Discussing the Conditional Probability from a Cognitive Psychological Perspective

Abstract

Probability signifies the most obscure and the least achievable content among other mathematics areas; particularly, the conditional probability concept that should not be left behind any standard course of probability from primary to university level. Moreover, understanding the conditional probability becomes more serious when the discussion fits into the field of teacher education, wherein the prospective mathematics teachers need not only to learn it but also to promote their pupils’ conditional probability reasoning. From this aspect, the current study aims at exploring the prospective mathematics teachers’ conditional probability reasoning from a cognitive psychological perspective that focuses on how their minds work. Accordingly, the generic inductive approach has been employed. Hence, a purposive sample of the university students who study in a four-year mathematics teacher preparation program has been selected. After analyzing the school curriculum of probability, an authentic conditional probability situation has been utilized. Following this, the students’ interpretations have been translated, coded, and categorized using NVivo software. As a result, the generalizer (58.8%), conservative (11.8%), correlational (23.5%), and the rational thinker (5.9%) have been defined as the primary models of conditional probability reasoning. Furthermore, while the generalizer and conservative thinkers both share the anchoring and adjustment bias, the illusion of validity has been operated by only the conservatives. Besides, the one-step, availability, causality, and gambler fallacy, were the correlational thinkers' assigned biases. On the other side, the rational thinkers have reached a high level of contextual knowledge, with understanding the idea of sample space reduction.