Does half a pizza equal half a box of chocolates?

Singer‐Freeman, Karen; Goswami, Usha

doi:10.1016/s0885-2014(01)00066-1

Cited by 89 publications

(54 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our results support previous findings (Schlottmann, 2001;Singer-Freeman & Goswami, 2001) indicating that proportional reasoning is possible early in life when using an intuitive task; nevertheless 5-year-olds were more accurate than 4-year-olds in rating proportions. In line with previous results (Frick & Newcombe, 2012), a similar age effect was found for children's ability to locate targets presented on maps.…”

Section: Discussionsupporting

confidence: 91%

“…On the one hand, 5-year-olds can successfully rate probabilities of events on a continuous scale (Schlottmann, 2001), and 3-and 4-year-olds can match proportions across substances (e.g., half a pizza equals half a chocolate bar; Singer-Freeman & Goswami, 2001). On the other hand, same-aged children had difficulties in finding the matching proportion between two alternatives (Boyer & Levine, 2012;Spinillo & Bryant, 1991).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The relation between spatial thinking and proportional reasoning in preschoolers

Möhring

Newcombe

Frick

2015

Journal of Experimental Child Psychology

View full text Add to dashboard Cite

Previous research has indicated a close link between spatial and mathematical thinking. However, what shared processes account for this link? In this study, we focused on the spatial skill of map reading and the mathematical skill of proportional reasoning and investigated whether scaling, or the ability to relate information in different-sized representations, is a shared process. Scaling was experimentally manipulated in both tasks. In the map task, 4- and 5-year-olds (N=50) were asked to point to the same position shown on a map in a larger referent space on a touch screen. The sizes of the maps were varied systematically, such that some trials required scaling and some did not (i.e., the map had the same size as the referent space). In the proportional reasoning task, children were presented with different relative amounts of juice and water and were asked to estimate each mixture on a rating scale. Again, some trials required scaling, but others could be solved by directly mapping the proportional components onto the rating scale. Children's absolute errors in locating targets in the map task were closely related to their performance in the proportional reasoning task even after controlling for age and verbal intelligence. Crucially, this was only true for trials that required scaling, whereas performance on nonscaled trials was not related. These results shed light on the mechanisms involved in the close connection between spatial and mathematical thinking early in life.

show abstract

Section: Discussionsupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

The relation between spatial thinking and proportional reasoning in preschoolers

Möhring

Newcombe

Frick

2015

Journal of Experimental Child Psychology

View full text Add to dashboard Cite

show abstract

“…Findings suggested that children as young as 8 years old were able to consider both components that constitute a proportion and integrate them in a normative proportional way 2 . These results stand in contrast to previous claims that proportional reasoning does not emerge before the age of 11 years (Moore et al, 1991;Noelting, 1980;Piaget & Inhelder, 1975) and confirm other findings that even younger children are able to reason about proportions (Acredolo et al, 1989;Boyer & Levine, 2012;Boyer et al, 2008;Jeong et al, 2007;Schlottmann, 2001;Singer-Freeman & Goswami, 2001;Sophian, 2000;Spinillo & Bryant, 1991, 1999. In line with previous paradigms showing earlier success in children's proportional reasoning, it is possible that the presentation of continuous proportional quantities and the nature of the response mode (spatial ratings that are more intuitively graspable) led to children's success on our proportional reasoning task.…”

Section: Discussionsupporting

confidence: 71%

“…That is, children's formal fraction knowledge may have helped them to encode spatial proportions and to reproduce them on the rating scale. Even though this possibility cannot be eliminated by our correlational results, it seems unlikely in light of many studies (Acredolo et al, 1989;Boyer & Levine, 2012;Boyer et al, 2008;Jeong et al, 2007;Schlottmann, 2001;Singer-Freeman & Goswami, 2001;Sophian, 2000;Spinillo & Bryant, 1991, 1999 showing signs of proportional reasoning at an age when understanding of formal fractions is not present (Hecht & Vagi, 2010;Schneider & Siegler, 2010;Stafylidou & Vosniadou, 2004). Nonetheless, future studies using longitudinal designs or training components are needed to pin down the causal direction of the relation we have identified.…”

Section: The Relation Between Proportional Reasoning and Fraction Undmentioning

confidence: 79%

“…For example, several studies have demonstrated that 5-to 6-year-olds showed successful proportional reasoning when presented with continuous amounts as opposed to discrete amounts (Boyer, Levine, & Huttenlocher, 2008;Jeong, Levine, & Huttenlocher, 2007;Spinillo & Bryant, 1999). Children also showed earlier competence at the age of 3 to 4 years when asked to produce equal proportions, possibly by tapping their ability to reason by analogy (Goswami, 1989;Singer-Freeman & Goswami, 2001). Analogical reasoning may build on similar cognitive competencies as proportional reasoning, because it often also requires an understanding of relations between relations (e.g., bananas are related to fruits like cucumbers are related to vegetables; cf.…”

Section: Such Findings Documenting Children's Difficulties With Fractmentioning

confidence: 99%

See 1 more Smart Citation