EASING THE TRANSITION TO THIRD-LEVEL FOR FIRST-YEAR MATHEMATICIANS

摘要

Despite students' prior high achievements in mathematics, it was observed over a period of years among a first-year cohort of almost 80 students studying Pure and Applied Mathematics/Theoretical Physics in Trinity College Dublin that a large number struggled significantly with the transition to thirdlevel. A number of factors were identified as being potentially responsible for this, including larger class sizes, a more Abstract form of mathematics, and general difficulties settling into a class in which a noticeable proportion of the students did not possess good social skills. To avoid students dropping out or failing first year, it was decided to introduce a carefully constructed problem-solving module into the students' timetable. This module, while addressing challenging areas from the general first-year programme, was delivered to students in small groups, once a week, with the focus on pair/group work. Attendance was compulsory, and all marks for the module were awarded based on attendance and participation, with no final examination. The idea behind this was to ensure that students maintained contact with their programme at least once a week, and that they were encouraged to participate in each class, despite their initial misgivings. The pace was considerably slower than in lectures, and students were encouraged to discuss their approaches to various problems with others in their group. Pairs of students working together was mutually beneficial, as weaker students often found it easier to learn from a peer; while stronger students developed techniques to better articulate their problem-solving approach. Students were deliberately paired differently every week, with the dual purpose of allowing them to experience working with students of various abilities, and also to encourage greater mixing among the class. This module assisted students in developing general problem-solving skills, as methods of approaching previously unseen problems were examined on a weekly basis. In addition, it forced them to collaborate with classmates on problems and agree on a single solution; an approach with which some of the brightest students struggled noticeably. The ability to explain complex mathematics in simpler terms will be a vital one for many of these students once they become part of the workforce. At the end of each term, students were given an anonymous questionnaire to complete, to ascertain the benefit of the module. The feedback obtained in this way, over a series of three years, was extremely favourable, with the vast majority of students acknowledging that, although they found it difficult initially, the pair-work proved to be invaluable to their learning and fostered academic cooperation among their classmates.