Wenke Möhring

Picturing perspectives: development of perspective-taking abilities in 4- to 8-year-olds

Although the development of perspective taking has been well researched, there is no uniform methodology for assessing this ability across a wide age span when frames of reference conflict. To address this gap, we created scenes of toy photographers taking pictures of layouts of objects from different angles, and presented them to 4- to 8-year-olds (N = 80). Children were asked to choose which one of four pictures could have been taken from a specific viewpoint. Results showed that this new technique confirmed the classic pattern of developmental progress on this kind of spatial skill: (1) 4-year-olds responded near chance level, regardless of layout complexity, (2) there was a growing ability to inhibit egocentric choices around age 6 with layouts of low complexity (one object), (3) performance increased and egocentric responses decreased dramatically around age 7, (4) even at age 8, children still showed considerable individual variability. This perspective taking task can thus be used to address important questions about the supports for early spatial development and the structure of early intellect.

Development of mental transformation abilities

Mental representation and transformation of spatial information is often examined with mental rotation (MR) tasks, which require deciding whether a rotated image is the same as or the mirror version of an upright image. Recent research with infants shows early discrimination of objects from mirror-image versions. However, even at the age of 4 years, many children perform at near chance level on more standard measures. Similar age discrepancies can be observed in other domains, including perspective taking, theory of mind, and intuitive physics. These paradoxical results raise the questions of how performance relates to competence and how to conceptualize developmental change. There may be a common underlying mechanism: the development of the ability to imagine things and mentally transform them in a prospective fashion.

Spatial Proportional Reasoning Is Associated With Formal Knowledge About Fractions

Proportional reasoning involves thinking about parts and wholes (i.e., about fractional quantities). Yet, research on proportional reasoning and fraction learning has proceeded separately. This study assessed proportional reasoning and formal fraction knowledge in 8- to 10-year-olds. Participants (N = 52) saw combinations of cherry juice and water in displays that highlighted either part–whole or part–part relations. Their task was to indicate on a continuous rating scale how much each mixture would taste of cherries. Ratings suggested the use of a proportional integration rule for both kinds of displays, although more robustly and accurately for part–whole displays. The findings indicate that children may be more likely to scale proportional components when being presented with part–whole as compared with part–part displays. Crucially, ratings for part–whole problems correlated with fraction knowledge, even after controlling for age, suggesting that a sense of spatial proportions is associated with an understanding of fractional quantities.

The relation between spatial thinking and proportional reasoning in preschoolers

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. Childrens 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.

A Matter of Balance: Motor Control is Related to Children’s Spatial and Proportional Reasoning Skills

Recent research has shown close links between spatial and mathematical thinking and between spatial abilities and motor skills. However, longitudinal research examining the relations between motor, spatial, and mathematical skills is rare, and the nature of these relations remains unclear. The present study thus investigated the relation between children’s motor control and their spatial and proportional reasoning. We measured 6-year-olds’ spatial scaling (i.e., the ability to reason about different-sized spaces), their mental transformation skills, and their ability to balance on one leg as an index for motor control. One year later (N = 126), we tested the same children’s understanding of proportions. We also assessed several control variables (verbal IQ and socio-economic status) as well as inhibitory control, visuo-spatial and verbal working memory. Stepwise hierarchical regressions showed that, after accounting for effects of control variables, children’s balance skills significantly increased the explained variance in their spatial performance and proportional reasoning. Our results suggest specific relations between balance skills and spatial as well as proportional reasoning skills that cannot be explained by general differences in executive functioning or intelligence.

Where music meets space: Children’s sensitivity to pitch intervals is related to their mental spatial transformation skills

Relations have been found among various continuous dimensions, including space and musical pitch. To probe the nature and development of space-pitch mappings, we tested 5- to 7-year-olds and adults (N=69), who heard pitch intervals and were asked to choose the corresponding spatial representation. Results showed that children and adults both mapped pitches continuously onto space, although effects were stronger in older than younger children. Additionally, childrens spatial and numerical skills were tested, showing a relation between childrens spatial and pitch-matching skills, and between their spatial and numerical skills. However, pitch and number were not related, suggesting spatial underpinnings for pitch and number.

How Big Is Many? Development of Spatial and Numerical Magnitude Understanding

Abstract This chapter proposes that childrens spatial and mathematical developments are deeply interconnected because both domains involve magnitude processing. Magnitude can be conceptualized as applying to continuous quantities or collections of discrete entities and can also be treated either intensively (relative) or extensively (absolute). We suggest that young children may show an extensitivity bias because of a focus on extensive quantity as they learn about numbers and counting. Discrete presentation may prompt extensive thinking even when it is inappropriate. Here, we connect five domains of developmental research, which have traditionally been treated as separate: spatial estimation, spatial scaling, using number lines to represent integers, proportional reasoning, and fraction understanding. We discuss how childrens difficulties with coordinating intensive and extensive information may explain recurring response biases in these domains. In the last section, we consider how this theoretical framework sheds light on overall relations between spatial and mathematical thinking and how it may suggest new avenues for research.