How do students learn to apply their mathematical knowledge to interpret graphs in physics?

This paper describes a laboratory-based program in physics designed to help students build effective links between the mathematical equations used to solve problems in mechanics and the real world of moving objects. Through the analysis of straight line graphs derived from their own data students have been able to achieve a considerable development towards a concept of slope, or gradient, and how it relates to the concept of proportionality, but they continue to demonstrate a great resistance to applying their mathematical knowledge to physics. A model designed to help us apply current research ideas to this problem is described. The work described in this paper was carried out at Dickson College, a government senior secondary college (Years 11 and 12) in the Australian Capital Territory, where the author taught physics and biology.