Undergraduate difficulties: algebraic skills and mathematical comprehension.
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Many first year university students struggle with mathematics. Observations in senior mathematics classes in four New Zealand secondary schools highlighted potential undergraduate problems, especially with algebraic and mathematical reading skills. In this thesis, these two areas are investigated further. In the first part of the thesis, an analysis is done of algebraic tests given to first year university mathematics students. From the results there emerged five main categories of common consistent algebraic difficulties. These categories not only emerged the following year with a similar group, but senior secondary school and second year undergraduate mathematics students also displayed them. Overall, the conclusion was that these categories of algebraic difficulties formed from the research did not appear to improve with higher mathematical learning. A second area for the investigation of undergraduate difficulties was in the field of reading to learn mathematics. The results of a questionnaire survey confirmed that students were not only resistant to reading mathematical text, but they did not appear to have the skills to read expository text. Many students used a narrative, surface approach to mathematical reading that resulted in very little of a topic being understood. Further analysis using a variety of extracts, case studies, interviews and written answers led to the formation of a mathematical reading model based on generative comprehension research by Wittrock (1990) and interactive reading research by Dechant (1991). For mathematical text, critical linkages were often symbol-symbol linkages requiring a higher level of comprehension than narrative text. These critical linkages were predominantly located at an inner text layer. A major deterrent to reading mathematical text for students is the difficulty in locating these critical linkages in hard-copy text. Further investigations compared hard copy text with various types of software designed for self-study purposes. Some of the software was found to be better at directing students to these critical linkages while others were not so successful.