This book is about how to teach arithmetic using an inquiry method for homeschool and classroom teachers. A child's innate love of learning is encouraged through hands-on exploration, discovery, and the creation of models. The book is a collection of lessons, games, and activities. Black Line Masters and an answer key to the Student Work book are included. Subjects covered are subtraction, multiplication, division, regrouping in addition, patterns, fractions, place value into the thousands, and other general math topics.

This book synthesizes research findings on patterns in the last twenty years or so in order to argue for a theory of graded representations in pattern generalization. While research results drawn from investigations conducted with different age-level groups have sufficiently demonstrated varying shifts in structural awareness and competence, which influence the eventual shape of an intended generalization, such shifts, however, are not necessarily permanent due to other pertinent factors such as the complexity of patterning tasks. The book proposes an alternative view of pattern generalization, that is, one that is not about shifts or transition phases but graded depending on individual experiences with target patterns. The theory of graded representations involving pattern generalization offers a much more robust understanding of differences in patterning competence since it is sensitive to varying levels of entry into generalization. Empirical evidence will be provided to demonstrate this alternative view, which is drawn from the author’s longitudinal work with elementary and middle school children, including several investigations conducted with preservice elementary majors. Two chapters of the book will be devoted to extending pattern generalization activity to arithmetic and algebraic learning of concepts and processes. The concluding chapter addresses the pedagogical significance of pattern learning in the school mathematics curriculum. ​

Patterns in Arithmetic: Book 2 Parent / Teacher Guide and Student Workbook is about how to teach arithmetic using an inquiry method for homeschool and classroom teachers. A child's innate love of learning is encouraged through hands-on exploration, discovery, and the creation of models. The Parent / Teacher Guide is a collection of lessons, games, activities, Black Line Masters, and an answer key to the student workbook. The Student Workbook has worksheets necessary to complete the lessons. Subjects covered are subtraction, multiplication, division, regrouping in addition, patterns, fractions, place value into the thousands, and other general math topics.

Resnik expresses his commitment to a structuralist philosophy of mathematics and links this to a defence of realism about the metaphysics of mathematics - the view that mathematics is about things that really exist.