Teaching Concepts with Maple

May 14 2012 rlopez 1303
Maple

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Being easy to use is nice, but being easy to learn with is better. Maple’s ease-of-use paradigm, captured in the phrases “Clickable Calculus” and “Clickable Math” provides a syntax-free way to use Maple. The learning curve is flattened. But making Maple easy to use to use badly in the classroom helps neither student nor instructor.

In the mid to late ‘80s, as the movement to put computers in the classroom began, at least three researchers zeroed in on the idea to “resequence concepts and skills.” The traditional approach to math instruction, an approach written into countless texts, stresses skill development in the service of concept development. By-hand manipulative skills are necessary for exploring concepts when the only tools for that exploration are pencil and paper. They are a prerequisite for the acquisition of conceptual understanding.

Tools like Maple allow concepts to be explored before the manipulative skills are acquired. Maple draws the graphs, solves the equations, simplifies the expressions. Concepts can be presented and studied, using Maple in place of the not-yet-developed skills. More than that, Maple can be used to implement the steps of the relevant algorithms. Thus, Maple allows a student to see the big picture first, followed by a look at how the details, the steps of relevant calculations, fit into the big picture. All the while, it’s Maple doing the heavy-lifting; the student is learning where the bits fit, and why certain manipulations are needed.

Classroom experience shows that students learn the necessary skills more efficiently and effectively when they have a clearer idea of why they are necessary. They’ve seen what the “right answers” are supposed to look like, they know where the parts belong, and they understand what the goal is supposed to be. 

Maple makes this resequencing of concepts and skills easier to implement because virtually no time is spent learning the tool. Maple’s point-and-click approach to computing in its new interface means that conceptual development can take place right from the start, without a pause to teach a computing language. The simplicity of the tool is one thing, but its use in service of a better pedagogy is far more important. And that better pedagogy is well served by the ease-of-use of the tool.

The collection of examples made available on the Maple web site, in a new section called Teaching Concepts with Maple, illustrates this resequencing of concepts and skills. Each example shows how, after a statement of a problem, it can expeditiously be solved in Maple. Then, like peeling away the layers of an onion, various facets of the solution process can be explored, using Maple’s point-and-click technologies.  From a big-picture conceptual approach, to a mastery of details, Maple helps the student learn more quickly, and with greater insight and understanding.

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