My first blog for OCR features an innovative approach to using technology in the teaching, learning and assessment of Mathematics. The option was developed to allow students to experience how technology can be harnessed in the study of mathematics.
MEI’s position on the use of technology is:
“MEI believes that technology should be embedded within the teaching, learning and assessment of mathematics. It aids understanding and enables problems to be addressed that would be impractical or inefficient to tackle without it.”
Technology is already used by many students in their study of statistics but at MEI we wanted to show how technology can also be very effectively in pure maths.
Mathematical software is fantastic for automating processes that are time-consuming to perform by hand including arithmetic, graphing and even algebra.
Using technology in this way can change the emphasis so that students focus more on spotting patterns and observing mathematical relationships which can then be confirmed using analytical skills.
This is how students will use technology in FPT: they investigate a situation in mathematical software and then make conjectures, which they are then expected to be able to verify and explain.
Learning traditional pure maths skills is still important, and these are assessed elsewhere in A Level Mathematics and Further Mathematics. FPT allows students to see a bigger picture by delegating the technical work to the computer and focusing on the concepts.
It’s a mind-blowing moment when you first see all the solutions to a family of differential equations as a parameter varies, rather than struggling with one solution to one differential equation.
This approach has been commended by university mathematicians who have commented that it is consistent with how students might use technology if they continue their study of mathematics.
In the design of FPT we chose topics that were particularly rich when studied with technology. The topics are:
The investigation of curves topic involves students using a graphing tool to explore a family of curves such as for different values of k.
The technology allows for multiple cases of the family to be plotted quickly and accurately so that students can identify common or distinct features in the different cases.
What is unique to FPT is that students can also use a computer algebra system (CAS) for solving equations or differentiating in the same way that they’d use a scientific calculator for arithmetic in other areas of maths.
In the differential equations topic the students use technology to generate tangent (or slope) fields. These give a very visual representation of a differential equation and can help students understand its behaviour.
The differential equations are then solved using either CAS or a numerical method on a spreadsheet. The emphasis is on being able to describe the behaviour and not perform algebra or calculations by hand.
The number theory topic is often the most popular with students. In this topic students use the Python programming language to solve problems such as “which of the first 100 Fibonacci numbers are also square numbers?”
The small programs that the students write can check a large number of integers in a very short amount of time and then the students can use their mathematical skills to explain the results obtained.
There are a range of choices for the software that students can use in FPT. One of the choices is to use GeoGebra and Python, both of which are free. There are resources and support available on using these on MEI’s Integral resources platform.
Using these technologies in FPT can also have a positive impact in other lessons too: teachers who have taught FPT often comment that as a result they make greater, and more effective, use of technology elsewhere.
In the FPT exam candidates have access to the software, usually on a laptop; however, it is a written paper and their submission is a written script, just like for their other exams.
This reinforces the idea that technology is just a tool that allows students to access mathematical ideas but the important feature is that they can interpret and explain them.
It also means that it can be administered in a very similar way to their other maths exams and hence does not present additional barriers to schools and colleges.
In H645 OCR B (MEI) A Level Further Mathematics candidates take the mandatory Core Pure paper that accounts for 50% of their marks plus either a Major plus one minor, or three minor optional papers that contribute the other 50%. One of the attractive features of the OCR Further Maths specifications is that candidates can take additional minor optional papers, with their best grade combination counting.
This means that FPT can be offered to broaden the mathematical experience for students who are interested in the intersection of maths and computing.
At MEI we have produced a range of resources to support students with FPT: as well as a textbook there are full Integral resources and, with the support of OCR, we have offered a free online course for students this year.
With the resources available, FPT could be particularly attractive to students who want to self-study an additional option for Further Mathematics.
If you have any queries or questions, you can comment below, email us via firstname.lastname@example.org, call us on 01223 553998 or Tweet us @OCR_Maths. You can also sign up to subject updates and receive up-to-date email information about resources and support.
Tom Button - Mathematics Technology Specialist
Tom Button is the Mathematics Technology Specialist for MEI and the Technology Professional Development Lead for the AMSP. He tweets about maths and technology at @mathstechnology