Peer facilitated learning in Mathematics for Engineering: a case study from an Australian university

Abstract

The purpose of this case study is to discuss the effectiveness of peer assisted learning as an engagement strategy for first year engineering students. Studies have shown that engagement is critical to student success in higher education and that it requires a multifaceted approach that recognises the diverse needs of contemporary heterogeneous cohorts. By using the case study of a peer facilitator in a Mathematics for Engineers unit at an Australian University we hope to provide some insights into the Peer Assisted Study Session (PASS) model of student engagement and learning support. PASS is the nomenclature commonly used in Australia for Supplemental Instruction; a peer facilitated learning model that has been shown to improve students’ academic performance as well as assisting in their transition to the university environment. The authors are the coordinator of the PASS programme and a student facilitator from an Australian university. Kiyomi Dunphy, the student facilitator, provides insight into her experience of running weekly study sessions for students and this is supplemented with comments from the programme attendees. Rather than focusing on quantitative data, we have taken a qualitative approach, with the intention of explicating the model as it operates in our particular context.

Introduction

The agenda of widening participation in the tertiary sector compels universities to ensure that they consider the diverse needs and demands of students. As the student cohort becomes more heterogeneous and demands from the employment sector rapidly change, the process of learning and student development have become central concerns of higher education (Warren, 2002). The significance of the first year experience in facilitating student retention and success has been widely researched over the past decade (McInnis, 2001; Krause et al., 2005; Trotter and Roberts, 2006; Zhao and Kuh, 2004). Rather than taking an extra-curricular approach to the first year experience, it is now situated within the curriculum in recognition of the interconnectedness and interdependence of the many factors that affect students’ transition to university (Tinto, 2006). The curriculum, which encompasses academic, social and support dimensions, is seen to frame the ‘educational conditions in which we place students’ (Tinto, 2009, p2). Kift suggests that the curriculum, which is at the nexus of the student experience, is where ‘students are entitled to expect academic and social relevance, support and engagement’ (2009, p9).

Student engagement has become a critical facet of the first year experience and research is increasingly concerned with the many factors that influence it (Krause and Coates, 2008; Tinto, 2006). Studies into retention in Australian universities confirm the importance of the totality of students’ experiences, with the following factors being particularly relevant: supportive peer groups, ready access to responsive staff, ‘just in time’ and tailored support, explicit expectations and constructive feedback (Scott et al., 2008). In highlighting engagement as a condition for student success, Tinto asserts that ‘the more students are academically and socially involved, the more likely are they to persist and graduate’ (Tinto, 2009, p4). Learning communities are one approach that can contribute significantly to student engagement as they provide both academic and social opportunities and support (Zhao and Kuh, 2004). Tinto is a strong advocate of learning communities and, based on his research, he argues for the importance of structured collaborative learning environments. Such peer group learning can take many forms, ranging from informal study groups to structured sessions within tutorials (Alpay et al., 2010; Wilson, 2009; O’Shea, 2006).

This case study provides an overview of the Supplemental Instruction/PASS model of collaborative learning and looks specifically at how and why it can be helpful for engineering students studying mathematics. It then focuses on the particular programme run at our university, drawing on the experiences of Kiyomi Dunphy who provided peer facilitated sessions for five semesters in the compulsory unit Mathematics for Engineers 2. Case studies have many applications; in this instance the purpose is to ‘describe an intervention and the real-life context in which it occurred’ (Yin, 2003, p15). Proponents of the case study as a research method argue its merits as providing in-depth, specific and contextualised knowledge about the research topic (Yin, 2003; Berg, 2009). We acknowledge the debates about the generalisability of case studies (see for example Gomm et al., 2000), but we take the position that a case study adds to ‘existing experience and humanistic understanding’ (Stake, 2000, p24). As such, this case study contributes to discussions about pedagogical approaches to teaching engineering students in the current tertiary environment.

Supplemental Instruction/Peer Assisted Study Sessions

This paper is particularly concerned with the peer learning model of Supplemental Instruction (SI), which provides a demonstrated means for student engagement and creates learning communities for first year students. SI derives from an initiative developed by Dr Deanna Martin at the University of Missouri-Kansas City (Muhr and Martin, 2006; Martin and Arendale, 1994; Blanc et al., 1983). Charged with improving the retention rates of students, she based the SI programme on the philosophy of peer learning and focusing on study strategies for learning specific course content. A crucial component of SI is that it targets ‘high risk’ courses rather than ‘high risk’ students (Hurley and Gilbert, 2008). In this sense it is a developmental programme and therefore suitable for a range of students, from those anxious about passing the subject to those aspiring to high grades. SI has proved successful and is now a feature of hundreds of tertiary institutions in 29 countries across the world (Wilcox and Jacobs, 2008). The nomenclature of the programme varies; for example in the United States it is usually referred to as SI, in the United Kingdom the term Peer Assisted Learning (PAL) is preferred and in Australia it is most commonly called PASS (Peer Assisted Study Sessions). Supplemental Instruction/Peer Assisted Study Sessions will be referred to as SI/PASS for the remainder of this case study. The essence or ‘original genetic code’ (Martin and Blanc, cited in Couchman, 2008, p80) which makes SI/PASS distinctive from other peer learning programmes is a collaborative learning environment facilitated by trained senior students (PASS facilitators) who have successfully completed the subject it is running in and undergone SI/PASS training. The effectiveness of the SI/PASS model is underpinned by its strong theoretical frameworks which ensure sound pedagogical and innovative approaches to learning. A wide range of theorists (such as behaviourists, cognitive developmentalists, constructivists and critical theorists) have been drawn upon in creating a model based on optimising learning (Zerger, 2008).

The SI/PASS model has evolved to suit different contexts, thus there is a range of variables which differentiate programmes. For example, in many cases SI/PASS facilitators are paid to run sessions, whereas in other programmes they are volunteers. The amount of paid preparation time also varies — some SI/PASS facilitators are expected to attend the subject lecture while others are paid for one hour preparation per week. Each PASS session may also appear to an observer to be quite unique, especially when compared across disciplines. However, the ‘genetic code’ of providing a collaborative learning environment, where the student facilitator is not the expert but the guide, remains the same. Their role is to model learning strategies through developing activities and processes that enable students to learn actively and collaboratively. The facilitators ‘mirror the curriculum, rather than teaching new materials’ (Marra and Litzinger, 1997, p112) and their greatest challenge is to facilitate learning rather than re-teaching. As near peers, students who have recently studied the same subject (the student facilitators) model ‘how to learn’ in a safe and non-threatening interactive learning situation.

Substantial research into the effectiveness of SI/PASS finds that students who attend sessions tend to attain higher mean grades than their counterparts who do not attend, particularly where they attend regularly (Hurley and Gilbert, 2008; Etter et al., 2001; Martin and Arendale, 1994). It is difficult to isolate SI/PASS as the sole predictor of student success as there are many different determining variables. However, studies which control for variables such as student aptitude and the voluntary nature of attendance have found improvement in students’ performance amongst those attending the programme (Parkinson, 2009; Hensen and Shelley, 2003). Different forms of qualitative evaluation, including surveys and focus groups, tend to provide data that support stakeholders’ affirmation of the value of SI/PASS. As well as having some impact on grades, SI/PASS provides a social forum to counter the isolation that new students often encounter (van der Meer and Scott, 2009).

SI/PASS in engineering

SI/PASS runs successfully in both engineering and mathematics programmes (Cheng and Walters, 2009; Kieran and O’Neill, 2009; Wright et al., 2002; Marra and Litzinger, 1997). Lin and Woolston (2008) suggest that participating in SI/PASS enhances and diversifies the learning capabilities of engineering students, ultimately contributing to the quality of engineering graduates. They contend that the learning strategies applied in SI/PASS are complementary to the study of engineering which ‘combines many aspects of learning,understanding and creativity in its educational processes’ (p9). Engineering study requires an understanding of complex concepts at a fast rate as well as solving problems through the application of scientific and mathematical principles (Kieran and O’Neill, 2009). In a longitudinal study at their institution, Ambikairajah et al. (2006) found that, despite the need to master difficult concepts, many engineering students do not tend to spend sufficient time on independent study outside of class. For students who often juggle work and other commitments with their study, SI/PASS provides opportunities to participate in a regular, disciplined learning environment. Lin and Woolston (2008) conclude from their seven year experience of running SI in the College of Engineering at the University of Wisconsin-Madison that it impacts positively on students’ learning and engages them in a way that does not usually occur in traditional classes. Murray (2006), a strong advocate of SI/PASS, began offering it in engineering studies in 1993. He argues that it is largely responsible for reducing the failure rate in a Mechanics unit from 45% to below 10%. Mahdi (2006) set up a peer supporting learning programme based on SI in an electronic engineering course at the University of Limerick and found that the learning and academic performance of first year students improved. Similarly, Blat et al. (2001), drawing on five years experience of running SI in an engineering programme, assert that not only did it improve students’ academic performance but that it also impacted positively on the teaching and learning experiences of students and teachers and ‘promoted community building and the formation of study groups’ (p10).

The SI/PASS model is an evolving phenomenon that is necessarily adapted to suit specific contexts. PASS was initially introduced at our university in 2007 as a learning and teaching project. It was piloted in Mathematics for Engineers 1 and, in response to student demand, was extended the following semester to Mathematics for Engineers 2. Since that time PASS has continued to run in both subjects each semester. The subjects selected to run PASS usually have either relatively high failure rates or are those which students tend to find particularly challenging. Mathematics for Engineers 2 is a subject with a considerable failure rate which is exacerbated by a considerable proportion of students entering university without having completed the requisite mathematics in high school. This is not a singular experience; research has shown many students do not have the requisite level of preparedness for tertiary level engineering studies in Australian universities (Henderson and Broadbridge, 2007). It is also recognised that students need to understand the relevance to their engineering studies of the mathematics they are studying (Fuller and Jorgenson, 2004) and, in practice, this is not always made explicit (Wood, 2008).

PASS facilitators usually attend a two day training course which includes experiential learning and some pedagogical theory. They then offer weekly sessions that focus on study skills and learning course content. Although their sessions are monitored at times by the PASS coordination team, PASS facilitators work very independently and carry a large burden of responsibility to maintain the integrity of PASS and not slip into re-teaching. The students who are trained to facilitate PASS are selected on the basis of a combination of academic grades, communication skills and performance in an interview. They are often students who have attended PASS themselves and appreciate the opportunity to become facilitators. They determine the times to run their sessions based on their timetables and those of the students who may attend. Once they have chosen a suitable time they then promote PASS at lectures and through the subject’s e-learning site. The content of each session is prepared by the facilitator in response to students’ suggestions at the previous session. This might include lecture revision, homework exercises, problem solving, reading difficult texts, referencing practice, unit-specific study strategies or small group mind mapping of difficult concepts. There are many possibilities and PASS facilitators use existing materials and devise their own activities. Facilitators also need to be adaptive and responsive to the needs of the students as issues arise between sessions.

Evaluation

Evaluation of the programme is primarily carried out through a comparison of the grades of students who attend PASS with students who did not attend. This is supplemented with data from attendee and sometimes non-attendee surveys, as well as retention data and feedback from relevant staff. Table 1 shows the average mark differential between Mathematics for Engineers 2 students who attended PASS four or more times and non-attendees from this cohort. The percentage of students from the Mathematics for Engineers 2 cohort who attend PASS is reasonably low; however, the students who do attend PASS tend to maintain consistent attendance and, as Table 1 indicates, gain substantially higher marks on average.

Table 1 Average mark differentials between PASS attendees and non-attendees in Mathematics for Engineers 2

	No. of students enrolled in Mathematics for Engineers 2	Average mark differential (/100) between students who attended PASS four or more times and non attendees	% of cohort who attended four or more PASS session	No. of students who attended four or more PASS sessions
Spring semester 2007	188	23 marks	5%	9
Autumn semester 2008	92	22 marks	10%	9
Spring semester 2008	155	25 marks	11%	17
Autumn semester 2009	105	17 marks	19%	19
Spring semester 2009	190	19 marks	10%	19

The voices of students who run PASS sessions are not often included in the literature on SI/PASS as it tends to focus on outcomes for attendees. However, studies that have considered the impact of participation in the programme for PASS facilitators find that the students perceive gains in a range of areas such as interpersonal communication, self confidence, greater depth of subject understanding, group facilitation and employability (Congos and Stout, 2003; Couchman, 2009). In the following section, the reflections of Kiyomi, a final year Electrical Engineering student and long term PASS facilitator are provided as an insight into her experiences with the programme. Student feedback on her sessions is also included.

Insights of a PASS facilitator

I have been a PASS facilitator in the subject Mathematics for Engineers 2 for five semesters and this experience has enriched my life at university. I personally did not do as well as I would have liked when I studied this subject, but I was recommended for this role for my determination to improve and my good communication skills. As someone who struggled with the content, I feel I can empathise with students on a level that our lecturers/tutors cannot. Observing people struggle with concepts as I did evokes a strong desire in me to help them in a way that I wished I had been offered at the time that I was learning these concepts. PASS provides the opportunity to do this. The personal satisfaction experienced when overcoming any complications and ultimately achieving understanding is a practice I wished to instill into others.

I know that I have played my small part in developing the culture of peer learning in the School of Engineering. To encourage a peer learning culture and promote the PASS sessions I designed a poster with the phrase ‘Albert Einstein failed his first maths exam at university…if only he had attended PASS’. Since being involved with PASS, I now study more with my friends and where possible we find an empty classroom with a whiteboard. I have been pleased to hear that students who have attended PASS are also doing this outside PASS sessions. For example, one group of attendees formed a study group for other subjects and reported that their overall course improvement was outstanding as a result.

PASS is effective due to its open door policy with everyone being accepted regardless of their ability. Many of the attendees seem to enjoy the flexibility of attendance as there is no compulsion to stay for a whole session if they have other priorities such as part-time work. I also think they gain from it being a different learning experience as they are expected to be active learners. I often explain that I don’t have all the answers and am not qualified to teach this subject, however, as a student I can assist with ways to find the answers. ‘Tell me and I’ll forget, show me and I may remember, involve me and I will understand’ is a Chinese proverb that is a motto of our PASS programme as well as the slogan that ‘it’s two and half times more effective to study in groups than alone’, and these define what I feel makes PASS so effective.

The activities used in my sessions are based on peer learning theory. Those attending realise that studying together is more motivating and more effective than struggling alone. One activity I have done every semester is put the students in small groups to summarise their lecture notes. Each group is given a different lecture with the idea that we combine the efforts of all groups and make a basic study booklet. I usually run this activity just before their first class test, to have them revise earlier topics that they may have forgotten. I also encourage them to do the same for the remaining lectures as this booklet may help them with their final examinations. I have often found that in a group the students create a better summary of key points than if they were trying to do this for themselves. As part of this activity I show them my lecture summary that I used at the time I was studying the unit and highlight why I thought it was so helpful for me.

Throughout the sessions I feel it is important to address the needs of the students. For example, across the semesters there has been a common attitude among PASS attendees that polynomial long division is difficult. This knowledge is required to solve for factors when dealing with higher order differential equations. I remember when I was studying the unit that this skill was briefly mentioned by the lecturer without much detail about how to master it. At the time I also found this difficult, but I was determined to learn how to do it. When I did master it I was annoyed at how simple I eventually thought this was, and wished someone had just shown me a clear way of understanding the concept. To assist students and to help them avoid replicating my personal frustrations, I created a step by step example supplemented with practice questions. I often receive positive feedback on this resource, with students commenting that they could now understand the process.

I have also noticed that students find it difficult to make the distinction between the varying types of ordinary differential equations (ODE). It is important that students can distinguish between these more specific types of equations, as that defines the method they need to use to solve them. It was after several students had shown me their class test papers that I realised they could execute the methods correctly but were not sure when to use which method. To resolve this issue, we created together a question path that we could use to determine what type of question was being asked. We use several ‘yes’ or ‘no’ questions to eliminate the possibilities. For example, the line of questioning the students would have to start with would include ‘Is the ODE a first order ODE?’

This can be answered by a simple inspection of the question. If this resulted in ‘yes’ the students would narrow the possibilities to a first order separable ODE or a first order linear ODE. The next question would further the separation; ‘Does the ODE fit the linear criteria?’ If the three criteria needed to be linear existed, such as the leading coefficient was one or could be divisible to be one, the student could then conclude this was a linear first order ODE and solve accordingly. If it had not matched the needed linear criteria, then it could be concluded that it was a first order separable ODE, and again solved appropriately. There is little emphasis on really knowing how to spot the key differences between the types of ODEs, with more emphasis in class time placed on how to solve them. Hence students who attended PASS were able to gain greater understanding of the subject material and distinguish the varying ODEtypes.

Another activity which students always seem to enjoy involves some role play. In Mathematics for Engineers 2, students are required to solve application style questions which they often find difficult. The mathematics of the question may not be complex but it can be difficult to decode what the question is asking. A method that I have successfully used to tackle these problems is to choose key words as a group exercise and try to draw out as much information as we can from the question. Then two students are selected to act out the question. For example, in one instance, when we looked at the common question of the rate at which water moves between tanks, two students pretended to be tanks. I read the question aloud and when it was stated that the tanks were joined the two students clasped each other’s hands. This activity is often comical and quite different to exercises carried out in tutorials. It seems that the visual memory of the comical imagery serves as a reminder of how to solve the problem should they be presented with this task in an examination.

The students also seem to enjoy the activity I have called ‘Laplace Bingo’. This activity is one I play to assist the students in becoming familiar with the use of tables for Laplace transforms. The game is much like standard bingo. In a regular game of bingo each player is given a game card with, for example, nine numbers on it. One person will call out numbers at random, possibly drawn from a hat or a stack of cards, and each player will cross out corresponding numbers on their cards as they are called. The first player to cross off all the numbers on their card wins the game. Laplace Bingo follows this same process. The difference however, is that instead of numbers Laplace transforms are used. I would generally pick a function from a stack of cards I had created. However, the students could not simply cross that function off their card, as the cards were made up of solutions only. Therefore they would need to carry out the Laplace transform on each function that was called to be able to cross anything off their game cards.As they begin to seem more confident with the transforms, I proceed to call the cards at a faster pace. This has always proven to be a successful activity. On one occasion a student who had not been present at the session expressed he was upset as it was clear that his friends who had been to the session were far more competent then he was with using his Laplace transforms table. Many students claimed at the end of the session they did not require the Laplace table at all anymore.

There have also been several occasions where I have used warm up questions to start the session off and reviewed past examinations in groups or pairs. A number of work stations with different activities for small groups was also a common way of learning in my PASS sessions. For example, there may be two workstations with the students divided into two equal groups. One group may practice examination style questions on the whiteboard with different members of the team attempting to explain to the other students how they arrived at their answer. Meanwhile, another group may play noughts and crosses with mathematics whereby once the group has solved the question being asked they may place a nought or cross on the question matrices provided. During such activities I stand back and allow the students to achieve their results with minimal assistance from me.

Discussion about PASS generally focuses on the benefits for attendees; however, it often fails to recognise just how much it benefits the facilitators. As a result of being involved in the programme, my understanding of the subject material has heightened immensely. I have learned different methods and techniques for approaching mathematical problems from various students over the years. For example, a PASS attendee showed me how to use the tabular method for integration by parts rather than the formula and now I share this knowledge with students every semester. My enhanced knowledge has assisted me in subsequent subjects throughout my degree, particularly where Mathematics for Engineers 2 was a prerequisite. I received a Pass grade for Mathematics for Engineers 2, however, the first semester that I facilitated PASS, I was also studying Mathematics for Engineers 3 and I achieved a Distinction for the subject. I do not believe this improvement would have been possible if I was not continually practising the fundamentals and emphasising good study habits in PASS.

Attendee feedback

The following PASS attendee comments are taken from the 2008/2009 attendee evaluations. Two of the students claim that PASS was instrumental to their success in the unit and the formation of friendships is also a common theme. Some of the comments describe how PASS helped their learning processes.

Comments from Mathematics for Engineers 2 attendees:

The PASS Sessions were very well prepared with warm up phase questions, followed by higher degree of difficulty questions worked out as a team. Students would take turns in completing the questions while Kiyomi steered us in the right direction or helped when necessary. Material provided to us assisted us during class and also enabled us to carry on with work in our spare time.

Kiyomi was able to impart her knowledge enthusiastically through many different techniques through group activities, class handouts and whiteboard notes for the class. Kiyomi regularly revised course content and formulas required for each week so that we could remember them for the final exam […] My confidence in mathematics increased and I was able to build relations through PASS Sessions with other students to build a study network.

I’ve attended all her PASS sessions last year and believe me they really helped. Today I got a post from our university and it contained a certificate stating that I had scored the highest marks in Maths For Engineers 2. I believe that Kiyomi and her sessions were responsible for about 10-15% of my total marks. She really encourages students to work with each other and get involved to solve the problem. The sessions not only helped my learning but also helped me make friends and also increased my confidence level.

The way a number of the games and tasks were broken into teams helped me greatly in meeting people. I’m usually very shy however having the math to think about removed the awkwardness.

I was a student of Mathematics for Engineers 2 in the first semester of 2008 […] I found that the volume of knowledge and understanding of concepts required in this unit quickly became overwhelming within the first few weeks. When I didn’t do well in the first class test I knew that I needed to find some method of study that worked for me and around the same time I found out about the PASS sessions. Kiyomi was a godsend. Her organisation and knowledge of the subject was excellent and whenever unable to assist with a question on the spot, she would come prepared with a method to help in the following session. The use of props that aided us in learning the Laplace transforms made this component of the subject easy to learn and her assistance went beyond the scope of the unit to include various methods for equating coefficients and long division algebra. These foundations have not only served me well in this unit but also in other subjects such as Control Systems and Circuit Theory. Her innovative approach in assisting us with learning what we needed to know helped turn me around for this subject. Quite simply, without Kiyomi, I would have failed Mathematics for Engineers 2.

The unit coordinator was asked to provide feedback on her experience of the PASS program in Mathematics for Engineers 2:

Kiyomi has encouraged PASS attendees to develop useful study habits and has worked to develop cooperative learning skills and to promote a positive attitude in the students towards their capabilities and their potential. She has enabled many of the less confident students to achieve well at their mathematics. She encourages the students to develop the skills to enable them to be independent learners by being able to know how and have the confidence to source solutions from many areas including each other, their lecture and tutorial material and the staff involved in the unit.

Kiyomi has put a lot of time into the preparation of material for the PASS sessions, even developing fun games and aids to help the students gain a better understanding of some basic mathematics concepts essential for this unit. Kiyomi has been very cooperative with me as unit coordinator. She has always kept in contact throughout the semester to make sure she knows exactly what is required in the unit and to see in what ways she can also more effectively present the PASS sessions.

It is hoped that, by sharing the experiences of one PASS facilitator in a Mathematics for Engineers unit, readers will have gained some insight into the actual workings of SI/PASS sessions and the benefits that can accrue for both attendees and the student facilitators. This case study has not intended to argue for the efficacy of PASS based on quantitative data, but rather to suggest that PASS can be a worthwhile strategy that sits within a curriculum approach to engagement. The lives of tertiary students are becoming increasingly complex and each student brings their own unique context to the university experience. There is certainly not a ‘one size fits all’ answer to engaging students but, as one of a number of strategies, PASS provides a means for enhancing students’ academic and social experiences in a contextualised and supportive learning environment.