A Common Approach to the Teaching of Mathematics in G.C.S.E. Science

An Action Research Project by Tom Nadin (Science)

Context

The summer of 2018 would see our Y11 students taking the new (1-9), GCSE Science exams for the first time. These GCSE exams would include a significant amount of new content, foremost of which was increased focus on mathematical skills. For the first time in my (and most of my colleagues), teaching career students would be explicitly examined on their Mathematical skills in their Science exams. Although this was a cause of some anxiety to both myself and the Faculty we soon realised that it was also an opportunity to explicitly develop students skills in an area which would benefit them in their later lives as well as helping them to gain marks in their GCSE exams. It would also provide us with an opportunity to work closely with our colleagues in the Maths Faculty.

Introduction

The new GCSEs Science exams in 2018, were to examine students’ mathematical skills for the first time, with 10% of the Biology, 20% of the Chemistry and 30% of the Physics marks to be allocated to this purpose. Although we had always been used to teaching certain mathematical skills in Science, for example drawing and interpreting graphs and calculating averages and percentages, never were such a large percentage of the marks in the GCSE exams at stake. In addition to this, there was the potentially daunting fact that most of us had no experience of teaching a significant amount of new mathematical skills and content. The new GCSE would require us to explicitly cover the following areas of Mathematics.

  • Arithmetic and numerical calculation.
  • Handling data
  • Algebra
  • Graphs
  • Geometry and trigonometry

Some elements of this, for example parts of the algebraic, geometry and trigonometry content seemed particularly unfamiliar and daunting. However, it quickly became obvious that our best course of action would be to work closely with the Mathematics Faculty, both to find out how they taught these topics and also to develop a shared approach to teaching all of the common content, hopefully to the benefit of both Faculties.

Actions

Fortunately, our school has developed an action research based model of professional development which would allow colleagues from both the Science and Maths Faculties to meet and to work together.  The head of Maths, a Maths colleague and a colleague who taught both Maths and Science formed one such “Learning Focus Group”. At first our conversations were somewhat informal, but none the less extremely helpful, for example in ascertaining how and when certain content is taught in Maths. For example it quickly became clear that all of the mathematical content assessed at GCSE in Science was taught at KS3 in Maths. It also became clear that many of these skills, were not only also assessed at KS4 in Maths, but were areas in which students often did not do well. Clearly our work had the potential to be of benefit to both Faculties. We quickly agreed that we were most likely to have an impact on students if we chose to develop a limited number of, hopefully high impact, activities and resources rather than trying to change a huge number of things at once. We could then use these resources and run these activities with year eleven in the first instance. Our main actions are listed below.

1. Year eleven, off-timetable “Curriculum Enrichment Day”

At our school we have a rolling schedule of off timetable days, where Faculties or pairs of Faculties work with a year group for a day to run enrichment activities. Fortunately, once such day was already scheduled for March in which Maths and Science would jointly host year eleven all day. This seemed to be the perfect opportunity to work together to plan and deliver some activities to develop students skills in the shared mathematical content. We decided that we would focus on three key areas. These were, (1) averages and percentages, standard form, (2) significant figures and decimal places and (3) gradients and rates of change. The Science department were more confident in delivering the content related to these first two areas, so although we would plan the sessions together they would be delivered by Science teachers only, whereas the third area (gradients and rates of change), was an area in which we felt less confident so we decided that this would be team taught by both Maths and Science teachers. Possibly the most valuable aspect of this process was the two faculties working together to plan the activities. It was extremely useful to us in Science to see how our Maths colleagues approached teaching in these areas and I think, helpful to the Maths teacher to see examples of how the mathematical skills were used in Science. Not only that, but at the end of the process we had developed what we believed to be high quality resources which we could use with Year 11.

Below is an example of a shared maths and science question on which a part of one of these lessons was based.

Q1.

The speed-time graph for a car’s journey is shown.

TN graph

(a)     Estimate the acceleration at 6 seconds.

You must show your working.

………………………………………………………………………………………………………..

………………………………………………………………………………………………………..

………………………………………………………………………………………………………..

………………………………………………………………………………………………………..

………………………………………………………………………………………………………..

Answer ……………………………………………..m/s2

(3)

 

When evaluating the day, colleagues in both Maths and Science felt that it has been highly successful. When questioned, year 11 students also felt that it had been valuable and that they were now more confident in their maths skills in the areas covered. Interestingly, soon after the Curriculum Enrichment Day, year eleven sat mock exams in Science. It was noticeable that their responses to mathematical questions had improved, particularly in the “simple” questions where they had previously been making errors, for example in calculating averages or with decimal places.

2. Shared starter activities

We also wanted to develop a bank of resources we could use routinely in our lessons. We felt that these would be most impactful if we could use the same resources across both Maths and Science lessons, both reinforcing the content and the point that they were shared skills which applied in exactly the same way in both areas.  We decided that we would develop a range of starter activities to cover all of the shared content and that we would use these with Y11 in the first instance, with a view to rolling out across all year groups in the subsequent years. Fortunately through the schools membership of PiXL, we had access to some resources which we could use and develop to suit our own needs. We took these resources and updated them, using examples from both the Maths and Science curriculum and by adding some additional practice questions. We ended up with 18 starter activities which covered all of the content. We decided that we would incorporate all of these in to Maths and Science lessons. In Science students would experience all 18 starter activities twice. Once in their Chemistry lessons and once in their Physics lessons. We decided not to use their Biology lessons, partly because of the reduced mathematical content in Biology, but mostly because the Biology course has more subject content and we did not feel that there would be sufficient time to add in the maths skills and deliver all of it successfully.

Below is an example of a slide from the Maths starter activities.

TN standard form

3. Shared approach to learning and using equations in Triple Physics

An additional challenge for our students was having to learn off by heart 23 Physics equations which they were expected to be able to recall and use in exam conditions. In addition to this there were a number of equations which they would be provided with in the exams and be expected to apply. Whilst this was potentially an issue for all students, our analysis of the sample papers suggested that it was more likely to apply to those students doing higher tier and Separate Science papers (this turned out to be the case, with most equations given on the foundation tier papers in the final exams). In particular it appeared to be an issue for our Separate Science Physics students. Some had difficulty remembering the equations which was causing them additional anxiety and many were finding it difficult to apply the equations, especially where they were expected to rearrange them. Fortunately, although not entirely surprisingly, the large majority of the Triple Science students were also in the same (top) set for Maths. This provided an opportunity for these students Maths and Physics teachers to work together to address the issue. The science teacher developed strategies to help students remember the equations, this included physical resources for example flash cards and also in class strategies, for example chanting the equations. Both the Maths and Physics teachers provided opportunities to practice using the equations in class. This was particularly impactful when the Maths teacher used the Physics equations as worked examples, using them and also rearranging them. The large majority of students asked said that they found this to be extremely helpful in increasing their confidence in using and ability to remember these equations.

 

4. Consistent and simplified approach to revision

One of the greatest benefits of spending time working in this area, and particularly in collaborating with our colleagues in Maths, is that it really gave us the opportunity to engage with the mathematical content. It became increasingly clear that whilst at first the range of content had seemed rather daunting, in fact most of the time and in most of the exam questions available (and again it proved to be the case in the summer exams), it all boiled down to student understanding a set of core (and often quite simple), mathematical skills. This was particularly the case at foundation tier. In the Science Faculty we had already decided to run a series of revision lesson across the faculty from February onwards. We would re-cover key concepts from the entirety of the course, applying this understanding to and practicing exam questions. The question was, how could we use this as an opportunity to review the key mathematical skills? We decided that it would be helpful if we could condense these on to one slide which we could repeatedly share with students to reinforce these concepts.

Below is a copy of the slide we developed.

TN formulas

We regularly used this slide as both a starter and plenary in the revision lessons, asking student to apply part of it to practice exam questions specific to the Biology, Chemistry and Physics specifications. Below is an example of once such question.

TN exam q

Impacts

It is quite hard to quantify the impact of these actions in terms of improved outcomes. AQA’s exam analysis does not currently offer a breakdown of student responses based solely on Maths skills questions. However, I was able to focus on some specific questions in which students were asked to apply their mathematical skills. Although it was a slightly mixed picture, it did appear that in the majority of cases our students had achieved average marks which were above the AQA average. What is certain is that our student increased in confidence and ability in answering these questions from their November mock exams to their February mock exams, then again to their final exams in the summer.

It is also beyond doubt that collaboration between the two faculties greatly improved the confidence of Science staff in the teaching of the mathematical content. It also improved the understanding of our Maths colleagues of the mathematical expectations of student in Science.

Possibly, most pleasingly, the project created a spirit of collaboration between the Maths and Science Faculties which I am hopeful will continue to be fruitful in the future.

Next steps

From the very start of the project it was a deliberate decision to focus on a limited number of areas and to focus on year eleven with a view to rolling out resources to other year groups in the future. We now need to spread these resources (for example the maths starter activities), across schemes of work for other year groups. It would also be useful to continue our collaboration with Maths and to focus on year groups other than Year 11. For example to pinpoint where these skills are taught in Maths at Key Stage 3 and to coordinate our teaching of these areas in Science lessons.

One area which was particularly effective was the teaching and application of equations in Triple Physics.  We should take the strategies which worked well here, for example the use of the equations in Maths lessons and in-class strategies for learning the equations, for example chanting and apply these to all Physics groups at Key Stage 4.

Featured image: ‘Mathematics’ by geralt on Pixabay.  Licensed under Creative Commons CC0

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