Students often struggle to solve problems in science that require them to do mathematical calculations, rearrange equations or draw/analyse graphs. Here are 10 ideas to improve the transferability of skills, ideally across the whole curriculum, not just in science
(1) Collaborate with your maths department on the order of skills taught – The passage below is taken from the
The initial stimulus for collaborative work between the two faculties came from science teachers who identified that there were numeracy problems preventing students making rapid progress in science. Skills that should be transferable were not being applied by students outside of maths lessons. These were principally related to: changing the subject in equations; scaling graphs; drawing lines of best fit; and identifying types of graphs e.g. scatter or line? The problems were confounded by a mismatch in the order in which certain maths skills were taught in KS3 and applied in science. These timing issues meant that in science we were expecting high level skills that had not yet been fully covered in maths.
Another issue is that many students are taught in different maths sets to their science ones and so it cannot be assumed that they all have the same maths skills or have been taught techniques or language.
Data taken from science practical lessons could be processed in maths lessons so that the students can develop transferable skills. A joint maths and science day for students as outlined in teaching approaches has been shown to be beneficial to all. Looking at graphical analysis or molar calculations in a common way in maths and science helps everyone.
(2) Use common language and teach the terms explicitly.
To Maths teachers a line graph (and line of best fit) is a straight line, to science teachers, it could be curved. Students can often try to draw straight lines through what clearly looks like a curved set of points when asked to draw a line graph, because they are using the maths definition.
Range is a numerical value in maths, but can have multiple meanings in science – the range of a variable, graph or measuring instrument.
The term ‘variable’ is used infrequently in mathematics, but very commonly used in science, with students being expected to identify different categories of variable by age 11. In these categories is the term discontinuous used?
‘range’ is a numerical value in mathematics, but a quantity in science, linked to a specific variable.
(3) Try to standardise the approach to answering questions
A motorbike travels 20 miles in 10 minutes, how far does it go in an hour?
How did you work this out?
- By proportional reasoning? 60 minutes is 6 times as long as 10. So the distance is 6 times as long – 120 miles (it’s a fast bike)
- By working out how far it travels in one minute (20/10 = 2 miles) then multiplying by how many minutes
- By explicitly using the formula distance = speed x time
- By using triangles
Setting one of these problems and asking students how they worked it out is very interesting- then find out how the maths department would get them to answer it.
(4) Talk about the concepts in words before you introduce the formula. Equations are stories about relationships.
So for Newton’s second law you could talk about wanting to move a car that won’t start. It’s fairly intuitive that the harder you push it (the bigger the Force you apply) the bigger the change in motion (acceleration) of a car. But what would happen to the motion of the car when you push it as hard as you can, if it was very light? Or very heavy? From this thought experiment we can deduce that the change of motion is greater the bigger the force is, but also smaller the larger the mass so acceleration = Force/mass or a= F/m
Almost all of you will have learnt this as F=ma, is a=F/m more appropriate? Read on ..
(5) Consider the order you show students formulae
Does it matter if you show F=ma, a=F/m or m= F/a
or V=IR , I=V/R or R=V/I ?
remembering that equations tell stories, what story makes the most sense?
F = ma – Speeding up or slowing down a mass requires a force. The larger the force the greater the acceleration or deceleration for a given mass. Having a larger mass would require a larger force to maintain the same acceleration
or
a = F/m – The acceleration depends on the Force and the mass. The greater the force, the greater the acceleration. The greater the mass, the smaller the acceleration
or
a=F/m is generally more useful than the more usual F=ma as we are normally working out the acceleration having chosen the mass and the force. The story also makes more sense to me.
Similarly, I would introduce I=V/R rather than V=IR
(6) Rearranging the equation vs Changing the subject
Usually, students are told to rearrange the equations. For those with good maths skills that is fine. However, to many students, it is a mysterious process.
Consider changing the subject instead (With thanks to Helen Reynolds for this)
- The cat is sitting on the mat
- The mat is the thing the cat was sitting on
- Sitting is what the cat was doing on the mat
Here we have just changed the subject. All three statements say the same thing with the equals sign being represented by is. To some students, this is a revelation
Similarly using numbers can demystify algebra. So
6 = 2×3 or 3=6/2 or 2=6/3 are also equivalent statements and far more intuitive than using letters
(7) Use maths type starters in your lessons.
- Change the subject so If a = F/m what does F = ?
- I = V/R What would happen to the current if the potential difference got bigger/ Resistance got smaller etc.
- What would the gradient of a distance- time give you?
- An electric heater has a power of 2kW. How much energy does it transfer in one minute?
- What happens to the kinetic energy of a bird when it’s velocity doubles (and its mass halves?)
- Explain the story of this graph – Do we need more pirates?
(8) Triangles – A useful aid or the work of the devil?
Triangles are undoubtedly helpful for students who struggle to change the subject of equations. They shouldnt be used instead of trying to do the algebra. Triangles can be used to tell the stories and used as another alternative approach taught in combination with the other methods.
Theo Mr Neil Artkin
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