Introduction

Service teaching is teaching to students whose main studies lie outside our discipline area. For the students, this ranges from as little as one unit - for example a first year statistics unit required by biology, or business or psychology - through to a sequence of units, for example in engineering.

We have a fantastic opportunity to turn these students on to mathematics and statistics so that they learn the ideas deeply and integrate them with their discipline studies. We also hope they actively seek out further units in the area - perhaps take a mathematical sciences minor or even a double degree. In any case, we have a responsibility to provide them with the knowledge and skills that they require, and that they will apply in their course and their future work.

In addition to the usual considerations in teaching units, those taught to partner disciplines benefit from close interaction with the partner, provision of directly relevant examples, and careful attention to the career intentions of the students.

The contents of the preceding modules are also applicable to service teaching. In this module, we highlight some particular aspects of service teaching. Conversely, the teaching strategies outlined in this module could be used for any unit.

There is plenty of published material - though very little evidence-based research - on the sensitivities of service teaching, in particular attitudes towards service teaching, suitable teaching strategies, the practicalities of dealing with students and the partner faculties, and the pressures engendered by university funding. In what follows, we cite relevant literature in each section. Many, but not all, excerpts relate to service teaching for engineering, both in mathematics and statistics. The issues are similar when teaching for other disciplines (Broadbridge & Henderson, 2008, p. 1), but be aware that there is a difference between service teaching of a sequence of units, as would happen in engineering, and the provision of a single ‘general’ prerequisite unit such as statistics for business and biology, or discrete mathematics for computer science.

Caveat: Decisions on service teaching are made at faculty and university level. The lecturers may not be able to make changes. So check with your Head before making changes or talking to a partner faculty.

Learning Outcomes

At the end of this module, participants will be able to:

• understand the importance of service teaching for mathematics and statistics;
• explain how the needs and expectations of service unit students differ from those enrolled in the mathematical sciences;
• identify the main teaching strategies for service units in mathematics and statistics;
• apply these strategies to cater to and effectively engage students in service units;
• celebrate the opportunity to engage with cross disciplinary ideas and methods in mathematics and statistics.

Module Structure

The module proceeds as follows:

• Your role
• The need for relevance
• Teaching strategies
• The first year
• Celebrate.

Your role

In 2007, the Australian Mathematical Sciences Institute (AMSI) undertook a scoping project to examine mathematics education for 21st century engineering students (funded by the Carrick Institute for Teaching and Learning in Higher Education Discipline Based Initiatives Scheme). The project report, authored by Broadbridge and Henderson (2008), describes the important relationship which exists between the mathematics department and the departments for whom they provide a service: “Unlike in most provisions of service, in this case the service provider and client have very similar status, roles and job functions, even sharing the same employer.” (Broadbridge & Henderson, 2008, p 22); and “The welfare of many mathematics departments depends on their ability to respond to the needs of engineering education” (ibid., p 1).

The service unit is likely to stay with mathematics and statistics and not revert to the partner faculty (which may happen with little warning) if the service unit has good or, better still, excellent student experiences and outcomes exemplified by:

• high satisfaction on student surveys;
• high pass rates;
• students being able to apply mathematics skills in subsequent subjects; and
• plaudits by the students to the partner faculty;

Remember that there are pressures across the university for the student dollar, so naturally the partner faculty would like to have the funding that flows from these enrolments. It is easier to withstand these pressures if the students do well and the partners are kept happy.

Task 5.1 Context of service teaching in your university

1. Think about where service teaching of mathematics/statistics is placed in your university. This will change the context of your teaching. Is the teaching of mathematics and statistics carried out by the discipline (e.g. engineering, psychology, business) or is it taught by the mathematics/statistics department? Are you based in a mathematics/statistics department or in another area?
2. Identify the demographics of your student cohort, in particular identify non-mathematics/statistics majors and their degree programs.

Striving towards positive student experience benefits you, the students and the partner faculty. Therefore it is critical that you keep the students happy, and the partner schools/faculties satisfied, and then you will have the opportunity to teach some really interesting applications of mathematics and statistics to an engaged group of students.

However, at the beginning you may find that you have students who:

• are less motivated and less confident about mathematics
• do not really understand how the subject is relevant to them
• are accustomed to thinking within a framework that is less scientific and less deductive than you would expect.

Your teaching will need to:

• be more tightly structured with careful explanation and demonstration of process
• have greater support mechanisms
• relate to the partner discipline/s and the career aspirations of the students
• provide an introduction to (what will be seen as) useful applications of mathematical and statistical modelling.

Task 5.2 Career aspirations of your students

Do a short survey of your class to find out what their career aspirations are. For example, do a short written survey asking them to list:

• their degree or major (if you don't already have that information)
• their ideal job when they finish their degree
• what they do outside of university for fun (this may give you an idea of applications you could use such as sport or music)

Remember: you are the ambassador for mathematics and statistics in these classes - show your passion!

Bajpai et al. (1975) argued for enthusiasm from teachers: "For, if the teacher can find a challenge and an excitement in teaching mathematics to engineering students, there is a chance that the students may find a challenge and an excitement in learning." (pp. 361-2)

McAlevey, along with Stent (McAlevey & Stent, 1999), did a survey at Otago University, this time of business students' perceptions of the notion of good teaching in reference to statistics courses. Their starting point was that there have been many studies of students' perceptions of good teaching, but little on statistics teaching. Their assessment of what constitutes good teaching from the student perspective was, "interest created by the teacher, clarity, knowledge of subject matter, preparation, organization and enthusiasm." (p. 215)

Mathematicians and statisticians need to resist the (understandable) tendency to present their units as they would in their own disciplines. With your previous high level training you might believe that you can't discuss calculus without discussing limits, continuity or properties of functions, for example. Basically you can't teach all the background mathematics for service units - you will have to decide on the most important objectives and make sure that students are able to meet those. The partners want their students to be able to use calculus in their area, in which case the focus should be on what differentiation can tell you and when you should use it. Don't worry if you find yourself giving the students competency with techniques to do calculus or statistics without their having what you feel to be a full understanding of the development of the subject.

Søren Bisgaard (1998) emphasise the need for statistics courses to incorporate engineering examples. He contended that, "Many educators continue to insist that theory must precede examples and applications. However, engineers and other people with a practical bent prefer to see examples and motivation first." (p. 238)

Felder and Silverman (1988) describe the mismatch between the teaching style of some academics, and the learning style of (engineering) students; they propose teaching strategies (some of which we saw in Module 4) and some of which we present in the following sections) to reduce the frustration and disappointing outcomes this causes for both student and lecturer.

Task 5.3 Beliefs

Quickly review the Common myths about teaching undergraduate mathematics and The influence of teacher beliefs on student performance from Module 1. How does your attitude towards service teaching influence your students?

The need for relevance

Kümmerer (2001) presented a general discussion on the range of approaches used to teach mathematics to engineers, and pondered what mathematics means to them: "Their attitude towards mathematics expresses a good deal of respect - even though they believe that for them most of mathematics is useless." (p. 321) Mathematics may be regarded as simply a preparatory subject, something to be endured before the student starts physics or engineering. The drawback in this situation is, "that the whole motivation for a student is based on the promise of future applicability ... Such a course fails to relate mathematics to the intended applications." (p. 323)

The need for relevance was highlighted by a number of other writers as being important in assisting students with learning mathematics. Varsavsky (1995) stressed that a perceived lack of value can be detrimental to the students' acquisition of skills. "There is also a lack of motivation: too many students do not seem to understand the importance of mathematics in their engineering courses and in their future careers. Mathematics is mostly considered by students as a hurdle to be overcome in order to be awarded a degree." (p. 342)

Zanakis and Valenzi (1997) also undertook a survey of student perceptions at a university in Florida, USA, this time with an emphasis on anxiety, and looked at how student attitudes changed during a statistics course. Their motivation arose from poor student ratings of statistics courses, in spite of the need for these skills in the workplace:

"Business school undergraduates and alumni rank statistics lowest among their business course. Students perceive statistics courses to have little value in practice, to be extremely difficult, and only to be average in instructional effectiveness. ... Yet several surveys of business professionals consistently indicate statistical analysis is the most frequently needed quantitative methodology." (Zanakis & Valenzi, 1997, p. 10)

To make a mathematics course seem relevant to students in a service subject- and hence worth an investment of time - the subject has to be shown to be important for their own specialisation and future career. Obtain the lecture notes and textbooks of the partner discipline in order to see how these use mathematics and statistics. Make extensive use of examples and applications: "mathematics courses (for engineers) should be taught with a strong emphasis on applications...” (Easton & Steiner, 1996, p. 564).Think about whether you can use examples from their notes and use their jargon and notation. For example, if you can accommodate electronics students using ‘j’ instead of ‘i’ for the imaginary number SQRT(-1), it will give you time and energy to focus on deeper issues! It is also beneficial to be familiar with the other subjects the students are studying, so examples can be used from these; and refer to the subjects specifically by name or code, not just vaguely. However, Kümmerer (2001) pointed out, "In most cases a translation into the other language is necessary before students can recognize that one is discussing the same subject." (p. 331).

Task 5.4 Examples

Find an example in a textbook (or online resource) that you can use or adapt to use in a lecture in a service unit; if you do not personally teach such a unit, make it applicable to a unit taught by one of your colleagues. (Textbooks with titles such as Engineering Mathematics or Statistics for business/psychology make a good starting point for examples that you can adapt for your unit.)

Broadbridge and Henderson (2008, p. 12 and p. 27) discuss the practice of teaching mathematics entirely `in context’ and caution that this can be problematic in large multi-specialisation classes and also appears to cause less able students problems in then applying the same mathematics to different contexts. Recall point 6 of the Seven principles of learning in Module 1; while examples are important, they should enhance the learning outcomes achieved, rather than limit them.

Task 5.5 Relevant learning outcomes

Consider what students should be able to do as the outcomes of a service unit. In your response, discuss at least one of the following from Modules 1 and 2:

• Instrumental versus Relational understanding
• resources/heuristics/control/belief
• Anderson and Krathwohl’s framework
• general skills (graduate capabilities).

Post your response to the discussion board ; while you are there, respond to the other participants’ postings.

Teaching strategies

The AMSI report (Broadbridge & Henderson, 2008) describes the strategies reported by 27 Australian universities for service teaching of mathematics and statistics. Though often combined in various ways, these and other teaching strategies are presented below as separate items. Under each heading we also give one or two quotes from the extensive literature that exists in this area, particularly highlighting the benefits. (Note that much of this literature is best described as “good practice” literature and is based on case studies and surveys rather than controlled educational research. If you think you could contribute to this literature, read the section in Module 12 on Action Research.)

Tutorials

• Utilise tutorials to support lectures, as students tend to prefer them; for instance, "Of the teaching components used at Warwick (University), 64% of the students find the plenary session/lectures (of over 200 students) not useful compared to ... 22% for the personal tutor." (Shaw & Shaw, 1995, p. 167)
• Another benefit of tutorials is that they allow you to break a large multi-specialisation lecture group into focused tutorials, based on course or discipline e.g. electronic engineers, chemical engineers, business students, psychology students etc. You can then give a more general lecture, and contextualise the tutorial examples very specifically. This is also effective when your unit has the dual role of service and contributing to the mathematics or statistics major.

Small group/ project-based work

• Some of the benefits of small group work when there are large classes are: "This will foster team-work and mutual support among the students which, by improving their self-esteem, enhance learning. It will also allow the staff support to be better targeted on the more demanding problems." (McGregor & Scott, 1995, p. 126)

Small group work is also beneficial as it more closely resembles the students’ future working lives: "Essential changes ... now provide the engineering student training in practical projects involving small group work similar to that which will be found in their future working environment. These changes train engineers to carry out mathematical tasks in an environment which is much closer to that which they will encounter in their professional practice." (Worthy, 1996, p. 596)

Problem-based learning (PBL)

• Use real-life problems: "They are encouraged to tackle real problems to which they can contribute solutions and to develop personal values including ... the rules of the physical universe." (Easton & Steiner, 1996, p. 558)
• Here is an example of a real-life problem used by a previous participant in this module, described on the discussion board, which shows how problems can establish the relevance of your quantitative subject, and encourage general skills (teamwork, communication):

I run a second year modelling class and in the tutorial at the end of the first week, after hearing what modelling might and might not be, I give the students a list of questions of which the following is an example:
Suppose people enter the elevators in a skyscraper at random during the morning rush. The result will be several elevators stopping on each floor to discharge one or two passengers each.

1) Discuss schemes for improving the situation.

2) How could improvement be measured?

3) How could you model the situation to decide what scheme to adopt?

The idea of the tutorial is to break the students into small groups and give them a question each to think about. After about 20 minutes, a person from each group summarises the solution on the whiteboard and the remainder of the class offer comments and criticisms, as do I. The idea of the questions is to make students think about everyday things and how they might express them in a quantitative way.

"Students need to actually gather data, have goals in mind, and manage a data set to really appreciate what it is, what its characteristics are, and how it is interpreted. ... It is more natural to start with raw data and work toward solutions to questions heuristically, graphically, and intuitively. This sequence will also reduce student anxiety." (Zeis et al., 2001, p. 84)

Computer-based methods

• Barton and Nowack (1998) present a description about a statistics course developed for engineering students, which was a laboratory-style course based on a statistics computer package. Their approach was that, "The laboratory exercises reinforce material covered in lectures and link statistical concepts with engineering activities such as statistical process control (SPC) and design of experiments (DOE)." (p. 233)
• Computer algebra systems can quickly perform the calculations that you are likely to give the students, so there is an argument for saying that the students don't need to perform the mundane calculations. This is simplistic, because they do need a certain level of understanding to be able to use these packages and to interpret the output - you need to balance out the understanding and application. One employer said that "people who can do techniques are cheap; we need those who can think and create opportunities for our business.”
• However, be aware of potential frustrations and the need to anticipate the needs of a partner discipline. For instance, if SPSS is the standard for your partner area, then teaching with Minitab will be seen as irrelevant and a waste of time by students, and teachers from the partner discipline will also be frustrated.

Assessment

In the face of the pressure to have high pass rates in service subjects, it can seem tempting to “teach to the exam”; it is then galling to be told that the students you passed with gritted teeth do not know enough in later subjects! We will consider both formative and summative assessment in later modules. However, note at this stage that (perceived) assessment is a powerful driver of student activity. This means you must communicate reasonable expectations clearly, write authentic and valid assessment tasks, provide feedback during semester, and align the assessment to the intended outcomes of your subject (as negotiated with the partner discipline).

Task 5.6 Targeted tasks for partner degree programs

Write two mathematics or statistics exercises or problems suitable for tutorials/small group work/computer laboratories (combined as you wish) that have real world applications and are targeted to the partner discipline areas.

Support services

Early career teachers need to appreciate that most people find mathematics and statistics difficult. You will most likely have a gift for mathematics/statistics that your students don't have; what is basic to you may not be basic to your students! In addition to the support for learning inherent in each unit, some departments (and faculties) provide particular support.

"we can see from our survey ... that the weaker A-level students find the handouts less useful whereas they find the tutor more useful. This is a clear demonstration that the weaker students need more help and encouragement from members of staff and are less well equipped to work independently." (Shaw & Shaw, 1995, p. 168)

• Mathematics and statistics support services. Many universities run extra tutorials, both face-to-face and online, together with drop-in centres to help their students. (See Broadbridge and Henderson, 2008, pp. 13-16 for more detailed explanations of each of these services.)
• Peer-assisted learning. Students often find that explanations from more experienced students in their class, or from higher level students in the area, are easier to follow. This might be due to a combination of the smaller age gap and that the advisor has had recent experience of any learning difficulties. (This will be explored further in Module 11.)

Task 5.7 Support services for your students

• List the support services provided by your university for your students.
• List how these services are communicated to the students.
• Evaluate the effectiveness of these services. Are they meeting the students' needs? Your needs?
• Do you think support should be targeted to “at risk” students or to “high risk” units? (Both strategies have their proponents.)

The first year

Prior to the start of the unit, use information from students' high school results or other previous studies to channel students into units at the appropriate level of mathematics. This could be helped through:

• Diagnostic tests before students start - for example, both Macquarie and Murdoch Universities have online tests along with advice for students eg. Macquarie University's Assumed Knowledge of Mathematics quiz (Faculty of Business and Economics, n.d.)
• Bridging units for students identified as needing assistance - these are generally not for credit.

Because of the way service units function as a basis for later more specialised study in the student’s discipline, your unit may be among the first that they are studying at university. You will need to make them enthusiastic about general university learning as well as specific mathematics learning.

• Transition units for credit. These units are a common feature of university mathematics and assist many students to reach the required ‘starting' level in the area. Students who take these units have not had the opportunity to study mathematics at the required level, and many have come to tertiary level study through special entry pathways without the necessary preparation. Similarly, some mature-aged students may have prior study, but from some time ago, and may not have practised using it for many years. This can be particularly the case for disciplines requiring statistics, which may have no quantitative prerequisites for entry to their programs.
• Introduction to learning at university. You need to provide an introduction to scientific/deductive frames of thinking and ways of learning mathematics (recall Module 2). Campbell and co-authors (2007) describe the role of the first year program as serving:

“a number of purposes which typically include: a cultural and social transition for school leavers into higher education; the laying of the academic foundation upon which the individual grows and attains the desired graduate attributes as set by the program and by institution and professional accrediting bodies; and the beginning of formative development as a professional and citizen of tomorrow.” (p. 1)

Celebrate

Teaching and learning in cross-disciplinary contexts is a real privilege. The students are diverse and often focused on their careers. There are fantastic applications of mathematics and statistics in modern biology, information technology, commerce and engineering, and opportunities to work collaboratively with staff in other disciplines, both on teaching and research. Joint research (which to you may mean more of a consultant role) is an excellent way to establish a good relationship with a partner discipline, and can often convince students that you have the credibility to teach their subject.Suggested ways to celebrate student learning include:

• poster sessions, where students display posters of their work with staff from partner faculties invited
• miniconferences with student presentations
• student assignments double-marked by both faculties
• student awards for best/most innovative use of mathematics/statistics in engineering/biology/other partner disciplines.

Task 5.8 Celebrating learning

What does your department/school do to celebrate student learning in the quantitative disciplines? How could you increase the number of opportunities for this to happen?

Review and conclusion

Successful service teaching is essential to the survival of most mathematics and statistics departments, so expectations on you as the teacher are very high and probably a little daunting. But if you are systematic about catering to the needs of both the students and partner disciplines, and patient in appreciating their difficulties, then service teaching can be rewarding and even lead to productive research collaborations with other areas on campus.

Working across disciplines is exciting and interesting. Students may come with a range of learning styles and expectations and you need to be sensitive to the career aims of the students. However, quantitative and analytic skills are critical graduate capabilities that students need to demonstrate. The knowledge, skills and attitude you are teaching are a significant part of the academic profile that students need to demonstrate when they complete their degrees.

The next module, on in-class assessment, addresses how the teacher determines the current level of student understanding and skills, thus identifying gaps and misconceptions. This is particularly important for service teaching where students have a wide variety of backgrounds.

References

• Bajpai, A., Mustoe, L., & Walker, D. (1975). Mathematical Education of Engineers: Part 1. A critical appraisal. International Journal of Mathematical Education in Science & Technology, 6(3), pp. 361-380.
• Barton, R. R., & Nowack, C. A. (1998). A One-Semester, Laboratory-Based, Quality-Oriented Statistics Curriculum for Engineering Students. The American Statistician, 52(3), pp. 233-238.
• Bisgaard, S. (1998). Teacher's Corner - Discussion. The American Statistician, 52(3), 238-239.
• Broadbridge, P. & Henderson, S. (2008) Mathematics Education for the 21st Century Engineering Students – Final Report. Retrieved July 13, 2011 from http://www.amsi.org.au/images/stories/downloads/pdfs/education/21EngW.pdf
• Campbell, D., Boles, W., Murray, M., Iyer, M., Hargreaves, D. & Keir, A. (2007) Balancing pedagogy and student experience in first year engineering courses. Proceedings of the 3rd International Conceive Design Implement Operate (CDIO) Conference, Massachusetts, USA. Retrieved from: http://eprints.qut.edu.au/8054/1/8054.pdf
• Easton, A., & Steiner, J. (1996). A Core Curriculum in Mathematics for the Australian Engineer. Paper presented at the Second Biennial Australian Engineering Mathematics Conference, Sydney, Australia: Institution of Engineers, Australia.
• Faculty of Business and Economics. (n.d.) Assumed knowledge of mathematics, Retrieved February 22, 2011, from http://econometrics.mq.edu.au/quizzes/
• Kümmerer, B. (2001). Trying the Impossible - Teaching mathematics to physicists and engineers. In D. Holton (Ed.), The Teaching and Learning of Mathematics at University Level - An ICMI Study (pp. 321-334). Dordrecht: Kluwer Academic Publishers.
• McAlevey, L. G., & Stent, A. F. (1999). Undergraduate Perceptions of Teaching a First Course in Business Statistics. International Journal of Mathematical Education in Science & Technology, 30(2), pp. 215-225.
• McGregor, R., & Scott, B. (1995). A View on Applicable Mathematics Courses for Engineers. In L. Mustoe & S. Hibberd (Eds.), Mathematical Education of Engineers (pp. 115-129). Oxford: Clarendon Press.
• Shaw, C., & Shaw, V. (1995). Mathematics for First Year Engineering Students - Student performance and attitudes. In L. Mustoe & S. Hibberd (Eds.), Mathematical Education of Engineers (pp. 161-174). Oxford: Clarendon Press.
• Varsavsky, C. (1995). The Design of the Mathematics Curriculum for Engineers: A joint venture of the mathematics department and the engineering faculty. European Journal of Engineering Education, 20(3), pp. 341-345.
• Worthy, A. (1996). Mathematical Education of Engineers - Towards the year 2000. Paper presented at the Second Biennial Australian Engineering Mathematics Conference, Sydney, Australia: Institution of Engineers, Australia.
• Zanakis, S. H., & Valenzi, E. R. (1997). Student Anxiety and Attitudes in Business Statistics. Journal of Education for Business, 73(1), pp. 10-17.
• Zeis, C., Shah, A., Regassa, H., & Ahmadian, A. (2001). Statistical Components of an Undergraduate Business Degree: Putting the horse before the cart. Journal of Education for Business, November/December, pp. 83-88.