Activity Manual for Mathematical Reasoning for Elementary Teachers

Description

This resource provides hands-on, manipulative-based activities keyed to the text that involve future elementary school teachers discovering concepts, solving problems, and exploring mathematical ideas. These activities can be adapted for use with elementary students at a later time. Colorful, perforated paper manipulatives are provided in a convenient pouch at the back of the manual.

Table of Contents

Calvin Long received his B.S. in Mathematics from the University of Idaho. Following M.S. and Ph.D. degrees in Mathematics from the University of Oregon, he worked briefly as an analyst for the National Security Agency and then joined the faculty at Washington State University. His teaching ran the gamut from elementary algebra through graduate courses and included frequently teaching the content courses for prospective elementary school teachers.

 

His other professional activities include serving on numerous committees of the National Council of Teachers of Mathematics and the Mathematical Association of America, and holding various leadership positions in those organizations. Professor Long has also been heavily engaged in directing and instructing in-service workshops and institutes for teachers at all levels, has given more than 100 presentations at national and regional meetings of NCTM and its affiliated groups, and has presented invited lectures on mathematics education abroad.

 

Professor Long has co-authored two books and is the sole author of a text in number theory. In addition, he has authored over 90 articles on mathematics and mathematics education, and also served as a frequent reviewer for mathematics journals, including The Arithmetic Teacher and The Mathematics Teacher. In 1986, he received the Faculty Excellence Award in Teaching from Washington State University and, in 1991, he received a Certificate for Meritorious Service to the Mathematical Association of America.

 

Aside from his professional activities, Cal enjoys listening to, singing, and directing classical music, reading, fly fishing, camping, and backpacking.

 

 

Duane DeTemple received his B.S. with majors in Applied Science and Mathematics from Portland State College. Following his Ph.D. in Mathematics from Stanford University, he was a faculty member at Washington State University, where he is now a Professor Emeritus of Mathematics. He has been extensively involved with teacher preparation and professional development at both the elementary and secondary levels. Professor DeTemple has been a frequent consultant to projects sponsored by the Washington State Office of the Superintendent of Public Instruction, the Higher Education Coordinating Board, and other boards and agencies.

 

Dr. DeTemple has co-authored four other books and over 100 articles on mathematics or mathematics materials for the classroom. He is a member of the Washington State University President’s Teaching Academy, and in 2007 was the recipient of the WSU Sahlin Faculty Excellence Award for Instruction and the Distinguished Teaching Award of the Pacific Northwest Section of the Mathematical Association of America.

 

In addition to teaching and research mathematics, Duane enjoys reading, listening to, and playing music, hiking, biking, canoeing, traveling, and playing tennis.

 

 

Richard Millman received a B.S. from the Massachusetts Institute of Technology and a Ph.D. from Cornell University in Mathematics. He is a professor of mathematics and was director of the Center for Education Integrating Science, Mathematics, and Computing (CEISMC) at the Georgia Institute of Technology, which supports STEM outreach in K-12. He was formerly the Outreach Professor of Mathematics at the University of Kentucky, where he was involved in both preservice and in-service teacher training for mathematics teachers.

 

Dr. Millman has co-authored four books in mathematics, co-edited three others, and received ten peer-reviewed grants. He has published over 50 articles about mathematics or mathematics education and has taught a wide variety of mathematics and mathematics education courses throughout the undergraduate and graduate curriculum, including those for preservice teachers. He received, with a former student, an Excel Prize for Expository Writing for an article in The Mathematics Teacher and was a Member-at-Large of the Council of the American Mathematical Society. He was principal investigator and project director for ALGEBRA CUBED, a grant from the National Science Foundation to improve algebra education in rural Kentucky. He was the principal investigator of a Race to the Top grant from the Georgia Department of Education and another NSF grant, SLIDER, in which students use a curriculum based on engineering design in the context of building robots to learn eighth-grade physical science and math.

 

Rich enjoys traveling, writing about mathematics, losing golf balls, listening to music, and going to plays and movies. He also loves and is enormously proud of his grandchildren, with whom he enjoys discussing the conceptual basis of mathematics, among other topics.

Features for the future classroom demonstrate the relevance of the concepts students are learning and the ways in which the mathematical concepts will be employed in the classroom, provide perspective on the importance of learning the material, and engage students to learn by doing.

• The 8 Standards for Mathematical Practice (SMP) from the Common Core State Standards for Mathematics have been integrated throughout the text. These 8 standards encourage growing mathematical maturity, deepening conceptual understanding, and engaging with the subject matter. Instances where one of the SMP standards is particularly applicable are called out in the margins, helping future teachers to make the connection between the standards they may encounter as teachers, and the content and eventual implementation.

• Completely updated Into the Classroom features provide insights from active teachers, providing a window into their classroom via activities, projects, discussions, and ideas to engage children in the mathematics being covered in that particular chapter of the text.
• Integrating Mathematics and Pedagogy (IMAP) video references have been added to the Annotated Instructor’s Edition, making it easier to incorporate the IMAP videos into the classroom at relevant point-of-use. IMAP videos allow future teachers to see elementary and middle school students working out numerical concepts.
• Responding to Students (RTS) problems throughout the problem sets have been updated. These questions show how children try to use mathematical techniques and illustrate why future teachers will need a thorough understanding of mathematical content in order to answer students’ questions.
• From the NCTM Principles and Standards are extensive excerpts from The Principles and Standards to help students understand how what they are currently learning is reflected in what they will eventually be teaching.
• Highlights from History provide a cultural, historical, and personal perspective on the development of mathematical concepts and thought while illustrating the contributions that individuals have made to mathematics.
• The Chapter in Relation to Future Teachers is a brief concluding essay that puts the chapter into context, summarizing how the content fits into the bigger picture of teaching.
• Cooperative Investigations are activities that small groups can use to explore and discuss concepts. There is one Cooperative Investigation per chapter and additional Cooperative Investigations can be found in MyLab Math.
• Activity Manual annotations in the margins of the Annotated Instructor’s Edition indicate which activities are appropriate for each concept.

 

Strong pedagogical tools help students to understand the concepts and reason mathematically.

• Updated Chapter Openers begin with an introductory activity that introduces some of the principal topics of the chapter by means of cooperative learning. “Key Ideas” show the interconnections among the various parts of mathematics previously discussed and between mathematics and the real world.

• Examples are often presented in a problem-solving framework which asks students to independently obtain a solution that can be compared with the solution presented in the text. Solutions are frequently structured in the Pólya four-step format.
• Think Clouds serve as quick reminders and clarify key points in discussions.
• Hands On Activities begin each chapter, offering content-related games and puzzles that motivate the chapter. These can be easily adapted for use in the elementary classroom.
• Cooperative Investigations are activities that small groups can use to explore and discuss concepts. There is one Cooperative Investigation per chapter and additional Cooperative Investigations can be found in MyLab Math.
• Problem sets end each section and include a wide variety of question types.
• Understanding Concepts problems provide drill exercises and reinforce basic concepts.
• Into the Classroom problems pose questions that will help future teachers consider how they might clarify subtle and often-misunderstood points for their future students. These problems have been significantly increased and updated.
• Responding to Students exercises give future teachers insight into what mathematical questions and procedures children will come up with on their own, with ways to respond to them.
• Thinking Critically problems have students delve more deeply into the section topic. Many of these problems can be used as classroom activities or with small groups.
• Making Connections problems apply the section concepts to solving real-life problems and to other parts of mathematics.
• State Assessment problems provide examples of problems from the high-stakes standardized exams now used in many states. These problems help make future teachers aware of the types of knowledge that their future students will be asked to master.
• Writing exercises are interspersed throughout the problem types providing opportunities to convey ideas through written words and not just numbers and symbols.
• End-of-Chapter materials are designed to help students study efficiently.
• The Chapter Summary is in a table format, pulling together the Key Concepts, Vocabulary and Notation for easier study & review.
• Chapter Review exercises cover all of the main topics from the chapter to help students check their own understanding and prepare for a test.

Also available with MyLab Math 

MyLab™ Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math.

NEW! Media Update in MyLab Math features:

• NEW! Mathematics Education Insights videos provide an unscripted view into a real classroom in action. Your students will hear from and see teachers in action and watch children learning lessons, interacting with their classmates, asking questions in real classrooms. Watching and listening to the children provide insights into how children process information, work together, and eventually learn concepts. Worksheets are provided for each video as well as an implementation guide for instructors to help them integrate the ideas in these videos into their math for future teacher courses. 
• NEW! Common Core in Action videos feature experienced faculty shedding light on what the CCSS really mean for the classroom and for teachers.  Assessment questions are also available in MyLab Math.
• NEW! Common Core Assessment Analysis exercises require analysis and interpretation of sample CCSS exercises.
• NEW! Animations let students interact with the math in a visual, tangible way. These allow students to explore and manipulate the mathematical concepts, leading to more durable understanding. Corresponding exercises in MyLab Math make these truly assignable.
• NEW! Assessment questions for lecture videos allow instructors to create assignments around lecture videos within MyLab Math.
  
• NEW! Mindset material has been added to the course. This content encourages students to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as a learning opportunity – so often a major hurdle for developmental math students.
• UPDATED! Flashcards reinforce key vocabulary from the text in an interactive online format on any device, perfect for review on the go. 

The courses include all the robust features of MyLab Math, plus these additional highlights:

• “Show Work” questions enable professors to assign questions that require more detailed solutions to prove conceptual understanding, which is highly emphasized in the new Common Core State Standards.
• Getting Ready section provides an opportunity for remediation in areas where students may need a little more support.
• Integrating Mathematics and Pedagogy (IMAP) videos, by the San Diego State University Foundation, provide future teachers a view into how students learn and solve problems. A correlation shows which videos align with specific chapters and provides context to help instructors determine where and how to use them in their courses.
• Exercises that are based on IMAP videos are assignable online. Instructors may ask students to watch a brief video and answer related questions, testing students’ understanding of concepts and content in the context of children’s reasoning.
• Videos are available based on ideas from the Responding to Students exercises in the text. Sue Glascoe of Mesa Community College created these using the latest technology, offering a fresh new look for online and video instruction.
• Interactive homework exercises in MyLab Math are correlated to the exercises in the textbook, and they regenerate algorithmically to give students unlimited opportunity for practice and mastery. The software offers immediate, helpful feedback when students enter incorrect answers.

Reach every student with MyLab 

• Deliver trusted content: You deserve teaching materials that meet your own high standards for your course. That’s why we partner with highly respected authors to develop interactive content and course-specific resources that you can trust — and that keep your students engaged.
• Empower each learner: Each student learns at a different pace. Personalized learning pinpoints the precise areas where each student needs practice, giving all students the support they need–when and where they need it–to be successful.
• Teach your course your way: Your course is unique. So whether you’d like to build your own assignments, teach multiple sections, or set prerequisites, MyLab gives you the flexibility to easily create your course to fit your needs.
• Improve student results: When you teach with MyLab, student performance improves. That’s why instructors have chosen MyLab for over 15 years, touching the lives of over 50 million students.

Media Update in MyLab Math features:

• Mathematics Education Insights videos provide an unscripted view into a real classroom in action. Your students will hear from and see teachers in action and watch children learning lessons, interacting with their classmates, asking questions in real classrooms. Watching and listening to the children provide insights into how children process information, work together and eventually learn concepts. Worksheets are provided for each video as well as an implementation guide for instructors to help them integrate the ideas in these videos into their math for future teacher courses.
• Common Core in Action videos feature experienced faculty shedding light on what the CCSS really mean for the classroom and for teachers.  Assessment questions are also available in MyLab Math.
• Common Core Assessment Analysis exercises require analysis and interpretation of sample CCSS exercises.
• Animations let students interact with the math in a visual, tangible way. These allow students to explore and manipulate the mathematical concepts, leading to more durable understanding. Corresponding exercises in MyLab Math make these truly assignable.
• Assessment questions for lecture videos allow instructors to create assignments around lecture videos within MyLab Math.
  
• Mindset material has been added to the course. This content encourages students to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as a learning opportunity – so often a major hurdle for developmental math students.
• Updated Flashcards reinforce key vocabulary from the text in an interactive online format on any device, perfect for review on the go,