The accumulation of ideas concerning the teaching of elementary calculus includes recommendations which are still not in widespread use. Research into students’ understanding of calculus suggests that there are many learning difficulties which current teaching methods are not helping students to overcome. The introduction of calculators and microcomputers to school mathematics classes provides us with the illustrative and computational power to practise methods based on practical investigation and intuition which should help to meet the needs of students beginning calculus and lead to greater understanding.