Online assessment of graph theory

Abstract

The objective of this thesis is to establish whether or not online, objective questions in elementary graph theory can be written in a way that exploits the medium of computer-aided assessment. This required the identification and resolution of question design and programming issues. The resulting questions were trialled to give an extensive set of answer files which were analysed to identify whether computer delivery affected the questions in any adverse ways and, if so, to identify practical ways round these issues. A library of questions spanning commonly-taught topics in elementary graph theory has been designed, programmed and added to the graph theory topic within an online assessment and learning tool used at Brunel University called Mathletics. Distracters coded into the questions are based on errors students are likely to make, partially evidenced by final examination scripts. Questions were provided to students in Discrete Mathematics modules with an extensive collection of results compiled for analysis. Questions designed for use in practice environments were trialled on students from 2007 – 2008 and then from 2008 to 2014 inclusive under separate testing conditions. Particular focus is made on the relationship of facility and discrimination between comparable questions during this period. Data is grouped between topic and also year group for the 2008 – 2014 tests, namely 2008 to 2011 and 2011 to 2014, so that it may then be determined what factors, if any, had an effect on the overall results for these questions. Based on the analyses performed, it may be concluded that although CAA questions provide students with a means for improving their learning in this field of mathematics, what makes a question more challenging is not solely based on the number of ways a student can work out his/her solution but also on several other factors that depend on the topic itself.