The demand for more HE students to take more courses in mathematics has increased significantly, as the use of mathematics has increased in disciplines like life sciences and outside sciences altogether. Even on traditional science and engineering courses undergraduates are becoming more diverse in their mathematical background and conceptual understanding of the discipline. University tutors spend more and more time delivering additional teaching classes. When doing so, most rely on traditional methods of delivery. However, such methods presuppose that the learners have a good memory and a considerable time to practice. These suppositions are particularly unrealistic in the times of broadening participation, dealing with large groups of undergraduates who have limited mathematics background, limited memory, limited proficiency in explanatory reasoning, limited interest in the subject and on top of that, limited time to cover a large amount of material and limited study skills, all aggravated by a limited contact with teachers. As the result, we have seen many calls for reform in mathematics education. We propose the approach, which dispenses with many false dichotomies and addresses all the above challenges by promoting ‘‘learning through questioning and analysis’’, leading to ‘‘competency through comprehension’’, enhanced learning outcomes and increased student and employer satisfaction.
The paper describes a specific approach to teaching most that an engineering student needs to know about differential calculus – in a very efficient manner. The approach is based on Socratic Dialogue directed at developing freshers’ explanatory skills. The emphasis is on creating conceptual understanding that leads to more efficient and deeper learning. We also report common student misconceptions and suggest how they can be overcome.