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 9: Beyond Patterns of Cubes—More Problems to Explore

### Beyond Patterns of Cubes—More Problems to Explore

Beyond patterns of cubes—more problems to explore

Detailed answers to the nontrivial questions under the section below titled “For Your Own Learning” can be found in the companion website for this book at www.corwin.com/algebraprek–12.

### 1. Function Misconceptions

The concept of function is complex. Research studies have highlighted a variety of misconceptions students accumulate over the school years. As with most misconceptions, the longer these misconceptions are held, the harder it is for students to “unlearn” them. Early experiences with functions can help prevent the two particular misconceptions listed below.

### Misconception 1

Constant functions are not functions. A function is called constant if all inputs are assigned the same output. In other words, as the inputs vary, the outputs ...