This is a series of applets drawn from the website mathMINDhabits [sites.google.com/site/mathmindhabits]
that is designed for teachers of mathematics who want to deepen their understanding of the mathematics they teach
and that their students are expected to learn.
Algebra in the middle and secondary grades is largely the mathematics of function. The topic of Functions is not normally taught early in a student’s algebra career. When the topic of functions is finally taught, it is taught with emphasis on the symbolic representations of functions. Research has shown that approaching algebra from the outset through the study of functions using both symbolic and graphical representations simultaneously and in parallel is a pedagogically powerful teaching and learning strategy.
Many people learn better and develop deeper understanding and intuitions about a subject if visual representations of aspects of the subject are prominent in the teaching and learning. All people learn better and develop deeper understanding and intuitions if they have the opportunity and the tools to explore their understanding and intuition by going back and forth between different representations of the a given mathematical object and the procedures for manipulating and transforming it.
The Cartesian graph provides a way to express functions with imagery in addition to the symbols we usually use for their representation. The increasingly wide availability of graphing calculators and graphing software for personal computers and mobile devices makes it possible for us as teachers to take advantage of graphical representations in the way we teach the mathematics we teach as well as in the way we ourselves understand the subject.