Learning More by Solving Series of Problems Martin Kollar, Comenius University, Bratislava Jozef Hvorecky, University Bellevue, Bratislava, Slovakia

Graphical calculator CASIO ClassPad 300 Flexible tool in teaching mathematics User friendly Students are motivated More than capable to cover high school needs

Series of problems on the given topic We use graphical calculator to visualize our ideas Students can easier discover the facts and connections between them We encourage our students to make suggestions, hypotheses We let the students decide whether they need more examples and how many of the topic given

An example: L’Hospital Rule It is a strong rule for computing limits. Basically it says We wanted to visualize this rule IT can do things you can’t do on the blackboard

Series of problems to discover L’Hospital Rule Problem 1. Compute Problem 2. Find If needed, we provide students similar couples of problems. Students discover the fact that every (differentiable) function zoomed many times looks like a straight line.

Captures of screen of CASIO ClassPad 300 We draw the graphs of the numerator and denominator functions. Next, we zoomed the graphs in the neighbourhood of origin.

Captures of screen of CASIO ClassPad 300 Every picture below is 2 times zoomed previous picture.

Answers to teacher’s questions What line is it? This line is the tangent in a given point. In the first problem with lines we saw that the result is in fact the ratio of slopes of these lines. Slope of a tangent in a point is the derivative. “Ahaaa” effect: This is a L’Hospital’s rule!

The workshop Further problems on the L’Hospital’s rule. Sensitivity of solutions of systems of linear equations Lines and circles in analytical geometry. Animations in planar geomerty.

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