The Probabilistic Reasoning of Middle School Students

Japanese and Thai Senior High School Mathematics Teachers’ Knowledge of Variability

“…Teachers who chose answer (c) might have a misunderstanding about probability; they might have focused on the probability of the individual event of one baby being either a boy or a girl (which is ½, as the task sets from its initial sentence) rather than on the difference in sample sizes of babies delivered by the two hospitals. This kind of answer is closely related to the misconception known as equiprobability bias, which is a tendency to view several outcomes of a random experiment as equally likely, usually while focusing on the likelihood of just one event (Batanero et al, 2014;Lecoutre, Durand, & Cordier, 1990;Watson, 2005). Moreover, the results obtained in this study contrast with those reported by Watson (2000), in which 18 out of 33 Australian preservice secondary mathematics teachers correctly solved a similar version of the "Two hospitals" task.…”

Análisis cognitivo de tareas de comparación de probabilidades por futuro profesorado de Educación Primaria

“…En este sentido, y dentro del campo de la probabilidad, diversos autores destacan que los profesores en formación poseen un conocimiento matemático y didáctico insuficiente (Batanero et al, 2012;Batanero et al, 2004;Gea et al, 2017;Gómez et al, 2013;Pereira-Mendoza, 2002;Vásquez y Alsina, 2015a, 2015b presentando ciertas limitaciones en la descripción y evaluación de respuestas de alumnos (Batanero et al, 2015;Mohamed, 2012). Un razonamiento proporcional insuficiente puede estar detrás de gran parte de los errores de interpretación de conceptos o aplicación de procedimientos, tanto en estudiantes, como en futuros profesores en el ámbito de la probabilidad (Begolli et al, 2021;Boyer y Levine, 2015;Bryant y Nunes, 2012;Langrall y Mooney, 2005;Van Dooren, 2014;Watson, 2005;Watson et al, 2007).…”

When One Shape Does Not Fit All: A Commentary Essay on the Use of Graphs in Psychological Research

“…Nowadays, visual inspection continuous to be largely recommended for understanding data set's meaning in exploratory data analysis, and is considered more useful than a solely strictly adherence to statistical testing to answer questions prompted by the experiment (Wixted and Pashler, 2002 ; Marmolejo-Ramos and Matsunaga, 2009 ). Also student's books and papers addressing mechanisms underpinning statistical reasoning have introduced a shift of perspective from drawing graphs to using graphs for making sense of data and evaluating hypotheses (Moore, 1998 ; Wild and Pfannkuch, 1999 ; Konold and Pollatsek, 2002 ; Bakker, 2004 ; Bakker and Gravemeijer, 2004 ; Pfannkuch, 2005 ; Watson, 2005 ; Garfield and Ben-Zvi, 2008 ; Matejka and Fitzmaurice, 2017 ). However, as we review below, a vast majority of research papers continue to adopt non optimal graphical representations.…”