Supporting students to develop concepts underlying sampling and to shuttle between contextual and statistical spheres

To stimulate students’ shuttling between contextual and statistical spheres, we based tasks on professional practices. This article focuses on two tasks to support reasoning about sampling by students aged 16–17. The purpose of the tasks was to find out which smaller sample size would have been sufficient for making reliable inferences. The research question addressed is: How can students be supported to develop concepts underlying sampling and to shuttle between contextual and statistical spheres? Design research was carried out to test whether the tasks had the potential to support students’ concepts underlying sampling and to find indications of what teachers should do to use this potential. Analysis of video recordings indicates that the students showed a balanced development of the concepts underlying sampling. They seemed aware of the purposes of the tasks and were able to apply their statistical knowledge but tended to forget to shuttle back

Young children's explorations of average through informal inferential reasoning

This study situates children's early notions of average within an inquiry classroom to investigate the rich inferential reasoning that young children drew on to make sense of the questions: Is there a typical height for a student in year 3? If so, what is it? Based on their deliberations over several lessons, students' ideas about average and typicality evolved as meaning reasonable, contrary to atypical, most common (value or interval), middle, normative, and representative of the population. The case study reported here documents a new direction for the development of children's conceptions of average in a classroom designed to elicit their informal inferential reasoning about data

Vocationalism varies (a lot): a 12-country multivariate analysis of participation in formal adult learning

To encourage adult participation in education and training, contemporary policy makers typically encourage education and training provision to have a strongly vocational (employment-related) character, while also stressing individuals’ responsibility for developing their own learning. Adults’ motivation to learn is not, however, purely vocational—it varies substantially, not only between individuals but between populations. This article uses regression analysis to explain motivation among 12,000 learners in formal education and training in 12 European countries. Although vocational motivation is influenced by individual-level characteristics (such as age, gender, education, occupation), it turns out that the country in which the participation takes place is a far stronger explanatory variable. For example, although men’s vocational motivation to participate is higher than women’s in all countries, Eastern European women have significantly higher levels of vocational motivation than men in Western Europe. This supports other research which suggests that, despite globalization, national institutional structures (social, economic) have continuing policy significance

Learning correlation and regression within authentic sciences

One of the key challenges in mathematics and science education in secondary schools is to establish coherence between these school subjects. According to this PhD thesis statistical modelling can be a way to let students experience the connections between mathematics and science. The purpose of this design-based research was to gain insight into how to support upper-secondary school students’ learning and understanding of correlation and regression models. The main research question was: What are characteristics of a valid and effective teaching and learning strategy to teach students about correlation and regression in such a way that they experience coherence between mathematics and the natural sciences? The design principle was to base the instructional activities on authentic problems in professional practices. We tested the evolving teaching and learning strategy in four studies. After a broad focus on statistical reasoning, the thesis zooms in on several specific concepts required: in particular measurement and sampling are considered important interfaces between mathematics and science. Last, the thesis zooms out and focuses more broadly on the coherence between mathematics, statistics, science and professional practices. In this thesis coherence is defined as the ability of students to make sense of the contexts so that they can apply scientific and mathematical knowledge when solving authentic problems. Based on four studies conclusions are made that the designed strategy to teach students about correlation and regression seems valid and effective. It seems valid because the strategy is in line with prevailing epistemological ideas of the involved school subjects (e.g., mathematics: calculate standard deviation, statistics: produce a formula for the regression line, biology: aerobic respiration, geometry: reasons for subsidence, physics: operation of a thermometer). It seems effective because the involved students learned to solve real-world problems by correctly using correlation and regression models. They also appeared to understand the concepts and process of modelling and were able to combine mathematical and statistical techniques with concepts of the natural sciences when solving real-world problems. The possible impact of this thesis for educational practice is multiple. Its scientific findings are directly applicable to educational practice. The practicality implies an effective intervention: an instructional unit and a research based student test that are realistically usable in the setting of secondary schools. Also, the developed set of design characteristics as criteria could be helpful for designers of similar teaching and learning strategies. The designed module provoked or inspired students to learn about statistics and that stimulated them to use it in other practices. The analysis shows that such a strategy works to teach students statistical techniques, that they can learn to understand the mathematical background, use mathematical tools and that the natural sciences offer powerful contexts to evoke students’ interests to learn and reason about statistics