of what American students are learning.These data suggests that while we continue to show improvement, we are not near where we want to be. Both TIMSS and NAEP data are referred to throughout the book.This chapter explains briefly how the movement toward shared standards began with the Curriculum and Evaluation Standards for School Mathematics, followed by the Professional Standards for Teaching Mathematics and the Assessment Standards for School Mathematics. Considerable attention is given to the content of Principles and Standards for School Mathematics, Curriculum Focal Points and the Common Core State Standards. It may be useful to use a time line to show your students the progression. The new Association of Mathematics Teacher Educators (AMTE) Standards for Preparing Teachers of Mathematics (AMTE, 2017) along with NCTM publication Principles to Actions (Appendix B) provide a focus on mathematical teaching practices. Perhaps a poster or bulletin board with these teaching practices would be a powerful reminder to refer to throughout the semester Pressures on teachers from state testing programs, the requirements of NCLB and the 2010 Common Core State Standards set of focused mathematics content standards and practices adopted by 43 of the 50 states (at the date of this publication) have a significant influence on what is happening in mathematics classrooms. You should encourage students to examine Appendix A of the main text, which contains the Standards for Mathematical Practice from the Common Core State Standards and the overarching domains. Although it is difficult to make general statements concerning these influences across states and provinces, teacher candidates should recognize the importance of discussing their own state/provincial standards in light of the vision of NCTM.You will not be able to adequately help your teacher candidates understand the standards documents in any one class or by having them read any chapter in this book. The task at this early juncture in the course is to heighten students’ awareness of the standards and then to consistently refer to them as you travel through your course. It is important to help teachers know that Common Core State Standards are not a curriculum but a statement of what is important in school mathematics. Most likely your own state or province has standards with which prospective and practicing teachers must be familiar. You may want to have students contrast the NCTM Standards and Curriculum Focal Points with the Common Core State Standards or those at the state/province level where you are located.Other Factors to Consider about School Mathematics The power of the individual teacher cannot be ignored. The last section in Chapter 1, An Invitation to Learn and Grow points out that the responsibility for excellent teaching and for significant learning by all students falls on the teacher. We added a section on how to create a whole school agreement with a cohesive mathematics message. How prospective and practicing teachers use this text and your course instruction to enhance their content knowledge develops their ability to persevere and demonstrates their positive attitude and passion for teaching mathematics. 3 / 4

Copyright © 2019, 2016, 2013 Pearson Education, Inc. All rights reserved.2 Their readiness for accepting change and their reflective disposition will play an important role in how their pre-K–8 students grow as mathematical thinkers.

SUGGESTED ACTIVITIES

Here are a few things that can be done to get students involved in the ideas just discussed.Introduce Principles and Standards Discuss the goals for students or read aloud the first paragraph of Chapter 1 of Principles and Actions (see Appendix

• How is this similar or different from what they experienced as elementary or middle school students? Is this what

they are seeing in their field experiences? How possible do they believe this vision is for their classroom?Point out the structure of the CCSS standards document. The standards define what students should understand and be able to do. The Clusters summarize groups of related standards. The Domains are larger groups of related standards (PPT Slide 1-5). The standards from different clusters and domains may sometimes be closely related, because mathematics is a connected subject. It is critical that your methods students also read the six principles listed on (PPT Slide 1-8 as well as the five process standards (PPT Slide 1-6). Although these are included in the text, it would be much better if students read the full discussion of these in the actual document. With a student membership to NCTM, your teacher candidates can access a Web version of the document or NCTM graciously allows guests to sign up for 120 days of free access which should cover the time frame of most courses.

The Five Content Standards Have students examine at least one of the five content standards or the domains from the Common Core State Standards (downloadable at www.corestandards.org). You might want to spend some time discussing how these standards are alike or different from the content in your state/province standards. Most importantly for pre service teachers, you want them to be aware of these documents to get an idea of what content is appropriate at each grade level.Another good discussion to have surrounds the issue of basic skills. What is meant when people say “basic skills” in mathematics? Do the standards documents support students having basic skills? (Absolutely!) A discussion concerning the pressures of high stakes testing and how this pressure influences what is taught in the classroom is most useful at this early point in the semester. If there are sample-released test items in your state/province that are available, compare those to the standards documents to see whether there are similarities and differences.

Introduce Professional Journals and Publications Pass out back issues of Teaching Children Mathematics and/or Mathematics Teaching in the Middle School. Point out some of the regular features of each journal that may be of interest. Encourage or require your students to become e-members of NCTM. This membership allows full-time students to select an electronic subscription to one of the journals—Teaching Children Mathematics, Mathematics Teaching in the Middle School or Mathematics Teacher (for high school)—and enable them to download 25 journal articles from a non-subscribed journal. They can also attend regional NCTM conferences for FREE!Also show students the NCTM Essential Understandings series including the new Essential Understandings in Practice, which provide details of how to teach the essential understandings effectively, Navigations books, and other valuable NCTM publications that they should consider for their personal professional libraries. Several of the publications, such as the Navigations books, each include a CD-ROM with other articles and several good applets that teachers will find quite valuable.

POSSIBLE ASSIGNMENTS

• Select one of the five process standards from Principles and Actions (see Appendix B) or one of the Standards for

Mathematical Practice from the Common Core State Standards (see Appendix A) and read it carefully. Discuss how this standard reflects a vision of mathematics that is different from the one you experienced as a K-12 student.Decide on two ideas that you think are most important for you as a future teacher to take from this standard. Create a “to learn” list of the things you most need to learn in order to implement that standard as a teacher of mathematics.Use this “to learn” list approach as a first step toward developing a personal professional growth plan.

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