The subject of algebra has always been important in American secondary mathematics education. However, algebra at the elementary level has been garnering increasing attention and importance over the past 15 years. There is consequently a dire need for ideas, suggestions and models for how best to achieve pre-algebraic instruction in the elementary grades. Planting the Seeds of Algebra will empower teachers with theoretical and practical knowledge about both the content and pedagogy of such instruction, and show them the different faces of algebra as it appears in the early grades. The book will walk teachers of young children through many examples of K-6 math lessons and unpack, step by step, the hidden connections to higher algebra. After reading this book, teachers will be better equipped to reflect on their teaching, renew their thinking, and change parts of their practice in order to transform their classroom culture into one where both students and teachers are attuned to algebraic thinking, reasoning, talking, writing, and doing.

Exploration II. Subtraction: More Than Just “Take Away”
Exploration II. subtraction: more than just “take away”

Addition and subtraction do not simply provide foundations for algebra (or vice versa); these arithmetic operations and algebra are intimately interrelated and mutually support learning in both domains.

National Council of Teachers of Mathematics (2011a)

Photo by Monica Neagoy

Rationale for Exploration II

  • The concept of subtraction holds a position of prominence in preK-2 mathematics.
  • Algebraic thinking must be modeled with basic mathematical concepts. Treating arithmetic in algebraic ways begins with addition and subtraction: Working with equivalent numerical expressions and equations is a good start.
  • Technology tools compute more rapidly and efficiently than we do, so the bar has been raised for teaching arithmetic: Algebraic reasoning with numbers is the higher goal.
  • Understanding subtraction is more ...
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