Mathematical modelling: from novice to expert

This study strives to understand how mathematical modelling is perceived by novice, intermediate and expert modellers, through comparing and contrasting their understanding and habits of modelling. The study adopted a qualitative methodology based on observations, interviews and surveys of 78 participants. This included 14 experts who are professors, 11 intermediates consisting of graduate students and post-doctoral fellows, and 53 undergraduates or novices. The study incorporated interviews of the professors and the post-graduate participants, while questionnaires were utilized to understand the perspective of the undergraduate students. The study revealed that the majority of expert participants see modelling as a collaborative effort. There is a dichotomy among them regarding whether mathematical modelling is the setting up of a mathematical model alone, which is deemed an art, or if it includes the solving of the model, which is more a science. These differences have implications on how modelling is taught and how novices and intermediates in turn will view the modelling process. Experts also vary in their opinion on whether models must be verifiable or not. One key feature of the experts approach is that they begin by assuming that they do not understand the question asked and work to ensure that they do. This is despite their superior ability to solve problems. Intermediate participants were more forth- coming with their emotions on modelling than experts; they cited research as opposed to collaboration as their primary means of dealing with barriers arising during the modelling process, and gave credit to intuition as a skill needed for solving - something not mentioned among the experts. Novices were the most descriptive about their feelings when modelling. They conveyed a tendency to be more passive when encountering barriers, waiting for help or giving up as opposed to actively working through the problems. Many of our results, including those mentioned above, have implications for the teaching of effective mathematical modelling.