Using computer algebra to encourage a deep learning approach to calculus

The underlying concepts and proofs of introductory calculus involve difficult and abstract ideas that present a mountainous obstacle to many students. A tempting ‘solution ’ for lecturers is to focus the teaching at this stage on techniques. This may have the advantage of ensuring acceptable pass rates but helps neither the students nor the teaching staff in the long term. Computer algebra systems offer both an opportunity and a challenge to present new approaches that assist students to develop better understanding of the basic concepts. They can be used to change the emphasis of learning and teaching of calculus away from techniques and routine symbolic manipulation towards higher-level cognitive skills that focus on concepts and problem solving. Two of the key indicators of deep learning and conceptual understanding are the ability to transfer knowledge learned in one task to another task and the ability to move between different representations of mathematical objects. Computer algebra systems are multiple representation systems, that is, they have the ability to facilitate graphical, algebraic and numerical approaches to a topic. The author will describe how carefully structured worksheets are used with Derive to ask questions then let the students provide the answers in such a way that they can construct their own knowledge. This allows learners to ‘discover ’ rules, to make and test conjectures and to explore the relationship between different representations of functions and other mathematical objects using a blend of visual, symbolic and computational approaches. Students enjoy the power and versatility of computer algebra and are encouraged to become reflective, deep learners