Chapter 3

The Mathematics Lecture

The lecture is still the most common form of contact teaching in HE mathematics for anything but small groups (See Chapter 4). And of course there is a large range of approaches to such lectures. To accommodate this range we will take a fairly precise definition of a lecture.

A mathematics lecture is a contact period during which the main activity is a carefully paced presentation, by the lecturer, of a particular mathematical topic, with the intention that when the students leave they will have the means, materials and incentive to study and to learn that topic to the desired level.

Note that this definition does not imply a monologue from the lecturer, or absence of interaction with the students.We are here concerned with how we can give good mathematics lectures that efficiently and effectively support student learning. For this we will put together advice from experienced practitioners, results of educational research, commonly accepted good practice, and the views of students. Throughout, many examples are drawn from experienced practitioners, giving a range of perspectives.

Of course, the purpose of any lecture depends on the topic, the students and more besides. Properly designed a lecture can achieve a wide range of educational purposes. The really important thing is that the lecturer is clear about what they wish to achieve, and that they communicate this to the students. This is expressed in terms of the aims and objectives (i.e. learning objectives) of the lecture (Section 2.6). Normally the object of the lecture is to convey some important concept or technique, but it can also be used to good effect to inspire and motivate students, to impart values and change attitudes, encourage learning skills and develop transferable skills. The purpose of a particular lecture may perhaps be best appreciated when it is realised that lecturing time is actually prime time. It is the one occasion on which the lecturer can convey ideas, concepts, attitudes,etc to all of the students at once and to get across the key messages in the subject. At other times students will usually be learning independently or in small groups, supported by materials that we provide for them. Lecture time should therefore be quality time. Lectures may most productively be aimed at the key messages in the subject, at those areas where students are likely to experience the most difficulty, at establishing and encouraging higher order thinking skills, at developing attitudes and approaches that characterise the subject, and at motivating the students. We might summarise this as:

The key purpose of a lecture is to get across the most important messages about our subject to the maximum number of students.

The rest of this chapter can be found here.

Lists of supporting papers, not avalible in the book, can be found by following the links below.