Role of Algebra - MMAP/Pathways |
The core MMAP Application units address the areas of algebra and functions not only from different real-world contexts but from different mathematical vantage points. Then, Extension units help students solidify and codify their experiences, introducing and re-enforcing standard mathematical notation.
Units based on ArchiTech software, such as the Antarctica Project, provide opportunities to develop concepts of variable in two ways: The ArchiTech sliders-by which "global variables" such as outside temperature and insulation values can be manipulated-represent variables that are under the student's control. Students build tables comparing two variables such as "outside insulation" and "cost to build." An Extension, Direct and Inverse Variation, then helps students recognize and mathematically classify relationships between variables.
HabiTech-based units, such as Wolves and Caribou, allow opportunities for students to represent their knowledge of the world through algebraic functions and then track the results of those functions over time. Facility with algebraic notation, and with full words used for variables, is developed through using the software and the accompanying math opportunities. An Extension, Functions from Various Views, helps students compare functions found in HabiTech and Coding Toolbox.
Finally, units based on Coding Toolbox allow students to investigate functions from a more purely mathematical vantage point. Functions are used to build codes, the real-world context, and then learning about function properties-the relationship between domain and range, for example-enhances students' ability to break codes. A standard algebraic notation for functions-for example, y=x2+3--is used in the Coding Toolbox, as are terms such as range and domain. Extensions such as Equivalent Expressions help students learn the language and grammar of algebra, based on Coding Toolbox experiences.