Mathematical education has been much in the headlines during recent months and years, and the Department is pleased to be involved in an exciting one-year research project on mathematics at the interface of school and university. The main focus for the project is the phenomenon of persistent errors in basic mathematical manipulation and knowledge that appear in the work of many first-year university students, even those who are relatively able. Typical examples include writing
sin(x + y) = sin x + sin y,
or confusing a logical implication with its converse.
Preliminary analysis suggests that when it comes to more complex problems, for instance solving a differential equation, errors of a basic nature (such as going astray with fractions or standard integrals) cause more difficulties than "high-level" errors such as not recognising the form of the differential equation.
The aim of the project is to discover why these basic errors persist and to develop teaching methods and materials that will reinforce basic techniques and knowledge to the point where they can be used reliably in the course of tackling more complex problems.
The staff member of this Department involved with the project is:
and the project is being carried out in collaboration with Dr M. Grinfeld of the Department of Mathematics at the University of Strathclyde.
In May 2004, we received a grant for £1800 from the LTSN Maths, Stats and OR Network to run a pilot scheme of 'structured worksheets' at Strathclyde. The idea of these worksheets is to provide a bridge between the simple examples of mathematical theory that one often sees in lectures and the considerably more complex kind of questions that are found in exam papers. The worksheets come as a series, with the first sheet leading the student through step by step and asking them to fill in a few blanks along the way. As the series progresses, less and less information is given on the sheet, and so the student has to provide more and more of the details. As well as building up problem-solving ability at a steady pace, the worksheets help show students how to set out answers in a coherent form - something which is far from universally done at present!
Click here to see a web-log of progress on this scheme