Unasked But Answered: Comparing the Relative Probabilities of Coin Flip Sequence Attributes

An Investigation of the Representativeness Heuristic: The Case of a Multiple Choice Exam

“…Adding a further complexity in our research with prospective teachers is the contextualization of mathematics in situations of teaching and learning. In resonance with Chernoff and Mamolo (2015), we observed a tendency for participants to interpret the context with respect to what they as teachers might do in a similar situation, though this was not requested of them nor alluded to in the phrasing of the task. Comments that referred to what a teacher "would feel inclined to do" in response to the context seemed, on one hand, to shift focus away from a response to the mathematics.…”

“… The avoidance of theoretical probabilistic considerations was, in this instance, influenced by the two characteristics of the novel task: multinomial choices and contextual setting. To the best of our knowledge, research that has looked at multinomial sequences has identified that a "representativeness bias" (Fischbein, 1999, p.26; see also Chernoff & Mamolo, 2015) exists, though it has not delved into the specific characteristics of samples or events that make them appear as representative to the observer (e.g., what makes something "seem more random" in a particular context). For instance, Fischbein and Schnarch (1997) examined the responses of students in grades 5, 7, 9, and 11, as well as prospective mathematics teachers, to a question on the relative likelihood of winning the lottery when one player has chosen 6 consecutive numbers (from a total of 40) and the other has chosen numbers at random.…”

On the Occasion of an Anniversary, Eh: Confessions of a Canadian Math Ed Editor

“…Given the individuals involved and the strength of the proposal, it was an easy and resounding "yes" on my part. Beyond my initial support, I reviewed a few of the manuscripts that were submitted, and even contributed my own commentary (Chernoff, 2019). My involvement with this issue stands in stark contrast to the second special issue of the year, which was published solely in French.…”

“…By 2015, I had already been involved with @CJSMTE in a number of different ways. Having published in the journal (e.g., Chernoff & Mamolo, 2015 ; Chernoff & Russell, 2012 ), having reviewed a considerable number of manuscripts (15 in total between 2007 and 2015), and having served as an editorial board member (2012–2015), I was more familiar with @CJSMTE than any other math education journal at that point in my career. Ok, I have tried to convince myself for long enough now (i.e., 5 paragraphs) that I was indeed a viable candidate for the position, which brings us to 2015 and the start of my tenure as math ed editor of @CJSMTE.…”