Special tutorials to support pre-service mathematics teachers learning differential equations and mathematical modelling

Special tutorials both online and off-line were experimented in order to provide extra support for the senior pre-service mathematics teachers at an Australian regional university to improve their learning experience and achieve the best possible learning outcomes in an advanced mathematics course focusing on solving ordinary differential equations and applying mathematical modelling. Two types of special tutorials were offered to the students, the progressive tutorials on solving the same problem with different methods according to the learning progression and student’s instant requests, and the targeted tutorials to address the common problems shared by many students in attempting questions in the formal assessments. The experiments on these special tutorials indicated that the targeted tutorials were immensely useful for the students to either expand the scientific knowledge related to a real-world scenario described by words so as to begin problem solving with correct setting-ups or streamline multiple mathematical processes together to solve a complicated real-world problem described in words. This approach motivated most students to achieve their best possible learning outcomes. The progressive tutorials were effective in addressing student’s curiosity of solving the same problem by multiple techniques and hence improving student’s mathematical thinking and problem-solving skills in general. This exploratory study also found that there were common problems with a lack of general science knowledge and retention of the previously learnt mathematical techniques among most students. There also existed a portion of students who showed no interest in engaging with learning regardless of how much extra learning support provided to them.