Making Connections between Mathematics and Science

A CPD research project

With the introduction of the new AQA scheme of work in Science within the Science Faculty, it became apparent across the three sciences that students would be expected to use disciplines they had learned in the maths classroom, and apply them to scientific questions.

I was in the unique position that I was working in these two faculties so therefore had first-hand experience of the difficulties the students were experiencing.  Mathematics and science are different disciplines, each with their own purposes, traditions and practices, and this leads to some differences in the way language is used.

In science, we are used to terms such as ‘power’, ‘force’, ‘pressure’ and so on having different meanings in everyday language, compared with the precise definitions used in science. It is important for students to be able to recognise these differences when they move between contexts.

In a similar way, there are differences in the way that some terms are used in mathematics and science. One example is the term ‘line’, which has a more precise meaning in mathematics than the way it is often used in science. In mathematics, a line is, by definition, straight. In science, however, it is quite common to talk about ‘straight lines’ and ‘curved lines’.

Changing typical ways of talking is hard: a good compromise in science might be to continue to refer to ‘straight lines’, but to talk of ‘curves’ rather than ‘curved lines’. Another example is the use of the word ‘histogram’. In mathematics, this refers to a display of a distribution of data in which the bars represent ‘frequency density’ for each class interval; in science, the bars of a histogram normally represent ‘frequency’.

The aim of this action research was to:

• provide an overview of the mathematics relevant to science that may be studied by our students in both KS3 and KS4.

• clarify the meaning of the terms used where there are common misunderstandings or where there are different meanings in different contexts

• indicate as appropriate where there may be student misconceptions and problems in understanding

• identify, where relevant, approaches taken in mathematics teaching that may influence what is done in science lessons.

A common misconception for many students is the difference between mass and weight.  In everyday life, it is quite common to talk about the weight of things measured in grams (g) or kilograms (kg). These are the units shown on familiar items such as kitchen scales or bathroom scales, and it is usual to think of these as devices for weighing things. In science, however, an important distinction is made between the mass of an object and the weight of an object: the kilogram is a unit of mass and weights are measured in newtons (N).

It is not that science is correct and everyday language is wrong but that words are used in different ways in different contexts. Students need to understand these differences. Weight may be the more intuitive concept – heavy objects weigh a lot and are hard to lift up. Weight can be defined scientifically as the gravitational force exerted on an object, and most pupils know that things weigh less on the Moon than on Earth because there is ‘less gravity’. However, if an object is taken from the Earth to the Moon, there is still the same amount of ‘stuff’ or matter in it, even if it weighs less; its mass is a measure of the amount of matter in the object.

It would sound odd and out of place in a shop to talk about ‘finding the mass’ of some apples rather than ‘weighing them’.  However, in the school setting, students using a balance calibrated in grams should always talk of it as measuring mass.  In school maths, it is common to see the term mass used in its scientific sense, but it is possible that pupils may come across books and resources that use the term weight in its everyday sense.  In science, it is essential to understand the distinction between mass and weight, as well as being aware of how the terms may be used outside the science classroom.

In mathematics lessons students do not tend to consider the relationship between the variables represented by each axis of a graph, yet in science lessons this is an essential part of analysing data.  Students need considerable support in their science lessons to be able to interpret graphs to further their scientific understanding. In particular, interpreting the gradient of the graph presents considerable challenge.

Beyond science, it is useful for students to be aware of the implications of different ways that information can be represented. A particular difficulty for many people is understanding the difference between correlation and causation. As teachers most of us are of the philosophy that we need to prepare students for life beyond school, as well as provide them with the essential tools to succeed in learning science.

In our first meeting, our team shared resources. The teachers of Maths at GCSE decided that they would introduce some GCSE science questions into lessons at least once a week to give students the opportunity to become familiar with the fact that these were examples of maths in science. The teachers of GCSE science, would use maths starters in their science lessons.

In addition, a strategy was agreed that we would have a Curriculum Enrichment Day (a day when the normal timetable is suspended and  faculties have a large group of pupils for half or a whole day in order to undertake some extended work or project), that would involve teachers from both faculties working together. The first half of the day meant that teachers would work separately in their own field. Maths teachers revised  possible questions that could come up in the exam. Science teachers did the same for biology, chemistry and physics depending on their particular strength.

The final lesson of the day was a joint team teach with a science teacher paired up with a maths teacher. The focus was on particular topics in maths that cross over into science. The teachers would peer observe one another picking up tips and hints that would help with the teaching of a particular topic. Science teachers delivered maths for science numeracy up to three times after the Curriculum Enrichment Day, therefore each student had gone over a strategy or particular part of the numeracy at least three times.

Within science lessons, science teachers continue to deliver maths that is relevant in science using advice given by maths teachers. Resources have also been developed that are to be used at KS3. The impact of this will mean that the students will not get any great shock when they are expected to use this maths at GCSE as it will have been embedded to be part of the normal lesson where it applies. It is mainly in Physics and Chemistry lessons that these initiatives will have the greatest impact.

At a faculty level, for both science and maths, the incentives are better outcomes for our students, particularly our lower ability students. If mathematical questions are made accessible to students their overall attainment will be raised. At a whole-school level we can demonstrate to students that the skills they learn in maths are transferable. If students see that their maths skills can be applied in science then they should see that they can be applied to other subjects too. This recognition that skills are transferable and can be applied to solving problems in completely new situations should help our students take maths out into everyday life. We want our students to be equipped with the tools to question data throughout their lives.

The resultof these actions meant that teachers in both faculties have a better understanding of how and what was expected in their particular field. This means that we were able to be consistent across the subjects.  Also, many of the science teachers are now able to point out with confidence to the students that maths concepts being taught in a science lesson were not new and have already been taught to them by maths teachers.

Finally, we have been able to work together so that the students are better equipped to tackle the new GCSE courses in maths and science and as a result, we would hope to continue to see a rise in the results in both of these faculties.

Featured image: ‘homework’ by tjevans on Pixabay.  Licensed under Creative Commons CC0