Tag Archives: mathematics

What do school maths qualifications mean for university study?

“What’s this “ln” button on my calculator mean?”

The stories you hear from colleagues bemoaning the mathematical literacy, or lack of, amongst undergraduates. And graduate students too, actually.

This begs the question which I will try to answer with this post:

“What can students with a particular grade at GCSE Maths actually be expected to be able to do and does this have an impact on studying bioscience at University?”

First a little background. All students in state schools in England (Wales, Scotland and Northern Ireland have different systems) will follow the National Curriculum and GCSE Maths assesses students at the end of their compulsory education (age 16).

GCSE Maths can either be studied at Foundation Tier (which allows grades to be awarded between C through to G)  and Higher Tier (which allows grades to be awarded between A* through to C). If a student has studied Foundation Tier they will not have covered as much maths as those who’ve studied Higher Tier.

The report “Understanding the UK Mathematics Curriculum Pre-Higher Education” by Stephen Lee, Richard Browne, Stella Dudzic and Charlie Stripp of the MEI (launched by the Engineering Subject Centre and available on their website as well as at http://www.bioscience.heacademy.ac.uk/ftp/resources/pre-university-maths-guide.pdf ) has a rather sobering list of the knowledge and skills which are NOT covered by Foundation Tier students.

  • negative and fractional powers,
  • scientific notation,
  • solution of linear simultaneous equations,
  • reverse percentage calculations
  • plotting graphs of exponential functions
  • working with quantities which vary in direct or inverse proportion
  •  trigonometry,
  • cumulative frequency diagrams and histograms,
  • probability calculations

This list drew a sharp intake of breath and a communal sigh at the meeting “Mathematical Challenges for Biologists” organised by the Centre for Bioscience, The Higher Education Academy and held at the University of Reading Nov 2010. Many of the participants, mainly those teaching maths at first year university bioscience courses, recognised this description and had their suspicions confirmed.

It’s also worth noting, as Lee et al point out, that students with a B or C at GCSE Maths who have studied the Higher Tier will have an incomplete understanding of many of these topics.

What this means in effect is that someone with a B at GCSE maths may have limited ability to manipulate numbers commonly used in biology such as measurements made in microscopy in micrometres or concentrations in nanograms per litre. They are also unlikely to be able to recognise an equation for a straight line and may not be able to rearrange it. If they begin study of statistics at University level, they are unlikely to have a grasp of the basics of probability. This is fundamental stuff.

Logarithms and exponential decay are just not covered at all at GCSE level and this has important implications for the study of biochemistry, pharmacology and physiology where logarithmic scales are commonly used.

Another aspect worth noting is that much of the assessment of this knowledge is fairly formulaic with questions being relatively short and staged, leading the student almost by the hand. Changes to GCSE’s in Mathematics coming up in 2012 may help with this as there will be more emphasis on problem solving and hopefully some more challenging, longer questions.

So what does this mean for students studying bioscience at University? It means that either Universities require  AS Maths for entry to Bioscience degrees OR for students with GCSE Maths there must be some provision for learning these essential tools and concepts. They must know about logarithms and be able to use them. They must be able to recognise equations for straight lines, hyperbolae, exponential growth and decay and they must be able to rearrange these equations to get out the information they’re looking for.  They must be able to manipulate very small numbers in scientific notation and calculate concentrations and dilutions. Without this level of mathematical skill, I believe, students should not graduate as scientists.

Why is it important? Why do mathematics education within life sciences courses?

The developments in technology to increase the throughput of experiments in the biosciences has led to an explosion in data generation and a pressing need to find ways to make sense of that data. The advent of “Systems Biology” and “Computational Biology” has shone a spotlight on mathematical approaches and revealed some weakening cracks in the ability of biologists to understand the mathematics and the ability of those with mathematical skill and insight to communicate their ideas and results.

 The importance of mathematical approaches is expressed very elegantly in Joel Cohen’s essay title:

 Mathematics Is Biology’s Next Microscope, Only Better; Biology Is Mathematics’ Next Physics, Only Better.

 Joel E. Cohen, PLoS Biol. 2004 December; 2(12): e439

 The analogy is very powerful as Cohen comments:

 The discovery of the microscope in the late 17th century caused a revolution in  biology by revealing otherwise invisible and previously unsuspected worlds.

 And it is backed up with an array of fascinating examples where mathematics has had an impact upon biology from William Harvey’s analysis of blood circulation in 1628, through the Logistic equation for limited population growth (Verhulst in 1838), Pearson’s correlation coefficient, Markov’s chains, Fisher’s ANOVA, to the effect of dogs on the transmission of Chagas’ disease in Argentina (2001).

 Cohen’s argument is that those with some experience of, and insight into, mathematics can see things differently and with greater clarity.

 Charles Darwin was right when he wrote that people with an understanding “of the great leading principles of mathematics… seem to have an extra sense” (F. Darwin 1905).

 It is these principles of mathematics, rather than just the algebra-crunching and number-crunching that matter. It is like putting on a special pair of glasses to watch a 3D movie:

Those who understand the calculus, ordinary and partial differential equations, and probability theory have a way of seeing and understanding the world, including the biological world, that is unavailable to those who do not.

 This is a compelling argument for ensuring that all biological sciences students undertake some study of mathematics (not only statistics) within a biological context. The main advances in mathematics education within bioscience degree programmes, in the UK at least, has been the realisation of the importance of context. The mathematics needs to be presented within the biological context and assessed to sufficient depth. Relying upon school mathematics, even to A level standard, is usually not enough, but more of that another time.

 Cohen’s argument rests the responsibility of understanding the mathematical approaches largely upon the biologist and bioscience education and this is where I beg to differ. How many times have I attended a mathematical biology seminar (as a biologist not a mathematician) and found people speaking in another language. It seems once a mathematician learns the mathematical language they forget how to speak in English. I suggest that we need to spend considerable effort thinking about how to communicate the output of mathematical biology / systems biology / computational biology. Perhaps we need to work from both ends of the spectrum.