Abstract
Although it is thought that young children focus on the magnitude of the target dimension across ratio sets during binary comparison of ratios, it is unknown whether this is the default approach to ratio reasoning, or if such approach varies across representation formats (discrete entities and continuous amounts) that naturally afford different opportunities to process the dimensions in each ratio set. In the current study, 132 kindergarteners (Mage = 68 months, SD = 3.5, range = 62–75 months) performed binary comparisons of ratios with discrete and continuous representations. Results from a linear mixed model revealed that children followed an additive strategy to ratio reasoning—i.e., they focused on the magnitude of the target dimension across ratio sets as well as on the absolute magnitude of the ratio set. This approach did not vary substantially across representation formats. Results also showed an association between ratio reasoning and children’s math problem-solving abilities; children with better math abilities performed better on ratio reasoning tasks and processed additional dimensions across ratio sets. Findings are discussed in terms of the processes that underlie ratio reasoning and add to the extant debate on whether true ratio reasoning is observed in young children.
Highlights
Rational numbers are usually introduced at late stages in elementary education, children engage in ratio reasoning well before the onset of formal school
The literature review suggests that children’s approach to ratio reasoning may vary across representation formats because continuous and discrete representations naturally afford different opportunities to estimate the absolute magnitude of each dimension within each ratio set and across ratio sets
Our findings suggest that kindergarteners already follow an additive strategy to ratio reasoning and tend to focus on the magnitude of the target dimension across ratio sets as well as on the absolute magnitude of the ratio set
Summary
Rational numbers are usually introduced at late stages in elementary education, children engage in ratio reasoning well before the onset of formal school. When presented with two different jars containing blue and yellow beads (each jar reflecting different ratios of blue to yellow) and tasked to select the jar for which the probability of getting a blue bead is higher, 6-year-old children usually select the jar containing more blue beads, independently of the ratio blue to yellow in each jar (Falk et al, 2012). It is thought that such an error is a “conceptual misunderstanding” that reflects children’s inability to establish part–whole relations between the parts or dimensions of a ratio set (i.e., each jar) and that they rely on unidimensional heuristics We look at whether children rely on specific unidimensional heuristics to reason about ratios and whether this approach is consistent across different representation formats (continuous vs discrete) that naturally afford different opportunities to establish part–part relations and part–whole relations. Probability (probabilistic reasoning) and data analysis are core mathematical aspects to be developed from Pre-K2 to Grade 12 according to the National Council of Teachers of Mathematics (2000)
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