We have recently published our Design Guide for Open Online Courses (PDF file, 89 pages, 6 MB).

The guide, which has a short foreword by Maren Deepwell (Chief Executive, Association for Learning Technology) and Joe Wilson (Co-founder, Open Scotland), is a comprehensive summary of how we went about creating Citizen Maths. The guide shares our design principles, the techniques we used to put them into practice, and some of the changes we made in the light of experience.

Our aim is to provide — with the appropriate ‘translation’ to other contexts — a resource that will be useful to teams who are developing online education initiatives.

The guide is licensed under a Creative Commons attribution-only (CC BY) licence, which means it can be freely shared and reused.

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

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.

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.

The course is designed around five powerful ideas:

- Proportion
- Uncertainty
- Representation
- Measurement
- 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.

To date, over 12,500 people have registered for Citizen Maths, and over 22,000 have completed the Citizen Maths pre-course self-assessment.

]]>….it was just like having a tutor in my home working at my pace and my level, and the more I progressed, the more confident I felt of my own abilities….

Nicky Mitchell works as a Learning Support Assistant at a primary school in Maidstone, Kent. Last year Nicky completed Citizen Maths.

In this Womanthology article, Nicky explains the difference Citizen Maths made for her.

]]>Citizen Maths overviewA general introduction covering: - what the course is;
- who it’s for — learners, colleges, employers;
- benefits of the course design;
- short samples of the course videos;
- brief learner comments.
3 minutes long. Useful for anyone. |
View on YouTube |

Learners’ perspectiveWhat learners say about Citizen Maths: - how learners feel about the course;
- how the course demonstrates maths in everyday life;
- how it helps you understand maths in a non-threatening way;
- short samples of the course videos;
- benefits of learning online.
3 minutes long. Useful for learners who might be considering doing the course. |
View on YouTube |

Tutors’ perspectiveWhat tutors say about Citizen Maths: - who the course is for;
- how the course can be accessed across different platforms;
- the flexible structure of the course;
- the approach to teaching and learning;
- the range of learning activities.
4 minutes long. Useful for teachers in colleges, human resources managers in employers. |
View on YouTube |

Course screencastA screencast about : - what it feels like to do the course;
- benefits of flexibility in setting your own speed and repeating where necessary;
- examples of of learning activities;
- use of quizzes, spreadsheets and apps;
- topcis covered by the powerful ideas.
4 minutes long. Useful for learners. |
View on YouTube |

These come as PDF files in a range of sizes and formats: A3 poster, A4 leaflet, A5 flyer, A6 postcard, print-ready version of A3 poster design with bleed and trim marks (can be enlarged to A2).

If you’d like to include contact details of someone in your organisation who can provide local support for people doing the course, you can edit the PDF files of our “empty belly” versions, in A3 and A4. If you would like a supply of printed flyers or posters please contact us.

]]>We respect the fact that some people prefer to limit the number of cookies stored by their browser. For this reason we are providing a list of the cookies a user of the course may find that their browser stores, in case you wish to restrict this.

Names of cookies are indicated by italics in what follows.

In order for the Citizen Maths course to recognise who you are, you need to allow course.citizenmaths.com to set and use the *gtoken* cookie. Both citizenmaths.com and course.citizenmaths.com also use the *_ga* and *_gat* cookies for Google Analytics.

As explained in our privacy policy, the course runs on Google Course Builder software. Some of the activities also use Google Sheets (which is free and available ‘in the cloud’ for wide access). Google sets a number of cookies. We have not been able to test whether all of these are critical to the functioning of the course, but recommend that you allow your browser to set and use the cookies listed below. (Please note that Google’s Data Processing and Security Terms for its Cloud Platform mean that Google will not itself process any personal data relating to your participation in Citizen Maths.)

google.com

*SID**HSID**SSID**APISID**SAPISID*

accounts.google.com

*SMSV**ACCOUNT_CHOOSER**LSID**GAPS*

myaccount.google.com

*OTZ**OSID**_utma**_utmc**_utmz**_utmt_t10**_utmb*

security.google.com

*OSID*

docs.google.com

*S**lbcs*

Several activities through the course use the Scratch programming environment from Massachusetts Institute of Technology (see why), so please grant permission for scratch.mit.edu to set and use these cookies:

*_utma**_utmb**_utmc**_utmz*

Similarly,

- for those activities that use Geogebra, please allow
*_utmz*cookies from geogebra.org; - for the activity that uses Office of National Statistics data, please allow
*_cfduid*(and, less critically, Google Analytics cookies*_ga*and*_gat*) from ons.gov.uk; - for the activity that uses xe.com, please allow
*__asc*,*__auc*,*WT_FPC*(and, less critically, Google Analytics cookies*_ga*and*_gat*) from xe.com.

The following cookies are for sites which the course links to. Mainly this is for supplementary information and further research at your discretion, so you will still be able to complete the main part of the course even if you don’t accept these cookies.

drinkaware.co.uk

*_ga**_dc_gtm_UA-5152163-1**__atuvc**__atuvs**_ceg.s**_ceg.u**optimizelyEndUserId**optimizelySegments**optimizelyBuckets**optimizelyPendingLogEvents*

en.wikipedia.org

*CP**WMF-Last-Access**enwikiGeoFeaturesUser2**enwikimwuser-sessionId*

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*_ga**_gat**_gat_newView**nmstat**HSETRACK*

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*_ga**_gat**__cfduid**__atuvc**__atuvs**has_js**pagestyle**teztsize**_dc_gtm_UA-23620389-3*

- 51% of Britons admit their maths skills aren’t good enough to deal with everyday decisions like offers from supermarkets, phone, broadband, budget airline and utility companies.
- 84% believe that organisations are exploiting this lack of maths skills, making it hard for consumers to work out the best deals.
- Over a quarter of the population suspect they have fallen foul of this repeatedly over the last year.
- Britain’s ‘maths confusion’ may be costing consumers as much as £1billion a year.

The full text of our news release is available here Citizen Maths market research (1) 30.01.17

A release that links this to the wider issue of poor maths in the workplace is available here Citizen Maths research (2) 30.01.17

We have also just released a new video which features users talking about their experience with Citizen Maths.

]]>Citizen Maths cannot help you on its own to achieve GCSE Maths: but it does cover a some important parts of the curriculum; and it may be helpful in getting you started at becoming more confident with maths at GCSE level.

To gain GCSE in Mathematics, you are expected to be:

- fluent in skills;
- a problem solver;
- able to reason and interpret with
- number (eg calculating fractions and decimals),
- algebra (eg solving equations),
- proportion (eg scaling),
- geometry (eg properties of shapes),
- measures (eg area of a triangle),
- probability (eg randomness),
- statistics (eg pie charts).

Full details of what is required in GCSE, please see the GCSE requirements document (PDF, 589 KB).

Citizen Maths offers lessons which are set in real-life situations that are relevant to some of the GCSE requirements.

For example, under the GCSE requirements called ‘measures and accuracy’, Citizen Maths provides a good deal of support in using:

- mass
- length
- time and money
- estimation and rounding.

Aspects of fractions, decimals and percentages are also covered though not in full.

Citizen Maths gives plenty of support on:

- scale factors
- finding a fractional quantity
- simple ratios
- working with speeds.

Some other topics are touched on in Citizen Maths including:

- using ratio notation
- expressing a ratio as a fraction
- percentages
- comparing quantities as ratios.

These topics make up over a half of the GCSE content called ‘Ratio, proportion and rates of change’.

Citizen Maths includes help on formulas about circles and perimeters. There is some work on angles, rotations, reflections and polygons and on properties of shapes, but this makes up only a small amount of the GCSE content called ‘Geometry and Measures’.

There are lessons in Citizen Maths on randomness. There is also some work on:

- expected frequencies
- when probabilities add to 1
- the effect of increasing sample size and sample spaces.

However, these topics make up only a small part of the GCSE requirements on ‘Probability’.

Under the GCSE requirement called ‘Statistics’, interpreting charts and applying statistics are touched upon but much of the GCSE requirements in this area are not covered

The previous section summarises the parts of the GCSE requirements that are best supported by Citizen Maths.

But it is also important to note that a major benefit of studying Citizen Maths with GCSE in mind is that Citizen Maths emphasises *using* mathematics in a way that should make the mathematics more easily understood. In the words of the GCSE requirements document, Citizen Maths should help you to:

- acquire, select and apply mathematical techniques to solve problems
- reason mathematically, make deductions and inferences and draw conclusions
- comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context. (page 3,
*Mathematics GCSE subject content and assessment objectives*)

The videos of the to-camera tutors in the Citizen Maths lessons provide a very clear demonstration of these processes, all of which you will need to learn to succeed at GCSE.

There are substantial sections of the GCSE requirements that are not covered at all by Citizen Maths or are not covered in sufficient depth to really be relevant to GCSE.

Here are the GCSE requirements for “Subject aims and learning outcomes”. The requirements in underlined italics *are not* covered by Citizen Maths (the rest are, to some degree):

GCSE specifications in mathematics should provide a broad, coherent, satisfying and worthwhile course of study. They should encourage students to develop confidence in, and a positive attitude towards mathematics and to recognise the importance of mathematics in their own lives and to society.

They should also provide a strong mathematical foundation for students who go on to study mathematics at a higher level post-16. GCSE specifications in mathematics should enable students to:

develop fluent knowledge, skills and understanding of mathematical methods and concepts- acquire, select and apply mathematical techniques to solve problems
- reason mathematically, make deductions and inferences and draw conclusions
- comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context.

Students should be aware that mathematics can be used to develop models of real situations and that these models may be more or less effective depending on how the situation has been simplified and the assumptions that have been made.

.Students should also be able to recall, select and apply mathematical formulae

Table 1 gives an indication of the coverage.

(Note: mostly you can ignore the numbers, but they refer to heading numbers in the GCSE requirements document in case you want to look up more details there)

Subject content |
Citizen Maths covers |
Citizen Maths covers in part |
Citizen Maths does not cover |

Number | Structure and calculation | ||

Fractions, decimals and percentages | |||

Measures and accuracy | |||

Algebra | Notation, vocabulary and manipulation | ||

Graphs | |||

Solving equations and inequalities | |||

Sequences | |||

Some of ratio: 1,2,3,5,11 | Some of ratio: 4,6,9,12 | Some of ratio: 7,8,10,13,14,15,16 | |

Geometry and measures | Some of properties and constructions: 1,4,7 | Some of properties and constructions: 2,3,5,6,8,9,10,11,12,13 | |

Some of mensuration and calculation: 14,17 | Some of mensuration and calculation: 15,16 | Some of mensuration and calculation: 18,19,20,21,22,23 | |

Vectors | |||

Probability | Some: 2 | Some: 3,4,5,7 | Some: 1,6,8,9 |

Statistics | Some: 2,3,5 | Some: 1,4,6 |

Of the assessment objectives (page 13 of GCSE requirements document), CM covers: AO1 (though little emphasis on ‘accurately recall facts, terminology and definitions’; AO2 (though little on ‘present arguments and proofs’); AO3.

It is also true to say that Citizen Maths — in the words of the GCSE requirements document — does not emphasise that you ‘develop fluent knowledge, skills and understanding of mathematical methods’ (page 3, *Mathematics GCSE subject content and assessment objectives*). Citizen Maths has not been designed with this goal in mind.

If you were wondering whether Citizen Maths would help you get a GCSE, the answer is to some extent, but a quite a lot of further work would be needed. Perhaps you should think of Citizen Maths as:

- giving you a good grounding in the powerful ideas that it presents;
- an option that may help you to get over your initial worries about mathematics;
- a way to build confidence before you go on to tackle maths in more detail.

Citizen Maths may also be useful if you find yourself in a class where your classmates seem to get the mathematics quickly while you are struggling with basic ideas. If so, because Citizen Maths emphasises how to use the mathematical ideas it covers, it might help you to grasp the ideas in a better way.

As well as studying Citizen Maths, there are other resources which we think might complement our course in helping you achieve GCSE Mathematics. Take a look at:

- BBC Bitesize resources
- the adult focused BBC Skillswise at Level 2
- The US-focused Khan Academy has many helpful video tutorials
- The Mathematics Enhancement Programme GCSE from the Centre for Innovation in Mathematics Teaching.

This document sets out how you could use Citizen Maths to improve your maths in preparation to be a school teacher.

Alongside various other standards that you need to be reach, as a prospective teacher, you must satisfy the Department for Education about the level of your mathematical knowledge, including your appreciation of key concepts. In addition, you must take a test of your numeracy skills. You can find details on the Department for Education website.

In the test, you must demonstrate:

- your mental arithmetic skills relating to the four basic operations (+, -, x and ÷) , time, proportions (including fractions, decimals and percentages), measurement and conversions;
- Your written skills in interpreting data and solving problems involving time, money, proportions, measurements, averages, range and formulas.

If you study Citizen Maths thoroughly, you are likely to gain a better appreciation of mathematics, especially how the five powerful ideas of proportion, representation, uncertainty, measurement and pattern can be useful in your personal, social and working life. This level of understanding of key concepts is very important in becoming an effective teacher of maths.

Citizen Maths does not focus explicitly on mental arithmetic and we would recommend additional work in this area beyond what Citizen Maths can offer.

The written test for prospective teachers is likely to focus on computational techniques in the various topics listed above under what evidence of competence in maths is required. Citizen Maths does occasionally explain such techniques but it is not the main focus of Citizen Maths. We strongly believe that being able to use such techniques effectively is supported by a sound appreciation of the underlying concepts and so Citizen Maths should provide a good basis for another course which does emphasise those techniques.

The powerful-ideas-in-action in Citizen Maths on:

- proportion will support solving problems on proportion, fraction, decimals and percentages;
- representation will provide a good conceptual basis for data interpretation and solving problems with averages and range;
- measurement will be of direct help with solving problems on measurement in the written test.

The use of formulas appears throughout the work on the various powerful ideas, though formulas are perhaps most explicit in the powerful idea on measurement.

Good teacher trainee courses will provide support during the course to enable you to brush up your techniques in mathematics and we believe such support will be more effective if you have the sort of appreciation of proportion, representation and measurement that Citizen Maths offers.

As indicated above, Citizen Maths should provide a supportive grounding in numeracy but we would recommend further work on techniques to follow on from our course in order to prepare you for the mental and written tests associated with becoming a teacher.

The Citizen Maths Statement of Participation may not be specifically useful to you in gaining a teaching qualification, except perhaps as evidence for an interview to obtain an initial place as a teacher trainee.

]]>We will send you automated email messages to encourage you to achieve significant steps in the course — from just getting started to completing a unit or a whole Powerful Idea. The emails are triggered by your progress, and tell you what you need to do to achieve the next landmark.

You can opt in to receive these encouraging emails when you register for the course, or, if you’re registered, you can opt in or out of this service from your profile page.

Earlier in the year we did some usability tests with people working their way through the course. We found that they were looking for help on some topics (such as how to undo edits in Scratch) but couldn’t find it, even when it was there and (we had thought) easy to find.

We have now added a new Help page (you need to be logged in to the course to access this) that brings together all Citizen Maths help in one place. Hopefully it really is easy to find now.

If you want a quick way of looking to see which video mentioned a particular idea or calculation, or if you simply prefer to read than to watch and listen, you can now get transcripts of every Citizen Maths video. Just click on the link under the video.

The image on the right shows a screenshot of one of the videos in the course (related to chance and probability, part of the Uncertainty powerful idea, hence the roulette wheel) with the transcript window opened beneath it. Please click on the image to enlarge it.

We take learners’ privacy very seriously on Citizen Maths, and try to enable you to control your own data. With that in mind, we’ve made a change to clause 7 of our privacy policy so that, 24 months after a learner’s last login to Citizen Maths, we delete all their personal information including their progress in the course.

At the same time we archive a copy of the same profile and progress information, having first anonymised it by the removal of names and email address from the data.

]]>