# Further Pure Mathematics with Technology

Further Pure Mathematics with Technology is an exciting and innovative A Further Mathematics option that requires students to have access to technology for the teaching, learning and assessment.

## Why do Further Pure Mathematics with Technology (FPT)?

FPT is an A level Further Mathematics option that can be studied alongside (or after) studying the Core Pure element of A level Further Mathematics. This option builds on and extends students' knowledge of pure mathematics through using technology to perform mathematical processes quickly and accurately. They will observe the effect of changing parameters displayed in different representations, which is useful for aiding generalisation. Students will engage in investigative approaches to problem solving.

OCR(MEI) A level Further Mathematics allows students to take additional options, with the best scores contributing to their A level grade, so FPT could be offered to students as a useful additional option, without committing to it being part of their overall mark.

## FM videos for FPT

We have produced a series of short videos to support students learning the content of FPT. These break the content into sections and are designed to introduce students to concepts so that they can learn the material for each section by working through appropriate examples. This videos have been produced thanks to the sponsorship of OCR.

### Sample video

The videos are accesible via YouTube: FPT videos playlist

The videos are also freely available to registered schools and colleges through your Integral® account. All students at AMSP registered schools/colleges can also access the videos directly via a separate 'student account' that teachers can share with students. The student account features the videos but no other resources. For more details about the FM videos for other options and registering with the AMSP see: AMSP Further Mathematics resources.

## The content of FPT

Candidates are expected to know the pure content of A level Further Mathematics as well as the Polar Curves some of the Differential Equations content of A level Further Mathematics. Included in this module are:

• Investigations of Curves: exploring including curves with a graph plotter and Computer Algebra system (CAS). The curves can be expressed as cartesian equations, parametric equations and polar curves.
• Differential equations: exploring tangent fields with a graph plotter, analytical solutions with CAS and numerical solutions with a spreadsheet.
• Number Theory: writing programs to solve problems in the integers.

A suggested scheme of work is available:

## Assessment of FPT

FPT is assessed by a timed written paper that assumes that students have access to the technology. For the examination each student will need access to a computer with the software installed and no communication ability. A graphical calculator is allowed in the examination.

You may find the documents below useful:

## Software for FPT

Students are expected to have access to software for the teaching, learning and assessment that features a graph-plotter, spreadsheet and CAS. They will also need access to the Python programming language. Support for the using different types of software will be available in the free Integral teaching resources include instructions how to use it along with solutions to all the exercises and practice papers. Please see below for further details of allowed software. If you have any questions about appropriate software for FPT please contact MEI's Mathematics Technologies Specialist.

Approved software for use in the examination for FPT (updated March 2017):

• Geogebra (v5 or later)
• TI-Nspire software (any model with CAS)
• CASIO ClassPad software (any model with CAS)
• Mathematica (v11.0 or later)
• Maple (v2016 or later)
• Excel (any version)
• Gnumeric (any version)
• Apache OpenOffice spreadsheet (v4 or later)

Approved programming language for FPT (updated March 2017)

• Python (v 3.6 or later)

Students should use GeoGebra version 5. Version 5 can be downloaded from www.geogebra.org/download: selecting the "GeoGebra Classic 5" option. Students should not use GeoGebra 6.

When using Python students will need to learn an additional process that is not performed automatically in the software: how to calculate if an integer is prime. Guidance on this is given in the document: Advice when using Python

## Resources

Full integral resources for FPT and an FPT textbook will be available in 2018.

## CPD for Further Pure with Technology

MEI will be offering conference sessions about FPT during 2018/19 as well as other professional development.

You may find the podcast below useful:

Tom Button, MEI's Learning Technologies Specialist, talks to Craig Barton, TES adviser for secondary maths, about the success of, and the future for, the Further Pure Mathematics with Technology project.

TES Maths Podcast Special - Tom Button Interview

Lee, S & Button, T (2013)
Moving with the Times - A New A level Further Mathematics Unit: Further Pure Mathematics with Technology (FPT)

Button, T & Lee, S (2013)
Further pure mathematics with technology: A post-16 unit of study that uses technology in the teaching, learning and assessment.
Proceedings of the International Conference on Technology in Mathematics Teaching, Bari, Italy, July 2013.

An article on the development of Further Pure with Technology was published in issue 235 of the ATM magazine, Mathematics Teaching.
Further pure mathematics with technology: Developing a new A-Level mathematics unit that uses technology in the teaching, the learning, and the assessment - Tom Button