Exploring Threshold concepts in basic Statistics, using the Internet

Meyer and Land (2002) have introduced the notion of a threshold concept in student learning. By definition a threshold is an insight which is initially alien or counter-intuitive, is integrative in that it subsumes some previous knowledge and is transformative in that it leads to a different perspective of or within the discipline. The notion is suggested to be applicable in many disciplines. It is phrased in terms that the threshold nature of a concept is defined mainly by the student experience rather than simply an objective analytical process. Nonetheless past experience may lead teachers of statistics at tertiary level to surmise that threshold concepts in basic statistics will include the notion of patterns of spread or variation, randomness, sampling, the central limit theorem, and linear regression. Introductions to Bayes' theorem and interval estimation are further candidates. Hypothesis testing may present other difficulties. Some methods and results in an exploration of student perspectives will be presented. A class of over 465 students in their second semester course of undergraduate applied statistics (STA220) participated in a survey with a short list of 4 items via internet and PC lab access to a WebCT site supporting their current course. The 4 items addressed their experience in the earlier course (STA100), and were as follows: Explain in your own words the term random sample. The central limit theorem tells us something about the mean of a sample. State in your own words what the theorem implies. List three concepts you found very simple to learn about in STA100. List the three most difficult concepts that you learnt about in STA100. The motive for the exploration is the open question of whether or not two key concepts were clearly and articulately reported by the respondents, and whether there is initial supportive evidence for any particular concepts being experienced as threshold concepts by these students. As teaching effort aimed at plausible threshold concepts may lead to more successful student participation and learning, the diagnostic value of an internet resource that assists in collection of data may be substantial. Text editors may assist in the analysis of typed responses. Internet connections will allow for the quicker transfer of data and for rapid interchange of improved public domain material addressing concepts that appear to have threshold qualities