Read more about Mathematics for Elementary Teachers

Mathematics for Elementary Teachers

(11 reviews)

Michelle Manes, Honolulu, HI

Copyright Year: 2017

Publisher: University of Hawaii Manoa

Language: English

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Reviewed by Thomas Starmack, Professor, Bloomsburg University of Pennsylvania on 3/26/20

The book is somewhat dated and does not include current research based best practices like concrete, representational, then abstract. Like most authors, they make assumptions that students have the ability to understand abstract and start the... read more

Reviewed by Jamie Price, Assistant Professor, East Tennessee State University on 3/20/20

This book introduces the reader to the standards for mathematical practice (SMP) from the Common Core standards in the introduction. I appreciated this as these standards cover all grades and are a unifying theme of the Common Core standards, yet... read more

Reviewed by Shay Kidd, Assistant Professor- Mathematics Education, University of Montana - Western on 12/30/19

The content that elementary teachers need to have that is not covered in this book is graphing, probability, statistics, exponents, visual displays of data. The coverage of operations is very specific in the examples and does not cover the wide... read more

Reviewed by Ryan Nivens, Associate Professor, East Tennessee State University on 10/25/19

The book covers all the expected mathematical strands except for measurement and data/stats. There are some obvious connections to the strands of mathematical practice from the Common Core standards. While the abstract specifically lists MP1, MP2,... read more

Reviewed by Monica Rose Gilmore, Graduate Student, CU Boulder on 7/1/19

This textbook goes into depth about different mathematical concepts that are important for elementary school teachers to understand in teaching mathematics. However, the text is missing a focus on statistics and probability, which are key areas of... read more

Reviewed by Glenna Gustafson, Professor, Radford University on 5/22/19

This is book is fairly comprehensive and I feel could be used by most foundational courses in elementary mathematics. The structure and writing provide a good foundation for students learning the "why" behind the mathematics and becoming... read more

Reviewed by Karise Mace, Mathematics Instructor, Kuztown University on 5/16/19

This book is fairly comprehensive for a one-semester course, although it does not include much detail about several topics. The section on number systems barely touches on Roman numerals and only mentions Mayan and Babylonian counting systems.... read more

Reviewed by Desley Plaisance, Associate Professor, Nicholls State University on 4/29/19

This textbook seems to be appropriate for the first course typically taught for elementary teachers which usually includes topics of problem solving, place value, number and operations. Most books are able to be used for a second course which... read more

Reviewed by Lisa Cooper, Assistant Professor, LSUS on 4/26/19

This text covers many concepts appropriately; however, a few concepts are missing, such as; data analysis and statistics. For more than ten years, data-driven instruction has been a major focus in education along with many other uses. This text... read more

Reviewed by Demetrice Smith-Mutegi, Instructor/Coordinator, Marian University on 3/6/19

This text covers place value, numbers and operations, fractions, patterns, algebraic thinking, decimals, and geometry. However, elementary teachers are expected to also know and understand statistics and probability. This text does not address... read more

Reviewed by Kandy Noles Stevens, Assistant Professor of Education, Southwest Minnesota State University on 12/28/18

This text covers the areas applicable to elementary mathematics extremely well (with the exception of omitting probability and data analysis) and provides graphically visual boxes within the text to define terms and instructional strategies. ... read more

Table of Contents

I. Problem Solving

  • Introduction
  • Problem or Exercise?
  • Problem Solving Strategies
  • Beware of Patterns!
  • Problem Bank
  • Careful Use of Language in Mathematics
  • Explaning Your Work
  • The Last Step

II. Place Value

  • Dots and Boxes
  • Other Rules
  • Binary Numbers
  • Other Bases
  • Number Systems
  • Even Numbers
  • Problem Bank
  • Exploration

III. Number and Operations

  • Introduction
  • Addition: Dots and Boxes
  • Subtration: Dots and Boxes
  • Multiplication: Dots and Boxes
  • Division: Dots and Boxes
  • Number Line Model
  • Area Model for Multiplication
  • Properties of Operations
  • Division Explorations
  • Problem Bank

IV. Fractions

  • Introduction
  • What is a Fraction?
  • The Key Fraction Rule
  • Adding and Subtracting Fractions
  • What is a Fraction? Revisited
  • Multiplying Fractions
  • Dividing Fractions: Meaning
  • Dividing Fractions: Invert and Multiply
  • Dividing Fractions: Problems
  • Fractions involving zero
  • Problem Bank
  • Egyptian Fractions
  • Algebra Connections
  • What is a Fraction? Part 3

V. Patterns and Algebraic Thinking

  • Introduction
  • Borders on a Square
  • Careful Use of Language in Mathematics: =
  • Growing Patterns
  • Matching Game
  • Structural and Procedural Algebra
  • Problem Bank

VI. Place Value and Decimals

  • Review of Dots & Boxes Model
  • Decimals
  • x-mals
  • Division and Decimals
  • More x -mals
  • Terminating or Repeating?
  • Matching Game
  • Operations on Decimals
  • Orders of Magnitude
  • Problem Bank

VII. Geometry

  • Introduction
  • Tangrams
  • Triangles and Quadrilaterals
  • Polygons
  • Platonic Solids
  • Painted Cubes
  • Symmetry
  • Geometry in Art and Science
  • Problem Bank

VIII. Voyaging on Hokule?a

  • Introduction
  • Hokule?a
  • Worldwide Voyage
  • Navigation

About the Book

This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable exploring unfamiliar mathematical situations.

The primary goal of this book is to help you learn to think like a mathematician in some very specific ways. You will:

• Make sense of problems and persevere in solving them. You will develop and demonstrate this skill by working on difficult problems, making incremental progress, and revising solutions to problems as you learn more.

• Reason abstractly and quantitatively. You will demonstrate this skill by learning to represent situations using mathematical notation (abstraction) as well as creating and testing examples (making situations more concrete).

• Construct viable arguments and critique the reasoning of others. You will be expected to create both written and verbal explanations for your solutions to problems. The most important questions in this class are “Why?” and “How do you know you're right?” Practice asking these questions of yourself, of your professor, and of your fellow students.

Throughout the book, you will learn how to learn mathematics on you own by reading, working on problems, and making sense of new ideas on your own and in collaboration with other students in the class.

About the Contributors

Author

Michelle Manes, Associate Professor, Department of Mathematics, University of Hawaii