Chapter 4

Tutoring in Mathematics

The Purpose of Tutoring in Mathematics

Besides the lecture, the other main type of contact teaching in mathematics is the tutorial or exercise class. In this we include all such interactive teaching which is distinguished from the traditional lecture (Always remembering that the lecture should be more interactive than just a monologue) covered in Chapter 3 by some significant degree of interaction with the students. This may be through working with a number of teaching assistants in a large exercise class, a small group tutorial or discussion class, demonstration classes, or individual one-to one tutoring.

In general the purpose of tutoring is to:

 provide supported practice in problem solving

 stimulate an environment for learning by doing

 provide training in communication/team skills

 facilitate learning by discussion.

In mathematics the major uses of tutoring are in problem solving or exercise classes, where the tutor does not usually coordinate and manage the discussion process. Rather, students simply work through problems, and discussion amongst subgroups is generated spontaneously. Many mathematicians actually prefer to work on their own, but there may be activities in which a coordinated team approach is useful, say in modelling problems. The main point in such group teaching is that the focus is as much on individual support for the student, to help them over the difficult parts of the course. The primary features of tutoring in mathematics are therefore:

 active participation

 face-to-face contact

 purposeful activity.

As Mason ([53], p.71) notes, the main advantage of tutoring in mathematics is that we can enter students’ world, and can interrogate them, rather than trying to bring them into the lecturer’s world, which is what usually happens in the lecture. It is an opportunity to help the students through the most difficult  conceptual reconstructions (Principle 7), such as abstraction. Also, small group teaching allows students to ‘teach’ each other and this takes advantage of the old adage that you only really begin to understand something when you come to teach it. Morss and Murray ([56], p. 50) give a useful list of the aims of groups and associated activities. They emphasise that we should explicitly share these with the students, so they know the purpose of the group activities. The tutoring environment is also a good place to help students to learn how to learn (Principle 8). For example, when a student is stuck on a differentiation get them to write out everything they know about differentiation. Eventually they will find this is a useful ploy whenever they hit a sticking point. Eventually, they will get fed up of writing stuff out and will start running through it in their mind - that is, thinking deeper. The tutorial also gives students the opportunity to watch experts in action, warts and all.

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