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Pathways from the Past I: Using History to Teach Numbers, Numerals, and Arithmetic

William P. Berlinghoff and Fernando Q. Gouvêa
Oxton House Publishers
Publication Date: 
Number of Pages: 
[Reviewed by
Amy Shell-Gellasch
, on

Review of Pathways from the Past I: Using History to Teach Numbers, Numerals, and Arithmetic and Pathways from the Past II: Using History to Teach Algebra.

These two volumes, “packets” as the authors refer to them, are the perfect companion piece to the authors’ very successful Math through the Ages: A Gentle History for Teachers and Others (Oxton House Publishers, 2002). That volume is designed to give teachers (elementary through secondary primarily) a basic grounding in the history of topics that they are or will be teaching in the classroom. These packets provide the teaching modules and worksheets that allow teachers to easily embed history into the curriculum.

As the two subtitles would suggest, the topics covered are specific to the school curriculum. Though this is not specifically stated, the modules in packet I could be used in from about 3rd grade through precalculus. The modules in this volume are on writing whole numbers and place value, zero, fractions, and negative numbers. The modules in packet II would be appropriate for 5th grade (or whenever algebraic notation is first introduced) through Algebra II. Those topics include algebraic symbols, linear problems, quadratic equations, cubic equations, and imaginary numbers. Each packet includes an introduction on how and why to use history in the classroom. This is followed by an ever so brief flyover of the historical eras that the mathematics in question relates to. Each chapter is broken into about 5 lessons while each volume has just under twenty lessons. The lessons include a brief overview of the historical context of the topic and a short description of the mathematics. Each section also has a loss-leaf work sheet for in class use with notes provided in the test. These notes are designed for the teacher’s use, not the student’s, and contain suggestions for using the materials.

What I love about these lessons is that they are very short and to the point. All told, each lesson is about 2–4 pages. So a teacher can pick this up the night before if need be and have a mini historical lesson ready for the next day. Throughout the authors provide comments on how to implement the lesson, examples of questions to ask, and suggestions for further reading for the teacher.

By no means do these handy little volumes constitute a history of mathematics text. They give just enough information for immediate application to the classroom. A teacher who wants to learn more mathematics and feel more grounded (beyond what is presented in the authors’ title) would be well served to read any of a number of general history text such as Suzuki or Katz for a deeper understanding.

There are a multitude of teacher recourses on the internet for use in the classroom. But finding material on the right level and ready to use takes an inordinate amount of time. The overwhelming benefit of these volumes is that it is all right there at your fingertips. To my knowledge, there is nothing else like it on the market. If you are an elementary school teacher, a middle or high school math teacher, a math education instructor, or even a developmental or general education mathematics instructor at the college lever you will surely find a use for Pathways from the Past. You might not have realized you needed these volumes, but you do!

Amy Shell-Gellasch is an Associate Professor at Montgomery College and a volunteer researcher at the Smithsonian National Museum of American History. Her area of study is the history of mathematics and its uses in the classroom.

First Thoughts for Teachers

1. Writing Whole Numbers: Place Value

Sheet 1-1: Egyptian Hieroglyphics

Sheet 1-2: Babylonian Numerals

Sheet 1-3: Mayan Numerals

Sheet 1-4: Roman Numerals

Sheet 1-5: Hindu-Arabic Numerals

2. Zero Is Not Nothing: Properties of Zero

Sheet 2-1: Using a Placeholder

Sheet 2-2: The Number Zero

Sheet 2-3: Zero in Equations

3. Broken Numbers: Fraction Arithmetic

Sheet 3-1: Unit Fractions

Sheet 3-2: Place Value Fractions

Sheet 3-3: Name and Count

Sheet 3-4: Working with Parts

Sheet 3-5: Decimals

Sheet 3-6: Percent

4. Less than Nothing?: Negative Numbers

Sheet 4-1: What Are Negative Numbers?

Sheet 4-2: Adding & Subtracting Negative Numbers

Sheet 4-3: Multiplying & Dividing Negative Numbers

Sheet 4-4: Fitting In

Sheet 4-5: Powers and (Sometimes) Roots