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# Citizen Maths

An open online maths course for adults who want to improve their grasp of maths at NVQ level 2.

14 June 2017

### Background

Citizen Maths is a free open online maths course for:

• self-motivated individuals whose level of mathematical capability is at or above NVQ Level 1, but is not yet at NVQ Level 3, and who want to improve it;
• employers who want to provide staff (or trade unions their members) with a practical and flexible learning and development opportunity in maths;
• colleges and other learning providers who want to give enrolled learners an additional or alternative route to improving their maths.

Citizen Maths has been produced by a consortium led by Calderdale College with OCR and UCL Institute of Education (IOE), with funding from the Ufi Charitable Trust.

### Challenge

Data from the OECD’s 2013 “PIAAC” Skills Report, shows that about 1 in 3 of the UK’s adult population – say ten million people – have a current level of mathematical capability that would enable them to benefit from Citizen Maths. This represents a challenge that is very difficult to address through traditional methods of learning and teaching: many are disenfranchised by life circumstances from taking part in face-to-face courses; and the challenge would be also be very costly to solve conventionally. Of course, nothing like all people will have the necessary self-motivation, ICT access and ICT skills to use Citizen Maths. But the absolute number of people in the UK population for whom Citizen Maths should be suitable, is nevertheless large; and, if Citizen Maths is successful with learners, we will have made a contribution to solving the “intermediate level” maths challenge, at a low enough cost per learner for the course (and similar courses) to be offered more widely.

### Solution

The course is designed around five powerful ideas:
1. Proportion
2. Uncertainty
3. Representation
4. Measurement
5. Pattern

We use the case of ‘proportion’ below to illustrate how we create meaningful problems for all five powerful ideas.

Citizen Maths analyses ordinary contexts in which proportion is in fact powerful, such as when mixing, sharing, comparing and scaling. Another more complex situation is when trading off one quantity against another, which leads to the idea of inverse proportion. These five examples of how the powerful idea of proportion is brought into action then become the focus for designing meaningful problems, around, for example, mixing recipes or concrete, creating pie charts, looking for best buys, figuring out how the pinch gesture works in an iPhone, or deciding how many workers to deploy at the supermarket checkouts. The research by Dave Pratt and Janet Ainley on the design constructs ‘purpose’ and ‘utility’ fundamentally informed the design of meaningful problems.

As well as working on problems with paper and pencil, tools such as calculators and spreadsheets are freely adopted. This is because at times it is more important to focus on the conceptual underpinning of the powerful ideas than on the details of calculation.

The course makes extensive use of applets on the Web or, when nothing suitable is available, applets that are specially designed for the course. The aim of the applets is to offer an on-screen manifestation of the powerful idea, which the learner can manipulate to gain a feel for how the powerful idea behaves. Such a holistic sense of the mathematical idea helps the learner to see it as a somewhat concrete object prior to working in more detail on computational aspects of the concept.

In a way, the approach helps to make the concept more visible, countering the trend for mathematics to become ever more hidden in the technological world. To this same end, we adopt Scratch, a programming environment, through which the learner ‘teaches’ the computer how to do the mathematics. In return, the mathematics not only becomes more visible but also the learner sees the pay-off for getting the mathematics (i.e. the program) correct, and is offered immediate system feedback when that is not the case.