Let's Talk About Logs (in the new A Level)
In the new specifications, algebraic fluency alone will not be enough. It will be assumed and be part of the path to an answer that brings meaning to Logarithms.
In the old specifications, Logarithms have been highly algebraic and very computational in nature. Apart from questions on exponential growth and decay (which were a year 13 unit of work), the expectation was that you could manipulate and solve equations and at most sketch and transform some curves.
This week I attended a webinar run by Pietro Tozzi, Maths Specialist for Pearson, called ‘Getting Ready to Teach Pearson’s new AS/A level Mathematics specification from 2017’. This two hour presentation included a brief mention of the theme of modelling in the new A Level. I was particularly intrigued by Mr Tozzi’s comments on the new face of Logarithms.
Bringing modelling to Logarithms
The new specifications have elevated Logarithms from being a purely algebraic tool to a basis for analysing problems in context.
Students will need to be able to:
- Use Log rules to rewrite exponential equations in linear form
- Interpret experimental data and link it back to the model it represents
- Use mathematical reasoning to understand the limitations of a given model
How do the Overarching Themes come into it?
Here’s an example from Paper 1 of Edexcel’s Sample Assessment Material :
The context is that of the number of microbes in a culture over time. Students have to make sure they understand how the equations can be used to answer each part.
Looking through this part by part:
Part (a) : This is the only purely algebraic element. It does still require students to play around with constants to get the linear equation required so still a bit unfamiliarity there.
Prominent theme: Mathematical Argument
Part (b) : N needs to be estimated using the plot provided. The algebra here is trivial but what instigates the use of it is not. The axes of the plot will need attention here.
Prominent Theme : Problem Solving
Part (c) : This will stump some students - the tricky part is knowing how to start, what working to present and providing an explanation that is complete and answers the question.
Prominent Themes : Problem Solving, Mathematical Modelling, and Language
Part (d) : This one had be thinking for a few seconds longer than I would have liked. It goes back to the equation given at the very start and expects students to (with no hints at all) think about the instance when T=1
- Prominent Themes : Problem Solving and Mathematical Modelling
What does this mean for students?
Exam questions with more words to make sense of - which is a good change! Gone are the days of being given equations and asked to find unknowns - much deeper interpretation and problem solving will be expected of A Level students.
Mathematical models and their underlying assumptions will need to be analysed over and above manipulating the equations. On top of this, loopholes in models will need to be found and justified with algebra.