The Structural Relationships Between Conceptual and Procedural Knowledge in Differential Equations

The aim of this study was to investigate the relationship between conceptual and procedural knowledge of the second order linear homogeneous differential equations based on a structural model. students majoring in science and engineering at the shahid rajaee teacher training university in 2009-2010 were considered as a statistical population. the primary test consisted of 30 multiple-choice questions based on the goal-content’s table of the subject. thirty students from science and engineering department were chosen in a pilot study by the method of cluster sampling. after analyzing data, 15 questions were eliminated due to lack of consistency with other questions and also due to their difficulty and discrimination indices. finally, a multiple-choice test with 15 questions was designed. its reliability was satisfactory (α= 0.79). one hundred and twenty two students were selected by cluster sampling method. the experimental model of learner’s knowledge was compiled and by the use of structural equation modeling the direct and total effects of factors determined. analysis of the final data showed that there is a meaningful direct effect on knowledge of ‘concepts’ with knowledge of ‘modeling’ (p<0.01); knowledge of ‘algorithm’ with knowledge of ‘application’ (p<0.01); knowledge of ‘application’ with knowledge of ‘algorithm’ (p<0.01); and knowledge of ‘application’ with knowledge of ‘theorems’ (p<0.05). these results demonstrate that understanding concepts, algorithm, applications, and mathematics modeling has a positive effect on the relationship between conceptual and procedural knowledge. therefore, the outcome of challengeable tasks in the process of teaching could lead to students’ learning achievement in mathematics.