Combinatorial and Proportional Task: Looking for Intuitive Strategies in Primary Education

Abstract

The development of probabilistic thinking at school requires enhancing combinatorial and proportional reasoning. For this reason, 190 sixth-grade elementary school students (11–12-year-old), without previous instruction in the topic, solve a task consisting of five questions that address both types of reasoning. This study explores the problem-solving strategies used by schoolchildren. The results obtained indicate that, in general, the students do not show strategies in the answers to the combinatorial questions. In addition, it is observed that they have difficulties in understanding the proposed statements and arguing the issues that explicitly require a justification.

Videogames and open feedback systems to enhance probabilistic reasoning and engagement

“…One of the most highly valued mathematical skills is probabilistic reasoning, a crucial aptitude for addressing real-world issues and making informed decisions [18]- [20]. Probabilistic reasoning can be defined as the ability that allows one to make decisions based on given information, identify patterns, and utilize statistics to describe, model and interpret phenomena, ultimately enabling inferences [21].…”

“…Notably, Ricart and Estrada [20] emphasize the instructional aspect in nurturing this skill, as students who haven't received prior guidance on probability concepts tend to lack strategies for decision-making rooted in proportionality reasoning. In their study frequently cited in the field, Fischbein et al [18] identify the difficulty of distancing oneself from the conventional notion of "luck" as a factor affecting probabilistic reasoning.…”

Farewell to Virtual Environments and Welcome to Post-pandemic Mathematical Problem Posing and Solving

“…The evaluation by competencies is complex and multivariable while the continuous evaluation does it in a progressive way and takes advantage of providing feedback proactively to students, so that in problem solving, lectures and other activities the curricular strategy is used individually [12] as well as metacognitive strategies with the sole purpose of discovering the metacognitive needs for the area of mathematics and improve student learning. The use of psychometric tools in learning is of utmost importance and with the use of appropriate strategies it is possible to pose and solve mathematical problems [13] as well as to develop probabilistic thinking that still present difficulties in mathematical arguments and statements [14], this comes from or are caused by the topics that are presented with greater difficulty and with pattern errors despite focusing with constructivist meaningful learning [15].…”