Revisiting Mr. Tall and Mr. Short

Riehl, Suzanne M.; Steinthorsdottir, Olof Bjorg

doi:10.5951/mathteacmiddscho.20.4.0220

Cited by 7 publications

(1 citation statement)

References 3 publications

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“…Second, proportional missing-value problems with an integer ratio (i.e., the ratio between two numbers forms an integer number, e.g., 4:2) are easier to solve than those with a noninteger ratio (i.e., the ratio between two numbers forms a noninteger number, e.g., 6:4; Kaput & West, 1994; Karplus et al, 1983; Riehl & Steinthorsdottir, 2019; Tourniaire & Pulos, 1985). Third, enlarge problems, in which the target is bigger than the given situation so that there is an increase in quantities, are easier to solve than shrink problems, in which the target is smaller than the given situation so that there is a decrease in quantities (Riehl & Steinthorsdottir, 2014, 2019).…”

Section: Definition and Problem Characteristicsmentioning

confidence: 99%

The early development of proportional reasoning: A longitudinal study of 5- to 8-year-olds.

Vanluydt¹,

Verschaffel²,

Dooren³

2022

Journal of Educational Psychology

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The present study longitudinally investigated proportional reasoning abilities in early elementary school before the start of its instruction. Three aims were put forward: (a) distinguishing the different developmental states in young children’s understanding of missing-value proportional situations, (b) investigating how children transition through these states, and (c) exploring possible predictors that explain individual differences in young children’s development of proportional reasoning abilities. We longitudinally investigated 5- to 8-year-olds’ (n = 315) proportional reasoning abilities in a fair-sharing missing-value proportional reasoning task. First, results showed that the development of proportional reasoning already starts at a very early age and is still ongoing when children are in their third year of elementary school. Second, latent class analysis revealed five different early states of proportional reasoning. The understanding of one-to-many correspondence was identified as an essential stepping-stone toward success in more difficult proportional reasoning problems with many-to-many correspondences. Third, exploratory analyses revealed that the large individual differences in children’s development of proportional reasoning abilities were associated with socioeconomic status, language, spatial abilities, and numerical abilities. Theoretical, methodological, and educational implications are discussed.

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