University students’ skills in statistical literacy

Many reports draw attention to the significant and measurable decline over the last decade in students’ mathematical skills even among those with good A-level grades in mathematics. Evidence is provided from several independent sources (e.g. QAA 2002), that even students who are well-qualified do not possess the necessary manipulative skills in algebra and basic calculus. It is argued that numeracy, a critical feature of basic mathematical ability, does not represent an elementary skill. The capability to estimate, having a sense of size and relative importance of numbers, the ability to perform simple mental arithmetic, and specific topics such as percentage and ratio must not be taken for granted at university level or seen as only the concern of the very earliest level of education. The aim of this article is to illustrate the results of the direct assessment of students’ numeracy in a first year, introductory statistics course and the effects of basic numerical and graphical skills on students’ level of mastery of statistical concepts. Such results are part of a research project carried out at the University of Glasgow in the Academic Year 2001/2002. Numeracy at baseline was very variable and students demonstrated a wide range of numerical skills and abilities. Also at the two Follow-up tests students demonstrated very different levels of confidence with statistical concepts. Our analysis showed that there is a top group of students who are very comfortable with a wide variety of statistical concepts. On the other hand, there is also a group of students whose level of knowledge of statistical concepts is much poorer than that of the rest of the class. On average, Follow-up statistical knowledge was not significantly affected by students’ previous mathematical qualification but was significantly related to numeracy at both Baseline tests and Follow-up tests. These results confirm that numeracy is a basic key skill, but it must not be taken for granted at university level. Our analysis outcomes suggest that not to require students to learn formulae or carry out calculations by hand and emphasize application of statistics to real context – which is the education approach chosen by our course – might be necessary but not sufficient to guarantee an acceptable level of understanding of basic statistical concepts. A reappraisal of the course program and a teaching approach that allows more time to be spent on fewer, more basic topics might be a possible remedy in order to insure students’ understanding of fundamental statistical notions. Since the present research project is an observational study, the results presented can do no more than suggest a direction for future work and be considered as a general indication. We cannot claim that there is a cause/effect relationship between students’ poor numerical abilities at university entry and their subsequent difficulty in accumulating statistical knowledge, nor that numeracy is the only variable which determines the level of students’ mastery of statistical concepts. Nevertheless, we can state that there is a link between the two variables which appears to justify the concerns of those who see poor arithmetical ability as a barrier to subsequent learning. Such results can give rise to further work in order to assess whether the outcomes found are related to the specific context of the course analysed or can be extended and considered typical features of service courses in general.