Learning correlation and regression within authentic sciences

Abstract

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.