Contemporary theorists suggest that in New Times, new forms of knowledge will become more dominant. This is also applicable to mathematics where, in a data-drenched society/world, new ways of thinking mathematically will emerge. Robyn Zevenbergen’s work in theorising new numeracies has suggested that statistical numeracy is a form of mathematics and numeracy that will have increasing importance in New Times. This means that the emphasis in teaching the data sub-strand will shift from constructing graphs to include collecting data, organising data and most importantly being able to interpret data. The work in critical numeracy is particularly relevant here where educators must be able to instill in young people the capacity to look beyond the obvious and look beyond the information to see how that information is being presented to represent particular viewpoints.
Chance is commonly known as probability and is the measure of the likelihood of particular events occurring. Students often have misconceptions about probability or the chance of events happening.
Today’s graduates of school need to exit with the skills and knowledge of how to critically interpret data - whether in tables or graphs. In today’s world, people are bombarded with information. A key life skill is being able to critically appraise information being presented and be able to make sense of the information. The emphasis in the teaching of data and graphs moves somewhat away from constructing graphs. Rather there is now a need to not only construct but to interpret data forms and content.
Bar graph:
Pie graph:
Pie graphs (or circle graphs) are used to represent data as a proportion of a whole set. It is one of the more difficult graphs to construct as considerable pre-requisite knowledge is needed – fractions, angles, percentages – so it is often left until late in the primary years curriculum. However, with the use of technology, particularly spreadsheets, the tedium of calculating can be removed so that mathematical thinking is more the focus when using spreadsheets to construct pie graphs. However, in order to be able to evaluate the correctness of the representation, students still need to understand the underlying principles of construction of pie graphs.
Two methods can be used to teach the construction of pie graphs. The first is a very practical and hands-on approach and gives the students a ‘sense’ of how data are represented. The second is the traditional method where considerable calculations are used. When teaching pie graphs, an important teaching tip is to ensure that the data being used are ones that the students can use easily in terms of calculations.
Stem & Leaf:
Stem and leaf plots are a relatively new addition to the data strand. They extend the column graph concept so that the data can also be seen. The column graph is a useful tool but does not show any indication within a given set of grouped data. For example, if the scores on a test or football match are in the high end or low end of a data set, this is unknown when using a traditional column format. The stem and leaf format allows for the variability within a data set to be observed. Stem and leaf plots can also be used for single or double sets of data. The double sets can be useful on comparing two sets of data.
