Consulting in statistics is usually deferred until at least near the end of a first degree, but this article shows how some aspects can be effectively taught to students in upper secondary or early tertiary courses in a way which reinforces their learning of standard basic concepts. We suggest that the existence of a real client adds a degree of realism not available in other ways, and emphasizes to students the importance of blending statistical calculations with meaningful communication.
This article illustrates the use of spreadsheets as a simulation tool for solving a collection of probability problems.
This article shows how teachers can create useful classroom activities to underpin data-handling methods for pupils aged 7-19. We use the data base of responses from the UK CensusAtSchool project that are available for pupils and teachers.
This article compares the national curriculum data-handling specifications of the UK, South Africa, Australia and New Zealand and shows how data from the CensusAtSchool project can be used to enhance the data-handling capabilities of pupils in those countries. These data can also provide enhanced opportunities for the integration of ICT into core curriculum activities. Some ideas to enable teachers of statistics to create classroom teaching material with an international flavour are also provided.
Pupils in England and Wales are increasingly being asked to undertake investigative-type work, be it the new compulsory projects in data handling for GCSE Mathematics (age 14-16) (see Browne 2002) or the Key Skills topic application of number. This article shows how teachers can generate realistic project scenarios using real data and produce indicative model solutions from the same data. The projects range from simple presentational problems for data,through hypothesis testing to complex modelling scenarios.
This article uses a simple counter-intuitive example to point out a common misinterpretation of correlation.
This article discusses three statistical laboratories - on descriptive statistics, statistical inference and regression - for introductory statistics courses. They are presented in Minitab, SPSS (Statistical Pack-age for the Social Sciences) and Excel, three pack-ages widely used in statistics education, and are available from the Web.
In this paper I propose some basic elements of a model of knowledge structures used in comprehending and generating graphs, with emphasis on the concept of covariation and on the analogical character of graphical representation. I then use this competence model to attempt to organize and interpret some of the existing literature on misconceptions in graphing. Two types of common misconceptions, treating the graph as a picture, and slope-height confusions, will be discussed, as will the earliest recorded use of graphs in the work of Oresme in 1361. One of the motives for studying concepts used in graphing is that it may help us understand the nature of the more general concepts of variable and function and the role that analogue spatial models play in representation.
The influences on adult quantitative literacy were studied using information from the National Adult Literacy Survey, 1,800,000 individuals between 25 and 35 years of age and not in school. The major influences on quantitative literacy were educational background (t = 123-; df = 1; p<.0001), daily television usage (t = 1538; df = 1; p<.0001), and disability (t = 713; df = a; p<.0001). Education impacted television usage (t = 691; df = 1; p<.0001) and personal yearly income (t = 991; df = 1; p<.0001). Ethnicity affected income levels (t = 898; df = 1; p<.0001), which in turn influenced television viewing (t = 1514; df = 1; p<.0001). The results indicated that education seemed the key to increasing levels of quantitative literacy. Library usage, parents' education, and gender did not exhibit any relationship with quantitative literacy.
The Birthday Problem is "How many people must be in a room before the probability that some share a birthday (ignoring the year and ignoring leap days) becomes at least 50%?" Multiple approaches to the problem are explored and compared, addressing probability concepts, problem solving, modelling assumptions, approximations (supported by Taylor series), recursion, (Excel) spreadsheets, simulation, and student preconceptions. The traditional product representation that yields the exact answer is not only tedious with a regular calculator, but did not provide insight on why the answer (23) is so much smaller than most students' predictions (typically, half of 365). A more intuitive (but slightly inexact) approach synthesized by the author focuses on the total number of "opportunities" for matched birthdays (e.g., the new "opportunities" for a match added by the kth person who enters are those that the kth person has with each of the k-1 people already there). The author followed the model of Shaughnessy (1977) in having students give predictions in advance of the exploration and these written data (as well as interview data) collected from students indicated representative multiplier or representative quotient effects, consistent with the literature on misconceptions and heuristics. Data collected from students after the traditional and "opportunities" explorations indicate that a majority of students preferred the opportunities approach, favoring the large gain in intuition over the slight loss in precision.