Variability in student reasoning about radioactive decay as a stochastic process

For several years, we have been investigating student conceptual understanding of radioactivity, particularly regarding half-life. Although it is considered to be random when an individual nucleus undergoes the sudden process of radioactive decay, the duration of time within which half of a radioactive sample decays (i.e., the half-life) is a predictable quantity. Many students generally struggle with the idea that random behavior of individual agents can give rise to predictable patterns in the collective; specific to radioactivity, many students have said both in interviews and surveys that, if you are looking at an individual nucleus, half of the nucleus will have decayed after one half-life. Our findings have indicated, however, that this idea (of individual nuclei decaying in a predictably continuous manner) is often not a robust and intact mental structure; rather, in other contexts, the same students correctly discuss radioactive decay as being instantaneous and unpredictable. We developed a survey to measure this context dependency and administered it both to high school students in Austria and to college students at the University of Alaska Fairbanks. Using both cluster analysis and alluvial diagrams to organize our data, we find a great variety in answering patterns across the survey prompts, indicating that student ideas have not yet crystallized. Our paper thus provides experimental evidence in support of a “knowledge in pieces” model of student cognition about radioactivity as opposed to a “misconceptions” model.