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Seeing things in proportion: Unravelling the early development of proportional reasoning

Boek - Dissertatie

We might be unaware of it, but on a daily basis we are confronted with situations in which proportional reasoning is needed. Besides, there is unanimity about the important role of proportional reasoning throughout learner's mathematical development. In spite of that, many adolescents and even adults seem to be particularly bad at it. In Flanders one third of the children does not reach the required learning outcomes regarding proportional reasoning at the end of elementary school (AHOVOKS, 2016). Although proportional reasoning is so hard to apprehend, there are indications that some young children can already reason proportionally in certain situations (e.g., Boyer & Levine, 2012). More research about the early development of proportional reasoning is needed. Hence, the focus of the current doctoral research project was unravelling the early development of proportional reasoning. Three aims were specified. First, to map the early development of proportional reasoning abilities in 5- to 8-year-olds. Second, to investigate the development of relational preference in 5- to 8-year-olds and its association with children's proportional reasoning abilities. Third, to explore possible predictors of children's proportional reasoning abilities and their development at this young age. In order to fulfill these aims, we conducted seven empirical studies. Study 1 investigated the emergence of proportional reasoning abilities in 4- to 5-year-olds. Study 2 cross-sectionally investigated 5- to 9-year-olds proportional reasoning abilities, whereas Study 3 investigated the development longitudinally in a group of 5- to 8-year-olds. Together, these studies showed that the development of proportional reasoning takes an early start. Most children take many meaningful steps towards full-fledged proportional reasoning in the first years of elementary school, but there are large individual differences between children. Also, the early understanding of one-to-many correspondence was identified as an essential step towards solving more difficult proportional reasoning problems. Study 4 investigated the development of relational preference in 5- to 8-year-olds and its association with proportional reasoning. Study 5 examined the association between relational preference and word-problem solving in 6- to 7-year-olds. These studies showed that relational preference in young children plays a role in performance on early proportional problems presented orally and with manipulatives, as well as in performance and errors on written word problems. Study 6 explored the association between early patterning and proportional reasoning abilities and found that patterning ability in 4- to 5-year-olds is a unique predictor for emergent proportional reasoning ability one and a half years later. Study 7 investigated the association between language and proportional reasoning and indicated that not only general vocabulary, but also some specific proportional vocabulary concepts (e.g., double, three times more), are important for early proportional reasoning. In the last chapter of this dissertation we discuss the main findings of the different studies, in light of the existing literature, and end with some methodological considerations and educational implications.
Jaar van publicatie:2021
Toegankelijkheid:Closed