A common barrier to learning and progression in mathematics can often be providing a successful answer to a “W” question posed by a student; such as “When will I ever use this?” and “Why are we learning about this?”
There are numerous such examples and I am sure that many teachers have experienced the challenge of being put on the spot by an inquisitive student. Usually, when such a question has been asked, an unnerving silence fills the room as your audience awaits the response that may provide the inspiration for them to engage and explore a topic or the confirmation that this abstract world of mathematics has no relevance to their fast moving and ever-changing world.
Contextualised learning is of great importance in modern education as techno savvy teenagers can now amass great levels of information and knowledge from many sources whilst becoming experts in discarding anything which is not relevant to them. The challenge for us in education is to ensure that we can meet their needs whilst still providing them with a formal education that leads to successful outcomes at the end of a course of study. At The JCB Academy, we have designed a number of different ways to engage learners in mathematics and to provide answers to the “W” questions. The vision and ethos of the academy gives us a unique setting where the practical application of mathematics can be explored in detail due to the engineering context that learning is undertaken in. The diploma courses at KS4 and KS5, that are at the core of the programme of study for all students at The JCB Academy, are based around engineering challenges which are designed and delivered in consultation with our challenge partners. As such, there is a wealth of practical examples at our disposal that we can bolt on to our lessons or embellish for the purposes of learning mathematics.
After a number of different trials and many hours of planning, we have settled on a model of delivery that contextualises the learning using three methods: general links to engineering; direct links to the engineering challenges and extended tasks linked to engineering challenges. We explored a number of different delivery models, weighing up the pros and cons of each before settling on the methods listed above. The options that we considered were as follows:
Follow a traditional scheme of work with engineering/science based lessons. Some links to engineering challenges where appropriate.
Follow a traditional scheme of work with projects/challenges per half term that are linked to the engineering challenges.
Project/thematic based delivery model linked to engineering challenges.
The three methods that we have settled on using are a combination of options 1 and 2, providing us with a balanced approach to placing maths in context without having to completely rewrite our scheme of work and associated resources.
General links to engineering are provided on a regular basis as either a starter to a lesson, or as an extension activity in the main part of a lesson. They usually consist of simple short examples of how a single topic is linked to a practical scenario and they do not have to be related directly to our engineering challenges. Some successful examples that we have used are short research tasks such as investigating scientific and engineering formulae, identifying what the letters or symbols stand for in a formula and then substituting in values for each unknown. This short task has been used as a starter to a series of lessons on substituting and re-arranging formulae with the practical context provided from the outset.
Direct links to the engineering challenges are also provided in lessons in the form of a 15 or 20 minute task used to enrich the learning. They usually involve taking raw data or drawings from an engineering challenge and using them in a specific lesson, for example, we use data on the failure rates of genuine and non-genuine oil filters from the JCB challenge to calculate averages from a grouped frequency table. Since the students have already been involved in changing oil filters and calculating mean time to failure in their engineering lessons it is easy for them to see the relevance of the task.
The final method of placing maths in context involves developing extended tasks which explore the practical application of mathematics to a greater detail. They are delivered at the end of a block of teaching on a particular set of topics following a normal scheme of work and are usually run over 2 or 3 lessons at the end of each half term. The recent changes to assessment at GCSE level has allowed us to have more freedom to plan for project-based tasks within our normal scheme of work given that all assessments are now linear and are undertaken at the end of Year 11. This has given us the opportunity to take the time to explore mathematics in practical contexts. An example of such a task is a project which our Year 10 students recently undertook based around their Rolls Royce challenge. This task combined their knowledge of volume and surface area from the mathematics lessons with the design of a piston pump that they were familiar with from their engineering lessons. They calculated swept volume for a particular pump design, converted this to cubic metres and litres and eventually presented their results in the form of a poster. For our most able students the task was extended to investigating the stroke of a piston using trigonometry and lower ability students were able to consolidate their knowledge of how to calculate the volume of a cylinder and convert between metric units. An element of competition was also built into the task by awarding house points for the best posters and using them to update the displays in our classrooms. The students have engaged thoroughly with these project-based tasks and enjoy the opportunity to explore mathematics in context.
Although it may seem that a lot of the examples described previously are JCB or engineering related and the methods suggested are specific to the context of our academy, there isn’t any reason why they could not be applied in a different setting. We have also used many examples from the world of business and finance that the students enjoy. We have developed tasks that, for example, involve calculating the moving average for the price of gold or crude oil. Another engaging activity involved the students doing some fictitious investment on the stock exchange and tracking the percentage profit/loss made. Our PE department have also provided us with a large amount of data on the athletics carried out by our Year 10 students in the summer term. We can use this data to carry out a number of interesting statistical analyses by, for example, comparing each house and finding out which has the highest average long jump or the lowest range of times for the 100m sprint. These are all simple examples which could be applied in any context and have worked well to engage the students.
The outcomes from placing the learning in context for mathematics are clearly seen when we track the development of our Year 10s over an academic year. By dealing with non-standard numbers in unfamiliar contexts we have noticed an improvement in their confidence and resilience. These are often two of the most difficult characteristics for young people to develop in mathematics and it can be very challenging for teachers to find ways to promote these traits in a curriculum which is designed around assessment. By seeing numbers in the real world, students are provided with a hook for future learning and gain an insight into the world of numbers beyond the classroom. They also realise very quickly that many branches of mathematics combine when forming a solution to a complex problem and that the answers presented, particularly in an engineering context, are not always simple whole numbers. Whilst their exam papers might use neat and tidy dimensions or units, this is rarely the case in the real world, leading to some interesting discussions about unit conversions and why there are 1,000,000,000 mm3 in 1 m3. As a teacher, there is nothing more satisfying than having an extended conversation about the intricate nature of mathematics and its application to real world contexts with a group of young people who are suddenly opening the door to a whole new world of numbers. As we move towards the new curriculum in 2015, problem solving skills and multi-step solutions will start to take on a much greater relevance. Although the quality of written communication (QWC) has been assessed for some time in mathematics, with a move towards more functional skills style questions, it has been suggested that the new curriculum will be more challenging and will require students to be able to clearly plan out a solution to a complex problem. Having already been exposed to this type of problem solving by undertaking practical tasks linked to real world problems will be of great benefit to all.