Children’s multiplicative transformations of discrete and continuous quantities

When you don't have to be exact: Investigating computational estimation skills with a comparison task

“…It might be argued that the distance effect found in Experiment 1 is due to range-based analysis (Barth, Baron, Spelke, & Carey, 2009). The use of only 2D × 2D multiplication problems enabled participants to figure that the exact answers for all problems ranged from 500 to 10,000, and this is why any response to a reference number larger than 10,000 or smaller than 500 was fast.…”

“…This pattern is adaptive because in such cases the sense of magnitude strategy could not guarantee a correct response. It suggests that adults approach this task with a rough idea for the magnitudes of multi-digit multiplication problems based on their ANS (Barth et al, 2009;McCrink & Spelke, 2010). When faced with an estimation comparison problem, they first attempt to solve it using their intuitive sense of magnitude based on the ANS.…”

Comparing the magnitude of two fractions with common components: Which representations are used by 10- and 12-year-olds?

“…As examples, 6-year-olds can choose the game with the greater probability of winning when this is determined by a ratio of two continuous quantities (i.e., a doughnut divided into a red part and a blue part) (Jeong et al, 2007), and 4-year-olds are able to perform simple operations on fractional amounts or to match figures according to visuospatial ratios (Mix et al, 1999;Sophian, 2000). Barth, Baron, Spelke, and Carey (2009) showed that 6-and 7-year-olds are able to apply multiplicative transformations to discrete quantities and, in particular, to represent the half of a set and compare it with a third set. Their performance varies with the ratio between the to-be-compared quantities, suggesting that children operate on mental magnitudes.…”

Spatial Proportional Reasoning Is Associated With Formal Knowledge About Fractions

“…One possible reason may be that they promote a different understanding of how proportional components should be scaled. Scaling can be defined as a process of transforming absolute magnitudes while conserving relational properties, and it is therefore an important aspect of proportional reasoning (Barth, Baron, Spelke, & Carey, 2009;Boyer & Levine, 2012;McCrink & Spelke, 2010). The importance of scaling for proportional reasoning is evident in everyday life, for instance when one wants to adjust the amounts of ingredients for a cake for 4 people to 6 people, or prepare the same concentrations of syrup-water mixtures in different jugs.…”