Diagnostic Testing in Mathematics

Abstract

For a good number of years starting from 1990 a steady decline in the basic mathematics skill of students entering mathematics or courses at the university level that required the use of mathematics is well documented in the U.K. and elsewhere. The decline in 'A' level standards underpins the decline in the entry standard of our students. In the UK this has been noted, reported, well debated and acted upon. It has been observed and reported that the tail end of the first year undergraduate cohorts (deficient in basic skills) have grown to a sizeable and problematic proportion (and gave rise to "high failure rate") and something needs to be done. This "mathematics problem" was reported by a number of organisations: Institute of Physics (1994), Engineering Council (1995), Institute of Mathematics and its Applications (1995), London Mathematical Society (1995) ("Tackling the Mathematics problem"). In "Tackling the Mathematics Problem", it was pointed out that
(i) Mathematics, Science and Engineering Departments appear unanimous in their perception of a qualitative change in the mathematical preparedness of incoming students - even among the very best and
(ii) students enrolling on courses making heavy mathematical demands are hampered by a serious lack of essential technical facility - in particular, a lack of fluency and reliability in numerical and algebraic manipulation and simplification.

The Gatsby report (Measuring the Mathematics Problem, 1999) collected evidence of this decline including the impact of the new 'A' level Mathematics courses. For institution that relies on equivalent or similar 'A' levels examination format as in the UK for admission standards, the experience and formative growth of the British Universities in using Diagnostic testing and Support Centres is particularly relevant. The US universities face the same problem and the problem is tackled differently and sometimes quite controversially through nationally organised Calculus Reform initiative. The recent Professor Adrian Smith's Inquiry "Making Mathematics Count" recommends some wide ranging initiatives and voices concern once again about the failure of the 'A' levels in preparing the students for the requirements and expectations of higher education institutions. We propose that (i) schools and universities could use diagnostic tests for their students, share resources and development costs; (ii) IT support and particularly institution support is vital for success; (iii) What needs to be done after the tests; and share (iv) our experience of some pedagogic and technical issues, in particular, in the use of Questionmark Perception for diagnostic testing with regard to setting online questions (questions with random parameters.)