Classes in the balance: Latent class analysis and the balance scale task

Abstract

Latent class analysis (LCA) has been successfully applied to tasks measuring higher cognitive functioning, suggesting the existence of distinct strategies used in such tasks. With LCA it became possible to classify post hoc. This important step forward in modeling and analyzing cognitive strategies is relevant to the overlapping waves model for strategy development [Siegler, R. S. (1996). Emerging minds: The process of change in children's thinking. New York: Oxford University Press.]. However, so far, developmental trends were not part of the statistical model. Moreover, the theoretical importance of the fact that a few distinct classes were found was weakened because not all these classes represented pure strategies. To address these two issues, we model the development in class membership by incorporating age and working memory as covariates in the LCA model. Previous findings that the classes are well demarcated are replicated. A developmental sequence is supported by a strong effect of age on class membership and a moderate effect of working memory. Classification itself is hardly affected by the covariates: the problem of difficult to characterize classes remains. Nevertheless, classes describe large proportions of children's responses, classes are robust and fit a developmental trend, and some classes represent mixed rule use. In the discussion, the theoretical status of the overlapping waves model is clarified.

Inquiry-Based Learning and Conceptual Change in Balance Beam Understanding

“…Exploratory analyses with age and gender were conducted. Gender did not relate to the pretest, posttest, or difference score (posttest minus pretest), which was in line with gender being not significant as a covariate in an LCA on the balance beam test (Boom and Ter Laak, 2007). The present results showed that gender also did not relate to a difference score.…”

“…In addition to Strategies 1, 2, 4, and the Addition Strategy, two classes (out of six) did not match any strategy. A later study with 5-to 14year-old participants and two covariates of class membership (age and working memory) revealed comparable classes, but the class representing Strategy 4 was not found (Boom and Ter Laak, 2007). Boom and Ter Laak (2007) attributed the absence of Strategy 4 to the inclusion of only few older participants.…”

“…A later study with 5-to 14year-old participants and two covariates of class membership (age and working memory) revealed comparable classes, but the class representing Strategy 4 was not found (Boom and Ter Laak, 2007). Boom and Ter Laak (2007) attributed the absence of Strategy 4 to the inclusion of only few older participants. These studies show the feasibility of using LCA to identify strategy use and thus capture children's explanatory frameworks.…”

“…Regarding strategy use, it was hypothesized that five or six classes would be found and that Strategies 1, 2, and 4 and the Addition Strategy would be detected, as well as one or two classes that could not be classified, because that is what previous studies with LCA of balance beam performance showed van der Maas, 1997, 2002;Boom et al, 2001;Boom and Ter Laak, 2007). It was expected that accuracy in the present study would be lower than in the study by Boom et al (2001) because they used four age groups to estimate the classes and the present study targeted a single, younger age group, 10 years and 9 months on average.…”

Moving towards understanding: Reasoning about graphs in primary mathematics education

“…We indeed found a fade out effect for the intervention. Second, from a statistical point of view, this study is innovative in the sense that the used latent growth curve model incorporated categorical responses to the tasks, which allowed us to model gradual changes in levels of reasoning (Boom & Ter Laak, 2007). Third, our cohort-sequential research design enabled us to "re-use" student groups per instruction condition, whereby the groups served as their own control group, depending on the specific cohort.…”