Peer Tutoring in Mathematics for University Students
Carmody, Georgina, Wood, Leigh, Mathematics and Computer Education
A peer tutoring service has been implemented with volunteer senior students from third year mathematics and statistics classes. This simultaneously bridges the gap in the university budget and helps both the tutors' education as well as their students' education. In this paper we examine the peer tutoring experience.
There are several (not mutually exclusive) educational and administrative reasons why peer teaching in university mathematics is advocated:
* To improve the supply and quality of tutors for mathematics subj ects 
* To improve the learning of those who are doing the peer teaching 
* To prepare students for teaching situations in the workplace by participation in peer teaching programs
* To provide services that are outside the university budget
Much work has been done on looking at the benefits of peer education as a whole and of different aspects of peer education. Damon and Phelps  distinguish three approaches to peer education namely peer tutoring, cooperative learning, and peer collaboration. Cooperative learning is generally a team-based learning approach where students pool their resources on a particular topic, and in peer collaboration students simultaneously approach broad aspects of a topic, working together. With these two aspects of peer education, the students are generally on an equal level to one another whereas in peer tutoring, one student takes on the role of a tutor and the other(s) take the role of a student. The use of cooperative and collaborative learning in mathematics at university level is addressed by D'Souza and Wood .
Griffin and Griffin  investigated the positive effects of reciprocal peer tutoring at various educational levels. They found that peer tutoring is effective for increasing student achievement for both the tutor and the student, with the tutor often benefiting more than the student. Peer tutoring schemes have been implemented in a variety of subjects and educational levels. Carroll  discusses the effectiveness of senior medical students acting as co-tutors working in tandem with the academic tutor for first year biology students. Bush  describes a peer tutoring program used for introductory accounting courses as a possible suitable substitute to current laboratory classes. In both of these papers the senior students were paid as academic tutors and were able to relieve full-time academic staff while at the same time providing help to first year students.
Both Hopkin  and Houston and Lazenbatt  investigate the use of reciprocal peer tutoring within a class environment in higher education where each student (or group of students) in the class is responsible for a particular topic and then takes on the role of tutor, teaching that particular topic to the other students in the class. This type of peer tutoring fostered independent and responsible learning, and promoted greater levels of communication, student participation and a deeper understanding of the work involved for the tutors [1, 8].
Oates et al.  were unable to find sufficient numbers of suitably qualified tutors for their first year university mathematics subjects and so instituted a second year segment for an undergraduate mathematics degree, where students were taught how to learn and teach mathematics. They observed classes, wrote materials and reflected on their experiences. Students were then paid to conduct tutorials in their third year. The results were positive and the experience also showed that the peer teachers improved their own learning as discussed above.
Preparing students for a career in teaching has some of the same characteristics as preparing them for teaching other students. One essential difference is that the authences in the workplace are more diverse so the students need to be given diverse learning situations that reflect this. The study of the needs of graduates in this area is new and follows from studies of the needs of employers for mathematicians with wide-ranging communication skills . …