Assessing Students’ Difficulties with Conditional Probability and Bayesian Reasoning

Abstract

In this paper we first describe the process of building a questionnaire directed to globally assess formal understanding of conditional probability and the psychological biases related to this concept.We then present results from applying the questionnaire to a sample of 414 students, after they had been taught the topic. Finally, we use Factor Analysis to show that formal knowledge of conditional probability in these students was unrelated to the different biases in conditional probability reasoning. These biases also appeared unrelated in our sample. We conclude with some recommendations about how to improve the teaching of conditional probability.

Pre-service mathematics teachers’ understanding of conditional probability in the context of the COVID-19 pandemic

“…It refers to using P(A & B), probability of both A and B occurring, as P(A|B). This type of error was noted in several previous studies, including those with pre-service teachers (Díaz & Fuente, 2007;Estrada & Batanero, 2006). In a medical context we may encounter this, e. g., if, knowing that a disease is common to 2% of males, but 3% of females, in a town with 4500 male and 5500 female inhabitants, one concludes that the probability that a person diagnosed with the disease is male is calculated as 2%•4500/10000 = 0.9 % instead of 2%•4500/(2%•4500+3%•5500) ≈ 35%.…”

“…highly relevant in medicine, law, education, psychology, and other professional fields (Batanero et al, 2016;Díaz & Batanero, 2009;Díaz & Fuente, 2007).…”

“…Finally, at level 4, the numerical level, students assign correct numerical values to conditional probabilities, state the necessary conditions under which two events are related, and use numerical reasoning to compare the probabilities before and after a trial. Díaz and Fuente (2007) developed a general questionnaire to globally assess formal understanding of conditional probability and the psychological biases and difficulties related to this concept. Three of these are relevant for the present study.…”

“…The CI is also related to a well-known psychological difficulty, the perception of P(A|B) regarding causality. If B is perceived as a possible cause of A, P(A|B) is viewed as a causal relation, while if A is perceived as a possible cause of B, P(A|B) is viewed as a diagnostic relation Díaz & Fuente, 2007;Tversky & Kahnemann, 1982).…”

Razonamiento probabilístico de estudiantes de bachillerato al interpretar datos de la COVID-19

“…Estos problemas han sido investigados por distintos autores, que los han clasificado identificando en ellos algunas variables que afectan a su resolución (ej., Huerta y Bresó, 2017). Otros trabajos describen sesgos de razonamiento como no comprender la asimetría de las probabilidades condicionadas (Borovcnik, 2016) o confundir condicionamiento y causación (Díaz y de la Fuente, 2007).…”