The importance of specific mathematical language for early proportional reasoning

Vanluydt, Elien; Supply, Anne-Sophie; Verschaffel, Lieven; Dooren, Wim Van

doi:10.1016/j.ecresq.2020.12.003

Cited by 19 publications

(9 citation statements)

References 27 publications

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“…Interestingly, two studies looked into predictors of early proportional reasoning in the early years of elementary school, before the start of formal instruction in this topic. In a first study, Vanluydt, Supply, et al (2021) reported that not only general vocabulary but also some specific proportional vocabulary concepts are important for early proportional reasoning. In a second study (Vanluydt, Wijns, et al, 2021), they showed that patterning in 4- to 5-year-olds is a unique predictor of proportional reasoning ability 1.5 years later, over and above sex and numerical and general cognitive abilities.…”

Section: Definition and Problem Characteristicsmentioning

confidence: 99%

“…In the third study, we investigated the association between patterning and proportional reasoning and found that patterning abilities in the second grade of kindergarten predict proportional reasoning 1.5 years later ( Vanluydt, Wijns, et al, 2021). Fourth, we analyzed the association between specific vocabulary related to proportional reasoning, general vocabulary, and early proportional reasoning and showed that both types of vocabulary are associated with proportional reasoning in the second grade of elementary school (Vanluydt, Supply, et al, 2021). Compared to these four previous studies, the present study was the first to longitudinally investigate the development of early proportional reasoning from the first grade until the third grade of elementary school.…”

Section: Research Contextmentioning

confidence: 99%

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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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Section: Definition and Problem Characteristicsmentioning

confidence: 99%

Section: Research Contextmentioning

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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“…This identification of multiplicative relations also relies on a specific vocabulary, for instance, master ing "twice as many" or "more than half" (Staples & Truxaw, 2012). Some specific mathematical vocabulary concepts ("double", "three more") are even significant predictors of proportional reasoning at the beginning of primary school (Vanluydt et al, 2021).…”

Section: Proportional Reasoning and Misconceptionsmentioning

confidence: 99%

Enhancing cognitive flexibility through a training based on multiple categorization: Developing proportional reasoning in primary school

Scheibling-Seve

Gvozdic

Pasquinelli³

et al. 2022

J. Numer. Cogn.

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Proportional reasoning is a key topic both at school and in everyday life. However, students are often misled by their preconceptions regarding proportions. Our hypothesis is that these limitations can be mitigated by working on alternative ways of categorizing situations that enable more adequate inferences. Multiple categorization triggers flexibility, which enables reinterpreting a problem statement and adopting a more relevant point of view. The present study aims to show the improvements in proportional reasoning after an intervention focusing on such a multiple categorization. Twenty-eight 4th and 5th grade classes participated in the study during one school year. Schools were classified by the SES of their neighborhood. The experimental group received 12 math lessons focusing on flexibly envisioning a situation involving proportional reasoning from different points of view. At the end of the school year, compared to a control group, the experimental group had better results on the posttest when solving proportion word problems and proposed more diverse solving strategies. The analyses also show that the performance gap linked to the school’s SES classification was reduced. This offers promising perspectives regarding multiple categorization as a path to overtake preconceptions and develop cognitive flexibility at school.

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“…Recently, research on the role of language has started to focus on the specific terminology that is involved in a specific mathematical area (Purpura & Reid, 2016;Purpura et al, 2017). Such domain-specific mathematical terminology in the area of multiplicative reasoning has also been shown to predict performance on multiplicative reasoning one year later (Vanluydt et al, 2021).…”

Section: Chapter 14 Multiplicative Relations and Problem Solvingmentioning

confidence: 99%

Commentary on Part IV

Verschaffel,

Van Dooren

2022

Enabling Mathematics Learning of Struggling Students

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The importance of specific mathematical language for early proportional reasoning

Cited by 19 publications

References 27 publications

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

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

Enhancing cognitive flexibility through a training based on multiple categorization: Developing proportional reasoning in primary school

Commentary on Part IV

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