Could probability be out of proportion? Self-explanation and example-based practice help students with lower proportional reasoning skills learn probability

Abstract

Proportional reasoning failures seem to constitute most errors in probabilistic reasoning, yet there is little empirical evidence about its role for attaining probabilistic knowledge and how to effectively intervene with students who have less proportional reasoning skills. We examined the contributions of students' proportional reasoning skill and example-based practice when learning about probabilities from a reformed seventh grade curriculum. Teachers in their regular classrooms were randomly assigned to instruct with a reformed textbook (control) or a version revised to incorporate correct and incorrect example problems with prompts to explain (treatment). Students' prior knowledge in proportional reasoning skill separately predicted probabilistic knowledge at posttest, regardless of their prior knowledge in probability or minority status. Overall, students in the treatment condition improved more in their probabilistic knowledge, if they started with less proportional reasoning skills. Our findings suggest that example-based practice is beneficial for students with less prior knowledge of proportions, likely a key concept for developing probabilistic knowledge.

The Effect of Error Analysis-Based Learning on Proportional Reasoning Ability of Seventh-Grade Students

“…Kshetree et al (2021) found using the treatment of students' misconceptions and errors in learning mathematics to be significant progress in dealing with mathematical problemsolving at conceptual, procedural, and application levels. Begolli et al (2021) revealed that the combination of correct and incorrect worked examples improves the proportional and probabilistic reasoning for students.…”

“…Proportional reasoning is also considered an important way to develop algebraic thinking and to understand the meaning of function (Cai and Sun, 2002). Students' prior knowledge in proportional reasoning skills predicted the probabilistic reasoning positively, and students' failure in proportional reasoning leads them to make many mistakes in probabilistic reasoning (Begolli et al, 2021).…”

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

“…Creemos que el contexto de la probabilidad es además un hábitat propicio en el que poder poner en juego el razonamiento proporcional. En este sentido, Begolli et al (2021) sugieren que las conexiones explícitas entre las proporciones y las probabilidades pueden llevar a los estudiantes a desarrollar una comprensión más profunda del razonamiento probabilístico y proponen que puede ser beneficioso, para este último, equilibrar y coordinar la instrucción sobre la probabilidad con la instrucción sobre el razonamiento proporcional.…”

“…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).…”

Students’ Proportional Reasoning in Mathematics Through Covid-19 Pandemic Context

“…Proportional reasoning is one of the reasons that mathematics is important to understand. Understanding fractions, percentages, ratios, decimals, scales, and algebra, as well as student opportunities, all require the ability to reason proportionally (Begolli et al, 2021;Brown et al, 2020;Hilton et al, 2016;Hilton & Hilton, 2018;Im & Jitendra, 2020;Jacobson et al, 2018;Johar & Yusniarti, 2018;Ojose, 2015;Orrill & Millett, 2020;Pelen et al, 2016;Sawatzki et al, 2019). Additionally, much of mathematics includes proportional reasoning, including unity, statistics, algebra, opportunities, and social arithmetic.…”