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marketing people to use. But this description masks some crucial assumptions that are open to question:

¾ that the two “sides” share a sufficiently effective language to be able to communicate with each other;

¾ that the results (which are based on statistics) can be interpreted without some degree of shared knowledge of problem context and analytical technique.

Indeed, we heard that between marketing and data analysis there is a growing “grey area” in which marketing needs have to be expressed as analytical questions, and the results of statistical analysis have to be interpreted to make business decisions. The problem is that there are not enough marketing officers with a well-developed facility for mathematical thinking, and at the same time there are not enough analysts with a well- developed knowledge of marketing and the “real world”, and an ability to communicate in a non-technical way about the analysis that they do. The company has recognised the need for marketing groups to have a generally better level of statistical understanding, which we would call TmL. The data mining manager described to us his attempts to train marketing officers to interrogate the customer database for themselves:

We found the biggest restriction is... understanding analysis as a process, so if you gave them the manual and a database query, for example ‘how many people live with a Manchester postcode and have a charge card and spend over £500 per month’, they could follow the manual to get an answer – by clicking through the different options. But what is at issue here is not the nuts and bolts of doing database analyses, but the big picture of “analysis as a process”.

How might the TmL that underpin analytical thinking be developed by people such as these marketing officers? Our working assumption is that, in the workplace, training needs to happen in the context of the work with the aim to develop a situated appreciation of the analytical models in use, as expressed through the IT systems. Part of this training might be to make visible and then discuss how expert analysts use the tools available to support them in “doing mathematics”. For example, we noted how the analysts “knew” when ratio and relative change were core ideas, and simply divided one column of a spreadsheet by another “to see what happens”. This strategy helped them to get a feel for the key features and invariants underlying the models they were using. The point here is not only to do with the classical problem of “transfer,” the complex ways in which formal learning should transfer to workplace activity It is also a recognition that experience helps people to develop very rich and generally tacit understandings and ways to cope with the complexities of their workplace situations, and these understandings are partly mathematical. Training should help people to construct new understandings on the basis of this expertise. Mathematical practices at work are inseparably tied up with “everyday” activity at work, the tools used and how they are used to solve business problems and communicate relevant mathematical ideas. It is this expertise that should form the basis for further development of “functional” mathematics.


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