The Duston school is a co-educational secondary school with a sixth form provision and an outstanding Ofsted rating. As of September 2014, it is a designated national teaching school and in September 2015, it will become an all-through 4-19 school. The Duston School is also one of twenty Lead Schools for Core Maths, providing support to a network of other schools as they look to deliver mathematics to all post 16 pupils.
At Duston, Core Maths is delivered by a team of three teachers, who work in close collaboration to develop materials and content appropriate to a range of student abilities. Each topic spans a whole half term, during which students receive ‘warm-up’ sessions on methods and techniques which are either new to them or which they may need to revise before tackling related problems. One of the unique aspects of delivery at The Duston School is that because there are three small classes of Core Maths students, teachers are able to constantly refine and adapt content in light of student response. This means that by the time a teacher delivers a lesson to the third group of students, any difficulties students might have will have been anticipated and thoroughly prepared for.
All year 11 students were initially made aware of the Core Maths course via presentations and mini-taster sessions, although subsequently successful recruitment was mainly achieved through targeted discussion with B and C grade GCSE students.
While the school has always had an ‘Option Maths’ programme enabling students to do ten hours of maths lessons at GCSE level, Core Maths offers another option to students who want to carry on with mathematics after GCSE but who cannot do A-Level because they fall short of the A Grade criteria. Notably this year, several A Grade students are taking Core Maths rather than A-Level mathematics.
86 students have already enrolled on the course for next year, in part because Core Maths has now been timetabled into the enrichment block, making it more accessible for students. This is well over and above expectations and is likely to require additional staffing so that small class sizes can be maintained. Both teachers and students recognize that the popularity of the course, in spite of its newness, is also partly attributable to the trust the students have in the mathematics department. Students know that they will be well supported on the course.
Recruitment for 2015 has almost exclusively involved the promotion of Core Maths at open evenings for future sixth form students and their parents. At these events, as in other centres, some of the current Core Maths cohort have attended and spoken enthusiastically about their experience of taking the course.
One of the unique features of Core Maths at the Duston School is that there is a team of three maths teachers delivering the course to just 21 students. The largest of the three classes has just 10 Students. One of the classes is run after school in order to accommodate 3 students who due to timetabling restrictions would not otherwise have been able to take the course.
The team works very closely together to develop materials and resources for Core Maths. To date, they have taken a day out per half term to plan lessons and develop content. Students typically study one topic per term. Each week teachers introduce a set of related problems and activities that enable the students to learn and apply their mathematical skills and knowledge. At the end of each week, the teachers meet to reflect on how well the activities have worked, with a view to adjusting the planned activities for the following week as required.
By working in such close collaboration teachers can respond quickly if students encounter difficulty with any of the materials. If something doesn’t work with one class, this information will be shared across the team, so that the next class will receive a slightly adapted version of the task. Introduction of new materials is planned so that it varies which class will do an activity first.
‘It’s so good that we do have different classes with different teachers teaching it [Core Maths]. So then someone can go ahead and teach a lesson. They can report back instantly and say “look I’ve done this with the class, just a heads up, you might want to start inputting this into your lesson.” So then two days later lets say, I’m there teaching it and I can say right, I know this with an issue with the other class, so lets fix it.’ Core Maths Teacher
As Core Maths tasks are so discussion based, teaching in small groups gives all students the opportunity to contribute to class discussions about the problems they are working on. Teachers consider this to be a vital part of problem solving activity in the class.
Small class size also means that teachers can more readily support the needs of less able students. Students who are clearly able to work independently will be asked to begin a task while the teacher (and HLTA who is in most lessons) works with students who require more support to get started or to progress through the task.
‘You can set the higher ability ones off, on they go, then you can go off and sit with them – the ones who aren’t as confident and just make sure they’re happy doing it. Whereas if you just try to set them all off, you’ve got ones who are really reluctant because they think “I don’t even know where to start” and they can see the other students who are like “what about this” and trying all these different ideas. And so that is the really nice thing about having such a small group.’ Core Maths Teacher
Working in small classes also appeals to students who recognize that teachers are able to support them more if they are struggling with a problem and similarly they are able to support each other more.
‘It’s a lot more comfortable … you get a lot more help from teachers’ Core Maths Student
‘‘You definitely feel more engaged. Core Maths Student
‘We help each other out, it’s not just teachers’. Core Maths Student
The school policy at Duston is to have scaffolded resources in every lesson available across all subjects, an ethos which the Core Maths teachers are fully committed to.
So for example, a recent problem involved looking at how quickly the cat population would increase if people didn’t get their cats spayed. Students were given a poster showing different facts about the fertility of a female cat. On the basis of the information provided, they were required to make judgements and estimations in order to work out their answer. For students who might struggle with this level of engagement, teachers provided an answer page which prompted them to list their assumptions and their estimations. Teachers also gave students a structure for how to go about solving the problem.
As an extension task, the more able students were asked to focus on male cats as well as the female cats, and to think about how many female cats the males might come into contact with and the subsequent impact on the cat population.
With scaffolded resources, the task never changes, but the amount of additional information or help that is given to students depends on their ability.
‘We’ve branded it as ‘maths warm-ups’. Before we do any project, we spend probably half an hour, forty five minutes just going over the maths they need because some of them again remember what they learned last year. Some of them probably never even learned it last year. Like historgrams, some of our C Grade students never learned histograms, whereas some of our students knew them straight away.’Core Maths Teacher.
‘Warm ups’ are used by the Core Maths teachers at The Duston School as a way of ensuring that all students are up to speed on the required mathematical skills before they start working on a problem. For example, when students began working on a finance project recently, the teachers soon realized that they were at very different levels in terms of their ability to use spreadsheets. While some students were very familiar with spreadsheet functionality, some had never even used spreadsheets before. These students clearly needed some ‘warm-up’ sessions on spreadsheets. Given topics last a whole half-term, at least two or three lessons are dedicated to ‘warm-ups’.
‘We’ve added them [warm-ups] now and it really has made a big difference.’ Core Maths Teacher
The warms ups were originally developed as a response to student feedback that although they enjoyed project work they were missing ‘normal maths’. Students took a while to adjust to the fact that Core Maths is so different to GCSE Maths and requires a greater level of independent thinking and analysis of problems than they are used to. ‘Warm-up’ sessions support them in making that transition.
‘They missed doing maths was one of the things that came back in that first half term. they realised they just quite liked sitting there doing some questions every now and again. They enjoyed maths last year and they actually miss doing it a little bit.’Core Maths Teacher
For students who don’t need the extra support, they have the option to work on harder questions during these sessions. Students themselves find these warm-up sessions very helpful.
‘Because we’ve had a six maybe seven month gap since GCSE, we’ve forgotten most of the stuff or maybe it’s like in the back of our minds so they recap over it and then going into something that builds on it.’ Core Math Student
Four sets of resources have been developed by the team to date, each relating to one project per half-term. All topics end with an assessment. The assessment is developed by the team prior to the project kick off and will usually take about 90 minutes to complete. Questions typically come from exam specs and do not specify what students need to do, they have to work this out for themselves. Assessments are based on similar questions to those that have been encountered by students throughout the project. Students are then RAG rated against the competence criteria and receive feedback from teachers.
In the future, the team is planning to have an additional one-hour assessment at the end of each half-term to test students on their problem solving ability. Measuring progress on problem solving ability has been a particular challenge for Core Maths teachers to date.
Student response to the assessments is very positive and they embrace the opportunity to get feedback on their progress.
‘Your assessments show what you may have struggled on over the half term and then you can easily work on areas that you may not be as strong at. So then you can improve them and get them up to the standard you need.‘ Core Maths Student
‘And also if you get a high grade you sort of want to maintain that and not drop down.‘ Core Maths Student
‘Having to stay after school is quite a commitment and I think having the grades back after each assessment, to see you’re doing well is reassuring that you’re doing it for a reason.‘ Core Maths Student
While the majority of students taking Core Maths at The Duston School are Grade B or C students, there are also some A and A* students on the course. The course tutors have found that one of the advantages of this is that the brighter students challenge the Grade B and C students. Although they also note that it isn’t always the lower grade students who struggle with topics.
‘It’s surprising who does better on which task as well. It’s not necessarily the A and A* students who do best. Sometimes the C grade students grasp it better’. Core Maths Teacher
The Core Maths teachers at Duston school recommend covering one topic per half term in detail. While at other centres teachers may have struggled for content, having lots of layers to a project which students gradually work through over the course of a half term, circumvents this problem.
Finally, regular assessments have been well received by students. Not only do they make progress easier to track but teachers have also found that the assessments give the course greater credibility. This is especially important for a course which is not compulsory.
Some of the topics and resources which the Core Maths team at The Duston School has developed over recent terms are detailed below. Mindful of the fact that the course runs over two years, the team employs a flexible approach to the teaching of Core Maths.
‘It’s quite a nice relaxed atmosphere in essence … it’s not like A-Level … If you go off task for a half hour and discuss mortgages or something else you don’t feel like oh I’ve got to catch up that time … if they want to look at something else or ask questions, you don’t feel like I’ve got to get back on task you feel like you can actually go and discuss it.’ Core Maths Teacher
Gambling Project – which covered chance and probability in the context of Football accumulators and Blackjack. Students looked at how to convert betting odds to probability and how gambling is more likely to lead to a loss of money.
In this statistics based task, students began by looking at the exponential growth of Ebola. Teachers were keen to teach students to question the statistics behind newspaper headlines.
One of the first tasks they did was to look at a headlines which suggested that 45% of males who catch Ebola are over 20. Students were given some basic data and asked how to work out if this were true.
Students also looked at a New York Times article on how quickly a rumour would spread around a school and ultimately the world if it is shared with just one person. Students were asked to apply the principles of exponential growth to the spread of Ebola.
Throughout the term, the topic incorporated elements of standard deviation, frequencies and histograms. A number of maths warm-up sessions were needed as teachers found that students had forgotten a lot of the statistical analysis from GCSE.
At the end of the topic, using all the data that they’d been given, and the statistical analysis they had carried out, students were asked to submit a short (500 word) report either in support of or against the statement ‘Ebola is the most deadly virus of our generation’. In spite of students having found the topic challenging, teachers noted that the quality of the reportssubmitted were very high.
Teachers also found that the report writing task helped identify which students were still not comfortable with making assumptions and applying their statistical knowledge and which students could interpret data and really understand what was being communicated. Overall the quality of the writing in the reports was quite high, a fact which teachers believe to be potentially attributable to the fact that all students did well in GCSE English.
The topic started with how much a person earns after tax, National Insurance, pension contributions and student loan repayments. Three studies were presented, a single person, a young couple or a young couple with children, each got different amount of money saved and earn a different amount each year. The students had to chose which case study they wanted to be, and then stick with that throughout the project.
Students were asked to analyse how much monthly income their case study would be left with after National Insurance, tax etc. using the budget plan from a major bank to set out how much would be spent on mortgage, food, bills etc. They also researched how much it cost to run a car, looking at issues look fuel economy, typical mileage and insurance rates.
Students then looked at the process of applying for a mortgage, what types of mortgages are available and how different things might effect how much could be borrowed, e.g. whether someone had an existing loan or children. The last part of the project involves exploring whether building a house (taking into account cost of materials, labour etc) would be cheaper than buying one.