Using Frequent Tests to Enhance the Teaching of Basic Mathematics and Statistics
I teach a one-semester Mathematics and Statistics unit to first-year students on specialist and joint programmes in Economics. These students are a very cosmopolitan group with a wide range of mathematical ability, ranging from long-forgotten Grade C in GCSE to A-grade Maths A'level or its equivalent.
One of the main purposes of the unit is to make sure that all students acquire or reinforce a basic mathematical competence to prepare them for more advanced economics and quantitative units, which follow later in the year and in subsequent years. The students use one well-established textbook, which contains all the exercises they are expected to undertake.
Diagnosis and streaming
When the students first arrive in the University, I have little reliable information about their mathematical skills. So at the beginning of the semester I give them a 45-minute multiple-choice test, to diagnose their arithmetic and algebraic knowledge. This test does not count towards their final unit grade.
The multiple choice tests are marked by machine. An optical mark reader reads pre-formatted answer sheets on which the students have shaded their answers to a, b, c, d or e. This is a relatively old technology, but it has advantages:
- The marking of the tests and the provision of feedback to the students are automated. They do not take up much time.
- The tests are carried out under supervision. All the students sit down at the same time in a lecture hall, rather than independently logging onto a PC in a remote location.
The early diagnostic test is used to stream the students in tutorial groups. I find that it is particularly important to allow weaker students the time and space to air their difficulties, away from those who can answer problems more easily.
Further tests during the term
In week 5 and 9 of the unit the students are given further short (30-minute) tests on the Mathematics and Statistics that they have learned to date. These tests count in a small way (15%) towards their final unit grade. This is sufficient to motivate the students! To encourage the nervous, I allow the students to count the higher of the two test marks in their final grade. In other words they are allowed one catastrophe!
The students receive automated feedback on their test performance in the week following the test. They can identify areas of weakness fairly rapidly.
The final exam and value-added
The final exam, taken at the end of the semester, is a two-hour multiple-choice test. My experience over four or five years is that many students who begin the semester with very low scores, show significant improvement over the semester. I only wish this were true for all such students!