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 IV. Odd and Even Numbers: Beyond the Last-Digit Rule
Exploration IV. odd and even numbers: beyond the last-digit rule

I do not suggest avoiding the last digit rule, this would be impossible, but rather postponing it in order to achieve odd/even classification by essence and not by superficial features of the common representation [of numbers].

Rina Zazkis (2011)

Photo by Susan K Hamon

Rationale for Exploration IV

  • The concept of odd and even numbers holds a position of prominence in preK-2 mathematics.
  • Students and teachers need to explore more profound meanings of odd and even and representations of odd and even numbers. The algebra of odd and even numbers serves students now, in middle school, in high school, and in college.
  • Just as in many languages the word for “odd” ...
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