Post-16 maths for employability

The Sutton Trust have just published a report: “The Employment Equation: why our young people need more maths for today’s jobs” by Professor Jeremy Hodgen and Dr Rachel Marks of King’s College, London which demonstrates the need for young people to continue to study maths after GCSE. Of particular interest are two of their recommendations:

5. In general, students with at least a grade C at GCSE have already covered the critical mathematical techniques and concepts, but they do need to understand what they already know better. Any specialist mathematical techniques can be learnt in the workplace, provided students understand and can apply GCSE mathematics. The curriculum should also include more “simple maths in complex settings”, by providing students with problem-solving opportunities involving “messy” contexts that do not have straightforward solutions. Students should have many more opportunities to collaborate and discuss, working together to understand, interpret and communicate the mathematics they are involved in.

6. To allow students to more easily transfer their mathematical skills into the workplace they should use computers extensively, particularly spreadsheets and computer-generated graphs, to apply and learn mathematics. Competence in these skills matters in the workplace.

“Simple maths” is defined as:

…[that]  almost wholly within the GCSE curriculum, covering the core areas of:

  • Number, particularly mental maths, approximation, estimation and proportional reasoning
  • Using and interpreting calculators and spreadsheets
  • Statistics and probability, including data collection, interpretation and representation
  • Algebra, particularly graphical representation and diagrams
  •  Geometry and measures, including 2D and 3D representation

The report also notes the increased use of technology, particularly spreadsheets and automated approaches, which has led to a “black-box” mentality where employees have little understanding of what the software is doing. Therefore a combination of developing understanding whilst using software tools extensively in real-world problems  is recommended.

To what extent would this vision of post-16 maths help students entering bioscience degrees? It would certainly be better than the current situation where the majority of bioscience undergraduates  don’t take any maths during their A level studies and thus become rusty on the maths that they had done at GCSE.

However there are some additional  topics that are really essential for bioscientists namely scientific notation, exponentials and logarithms. I think you could argue that basic calculus in the sense of understanding rates of change could also be included. Many mathematics educators argue that bioscientists should at least do AS maths as they would then cover logarithms and basic calculus but then bioscientists argue that it could become difficult to recruit sufficient students and after all it’s really not that important. Or is it?

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More equations = fewer citations: part two

This post was triggered by reading Michael McCarthy’s blog post on “Statistical Inference in Ecology”. In it he asks about writing a chapter on statistical inference for an ecology textbook and is trying to tackle that perennial problem: how much maths can you include and still make it readable and understandable?

In section 2 of the chapter “A short overview of some probability and sampling theory” I thought the issue boiled down to the question:

When writing for a general bioscience readership should you use mathematical symbols such as these?integral

First there is the argument that equations put biologists off because of maths anxiety. There may be some truth in that but I think there is another argument. A sizeable proportion of biologists in the UK have never studied calculus so have no idea what an integral sign means. In the UK I’d estimate this proportion to be about two-thirds based on the maths qualifications bioscience students start their degree with and the mathematical content of a bioscience degree (ref). Obviously this varies widely so these figures are estimates but nevertheless a good starting point.

If a biologist hasn’t studied calculus then including an equation such as this is the equivalent of putting a quote in another language. Just the other day I was reading a novel which had lots of quotes of poems in French. I stopped reading because I wasn’t able to translate the French and the author didn’t translate it into English. And it’s a horrible feeling, leaving me pretty fed up and the book  in the recycling bin. It didn’t motivate me to go and learn French I’m afraid!

How would you translate this equation? A graph and narrative explanation is a integral graphpossibility. You could include the equation but provide a visual and narrative explanation alongside it so that the reader gets the message that the integral sign just means getting the area and the x and x+dx at the bottom and top of the integral sign just show you the two boundary points.

In my experience using multiple modes, for example narrative and visual, works best – does anyone have other ideas?

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More Statistics Resources: StatTutor

The Statstutor  website contains lots of stats support materials free of charge. There are some leaflets explaining statstutor and these are available free of charge to those in UK Higher Education.  Find out more…..

There is also a short  survey about Statstutor –  it contains only 10 questions and should take no more than three minutes. Click here to take the statstutor survey

As far as I can see there is little in the way of biological context at the moment though lecturers are encouraged to submit resources to share. More information about this is available on the communities page.

There are a range of types of resource:

Case Study Videos – watch and listen as a tutor helps students handle projects involving real data;

Video Tutorials – watch and listen to a tutor working through important topics in statistics;

Teach Yourself – these paper based resources provide in-depth treatment of important topics, with theory and worked examples (sometimes written to accompany the video tutorials above);

Tests and Quizzes – on specific topics to enable you to gauge your competency and decide whether further work is required;

Facts & Formulae Leaflets – electronic versions of the very popular leaflets distributed by the Higher Education Academy MSOR Subject Centre;

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Statistics resources: crossover between school and university?

By Dr Jenny Koenig posted 17th June 2013.

Many people are surprised when they discover that the statistics taught in university bioscience degrees overlaps significantly with that taught in schools.  It makes sense though because not all students will have done any statistics at school and if they have done some, for example in biology A level, they are unlikely to have a coherent “big picture” of what statistics is and how it fits together. Thus universities need to start from the beginning to ensure all students get the right grounding before they can move on to more complex ideas.

It follows that many of the resources produced for schools might be useful in HE and vice versa. The Wellcome Trust have published the latest edition of their “Big Picture” magazine, a free post-16 resource that explores issues around biology and medicine. The magazine itself contains many key ideas in basic statistics and links to real world examples and some careers aspects all of which are  genuinely useful for post-16 including HE.

There are also links to other resources well worth exploring. I particularly liked the cartoon on conditional risk and being a trekkie-fan I did a double-take at the StatTrek website which did look quite good – perhaps as a reference for students to follow up ideas after lectures. There are some biological examples of the use of a number of statistical tests (Chi-squared, Mann-Whitney U, T-test, Wilcoxon) and links to some large datasets. Again these could be useful links for students to revise and reinforce material introduced in lectures or large classes.

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Infographics – using gapminder in teaching

Posted by Dr Jenny Koenig, 10th June 2013.

You may have seen some Ted talks by Hans Rosling where he uses some

fascinating graphics to illustrate data. I’ve included links to a few at the end of this post and thoroughly recommend them  even though the latter two are getting a little old now. But we warned, you could find that time slips away…

The Gapminder software that Hans Rosling uses is available for teaching along with many datasets. There are also plenty of lesson plans. The datasets range from biomedical eg disease prevalence, mortality rates to environmental eg forest coverage, number affected by drought and can be downloaded as Excel spreadsheet files or visualised using gapminder. There are also lots of videos including an hour long “The Joys of Stats.”

I would be really interested to know if anyone uses Gapminder in teaching statistics. It strikes me as a good “hook” to get students interested. Do feel free to add comments below.

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Accessibility for Visually-Impaired Students in Learning Maths

Posted by Jenny Koenig 3rd June 2013

Emma Cliffe of the University of Bath brought to my attention, via the AccessMSOR Working Group email list ACCESSMSORWG@JISCMAIL.AC.UK), a number of resources relating to providing accessible online learning materials in maths and science subjects. I’ve picked out some ideas I thought were interesting and hope that this will encourage you to pursue the links further.

(1) The Accessibility in Maths wiki pages are THE place to go to for anything to do with accessibility and maths, there are links to lots of organisations and resources, well worth book-marking.

(2) From the RNIB Centre for Accessible Information, Cryer, H. (2013). Teaching STEM subjects to blind and partially sighted students: Literature review and resources.

This is a literature review covering all of the sciences, technology, engineering and maths. There is an interesting discussion about producing tactile diagram resources which can be really helpful in developing understanding.  For example the significance of size and shape or illustrating the different forms of waves and how they interact. There are, however, benefits and pitfalls to tactile diagrams and these are described with further references. Clearly these tactile approaches could be very useful in conveying some of the mathematical ideas of biology and the article also covers ways of getting across graphical ideas. There is a review of the technology involved in getting maths online – particularly the use of MathML and LaTeX, and a long list of resources including software and good practice guides.

(3) Accessible Content Creation in Mathematics

Chris Hughes and Scot Leavitt, April 3, 2013, Portland Community College, USA

 The main message here was that each visually-impaired learner will have different preferences for ways of learning and these could include a combination of the following:

  1. a refreshable Braille device
  2. a screen-reader such as JAWS reading web-pages where the maths is written in MathML.
  3. a paper copy with enlarged font.

There are a number of common formats which are really problematic for visually-impaired learners and these are:

  1. pdf files with Mathematical content
  2. Flash applets
  3. Java applets
  4. Powerpoint files

It was interesting to note that, at the time of writing, some quite widely-used formative assessment packages such as MyMathLab are not completely accessible for visually-impaired learners.

 Use MathType not Equation Editor: I was surprised to note that if you create a Word document with the equations written in MathType, the plug-in from Design Science, they are able to be converted into screen-reader suitable files. However if you create the equations in Word’s own equation editor then they are NOT able to be converted to a useful format.

Both the report and the accompanying video are available – the report is really well referenced and the video gives a good insight into how the project unfolded, the interaction with the blind learners is particularly informative.

(4) 5th AccessMSORWG workshop: Mathematical Study Without Pen and Paper: Experiences, Impacts and Options. 

20th March 2013 funded by the Higher Education Academy. Slides, notes on the feedback from group discussions and a short report on the day



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