Diagnostic
Testing in Mathematics
Tze Beng Ng
matngtb@nus.edu.sg
Mathematics
National University of Singapore
Singapore
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.)
