World of work How is mathematics used in the world of work? Tool WA-1: Mathematics in the world of work © 2016 mascil project (G.A. no. 320693). Lead partner University of Nottingham; CC-NC-SA 4.0 license granted. The project mascil has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013).

Overview Aims: To introduce examples of the real-life use of mathematics in the workplace; To compare differences between workplace and school mathematics. We will: Consider the examples; Discuss differences in the way mathematics is used in the workplace compared to a school classroom. The aim of this tool is to introduce teachers to examples of the use of mathematics in the world of work so they can discuss how workplace mathematics differs from school mathematics. The tool shows just a few instances of how mathematics looks in a few specific workplaces. These examples do not cover the full range since, as research demonstrates, mathematics in workplaces is often adapted or transformed and becomes bespoke to the specific workplace with its required outcomes.

Real-life use of mathematics in work How is mathematics used in work places? How is this use of mathematics different from school mathematics? Briefly discuss with the teachers that mathematics, as it is used in the workplace, can look very different to the way it appears in school. Often the mathematical processes are hidden in work routines and not clearly visible, even to those carrying out the work. It seems that what is taught and learned in school mathematics is separate from workplace mathematics and has little utility or purpose other than in classrooms to enable students to gain qualifications.

Examples Discuss your personal responses Ask the teachers to work in pairs, for about half an hour, to read the accounts of the use of mathematics in different workplaces from the Handout: Mathematics in the world of work. Ask them to discuss how they see the use of mathematics in workplaces and identify differences between the way it us taught and used in school compared to the use of mathematics in the workplace. They should make notes of their ideas. (Note that the first account is quite substantial but the others are much briefer. Omit the first description if you are short of time.) Discuss your personal responses Make a note of your main points

Discussion Share your responses as a group. Consider the following areas where differences may be identified: Impact of technology Integration of mathematics into larger activities Mathematics as a ‘tool for the job’ Mathematics becoming ‘fused’ into workplace routines Differences in conventions and notation. Bring the group back together and ask them to share their responses. They may come up with a range of suggestions – it will be interesting to compare their thinking with what we know from research in this field. Williams and Wake (2007), researchers in England, have identified the following important differences that you can use to stimulate further discussion. In workplaces: use of new technology requires the use of mathematical thinking in the workplace, but workers also continue to make use of low technology; typically mathematics only makes sense when considered as integrated parts of larger, purposeful, sustained activities, as opposed to the short fragmented mathematical tasks one often sees in classrooms; workers generally see mathematics as a ‘tool for the job’; expert use of mathematics often becomes ‘fused’ with the reality of the workplace – this means that the worker does not see or think about the mathematics but about aspects of the work (to outsiders without in-depth knowledge of the workplace this means that understanding the mathematics as a model of the workplace situation is difficult); there are many differences in conventions and notation when working mathematically.

Finishing off There are many research reports that provide further insight into the use of mathematics in the workplace. Before next time read at least one of these and be ready to discuss the main points that affect what you teach and how you teach it. There are many accounts within research papers of the use of mathematics in workplace situations. Those quoted in the handout can be found in the report below by Wake and Williams. Some further research accounts are also listed below. In the report for the Sutton Trust by Hodgen and Marks (2014) it is suggested that “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.” Before next time each of the group should be encouraged to read at least one of these reports (the references are given below) and be ready to discuss the main points that affect what mathematics they teach and how they teach it so that will be useful in the workplace.   References Bakker, A. & FitzSimons, G. (eds) (2014). Special Issue: Educational Studies in Mathematics, 86(2), 151-305. FitzSimons, G. E. (2013). Doing Mathematics in the Workplace: A Brief Review of Selected Literature. Adults Learning Mathematics, 8(1), 7-19. Hodgen, J., & Marks, R. (2013). The Employment Equation: Why Our Young People Need More Maths for Today's Jobs. Sutton Trust. Williams, J., & Wake, G. (2007). Black boxes in workplace mathematics. Educational Studies in Mathematics, 64(3), 317-343.