KEYNOTE 1 CAS as a mentor for the apprentice mathematician

The acceptance of calculator technology as an integral part of the mathematics curriculum in schools, colleges and universities is a continuing subject for discussion with the level and heat of the debate rising and falling periodically. It’s always the same issues and questions that are asked at all levels of the curriculum. “When pupils use calculators they will not be able to do ‘such and such’. Should we allow calculators in the classroom before pupils can do maths by hand? Should we allow calculators in the examination?” The debate is now exercising the minds of teachers in higher education with most mathematics and engineering departments in the UK banning graphic calculators from examinations and thus discouraging their use during the teaching and learning process. The use of Computer Algebra Software (CAS) such as DERIVE, Maple and Mathematica has been accepted (grudgingly by many) because they are only available on computers, and access to computers is ‘easy to control’. A calculator with a built in CAS such as the Texas TI-92 introduces a new dimension to the debate in higher education. In this lecture I will argue that CAS, both as software on a computer and on hand-held technology, should be an integral part of the student mathematicians tool kit. It is important that students are encouraged to use ‘appropriate technology appropriately’. There is a natural tension between the need for students to be able to do mathematics 'by hand ' and to rely on technology. By reflecting on a module of mathematics in a Mathematics Degree programme I will demonstrate the need for students to turn to technology as a natural approach to unpacking the theory. At the same time we will discuss the concepts and skills needed to be able to use the technology effectively. The lecture will also look at the results of some research with school students using the TI-92 and consider their beliefs of mathematics learning when they use such technology