Mathematics teaching has been an active field of research and development at the Department of Mathematics and Systems Analysis at Aalto University. This research has been motivated by a desire to increase the number of students that pass compulsory basic mathematics courses without compromising on standards. The courses aim to provide the engineering students with the mathematical skills needed in their degree programmes so it is essential that a proper foundation is laid. Since 2006, a web-based automated assessment system called STACK has been used on basic mathematics courses for supplementary exercises to aid learning at Aalto University.
In this thesis, computer-aided mathematics teaching and, in particular, automated assessment are studied to investigate what effect attempting to solve online exercises has on mathematical proficiency. This is done by using a Granger causality test. For this, the first two of three basic courses are examined. The concepts relating to learning and computer-aided mathematics teaching as well as the developments, including Mumie, made at Aalto University are first presented. Then, the statistical methodology, the theoretical framework and the test procedure for Granger causality are described. The courses and data, which was collected from STACK and used to quantify mathematical proficiency for the Granger causality test, are then reviewed. Finally, the results and implications are presented.
The Granger causality tests show that there exists a Granger-causal relationship such that mathematical proficiency affects the desire to attempt to solve exercises. This holds for both of the interpretations used for quantifying mathematical profiency and all variations of the penalty deducted for incorrect attempts. The results imply that the exercises are too difficult for the students and that students tend to give up quickly. Thus, the Granger causality tests produced statistically significant results to back up what teachers have always known: students are discouraged by failure, but encouraged by success. The results provide teachers with valuable information about the students' abilities and enable teachers to alter the teaching accordingly to better support the students' learning.
