Versatile thinking and the learning of statistical concepts

Statistics was for a long time a domain where calculation dominated to the detriment of statistical thinking. In recent years, the latter concept has come much more to the fore, and is now being both researched and promoted in school and tertiary courses. In this study, we consider the application of the concept of flexible or versatile thinking to statistical inference, as a key attribute of statistical thinking. Whilst this versatility comprises process/object, visuo/analytic and representational versatility, we concentrate here on the last aspect, which includes the ability to work within a representation system (or semiotic register) and to transform seamlessly between the systems for given concepts, as well as to engage in procedural and conceptual interactions with specific representations. To exemplify the theoretical ideas, we consider two examples based on the concepts of relative comparison and sampling variability as cases where representational versatility may be crucial to understanding. We outline the qualitative thinking involved in representations of relative density and sample and population distributions, including mathematical models and their precursor, diagrammatic forms

Are Africans, Europeans, and Asians Different “Races”? A Guided-Inquiry Lab for Introducing Undergraduate Students to Genetic Diversity and Preparing Them to Study Natural Selection

Many students do not recognize that individual organisms within populations vary, and this may make it difficult for them to recognize the essential role variation plays in natural selection. Also, many students have weak scientific reasoning skills, and this makes it difficult for them to recognize misconceptions they might have. This paper describes a 2-h laboratory for college students that introduces them to genetic diversity and gives them practice using hypothetico-deductive reasoning. In brief, the lab presents students with DNA sequences from Africans, Europeans, and Asians, and asks students to determine whether people from each continent qualify as distinct “races.” Comparison of the DNA sequences shows that people on each continent are not more similar to one another than to people on other continents, and therefore do not qualify as distinct races. Ninety-four percent of our students reported that the laboratory was interesting, and 79% reported that it was a valuable learning experience. We developed and used a survey to measure the extent to which students recognized variation and its significance within populations and showed that the lab increased student awareness of variation. We also showed that the lab improved the ability of students to construct hypothetico-deductive arguments