Further Pure Mathematics with Technology: Developing a New ?-Level Mathematics Unit That Uses Technology in the Teaching, the Learning, and the Assessment

By Button, Tom | Mathematics Teaching, July 2013 | Go to article overview

Further Pure Mathematics with Technology: Developing a New ?-Level Mathematics Unit That Uses Technology in the Teaching, the Learning, and the Assessment


Button, Tom, Mathematics Teaching


Tom Button documents the essential features of the development process

Further Pure Mathematics with Technology (FPT) is a new optional A-ievei Further Mathematics unit developed by Mathematics in Education and Industry (MEI). It requires students to have access to technology, in the form of a graph-plotter, spreadsheet, programming language and computer algebra system (CAS) for the teaching, learning and assessment. This article describes the development of the unit, including the rationale for the design decisions, and the implications for future developments of this type.

The development process

Although there have been a number of projects in England in the past 20-30 years to integrate the use of technology into teaching and learning in mathematics there are still many classrooms where technology is not used effectively. This issue was raised by Ofsted's 2008 publication, Understanding the Score:

"Several years ago, inspection evidence showed that most pupils had some opportunities to use ICT as a tool to solve or explore mathematical problems. This is no longer the case ... despite technological advances, the potential of ICT to enhance the learning of mathematics is too rarely realised. "

The lack of realising this potential can be partly attributed to the lack of technology in the assessment of mathematics. In GCSE examinations students are allowed a scientific calculator, but not a graphical calculator, for some of the assessment. At ?-level students are allowed a graphical calculator in all but one of their examinations; however, these examinations are designed to be graphical calculator neutral, that is - having a graphical calculator should offer no advantage to a student. It is not surprising that as the technology is not expected to offer an advantage in the examination that many teachers do not exploit its use for teaching and learning.

In addition to this there are no examinations where computer algebra systems (CAS) are allowed. The Joint Council for Qualifications requirements for conducting examinations (2012) state:

"Calculators must not... be designed or adapted to offer any of these facilities: -

* symbolic algebra manipulation;

* symbolic differentiation or integration;"

As a consequence of this there have not previously been any mathematics examinations in England that have the allowed the use of CAS. As a consequence of this CAS is rarely used in the teaching and learning of mathematics in English schools. This is missing an opportunity to take advantage of the benefits of using CAS. In The Case for CAS (2004) Böhm et al suggest that these benefits include making concepts easier to teach, supporting visualisations, saving time on routine calculations, and improving students' perception of mathematics.

In 2008 MEI, in partnership with Texas Instruments, convened a seminar and invited leading experts to discuss 'Computer Algebra Systems in the Mathematics Curriculum'. One of the main findings of this event was:

"An ICT-based qualification, where students have access to appropriate devices in the classroom and examinations would be useful. It could be a much more realistic qualification that allowed them to be better problem-solvers and mathematicians. "

In this context MEI wanted to drive the debate forward by exploring the possibility of having part of the ?-level course involve the use of technology, including CAS, in a way that its use would be expected in the assessment, and consequently this would drive its use in the teaching and learning. The aim of this is to support the evolution of the role of technology in the mathematics curriculum from a computational tool, to a tool that allows for observation and conjecture as part of the mathematical process, as identified by Trouche (2004). MEI approached OCR, the examination board who administer the MEI ?-level, who gave full support to the development of a new unit in the ? …

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