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.

# Chapter 1: Making 7—The Lesson: (Grades PreK-K)

### Making 7—The Lesson: (Grades PreK-K)

For much of the 20th century, learning single-digit addition and subtraction has been synonymous with memorizing math facts. The predominant learning theory supporting this view was stimulus-response: A card with “3 + 4” flashed before children's eyes was the stimulus, and the memorized, isolated answer of “7” was the expected response. Despite all we now know about how the brain learns mathematics (Dehaene, 1997; Sousa, 2008), in many schools, memorizing mindless math facts is still stressed by some parents … and teachers.

Making 7 explores alternatives to rote memorization and fosters sense making of single-digit addition combinations. The lesson described below took place in the classroom of Ms. Brady, an extraordinary kindergarten teacher. Ms. Brady had ...