The traditional approach to teaching maths and stats modules is to deliver a lecture or more per week. Despite emerging discussions of a problem-based learning approach few lecturers have fundamentally changed their teaching style. Nevertheless, maths and stats modules are ideal for trialling such an approach. Typically maths and stats students in schools and colleges learn by a relatively light touch lecture style teaching, involving short demonstrations and a high proportion of practical work undertaken by the students. However there is reluctance to move to this format in Higher Education. Partly this seems to be due to a difficulty in identifying how this approach could be formulated in a university context. It is also undoubtedly more difficult to plan for such an approach given the resource constraints that ever larger cohorts entail.
Despite these challenges, it is worth considering the problem-based approach. A basic overview of the structure of the approach is:
The problem-based style of learning can be used in a variety of different formats. One set-up would be for all the teaching sessions to be designed around setting groups of students the task of working through problem sets. The role of the teaching staff in the classroom is then to offer advice as needed. This could be followed by the presentation of the group findings. In this set-up there would be no lectures, essentially meaning the sessions are workshops/clinics. A drawback of this approach is that students may not recognise the sessions as part of a ‘proper’ module and therefore be less willing to fully engage. If this approach were used successfully there would be a need for very clear guidelines on expectations and learning outcomes.
Another issue that is arises with respect to the problem-based learning approach is that students may become reliant on the group, meaning that they may struggle to carry out problem solving in an independent context. Therefore if you undertake the problem-based learning approach it may be sensible to also consider incorporating individual assessment into your maths/stats module, both formative and summative.
Lectures can provide a useful function, even in a practical subject that lends itself to learning-by-doing. Lectures can act as signposts so that students become aware of what should be their current level of learning and the expectations for future learning. Lectures also provide an effective mechanism for delivering material to a large number of students, avoiding the repetition that can prove very draining for staff teaching on a one-to-one basis. However, the effectiveness of a large group lecture depends on a number of factors. Teaching staff often find lecturing maths and stats in modules to be problematic due to the diverse ability of the students. It takes a very well planned and skilled member of teaching staff of deliver a lecture that students, across the ability spectrum, successfully learn from. Alternatively you may find that you have a group of students with very weak skills and in this context lecturing may not be a useful teaching medium. In contrast to the lecture, one-to-one sessions allow teaching staff to build up an understanding of the range of experience, ability and confidence of different learners and the unique barriers they may face.
Supplementing student-focused workshops with occasional lectures (not on a weekly basis) may be an appealing alternative. The lecture allows for sign-posting key techniques whilst seminars/tutorials with one-to-one support can be used to focus on the range of challenges arising from a diverse student body. The merits of these different approaches, broadly outlined in this section, centrally depends on the composition of your group of learners.
The diversity of maths ability of a cohort will vary depending on entry requirements. For example, it is likely to be much larger in those programmes that require only a minimum of GCSE-level maths compared with those that require A-level maths and, hence where students have more recent and similar experience. The level of overseas student recruitment adds another dimension to this. Where diversity is an issue, you may also wish to consider offering a preliminary module in order to narrow the gap between your diverse range of learners, with attendance dependent on a screening test on entry. If a preliminary module is in place, this may allow a more ‘traditional’ approach to be used in subsequent modules, including a weekly lecture series.
Whatever the degree of variation in entry qualifications, in order to effectively teach a range of learners you must be able to identify the skills of different students. Therefore in the next section we will consider the merits of screening and streaming students.