Algebra at A-Level

Pages from Algebra at A-Level

Computer algebra systems (CAS) can be used to solve equations, to factorise or expand algebraic expressions, to differentiate or integrate functions, or to find the answer to any problem where there is a routine algorithm that can lead to a solution. In 1995 the ATM published this influential booklet which discussed the implications of CAS for pre-university mathematics education.

Since then CAS technologies have been integrated with graphing capabilities, and enhanced to form functional programming environments. Technology can now deliver CAS functionality 1-to-1 on smartphones and tablet computers. New qualifications are being offered in pure mathematics with technology which permit the use of CAS systems in examinations, and there is growing interest in Extended Project Qualifications (EPQs) in science and engineering. CAS can provide a foundation for Mathematics EPQ.

The 1995 ATM booklet explored a number of questions that might arise as computer algebra systems and related technologies became widely available.

“How will we spend the time that we save when certain techniques are redundant?
“Will we decide that the mathematical concepts are most important and that our students really need a better understanding of the work they are doing?
“Will we want to spend more time on problem solving?
“Should we give more emphasis to the notion of proof. or mathematical elegance?
“What about the study of the historical development and cultural significance of areas of mathematics?
“Should we pay more attention to the contexts of the problems that we address and encourage our students to make decisions about which computations are necessary and to interpret the results?
“What should be in the mathematics curriculum?''

ATM has set up a Working Group to update this booklet and give guidance to teachers about how they can use CAS technology across the curriculum — a technology that relates to learning and teaching even though it isn't generally allowed in assessment. The government's guidance for the 2017 A level states “The use of technology, in particular mathematical and statistical graphing tools and spreadsheets, must permeate the study of AS and A level mathematics.” This statement has recently been strengthened by additional guidance that awarding bodies need to justify how they are meeting this in their assessment strategies. The Working Group is keen to learn from members about how they are applying CAS systems and languages such as Derive, Autograph, Mathematica and Haskell. If you have any comments or feedback please contact ianbenson@atm.org.uk.

Available to download here.