Math Concepts Strand Overview
This strand contains a wide variety of lessons that are arranged by topic. You will find lessons related to fractions, geometry, functions, and other common pre-algebra topics. It is important to understand what these lessons are and what they are not. These lessons are meant to integrate technology (either spreadsheets or calculators) into the learning process. The lessons also help students extend their mathematical understanding either through helping students visualize mathematics or by applying the mathematics to everyday settings. Finally, the lessons use common technologies such as the spreadsheet and the calculator as tools that can compensate for "nagging problems" associated with procedural skills like dividing decimals or multiplying multidigit numbers.
These lessons are not a complete curriculum. We do not advise that you try to use them in any kind of sequential order day-after-day. They are meant to extend mathematical understanding, not to replace a daily curriculum. In that regard, we strongly advise that you use a NCTM-based curriculum for your regular instruction. Programs such as Connected Mathematics (Lappan, Fitzgerald, Friel, Fey, & Phillips, 1996) or Math in the Mind's Eye (Bennett, Maier, & Nelson, 1994) provide an excellent conceptual foundation for learning secondary mathematics. They are highly useful because they focus on conceptual understanding and incorporate a variety of ways to visualize concepts. We have found graphic or pictorial representations of math concepts to be particularly useful for academically low-achieving students or those in special education. Getting students to learn mathematics through "multiple representations"-math symbols, computational procedures, diagrams or pictures, verbal descriptions or arguments-is a practice that is strongly supported in current math research. We cite some of the major studies in this area in the Research Support section of this site.
We suggest that you first look through the lessons to get an idea of how they are structured and how you might use them as extension activities. Each lesson has an overview or objective statement, and each one typically includes files you can download for use with the lesson. You might want to print out the lessons so that you can examine them in detail.
Finally, you will probably want to start with instruction in how to use the spreadsheet. We provide some lessons in helping students learn the basic features of a spreadsheet (see Spreadsheet Basics). We also suggest that you first take a class or read an introductory manual on basic spreadsheet features before you have students work on spreadsheets, if you are not comfortable with a program like Excel. While our lessons do not require students to use complex spreadsheet features, a number of "How do I do this?" questions are likely to arise. Our Spreadsheet Basics lessons are not meant to be a comprehensive introduction to spreadsheets. Any number of commercial materials, including the manuals and help menus of the spreadsheet program, would serve that function.