Use of WebTests in teaching mathematics for economics
There are a number of challenges facing all people who are asked to teach mathematics to economics students. These include: low levels of confidence with respect to mathematical ability; limited fluency in algebra; limited understanding of the usefulness of mathematical principles in economic argument; and difficulties in recognising the mathematical representation of a problem within economic theory. In some ways, the last of these is the most problematic. Students often seem to understand the elements of an economic model when described verbally or diagrammatically, and can solve mathematical problems when it is presented in a fairly compact form. However, understanding how to convert a verbal description of an economic model into mathematical form is an art that can only be learned through extensive practice.
In this note, I have space only to describe the ways in which we have used WebTest, a computer based assessment engine developed within the Department of Mathematics at Heriot-Watt University, and maintained by its Learning Technology Centre, to address some of these problems. However, although I started out attempting to use WebTest as a means of generating additional mathematics questions for students within the constraints of existing teaching programmes, through observing how students used the material, it quickly became apparent that for this application to be successful, it would be necessary to restructure the course around WebTests.
During the first two terms of the second year of our four-year degree in economics, students receive a course of 32 lectures entitled Using mathematics in economics. From the very start of the course, there is an emphasis upon economic modelling. Thus the equation of a line might be taught in the context of the effect of changes in price upon demand for a good, or the consumption function of an economy. As lectures progress, applications become more sophisticated and complete, so that by the end of the lecture series, we consider standard problems in the theory of choice and analyse the standard IS-LM model.
The WebTests are a series of fourteen problem sets that examine students' knowledge of particular economic applications of mathematics. Tests are available online, and each question contains a number of random parameters, determined separately in each realisation of the test being used - generally sufficient so that no matter how many times the student generates a test, they will not obtain the same question twice.
Tests are assessed on a pass-fail basis, with a score of 70% being required to pass. Students can try each test as often as they wish. Tests are structured so that students should be able to score 40% or so without any particular knowledge, and pass after two or three attempts. Since each realisation of the test is different, and questions are quite sophisticated, students tend to learn techniques for solving types of problem, rather than specific questions.