Facilitating Communication about Measurement, Exponents, and Scientific Notation

Introduction

As students move from the middle grades to the secondary grades, they move from primarily modeling linear phenomena which have constant rates of change to studying non-linear phenomena which have variable rates of changes. Exponential functions are an important class of functions with non-constant rates of change and provide students an opportunity to revisit, reflect and refine their previous experiences involving numbers (e.g., properties of exponentials, scientific notation), issues of measurement (e.g., problems of scale), and geometry and spatial sense (e.g., visualization of exponential growth) (See Related 9 - 12 Patterns, Functions, & Algebra Standard). Students need ample opportunities to organize and consolidate their thinking about exponentials.

All students need extensive experience listening to, reading about,writing about, speaking about, reflecting on, and demonstrating mathematical ideas in order to develop the ability to express mathematical ideas coherently. Students also need to reflect on the thinking of others to broaden their understanding about their own strategies and alternative strategies for solving a problem. Active student participation in learning through small- and large-group discussions provides multiple opportunities for questioning, listening, and summarizing.

The teacher plays an important role in facilitating and fostering communication so that powerful mathematical understanding is developed (See Related 9 - 12 Communication Standard). Not only do teachers need to encourage their students to communicate mathematically, they also need to model good communication skills. The ability to pose questions that elicit, extend, and challenge students' thinking is an essential part of creating a classroom environment where intellectual risks, sense making, and deep understanding are expected.

The class shown in the following video clips is engaged in solving problems which require the use of very large numbers, prompting consideration of the value of scientific notation. The teacher relates the notions of scientific notation and exponents to the way Alice changes size in the story of Alice in Wonderland.

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