Math for Teachers: An Exploratory Approach

Author(s): Robert G Stein

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Math for Teachers: An Exploratory Approach, by Robert G. Stein, gives those who teach K-8 mathematics the opportunity to build a strong foundation for teaching mathematics. This strong foundation gives the reader confidence, joy, and satisfaction.

Math for Teachers uses an exploratory approach to mathematics. These challenging, guided explorations, many found nowhere else, are open-ended and foster independent learning.

The new second edition has been rearranged to flow more smoothly and includes new chapters on statistics and probability. In addition, pictures, diagrams, and uses of manipulatives have been enhanced to provide more concrete foundations for abstract ideas and to model how the material can be taught in schools.

Math for Teachers: An Exploratory Approach includes:

  • History used throughout to enrich, clarify and humanize mathematics.
  • Practical teaching tips and discussions about math curriculum.
  • Coverage of mathematics through grade 10.
  • The belief that students need to master both basic skills and underlying concepts in order to use mathematics effectively.
Robert G Stein

Many teachers have experienced the frustration of teaching long division to an unwilling pupil. Helping students learn would be so much easier if you could only help them understand why the division works and convince them that it will be useful to them later in mathematics. Robert Stein has succeeded in writing a book that helps teachers accomplish this goal and many other similar ones.

Math for Teachers: An Exploratory Approach covers elementary and middle school mathematics, as well as the foundations of algebra. The book is written with the teacher in mind, but it contains activities and exercises that are appropriate for students. Teachers can easily pull out the loose-leaf pages to photocopy for their students.

Two common themes dominate Stein’s approach. First, he wants teachers and students to be able to answer the question, Why does it work this way? Second, he wants them to realize that the algorithms used in arithmetic lay the foundation for understanding higher mathematics. For example, his treatment of fractions carefully notes that students who cannot manipulate numerical fractions will struggle when faced with algebraic ones. He analyzes the topics that must be understood before students work with fractions and proposes an order for introducing arithmetic with fractions. We especially appreciated his notes about improper fractions not really being improper and about calculators not negating the need for carefully teaching arithmetic.

Stein includes frequent historical notes detailing some of the most entertaining tales from the history of mathematics. Readers will learn about Euclid, Euler, and Gauss, as well as when algebra was first used.

Stein has developed a creative set of exercises that serve as a continuation of the learning process. He supplies answers for most of the exercises; but when a hint will suffice, he supplies one instead of the answer. At the close of each chapter, a vocabulary list includes section numbers that refer readers to the definition. The book also contains a self-test to help readers confirm that they clearly understand the material covered. We highly recommend this book to any teacher, particularly of grades K-9, who would like to increase his or her understanding of the foundations of mathematics or have a collection of interesting activities and problem sets for his or her students.

From a review of an earlier edition in the April 2004 issue of “The Mathematics Teacher.”
By Patrick Farrell, teacher, and Travis Wallace, student; Main School of Science and Mathematics, Limestone, ME

Math for Teachers: An Exploratory Approach, by Robert G. Stein, gives those who teach K-8 mathematics the opportunity to build a strong foundation for teaching mathematics. This strong foundation gives the reader confidence, joy, and satisfaction.

Math for Teachers uses an exploratory approach to mathematics. These challenging, guided explorations, many found nowhere else, are open-ended and foster independent learning.

The new second edition has been rearranged to flow more smoothly and includes new chapters on statistics and probability. In addition, pictures, diagrams, and uses of manipulatives have been enhanced to provide more concrete foundations for abstract ideas and to model how the material can be taught in schools.

Math for Teachers: An Exploratory Approach includes:

  • History used throughout to enrich, clarify and humanize mathematics.
  • Practical teaching tips and discussions about math curriculum.
  • Coverage of mathematics through grade 10.
  • The belief that students need to master both basic skills and underlying concepts in order to use mathematics effectively.

Robert G Stein

Many teachers have experienced the frustration of teaching long division to an unwilling pupil. Helping students learn would be so much easier if you could only help them understand why the division works and convince them that it will be useful to them later in mathematics. Robert Stein has succeeded in writing a book that helps teachers accomplish this goal and many other similar ones.

Math for Teachers: An Exploratory Approach covers elementary and middle school mathematics, as well as the foundations of algebra. The book is written with the teacher in mind, but it contains activities and exercises that are appropriate for students. Teachers can easily pull out the loose-leaf pages to photocopy for their students.

Two common themes dominate Stein’s approach. First, he wants teachers and students to be able to answer the question, Why does it work this way? Second, he wants them to realize that the algorithms used in arithmetic lay the foundation for understanding higher mathematics. For example, his treatment of fractions carefully notes that students who cannot manipulate numerical fractions will struggle when faced with algebraic ones. He analyzes the topics that must be understood before students work with fractions and proposes an order for introducing arithmetic with fractions. We especially appreciated his notes about improper fractions not really being improper and about calculators not negating the need for carefully teaching arithmetic.

Stein includes frequent historical notes detailing some of the most entertaining tales from the history of mathematics. Readers will learn about Euclid, Euler, and Gauss, as well as when algebra was first used.

Stein has developed a creative set of exercises that serve as a continuation of the learning process. He supplies answers for most of the exercises; but when a hint will suffice, he supplies one instead of the answer. At the close of each chapter, a vocabulary list includes section numbers that refer readers to the definition. The book also contains a self-test to help readers confirm that they clearly understand the material covered. We highly recommend this book to any teacher, particularly of grades K-9, who would like to increase his or her understanding of the foundations of mathematics or have a collection of interesting activities and problem sets for his or her students.

From a review of an earlier edition in the April 2004 issue of “The Mathematics Teacher.”
By Patrick Farrell, teacher, and Travis Wallace, student; Main School of Science and Mathematics, Limestone, ME