David H. Uttal

The Malleability of Spatial Skills: A Meta-analysis of Training Studies

Having good spatial skills strongly predicts achievement and attainment in science, technology, engineering, and mathematics fields (e.g., Shea, Lubinski, & Benbow, 2001; Wai, Lubinski, & Benbow, 2009). Improving spatial skills is therefore of both theoretical and practical importance. To determine whether and to what extent training and experience can improve these skills, we meta-analyzed 217 research studies investigating the magnitude, moderators, durability, and generalizability of training on spatial skills. After eliminating outliers, the average effect size (Hedgess g) for training relative to control was 0.47 (SE = 0.04). Training effects were stable and were not affected by delays between training and posttesting. Training also transferred to other spatial tasks that were not directly trained. We analyzed the effects of several moderators, including the presence and type of control groups, sex, age, and type of training. Additionally, we included a theoretically motivated typology of spatial skills that emphasizes 2 dimensions: intrinsic versus extrinsic and static versus dynamic (Newcombe & Shipley, in press). Finally, we consider the potential educational and policy implications of directly training spatial skills. Considered together, the results suggest that spatially enriched education could pay substantial dividends in increasing participation in mathematics, science, and engineering.

Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics

This article offers a new perspective on the use of concrete objects to teach mathematics. It is commonly assumed that concrete manipulatives are effective because they allow children to perform mathematics without understanding arbitrary, written mathematical symbols. We argue that the sharp distinction between concrete and abstract forms of mathematical expression may not be justified. We believe instead that manipulatives are also symbols; teachers intend for them to stand for or represent a concept or written symbol. Consequently, research on how young children comprehend symbolic relations is relevant to studying their comprehension of manipulatives. We review evidence that many of the problems that children encounter when using manipulatives are very similar to problems that they have using other symbol systems such as scale models. Successful use of manipulatives depends on treating them as symbols rather than as substitutes for symbols. A persistent dilemma for teachers of mathematics concerns how to help children understand

Cultural Values, Parents' Beliefs, and Children's Achievement in the United States and China'

This paper describes traditional and modern Chinese cultural values regarding educational achievement and how they are reflected in the beliefs of parents and children. Chinese philosophy traditionally has emphasized human malleability and the value of self- improvement. Chinese parents set higher standards and work more often with their children on homework than their American counterparts, and Chinese cultural values help to ensure that children work diligently. These factors may help to explain the superior performance of Chinese children in cross-national comparisons of mathematics achievement.

Grasping the Nature of Pictures

The role of experience in the development of pictorial competence has been the center of substantial debate. The four studies presented here help resolve the controversy by systematically documenting and examining manual exploration of depicted objects by infants. We report that 9-month-old infants manually investigate pictures, touching and feeling depicted objects as if they were real objects and even trying to pick them up off the page. The same behavior was observed in babies from two extremely different societies (the United States and the Ivory Coast). This investigation of pictures occurs even though infants can discriminate between real objects and their depictions. By the time infants are 19 months of age, their manual exploration is replaced by pointing at depicted objects. These results indicate that initial uncertainty about the nature of pictures leads infants to investigate them. Through experience, infants begin to acquire a concept of “picture.” This concept includes the fact that a picture has a dual nature (it is both an object and a representation of something other than itself), as well as knowledge about the culturally appropriate use of pictures.

Seeing the big picture: map use and the development of spatial cognition

This paper considers the relation between the development of spatial cognition and children’s use of maps and models. A new theoretical perspective is presented that takes into account the influences of maps on the development of spatial cognition. Maps provide a perspective on spatial information that differs in important ways from the perspective gained from direct experience navigating in the world. Using and thinking about maps may help children to acquire abstract concepts of space and the ability to think systematically about spatial relations that they have not experienced directly. In addition, exposure to maps may help children to think about multiple spatial relations among multiple locations. The results of previous studies that have demonstrated developmental differences in children’s cognition of large-scale environments are examined from this theoretical perspective. This review suggests that the development of spatial cognition consists partly of the acquisition of models of large-scale space, and that maps influence the development of the modern Western model.

Spatial Thinking and STEM Education: When, Why, and How?

Abstract We explore the relation between spatial thinking and performance and attainment in science, technology, engineering and mathematics (STEM) domains. Spatial skills strongly predict who will go into STEM fields. But why is this true? We argue that spatial skills serve as a gateway or barrier for entry into STEM fields. We review literature that indicates that psychometrically-assessed spatial abilities predict performance early in STEM learning, but become less predicative as students advance toward expertise. Experts often have mental representations that allow them to solve problems without having to use spatial thinking. For example, an expert chemist who knows a great deal about the structure and behavior of a particular molecule may not need to mentally rotate a representation of this molecule in order to make a decision about it. Novices who have low levels of spatial skills may not be able to advance to the point at which spatial skills become less important. Thus, a program of spatial training might help to increase the number of people who go into STEM fields. We review and give examples of work on spatial training, which show that spatial abilities are quite malleable. Our chapter helps to constrain and specify when and how spatial abilities do (or do not) matter in STEM thinking and learning.

The initial segment strategy: A heuristic for route selection

People often choose one route when traveling from point A to point B and a different route when traveling from point B to point A. To explain these route asymmetries, we propose that people rely on a heuristic (the initial segment strategy, or ISS) during route planning. This heuristic involves basing decisions disproportionately on the straightness of the initial segments of the routes. Asymmetries arise because the characteristics that favor selection of a particular route in one direction will usually differ from those that favor selection when traveling in the opposite direction. Results from five experiments supported these claims. In the first three experiments, we found that subjects’ decisions were asymmetric and involved a preference for initially straight routes. In Experiment 4, we confirmed that the ISS is a heuristic by demonstrating that people rely on it more when under time pressure. However, people can choose the optimal route when instructed to do so. In Experiment 5, we generalized the findings by having subjects select routes on maps of college campuses. Taken together, the results indicate that the ISS can account for asymmetries in route choices on both real and artificial maps.

Exploring and Enhancing Spatial Thinking Links to Achievement in Science, Technology, Engineering, and Mathematics?

Although neglected in traditional education, spatial thinking plays a critical role in achievement in science, technology, engineering, and mathematics (STEM) fields. We review this relationship and investigate the malleability of spatial thinking. Can spatial thinking be improved with training, life experience, or educational interventions? Can improving spatial thinking improve STEM achievement? Research indicates that the answer is “yes” to both questions. A recent quantitative synthesis of 206 spatial training studies found an average training improvement of 0.47 standard deviations. Training effects lasted for months in studies examining durability and transferred to tasks that differed at least moderately from training tasks. A few studies indicate that spatial training can improve STEM learning, although more research needs to be done on this issue. We argue that including spatial thinking in STEM curricula could substantially increase the number of Americans with the requisite cognitive skills to enter STEM careers.

The Origins of Pictorial Competence

Pictorial competence, which refers to the many factors involved in perceiving, interpreting, understanding, and using pictures, develops gradually over the first few years of life. Although experience is not required for accurate perception of pictures, it is necessary for understanding the nature of pictures. Infants initially respond to depicted objects as if they were real objects, and toddlers are remarkably insensitive to picture orientation. Only gradually do young children figure out the nature of pictures and how they are used.

Chapter Four – Spatial Thinking and STEM Education: When, Why, and How?

Abstract We explore the relation between spatial thinking and performance and attainment in science, technology, engineering and mathematics (STEM) domains. Spatial skills strongly predict who will go into STEM fields. But why is this true? We argue that spatial skills serve as a gateway or barrier for entry into STEM fields. We review literature that indicates that psychometrically-assessed spatial abilities predict performance early in STEM learning, but become less predicative as students advance toward expertise. Experts often have mental representations that allow them to solve problems without having to use spatial thinking. For example, an expert chemist who knows a great deal about the structure and behavior of a particular molecule may not need to mentally rotate a representation of this molecule in order to make a decision about it. Novices who have low levels of spatial skills may not be able to advance to the point at which spatial skills become less important. Thus, a program of spatial training might help to increase the number of people who go into STEM fields. We review and give examples of work on spatial training, which show that spatial abilities are quite malleable. Our chapter helps to constrain and specify when and how spatial abilities do (or do not) matter in STEM thinking and learning.