Once the format of the teaching sessions and method of assigning students to various sessions has been decided the key issue of making maths interesting for students with diverse skills must be given some thought. One of the most obvious initial steps is to illustrate key maths and stats techniques using economic examples. This approach can help weaker students understand the concepts better as they are then able to identify the relevance of the maths techniques in terms of economic applications. In addition, stronger students may be stretched by attempting more advanced economics applications using their maths skills. However, this alone is often not sufficient unless the examples are familiar from the core economics modules students are studying concurrently. This can be more difficult than it appears in year one since students may have limited exposure to maths and stats within the core economics modules, making the linking more difficult, or there may be issues relating to the sequencing of the economic concepts and the relevant mathematical or statistical technique. Further, this may be further compounded by the need to cover maths and stats techniques in the first year that will be used in economics modules later in the degree programme. Ideally module leaders from a range of maths, stats and core economics modules need to sit down together and agree on the linkages, common examples and sequencing where possible. Staff teaching core economics modules at stage one may be reluctant as they can take the view that they are being asked to spend time teaching maths and stats within their modules and that this should be placed elsewhere. To overcome this, the discussion should focus on how a linked up coherent approach can make the job of a core economics module leader easier.
Maths and stats teaching and learning usually requires a cycle of demonstrating and practicing a technique. The extent to which this cycle needs to be pre-empted or followed by an economics application requires thought. Some learners prefer to become very confident with a technique before considering applying it to an economics context. Other students need to understand why they are learning a technique before they can engage with the learning process. Evidence suggests that the more effective approach will depend on the educational/cultural background of your particular group of learners. Leung (2001) provides a discussion of the differences between East Asian and Western maths education. The author draws a distinction between the East Asian approach to content (i.e. basic knowledge and basic skills) and the Western focus on process (i.e. understanding how knowledge is arrived at). Therefore you should consider the diversity of skills and educational background amongst your students and adapt your approach accordingly.
In terms of delivery, the current dominant approach to lecturing in UK HE is to use Powerpoint slides. In the context of maths and stats teaching the use of Powerpoint can be useful in that it provides to students with an outline of the structure of the lecture and key points. Nevertheless, an over-reliance on Powerpoint is often unhelpful as weaker students need practice following detailed examples, which is difficult to illustrate on slides without making them very cluttered. Moreover, good students tend to lose interest unless they are stretched to solve difficult problems.
‘Chalk and talk’ is often criticised in the current education literature as a sign of the outdated teaching styles employed in economics. However this technique should not be completely disposed of as there is merit to it. Seeing a tutor solve a problem in real time is often re-assuring for students. Therefore a balance between demonstrating a technique with ‘chalk and talk’ while summarising the key points on a Powerpoint slide may be a sensible.
Even when the student body allows for a passive lecture experience it is unlikely to prove enjoyable for either lecturer or student. There are a number of possibilities as to how lectures can be made a more active learning experience for a range of learners. Below is a list of suggestions:
1. Go through a demonstrate-and-practice cycle in the lecture slot by asking students to solve another similar example to the one demonstrated. You can encourage stronger students to work with and encourage weaker students.
2. Ask students to complete a paper-based multiple-choice quiz at the end of the lecture. The key to ensuring engagement with this activity is to walk round the lecture room and provide feedback on interim answers. If you simply stand at the front of the lecture you may find a large number of students do not even attempt the questions. The simple act of walking up the aisle of a lecture can maintain concentration on the exercise for most students. You could ask students to mark their neighbour’s answers and ask for a show of hands regarding number of correct answers on the paper marked by each student. This should provide information as to how well you are delivering to your range of learners.
3. You can use online software such as Quizdom to run quizzes during and at the end of the lectures. If suitable software can be downloaded onto student mobile phones this may ease the organisation of this kind of testing. Alternatively students could be provided with a personal handset at the start of the year by the department for a paid deposit. If this system can be made operational it provides a very effective mechanism to ensure active learning. The advantage of on-line testing in real time during the lecture is that students can actually see whether most students have obtained the correct answer. This provides a good opportunity for students to benchmark their understanding against other students. The lecturer can also recognise where there is a broad lack of understanding and attempt to address this in future sessions. In addition, a lecturer should be able to identify any gap in learning between students with different abilities as results are easily stored.
4. At the start of the lecture series create teams of students, with the number in each team determined by the size of the class. You need to give some thought to the rules for defining how these teams can be set-up. In other words, you do not want teams organised by maths ability so you may suggest that each team should be comprised of students from a particular number of countries of birth. Alternatively, if most of your students are born in the UK you may suggest a composition according to GCSE or A-level results. You could agree on a prize for the winning team, or it may be best to keep it a surprise. Each week you could set a maths problem and note the team with the first right answer. To encourage attendance you could set a minimum number of students per team that must be present in each lecture otherwise the team will be disqualified. The difficulty of the questions set each week should depend on the length of time required for the lecture. This type of activity should develop mentoring within teams of students with diverse abilities.
5. You may consider showing short videos illustrating the economic application of a particular technique. A number of videos are available from the METAL project. This may provide weaker students with an understanding of the usefulness of maths techniques as well as stretching stronger students.
Turning to consider seminars and workshops the following possibilities are available:
1. The traditional approaches to seminars are either to ask students to present their answers on the board or to ask students to work through the questions individually with one-to-one support on hand. If the majority of students have attempted the questions in advance then going through the answers on the board may be a sensible approach. However weaker students may not know how to start the questions. To overcome this problem provide a quick example then ask them to try the problems individually with support. Weaker students often favour the individual work with support option. Whichever broad approach is used, and this may vary from session to session, adding in another dimension (ideas below) to part of the session may keep things interesting (ideas below).
2. It may be worth considering setting up groups and suggest that these are study groups that can meet outside the teaching sessions. You may wish to offer these groups access to a room to meet at another time in the week following the session. The composition of these groups is important and you need to have a classroom set-up to facilitate this type of session.This approach may work best with weaker ability students.
3. It may be appropriate to ask students at a later stage in their studies to come along to teaching or study sessions and act as mentors. This may be helpful with groups of weaker students who may struggle to attempt the questions without support. Mentors may be encouraged to engage with this activity as it positively reflects on their CV. Alternatively you may wish to consider awarding credits as part of a mentoring module for this activity or provide some remuneration. However, if willing volunteers can be found without the promise of credits or remuneration they may be the most valuable assistants.
4. Another option worth exploring within a workshop setting is to encourage students who have finished the problems to ‘teach’ other students. You would need to explain that teaching ensures deeper learning.
5. Question Time! At the end of a session you could split students into groups. Ask each group come up with a question and have a worked solution. This activity ensures that students are aware of the broad set of questions within a ‘type’ and thus the common approach to their solution. Ask the groups to solve each other’s questions and then have an answer session to establish whether the correct answer has been arrived at. Alternatively have each group ask the next to solve a question until no group can answer a particular question and the winning group is the only one left. The tutor can get involved in this type of activity by being a group in their own right or helping a weaker group. This can work well as a wrap-up session as the stronger students are encouraged to stay until the end.
6. Provide students with some questions to practice a particular mathematical or statistical technique. Split the students into groups and ask the students to come up with a question applied to economics and present the solution. This could be presented on an overhead transparency or you may wish to encourage students to bring along a laptop to type up their answer before showing this via an overhead projector. This approach may allow a tutor to engage stronger students.
7. You can use online software such as Quizdom to run quizzes at the middle or end of sessions. (See previous section regarding further considerations for using this type of system).
8. The reality of the focus on assessment is that students may engage with sessions only if they can clearly identify a link with the seminar/workshop material and the assessment for the module. Therefore you may wish to include past exam paper questions as part of the classroom work. Alternatively, encourage students to attend sessions by explaining the questions will be of a similar ‘type’ to that included in the module assessment. It is important to stress that the full range of learners will be formally assessed in the same way. This should encourage weaker students to put in more time to ‘catch-up’.
9. Computer-based learning can complement traditional delivery and help embed concepts. See section 2.4 for a further discussion.