Set in the heart of London, just a stone’s throw from the hustle and bustle that is Oxford Street, St. Marylebone Church of England School is an outstanding comprehensive school for girls. It offers a mixed sixth form provision which is currently attended by around 300 students.
The lead Core Maths teacher at the school is a strong advocate of Core Maths. More so than GCSE maths, he recognises that the course provides a valuable opportunity for students to see how mathematics can be used in their future studies or careers.
‘Core Maths is a bridge for students who enjoy maths and want to see where maths can take them.’
There were some initial concerns about the ease with which students might be recruited to the Core Maths course at St. Marylebone. Given it’s not compulsory, students were effectively being invited to study Core Maths in addition to their four mandatory A-Level subjects. In the end, nine students signed up to the course. The Core Maths teacher noted that each student had a particular reason for wanting to study the subject, whether it be that they had started A-Level maths and found that it wasn’t right for them, or that they were simply attracted by the opportunity to continue studying mathematics in some form after GCSE.
All nine students have remained on the course so far. This is in spite of the teacher’s concerns that retention might be an issue as students prioritised other AS subjects. Clearly Core Maths is meeting student need and the positive feedback from students would seem to reflect this.
One student who had taken AS level maths for a year noted –
‘I did the stats module for the AS and I really struggled with it, but I think in Core Maths I grasped what I hadn’t the year before because it was explained in a lot more depth and it was more of a simplified version so I picked it up a lot quicker this year.’
Another student said -
‘It’s not as easy as GCSE, it’s harder than that, but it’s not as hard as AS maths. So it’s kind of like an in-between.’
St. Marylebone offers students a two-hour slot each week and requires one hour study outside of class. This year the school has been trialling the use of ‘flipped learning’, a term traditionally used to describe how instead of doing the learning in school and the practice at home, students do the reverse. In using this approach, teachers are seeking genuine intellectual engagement with subject content before students come into the classroom.
Where this approach has been used in Core Maths, students have usually been given a video to watch or some questions to research ahead of the lesson. Typically the required preparation time is around a half hour. As the year progressed, the Core Maths teacher found that students came in to the lesson motivated to talk about what they’ve learned outside the classroom. He described the approach as a strategy for ‘‘the challenge of encouraging students to engage with problem solving’.
One example of where flipped learning was used in Core Maths was in relation to Fermi Estimation problems. Using an initial problem – how many piano tuners are there in London? - students were given a video to watch ahead of the lesson with some information that would help them to work out an approximate answer during the lesson. Students came to the lesson willing and able to engage with the problem. The teacher found that the natural next step that flowed from this was for students to come up with their own FE problems. Ideas offered included estimating how many heartbeats will a person have in a lifetime.
Flipped learning has also been used to teach financial management.
The ‘flipped learning’ method is very engaging for students and the Core Maths teacher noted that it is somewhat easier than preparing standard lessons. One of the somewhat predictable challenges initially however, was to do with managing those students who had not done any of the preparatory work. If the strategy is to work, there is an obvious need to encourage all students to engage with the process. If only some do and there are no consequences for those that don’t, then the risk is that gradually all students will lose interest in looking at the material provided ahead of the lesson.
The Core Maths teacher at St. Marylebone dealt with this issue by structuring lessons so that students who had done the advance preparation were given an opportunity to contribute and pass on their enthusiasm for a topic. Simultaneously those students who haven’t are encouraged and enabled to be part of the discussion. The Core Maths teacher found that when he next set a task ahead of the lesson, more students looked at the materials and did the preparatory work. He also noted that weaker students do not disengage from the process, they very much want to be part of it. The Core Maths teacher can see the benefits of asking students to come better prepared to lessons in the future to teach elements of Core Maths that have been taught using more traditional methods this year. Students also seem to have responded positively to the strategy as is clear from the comments below.
‘Sometimes I feel like it’s just to give us an introduction and a very, very basic understanding of what we’re doing……. It seemed like a strange way to do it but actually it was quite useful.’
‘… because it’s a new course as well it kind of eased us into it which was good,’
‘When he would email us the videos to watch, I’d be a bit confused about what they were for. But then when we’d come into the lesson I’d be like I’m actually I’m quite glad he gave us the video, it kind of made sense.’
Flipped learning is not always used at St. Marylebone. Sometimes lessons begin with an open-ended task which will perform much the same function as flipped learning. Students might be given a sheet with some minimal information on it. For example in one lesson students were given a graph on which was plotted the number of beds per hospital in London and the number of hospitals in each category e.g. 100+ beds, 500+ beds. Students had to work out what was being represented and why it was being represented in this way. The teacher found that students naturally worked out that area rather than height meant frequency and how many hospitals there might be in London. It engaged real debate not only about the mathematical concepts but also the issue of how different hospitals might have different numbers of beds.
During the year, a method of peer assessment designed to encourage students to engage more with the problem solving aspect of Core Maths was trialled. In particular the aim was to enable students to see that there can be different solutions to any particular problem and to support them in making comparative judgements about which solution might be best.
Students submitted a piece of work for the teacher to mark. The work was initially returned to them unmarked, with a simplified set of solutions and associated marks for each. Working in pairs students had to discuss and mark their partner’s work. Only at the end of this exercise did they then receive their actual marks and a brief set of comments from the Core Maths teacher. The Core Maths teacher found that the task provided a valuable opportunity for students to reflect on their learning, consider what they had done right and explore what someone else had done differently.
End of Year Assessment
The Core Maths teacher at St Marylebone sees assessment as having an important role to play in keeping students motivated. Students are assessed at the end of every topic. In addition, students took an end of year mock exam (deliberately timetabled for after the AS level exams) which was intended to provide recognition of the learning that has taken place this year and to give students a sense of achievement. The hope is that this will also increase the likelihood of students continuing with the course.
In addition, students will receive a predicted grade, reminding them of the value of Core Maths in relation to next year’s university applications. The Core Maths teacher is hopeful that students who might be at risk of getting a C or D grade in other AS level subjects will be motivated to continue with the course if they see that they have a realistic chance of getting a B or an A in Core Maths.
A lot of thought and consideration was given to the structure of the end of year assessment. The final paper consisted of multiple-choice questions, short answer questions and genuinely unstructured questions of the sort that are likely to appear in the eventual examination. Marks were equally divided across all three sections. This blend of closed and open ended questions was intended to given all students an opportunity to demonstrate what they had learned throughout the year while also assessing their problem solving skills. The marks across all three sections will give teachers an insight into whether students have developed the necessary problem-solving skills in the first year of the course.
The initial experience of teaching Core Maths at St. Marylebone has convinced the teachers there of the importance of making sure students have the right experience in the first month of the course. In part this means counteracting any sense that students are only doing Core Maths because they are not smart enough to do A-Level maths. The bigger but related challenge is to make Core Maths feels different to GCSE mathematics as early in the course as possible, whilst also generating a sense of achievement amongst students that they have acquired new skills.
Having lessons that look too much like GCSE at the start of the year could result in a classroom full of disaffected students. Similarly expecting students to tackle open-ended problems from day one is likely a step too far. However, incorporating an element of problem solving that students can master early on will provide a sense of achievement that students will find motivating. Starting off with financial management, or anything that has a ‘real-world’ feeling is recommended. These topics can be new enough to feel interesting and accessible enough so that students feel that they are learning something new.
Getting the structure and content of lessons right early on is viewed by teachers at St. Marylebone as absolutely critical. Ultimately this will impact on how easy or difficult a teacher will find the delivery of the course for the rest of the year. For the teachers at St. Marylebone this will likely mean beginning the course with Fermi estimation when the new cohort starts in September. Fermi estimation requires students to engage with high level thinking in a way that is quite different from GCSE, but can be approached in an accessible way via problems that only require one or two estimates and a relatively straightforward calculation.