Home Articles Reader Opinion Editorial Book Reviews Discussion Writers Guide About TCRecord
transparent 13

The Foundations of Mathematics

reviewed by Jenni L. Harding-Dekam - June 04, 2015

coverTitle: The Foundations of Mathematics
Author(s): Ian Stewart & David Tall
Publisher: Oxford University Press, Oxford
ISBN: 019870643X, Pages: 432, Year: 2015
Search for book at Amazon.com

Foundations of Mathematics: An Active Approach to Number, Shape, and Measures in the Early Years is a mathematics text revealing practical ways to bring mathematics into your preschool or early childhood learning environment. The authors of this book have extensive mathematics experiences with young children. Carole Skinner is an early years math specialist in the United Kingdom and Judith Stevens is an early learning consultant and author specializing in math.

This book is organized into eight chapters: all about the number, doing calculations, working with shapes, learning to measure, solving problems, collecting and sorting, stories and rhymes, and math outdoors. Each chapter articulates the mathematics content being addressed with the defining of concepts and vocabulary to be used with children. Experiences and activities provide modeling on how to teach this math content. Open-ended questions conclude each section, and provide students with math challenges to complete at home.

The chapter on working with shapes focuses on 2D and 3D shapes by identifying them in terms of faces, sides, regular, and irregular shapes. These characteristics of shape are emphasized in order to build children’s understanding of geometric vocabulary while providing a foundational understanding. In this chapter the authors explain shape, position, direction, and movement for explicit knowledge of different orientations. Next the authors investigate patterns and symmetry in actual objects that children can manipulate. This chapter also provides recommended mathematics children’s literature.

The role of the teacher during instruction is clarified in the next chapter through examples of activities for children. These activities and experiences are spread throughout each section and present hands-on ways for them to explore geometry. The section on enriching provisions explains how mathematical shape and spatial materials encourage mathematical thinking through play. There are nine open-ended questions and enabling statements about shape that teachers can use to guide students to a deeper understanding of concepts. The concluding section provides three activities children can do at home to reinforce shape learning with their families using ordinary items and family encounters.

The next chapter doing calculations emphasizes how to use number lines, tracks, and dominoes for calculations. Addition and subtraction aspects are articulated to create early numeracy. Multiplication and division are explained as repeated addition and subtraction through grouping. This chapter could be stronger if it outlined how to have children take the next step in grouping by creating multiplication arrays with objects in order to physically observe a grouping of numbers.

The stories and rhymes chapter shares specific ways to bring traditional stories, rhymes, and contemporary stories into mathematics learning. In the early years, it is important to create learning environments where instruction is integrated (mathematics and language arts in this case) because this is how children learn in their natural world. A reference section with counting books and rhymes is included.

The math outdoors chapter reveals ways children can continue their learning outdoors where they can see, touch, smell, hear, and taste mathematics. This allows children to use all of their senses to make sense of math. This discovery happens by extending indoor learning experiences outdoors through outdoor role play, creating math learning zones and resources, and playing games while keeping score. These outdoor activities engage children by being messy, noisy, and full of movement.

This book capitalizes on teaching mathematics to the “whole child” (Enslin, 2011). There are explicit directions on how to use indoor and outdoor activities to keep mathematics learning innovative. Suggested activities are both dependent (teacher and children together), independent (child alone), and in pairs (child learning with another child). Learning is accomplished by teacher-created activities (objects, imaginative play props), explicit teaching (number nursery rhymes, games), and the discovery of concepts by children (experimenting with mathematics in structured and unstructured situations). Children learn mathematics through hands-on and minds-on experiences.

In conclusion, Foundations of Mathematics: An Active Approach to Number, Shape, and Measures in the Early Years explains how to create mathematical understanding for 3- to 7-year-olds. This book would benefit early childhood teachers, specialists, leaders, childcare providers, and parents. It clearly articulates how to set up these mathematical open-ended learning experiences where children can understand their world.


Enslin, P. (2011). Liberalism, education and schooling – by T. H. McLaughlin. Educational Philosophy and Theory, 43(7), 788–790.

Cite This Article as: Teachers College Record, Date Published: June 04, 2015
https://www.tcrecord.org ID Number: 17982, Date Accessed: 12/6/2021 5:54:25 PM

Purchase Reprint Rights for this article or review
Article Tools
Related Articles

Related Discussion
Post a Comment | Read All

About the Author
  • Jenni Harding-Dekam
    University of Northern Colorado
    E-mail Author
    JENNI L. HARDING-DEKAM is an Associate Professor of Educational Mathematics in the School of Teacher Education at University of Northern Colorado. She is a former elementary school teacher and instructional technology specialist. She currently coordinates the Master’s of Arts in Teaching: Elementary Education Licensure Program working with multiple Partner Schools across Colorado. Dr. Harding-DeKam is passionate in several areas of education including mathematics instruction, quality instruction for children, improving teacher education, diversity in classrooms including ethnomathematics, culturally responsive classrooms, STEM learning for English Learners, and doctoral advising. Recent publications include Creating Number Sense by Incorporating Math Structure, The Power of Multicultural Mathematics Picturebooks, and Defining Culturally Responsive Teaching: The Case of Mathematics.

    Harding-DeKam, J. L. (2015). Creating number sense by incorporating math structure. The Colorado Mathematics Teacher, Winter, 15-16, 15–16.

    Loyd, S., Harding-DeKam, J. L., & Hamilton, B. (2015). The power of multicultural mathematics picturebooks. Colorado Reading Journal, 25, 5–10.

    Harding-DeKam, J. L. (2014). Defining culturally responsive teaching: The case of mathematics. Cogent Education Journal 1(1), DOI 10.1080/2331186X.2014.972676.

Member Center
In Print
This Month's Issue