A very common reason why students fail to do well in physics is they struggle to do the mathematical questions. There are many reasons for this
- Lack of maths skills
- Inability to transfer skills. from maths lessons. Maths tends to deal with numbers, and physics with quantities. In maths, many students who can rearrange something like a=bc and do calculations cannot do the same thing for F=ma. They also fail to see how the formulae can be used to give the units.
- Graphs in physics tell stories, in maths, they tend to be abstract relationships. The gradients calculated from y = mx+c do not represent a quantity as they do in physics. In physics, the gradient of a displacement time graph tells you the rate of change of displacement, which is the velocity. The gradient of a velocity-time graph tells you the acceleration. The area under a velocity-time graph tells you the distance travelled.
- A line of best fit in maths is nearly always a straight line. In physics, it may be a curve.
It seems evident that the physics and maths departments should work together to produce a common approach.
Before we look at Science stories it may be helpful to see how we might change the subject in English and Maths lessons to show commonality.
Literacy stories
- The cat sat on the mat
- The mat is where the cat sat
- Sitting is what the cat is doing on the mat
These three statements all tell the same story but have been rearranged to change the subject
Maths Stories
- 6 = 2 x 6
- 3 = 6/2
- 2 = 6/3
These three statements all tell the same story, the relationship is the same, but has been rearranged to change the subject
Science Stories
- F = ma
- a = F/m
- m = F/a
These three statements all tell the same story, the relationship is the same, but has been rearranged to change the subject
This can be a revelation to some students!
There are 4 main types of stories our students encounter at GCSE
- F = ma – Proportional eg F = ma
- Ratio eg a = F/m
- Accumulation s = vt
- Squared relationship – Ke =½ mv2 squared with with velocity
Proportional Relationships
We mostly teach proportional relationships. Doubling a factor on one side of the = sign doubles the other side. These give rise to straight-line graphs
So for F = ma if the force is doubled, then acceleration is also doubled (if the mass is unchanged)
For V = IR if the resistance is doubled, then the potential difference must also be doubled to keep the same current
Ratios
- a = F/m
- I = V/R
- x = F/k
Ratios usually tell better stories in all of the above the consequence = cause/constraint
acceleration is the consequence of the force, with mass being the constraint
current is the consequence of the potential difference with the resistance being the constraint
If we want a large consequence we need a large cause and a small constraint.
What effect does doubling the cause have on the consequence?
What effect does doubling the constraint have on the consequence
So what story does a = F/m tell us?
Is this a better story than F = ma?
Accumulations
- s = vt
- E = `Pt
- E = VIt
Accumulations (which are also proportional) tell us that over time that the quantity increases.
The longer you move for the further you travel
The longer you leave an appliance on for the more energy is transferred. Note that the more powerful the appliance the more energy is transferred in the same time compared to a less powerful one
Leaving an appliance on for twice as long, doubles the energy transferred (and hence it’s cost to run)
Squared Relationships
- Ke =½ mv2
- P = I2R
Squared relationships tell us that doubling the squared quantity eg the velocity, quadruples the kinetic energy
With the power relationship, we should be able to tell the story of what we want low currents through power lines in order to reduce power losses.
Have your students practice telling the stories, models for all are attached below
Stories of Graphs – Coming Soon!!
English