The usual way to make string diagrams using rubber bands or yarn on a board with nails does not allow much exploration. Mary Boole meant them as exercises in visualization. Building these diagrams using spreadsheets not only shows their versatility and capability for artistic expression, it helps students get used to using ordered pairs and axes of different sorts and thus builds their graphic sense. There are so many possibilities that you might think of having contests for the most interesting and thought provoking diagrams.
Tag: functions
String Challenge
Strings need not begin and end on axes that are at right angles to each other which we call Cartesian. It is quite interesting that Descartes himself did not use axes at right angles. We consider this a challenge because students have to figure out how to move both the axes and the lines. Once you understand the process there is no end to the beauty of the string diagrams you can make. We suggest you check out the Web and Wikipedia for more ideas.
Composition of Functions
One of the most powerful aspects of the mathematics of functions is our ability to treat them as abstract quantities (essentially numbers) and then combine them with standard operations. But with functions we can go further and develop a new operation we call composition or taking a function of a function. We give students the opportunity to explore composition by using different functions and by seeing their result on graphs. This is very powerful and great fun to push imaginations.
Inverse of a Function
Spreadsheets make it very easy to switch axes and add graphs. They enable students to play with what may have been difficult and abstract concepts like the inverse of a function. You may want to approach the inverse of a function by challenging students to fill in a table of values with a rule that creates a mirror of that function. So you can approach the inverse of a function either as the interchange of axes or as a symmetry issue. Either one works well on spreadsheets.
Polynomial Functions
Polynomial functions are not limited to the highest term and while that term is most important in determining the shape of its graph, additional terms play a role. Try out additional terms to see how they affect the shapes of the graph. Focus on the patterns!