Faculty of Education - Theses

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Subject: Study and teaching (Secondary) × Subject: Victoria × Start date: 1991 × End date: 1991 × Author: Ryan, Julie ×

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    Students' early understanding in calculus
    Ryan, Julie ( 1991)
    Students' Early Understanding of Calculus The study undertaken here looked at difficulties associated with the first principles approach to the derivative of a function and concentrated in particular on the first five lessons in calculus as experienced by a typical group of nineteen year 10 students who were preparing to take calculus at year 11. A traditional teaching approach was contrasted with an alternative computer teaching approach and both approaches were analysed for success in terms of conceptual understanding, skill acquisition and student perceptions of whether the work was easy to understand. As calculus has served as a critical filter for further study in mathematics, teaching methodology and student attitudes to the topic were a focus of the study. It was found that the students in the study had a limited concept image for gradient ('measure rise/run') and that a greater development of the global ideas associated with the gradient of a straight line needed to be a focus of learning before the idea of gradient of a curve should be introduced in beginning calculus. It was found that the use of a tangent to a curve at a point to measure gradient of the curve was not a spontaneous intuition and it is recommended that more time be given to this notion in the first principles approach to differentiation. The traditional first principles approach was found to be too cognitively demanding for the students who demonstrated a 'rush to the rule' for meaning. Students undergoing the computer treatment also demonstrated this 'rush to rule' and therefore very gradual development is recommended for students in their first encounters with calculus.