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

Abstract

During the last two years, the COVID-19 pandemic had a secondary effect of increased media content loaded with mathematical, often probabilistic information (and misinformation). Our exploratory study investigates the probabilistic intuitions, misconceptions, biases, and fallacies in conditional probability reasoning of mathematics teacher candidates in the context of the pandemic. The pre-service mathematics teachers who participated in our study were given a questionnaire with five contextual conditional probability problems, all formulated similarly to media statements often encountered when discussing the COVID-19 pandemic. Our findings confirm the previous findings on biases and fallacies related to conditional probability problems with a social context. They were also indicative of several types of errors (both numerical and logical) as more common than expected. Our results also reveal that pre-service mathematics teachers apparently separate the content learned in the classroom from the application of the knowledge in critical examination of the information to which they are daily exposed by the media.

Probabilistic Modeling for Conditional Statements

“…(5) (6) Also the cdf can be evaluated to be: (7) It is required in this research to evaluate theoretically the probability mass function after passing the random variable in if statement and sort function.…”

“…In order to find the individual pmfs of and before and after passing through the code, it is needed to resite the laws of joint probability of independent events A and B [13]: (12) (13) Also this can be expanded to multiple d events (where d here is the dimension or the number of random variables): (14) (15) In order to calculate the joint pmf of the two independent random variables and , then from eq (12) and eq (6), it can be conluded that:…”

“…Again, unified plot is made after each stage. The summary of the methodology was included in the Fig (6).…”

“…The contemporary design trend of embedded applications necessitates the analysis and optimization of performance and power in all the system's components, particularly in the early design stages when several solutions are contrasted. The need of a quick examination of the program, performed across the full development/compilation phase, especially from the source level down to the assembly, is being reinforced by the current pervasiveness of microprocessor-based architectures, to this end, the subject of establishing limits on the processing time of a process running on a microprocessor was examined in several research publications [5][6][7]. Unfortunately, given the capabilities of the present Processor, this work is getting harder and harder.…”

“…Because the target application is frequently real-time constrained, several analyses approached the issue at a coarse granularity, concentrating primarily on the WCET (Worst Case Execution Time). The issue generally has two sides; the first is analyzing the program routes to find out which instructions will be executed and how they will affect the WCET, while the second is micro-architectural analysis, or modeling of the hardware system running the software [6][7]. The authors in [8] suggested a technique for obtaining probabilistic distributions of execution durations using static analysis.…”