A DEVELOPMENTAL APPROACH TO MATHEMATICS TESTING FOR UNIVERSITY ADMISSIONS AND COURSE PLACEMENT

Decisions on admissions to university and placement into university courses are usually based on the results of achievement (as in secondary school exams) and/or aptitude (in intelligence-type tests and SAT). This paper argues that in a situation where educational provision at secondary school level is highly unequal, a third approach to testing offers an alternative which is preferable both on grounds of theory of cognitive psychology and because it yields much better discrimination.The Alternative Admissions Research Project at University of Cape Town has developed a mathematics test according to the dynamic testing approach as advocated by Miller (1990) for admission of African students from grossly under-resourced schools, as well as for placing these and other students into a diversifying first year curriculum. This approach aims to assess the ability of a candidate to learn from authentic academic material within the test. This paper focuses on the reasons for the development of the mathematics test and the process by which the test questions were developed and piloted. The reliability of the test and correlations of this test with subsequent mathematical performance data are discussed.Following the encouraging data for the test as an admission mechanism, the value of the dynamic testing approach for furnishing additional information for placement into an increasingly varied curriculum at first year level was investigated. This enabled the piloting of more topics and more comprehensive validation of this type of testing. The paper concerns itself with the reliability and predictive value of each of the topics in this placement test for a range of core courses in various faculties and the extent to which these tests can identify potentially at risk students who should be placed onto an appropriate curriculum.     

Comprehension tests in mathematics

An alternative way for testing a student's understanding of theory in a tertiary mathematics course is presented. Two sample questions are provided and advantages and disadvantages of the method are discussed. We argue that the method is an acceptable and flexible means of testing students, and can be adapted to be used in other contexts as well. This revised version was published online in July 2006 with corrections to the Cover Date.