Rule transition on the balance scale task: a case study in belief change

Abstract

For various domains in proportional reasoning cognitive development is characterized as a progression through a series of increasingly complex rules. A multiplicative relationship between two task features, such as weight and distance information of blocks placed at both sides of the fulcrum of a balance scale, appears difficult to discover. During development, children change their beliefs about the balance scale several times: from a focus on the weight dimension (Rule I) to occasionally considering the distance dimension (Rule II), guessing (Rule III), and applying multiplication (Rule IV;Siegler, 1981). Because of the detailed empirical findings the balance scale task has become a benchmark task for computational models of proportional reasoning.In this article, we present a large empirical study (N = 420) of which the findings provide a challenge for computational models. The effect of feedback and the effect of individually adapted training items on rule transition were tested for children using Rule I or Rule II. Presenting adapted training items initiates belief revision for Rule I but not for Rule II. The experience of making mistakes (by providing feedback) induces a change for both Rule I and Rule II. However, a delayed posttest shows that these changes are preserved after 2 weeks only for children using Rule I. We conclude that the transition from Rule I to Rule II differs from the transition from Rule II to a more complex rule. Concerning these empirical findings, we will review performance of computational models and the implications for a future belief revision model. It is one Thing, to show a Man that he is in an Error, and another, to put him in possession of Truth. Keywords

Preschoolers perform more informative experiments after observing theory-violating evidence

“…Studies on young children's learning in other knowledge domains have also demonstrated children's difficulty with taking into account a second subordinate dimension. Training studies on the balance scale task demonstrated that for the Rule 1 group (children who take into account only the weight dimension in determining which side will go down), feedback alone was insufficient for theory revision, but increasing awareness of the relevance of the distance dimension led some children to change their theories (Jansen, Raijmakers, & Visser, 2007;Jansen & Van der Maas, 2001;Siegler, 1976). The literature on cognitive flexibility offers different theoretical explanations for young children's difficulty with switching attention between dimensions.…”

Microdevelopment of peer interactions and scientific reasoning in young children /Microdesarrollo de la interacción entre pares y el razonamiento científico en niños pequeños

“…As a result, this study illustrates the intra- and inter-individual trajectories of the co-occurring processes — interaction and reasoning — in a single session by using techniques that highlight the temporal changes and patterns of behaviours. Although previous studies have been done at the group level to model learning in the balance scale task (see Jansen, Raijmakers, & Visser, 2007; Schmittmann, Visser, & Raijmakers, 2006), this study takes a different approach. Here, the emphasis is not on the content of the task, but on the processes of reasoning and interaction from moment to moment.…”

“…Por consiguiente, el estudio ilustra las trayectorias intra- e inter-individuales de los procesos concurrentes (interacción y razonamiento), utilizando técnicas que ponen de relieve los cambios temporales y los patrones de comportamiento. Aunque estudios previos han sido realizados a nivel grupal para modelar el aprendizaje en la tarea de la balanza (véase Jansen, Raijmakers, & Visser, 2007; Schmittmann, Visser & Raijmakers, 2006), nuestro estudio adopta un enfoque diferente. Aquí, el énfasis no se centra en el contenido de la tarea, sino en el proceso de razonamiento y en las interacciones observadas momento a momento.…”

Identifying Qualitative Between-Subject and Within-Subject Variability: A Method for Clustering Regime-Switching Dynamics

“…Human dynamic processes vary within a subject over time and differ between subjects at all behavioral, physiological, emotional, attentional, and cognitive levels (Molenaar et al, 2003). Widespread examples include but not limited to change processes in belief and attitudes (van der Maas et al, 2003;Jansen et al, 2007), affective experiences (Cole et al, 2004;Kuppens et al, 2010;Hamaker et al, 2015), and executive functions (Zelazo, 2016). The within-and betweensubject variabilities can be quantitative as well as qualitative in nature (Pintrich, 1988;Van Geert, 1991;van der Maas and Molenaar, 1992;van Dijk and van Geert, 2007;Stephen et al, 2009).…”