**Juliette Stephenson**

University of Exeter Business School Published January 2010

### Introduction

I first attended a workshop trialling the METAL resources back in Sept 2007 and my feedback was then incorporated (e.g. making the activity sheets independently available of the T&L guides). I offered to take part in this review and to help evaluate the final project resources in the context that I deploy them. I am keen to contribute to Economics Network activities and projects as they are extremely valuable in promoting good practice in economics education. Finally in my role as Head of Student Learning I am always particularly interested to discover and use different resources that can enhance our students’ learning; disseminating these to other colleagues where possible.

### Context

I coordinate and teach both our core Mathematics modules for level 1 Economics students. These modules are also taken by students from other programmes as optional electives, in particular from the Business Economics programme and some from Business & Management. In addition, there are some Year 2/3 students who are ‘filling in gaps’ in their mathematical skills.

I used some of the METAL resources last year on both modules, however this review is focusing on my recent use in Semester 1 09. The module (BEE1020 Basic Mathematical Economics) is designed for students without A-level Maths (or equivalent); essentially, these are students without knowledge of basic calculus. Therefore by the end of the course all students should be able to demonstrate simple optimisation techniques, in particular applying them within an economic context.

There are 164 students enrolled on this module, 60% with only GCSE level Maths. This is a very mixed ability group with varied expectations amongst students. Some are very competent at Maths, simply not having had the space within their A-level programme to take it up. At the other end of the spectrum are those who gave up after GCSE with a sigh of relief… only to discover as economists they need Maths after all! Many of these students lack confidence, with a tendency to over-complicate problems, and the module presents a huge challenge. While others, conversely, enjoy rediscovering maths. Most, however, gain a real sense of achievement; in particular, not surprisingly, when the maths is applied to economics and “everything comes together”.[1]

### Use of resources

**Case 1).** Having started this module with a review of basic arithmetic and algebra, we then moved on to equations in week 3 – beginning with Linear Equations. This seemed the first point that we could usefully apply mathematics to economics.[2] Having previewed the METAL project videos I decided to use *2.01 Linear Fractions - Budget Lines.* I introduced the topic in the first one hour lecture (starting with ‘general form’ and ‘solving equations with one/two unknown variables’). Then we watched the video by way of an introduction to ‘formulating equations’ i.e. some application of techniques. The video provided a good stimulus to a short discussion on why and how we ‘model’ in economics (with reference to the context of consumer choice/budget lines etc.) I then set a problem for students to work on individually (based upon T&L guide 2 Section 6: The Equation of a Straight Line: Economic Examples *a) A worked example to understand prices and costs*); finishing the lecture with a final worked example (S&D which included transposition i.e. inverse demand functions).

The second lecture on linear equations included a section on solving simultaneous equations. So this time I suggested that students could view video *2.06 Solving Simultaneous Equations - French Wine *independently as an optional follow up activity to reinforce this topic. Finally, I set the *Graphs and co-ordinates: Activity One and Two worksheets* as supplementary support, in particular for those students who needed to revisit this topic[3].

**Case 2).** Each week for this module students have 2* one hour lectures plus a one hour tutorial. A homework exercise is also set weekly and returned in the following tutorial (as part of the formative assessment). From this I could see that a number of students were still having problems with some of the initial arithmetic and algebra. I therefore decided to use the *Question Bank: Numbers *as a source of additional practice questions. There was good feedback from this; in particular students liked the explanations that accompanied the marking. I used other Question Bank topics later in the course: *calculus *and *economic applications*. This was less successful: the questions on *differentiation rules* use sin/cos/tan frequently. I do not include this on my course for the reason that this is not normally used in economics.

### Focus Group feedback/application

Finally, as part of the review, I decided that the most useful thing that I could do would be to get direct feedback from students on the METAL resources. I asked for volunteers and had a small focus group of 6 students. In addition a number of other students used some of the resources and sent me email feedback. This took place in week 8 in order to allow for the greatest range of topics.

I then decided to follow up some of the suggestions, in particular to use the videos as an *introduction* to a topic. My final topic on the module is integral calculus so I chose *5.14 The Diamond Water Paradox* - part one and two. This was set, explaining it was an introduction to the topic and that I would start the next lecture with a couple of short questions based upon these videos. I am also involved with an Integrative Technology project where we are trialling a range different technologies. This therefore was an opportunity to use the Audience Response System (ARS)[4] and I wrote the questions as interactive slides. I started the lecture with these questions: including one question to check how many students had never covered the concept of Integration before. I found that 76% of those who had no prior knowledge of topic answered one or more questions correctly. The last use of the METAL resources, again suggested by a student, was as a revision exercise. I set videos *5.06 – 5.09 Differentiation - Prices in monopolistic markets* as a homework task; this was followed up in next lecture with further questions (using the ARS clickers). The level of the maths was just right, students scored well and were pleased to see the results.

### Constructive suggestions for improvement

I have had a positive experience using these resources and I will be incorporating them again into this module. However I think there are ways in which they could be improved upon. These generic comments are therefore made in the spirit of ‘constructive criticism’.

- Resources (video animation, activity sheets) desperately need proof reading: missing symbols, wrong use of symbols etc.[5]
- Some terms misleadingly used interchangeably e.g. functions/equations; demand and inverse demand functions.
- Lack of compatibility with Macs, in particular downloading the Question Bank.
- Activity sheets need consistent voice – written to student or lecturer?
- Guidance to lecturers for use of some Activities is incomplete.
- Case studies: would be useful to have the mathematical content highlighting/indexing.
- Question Bank - optimisation –many use same format?

### Conclusion

As part of a portfolio of resources[6] to support first year quantitative modules, the METAL project makes a useful contribution. Their strength lies with the application to real life economic situations and problems. This can make a topic come alive and provide a stimulus for discussion. However there is a trade off: with limited resources (huge time pressures to get through material) the bigger picture can seem like a luxury. This might also explain the view of several students that the materials were “too gimmicky” and “long”. Setting them as supplementary exercises and as an introduction to topics seems a valuable use. Finally, I would use some of these materials to reinforce the maths concepts within a level one/introductory Economics Principles course.