Writing problem-centred activities

‘Knowing mathematics is doing mathematics. We need to create situations where students can be active, creative, and responsive to the physical world. I believe that to learn mathematics, students must construct it for themselves. They can only do that by exploring, justifying, representing, discussing, using, describing, investigating, predicting, in short by being active in the world.’

There are several stages in writing problem-centred activities that provide opportunities for learners to develop, practise and apply their functional mathematics skills. Identifying a context or topic that is realistic and purposeful is the first and critical stage in writing problem-centred activities.

A subject teacher, working alone, may be able to identify contexts where functional mathematics opportunities occur naturally and can be used to contribute to the main subject learning. However, it can be very effective for a subject teacher and a functional mathematics expert to work in partnership to identify contexts and develop authoritative problems. This combination of knowledge and expertise will produce activities that achieve both aims: subject focus and mathematics process.

The following activity was devised by an electrical engineering supervisor and a functional mathematics teacher working together. While soundly rooted in the vocational context, it has been designed to ensure that learners have the opportunity to practise and apply their functional mathematics skills.

Resistance and temperature

Scenario

Your supervisor has given you the job of rewiring a house that has been heavily insulated in the loft. The resistance of wire increases with temperature. In the height of summer, the temperature in the loft can reach 50°C.

Task

Investigate whether the 2.5 mm² annealed copper wire usually used for this purpose will be suitable for this particular job. It is unlikely that many functional mathematics teachers will have the knowledge of the engineering context to be able to develop this activity on their own. The expertise of the engineering supervisor is critical to ensuring that the context is authentic but they will need guidance from the functional mathematics teacher if they are to get the level right.

Partnership teaching, where the subject specialist and the functional mathematics teacher work together to plan, prepare and deliver the lessons, can also be highly effective. This collaborative working enables the functional mathematics teacher to identify the mathematical skills that underpin the subject content and devise relevant activities that will provide opportunities for learners to practise and apply their functional mathematics. This, in turn, will help learners to achieve their core learning aims.

In other provision, the activity can be led by the learners’ expressed interests. The following activity has been devised to encourage a learner with a keen interest in competitive weightlifting to develop and apply mathematical skills.

Weightlifting competition

Scenario

You are taking part in a weightlifting competition in 12 weeks’ time and have high hopes of winning a trophy. You know that you will need to prepare a detailed programme of training for the coming weeks.

Task

Using the template provided, plan a programme of training for the 12 weeks that will ensure that you are at peak fitness for the competition. The activity could be adapted for a learner who is keen on another sport.

Another way to challenge learners to apply their functional mathematics skills is to suggest that they develop an activity for another learner. This will enable them to identify and demonstrate their knowledge and understanding of the functional mathematics skills as well as using a range of other skills.

Dimensions and deviations

Scenario

Many thousands of bricks are used every day in the construction industry. Bricks should be made to British Standard 3921:1985*, which outlines the coordinating size and work size of bricks and the dimensional deviation allowed.

Task

In your workplace, test a sample of bricks to determine if they meet the British Standard.

*You would need to ensure that learners are aware of and have access to the relevant British Standard. This type of activity could be usefully introduced after learners have covered the knowledge about brick sizes and British Standards in their subject learning.

Everyday topics that are of interest to learners can be used as a basis for activities, for example deciding on the best buy from a range of options; fundraising to support a local environmental issue; finding the cost of a holiday for four.

New home for newts

Scenario

An article in your local paper highlights the threat to the population of newts in the park near your home due to the rubbish being dumped by visitors. You decide to enlist the help of friends to raise £100 to clean up the pond and make it environmentally safe for the newts.

Task

Consider the different ways you could raise the money and decide on the best option to put to your friends.

• Learners themselves can provide ideas for functional mathematics. Many learners will have an interest that can be harnessed to provide a scenario for an activity, for example sports, hobbies, leisure pursuits, cars. The following activity was devised for a learner who had a keen interest in Formula One motor racing.

Formula One

Scenario

Formula One is a very expensive sport. It is important that a team does well in the Constructors’ Championship if their sponsors are to continue to provide the money to run the team.

Task

Investigate how the different teams in Formula One have performed over the last ten years. Present your findings to a group of your fellow students. Decide which team you would advise a sponsor to support next year and explain your reasons.

Many purposeful activities will enable learners to use a range of functional skills, not just in mathematics. In many of the activities in this section there are opportunities for learners to develop and practise ICT skills, for example searching the internet, producing a graph to present data, and English skills, such as writing a questionnaire, producing a report, engaging in discussion.In the real world, functional skills are not used in isolation. Making the links with other functional skills will increase learners’ opportunities to use and apply the skills in a range of contexts.

Having decided on the context or topic, you will need to consider:

• the purpose of the activity

• the scenario

• what learners will be expected to do

• what results learners should produce

• how the functional mathematics process skills of representing,

analysing and interpreting can be used to complete the activity. Presentation and the use of language are important. Activities should be concise and should be written in language that learners will understand. Structure, style and readability are all important.

If you are developing a number of activities, it will help learners in the early stages if they all contain the same elements and follow the same format; learners will know what to expect. However, as learners become more

confident in their mathematical skills, it may be appropriate to devise activities that are less structured, allowing learners to use a greater degree of autonomy to determine the processes and information required. This is particularly relevant for higher-level learners, but it is worth noting that real world problems tend not to come in a structured format, so learners at every level will benefit from being provided with activities that vary in the degree of structure.

A structured activity should include:

• the title – short and informative, but exciting the interest of the learner

• an overview – this may be through a scenario, but should set the scene for the activity and outline the context

• the task or tasks – what the learner has to do

• the outcome – what the end result should be; what the learner should produce

• resources – any materials required to complete the activity, or guidance as to where they can be found, as appropriate to the level of the learner

• the timescale for delivery of the completed task.

It may also be useful to show the links to main subjects, if appropriate.

Key points for good style include the following.

• Address the learner directly in your writing – use ‘you’.

• Avoid the passive wherever possible.

• Avoid ambiguity. It is easy to make assumptions – you know what is involved but learners may not.

• Keep paragraphs short and to the point.

• Use simple direct words rather than complex or formal language.

• Use short sentences.

• Use words that learners are likely to know and understand. Define any new technical terms at the first time of use.

• Use bullets or numbered lists as appropriate.

An activity should be clear, easy to read and attractive to learners. Here are some Do’s and Don’ts to keep in mind.

• Don’t try to fit too much on a page.

• Do avoid clutter; use lots of white space.

• Do use a typeface that is easy to read.

• Don’t use lots of different typefaces.

• Do use headings where appropriate, but don’t use unnecessary capital letters.

• Don’t use images that are not relevant to the activity.

A task or activity should be considered in terms of its level of demand in relation to its complexity, familiarity, technical demand and the independence required of the learner. An activity can be differentiated for different levels and, where appropriate, to meet the needs of individual learners. For example, activities could provide

more or less learner support. For lower-level learners this might mean providing additional guidance in the form of resources, more teacher input, or breaking down the task into smaller chunks. For higher-level learners it could mean more demanding outcomes, greater complexity in the tasks required, and multi-stage interrelated tasks.

This stage also provides an opportunity to identify links with other functional skills. The following activity requires functional mathematics, but learners will be able to approach the activity with more confidence if they are able to apply functional English and ICT skills as well.

Travelling on the job

Scenario

You have just got a new job in the London area as a computer technician. It will mean regular travel by car to offices in Central London (SW1), Slough, Epsom, Bexley, Chigwell and Watford.

Task

Your employer has promised to help with the removal costs to relocate from Newcastle if you can provide an estimate. Where would be the best place to live, taking into account the travel costs and time taken?

The activity can be adapted to make it more relevant for learners by using local places and contexts.

Learners could use their functional ICT skills to search for and determine the mileages between the offices using a route planner. They could also use their functional ICT and functional English skills to present the final estimate to the employer. With all problem-centred activities, it is important to give effective formative feedback, as this will enable learners to confirm their skills and identify areas for further development. It is worth identifying opportunities for formative assessment at this stage of the writing process.

Learners’ feedback on an activity will help to tell you whether it was effective, although you will need to be clear about the type of feedback you want. You could ask learners for their opinion of an activity informally through group discussion, or formally through a short questionnaire.

With support and encouragement, learners are usually keen to express their views. Key areas you might want to ask them about include the following.

• Did you find the activity easy to understand?

• Did you have or could you find all the source material you needed to complete the activity?

• What skills did you use to complete the activity?

• What did you like about the activity?

• Was there anything you didn’t like or found difficult?

• What did you learn from the activity?

This feedback will enable you to revise or adapt the activity to meet different learners’ needs and interests. It may also generate further ideas for activities and engage learners in the development process. In fact, you could add a final question asking learners for suggestions that could be used for writing future activities.

• Be open to finding sources of ideas and activities in the most unlikely places.

• Listen to learners – they may provide ideas or topics of interest that you can develop.

• Be aware of links with other functional skills and other subjects, courses and programmes.

• Working in partnership with a colleague can enhance the process of writing activities and increase the stock of ideas.

Learners who are functional in their mathematics can transfer their mathematical skills to a wide range of contexts. They can select the appropriate techniques and carry out calculations to solve different problems. They can use mathematics in their everyday lives, including in their work at school or college, in their jobs, in making shopping decisions, or in managing their personal finances.