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Being able to estimate quantity is important in everyday life and for success in the STEM disciplines. However, people have difficulty reasoning about magnitudes outside of human perception (e.g., nanoseconds, geologic time). This study examines patterns of estimation errors across temporal and spatial magnitudes at large scales. We evaluated the effectiveness of hierarchical alignment in improving estimations, and transfer across dimensions. The activity was successful in increasing accuracy for temporal and spatial magnitudes, and learning transferred to the estimation of numeric magnitudes associated with events and objects. However, there were also a number of informative differences in performance on temporal, spatial, and numeric magnitude measures, suggesting that participants possess different categorical information for these scales. Educational implications are discussed., (Copyright © 2016 Cognitive Science Society, Inc.)

There are many continuous quantitative dimensions in the physical world. Philosophical, psychological, and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time and mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, and density) and number can be conceptualized discretely or continuously (i.e., natural vs real numbers). Variation on these quantitative dimensions is typically correlated, e.g., larger objects often weigh more than smaller ones. Number is a distinctive continuous dimension because the natural numbers (i.e., positive integers) are used to quantify collections of discrete objects. This aspect of number is emphasized by teaching of the count word sequence and arithmetic during the early school years. We review research on spatial and numerical estimation, and argue that a generalized magnitude system is the starting point for development in both domains. Development occurs along several lines: (1) changes in capacity, durability, and precision, (2) differentiation of the generalized magnitude system into separable dimensions, (3) formation of a discrete number system, i.e., the positive integers, (4) mapping the positive integers onto the continuous number line, and (5) acquiring abstract knowledge of the relations between pairs of systems. We discuss implications of this approach for teaching various topics in mathematics, including scaling, measurement, proportional reasoning, and fractions., (© 2015 Wiley Periodicals, Inc.)

Improving mathematics and science education in the United States has been a matter of national concern for over half a century. Psychology has a vital role to play in this enterprise. In this article, the authors review the kinds of contributions that psychology can make in four areas: (a) early understanding of mathematics, (b) understanding of science, (c) social and motivational aspects of involvement in mathematics and science, and (d) assessment of learning in mathematics and science. They also examine challenges to psychology's playing a central and constructive role and make recommendations for overcoming those challenges.

Previous research has shown sketching to be useful tostudents solving math problems. The present studyexamines which aspects of middle school students’sketching are related to, or predict, successfullyanswering math problems. The effects of individualdifferences in cognitive factors – working memory,spatial ability, and prior math knowledge – on answeraccuracy are also analyzed. Stepwise regressionanalysis indicates that prior math knowledge and theinclusion of numerical representations of key problemrelationships in sketches positively predict answeraccuracy, whereas including irrelevant relationships ina sketch is associated with lower answer accuracy.Methodological implications for future research arediscussed.

Understanding the development of spatial skills is important for promoting school readiness and improving overall success in STEM (science, technology, engineering, and mathematics) fields (e.g., Wai, Lubinski, Benbow, & Steiger, 2010). Children use their spatial skills to understand the world, including visualizing how objects fit together, and can practice them via spatial assembly activities (e.g., puzzles or blocks). These skills are incorporated into measures of overall intelligence and have been linked to success in subjects like mathematics (Mix & Cheng, 2012) and science (Pallrand & Seeber, 1984; Pribyl & Bodner, 1987). This monograph sought to answer four questions about early spatial skill development: 1) Can we reliably measure spatial skills in 3‐ and 4‐year‐olds?; 2) Do spatial skills measured at 3 predict spatial skills at age 5?; 3) Do preschool spatial skills predict mathematics skills at age 5?; and 4) What factors contribute to individual differences in preschool spatial skills (e.g., SES, gender, fine‐motor skills, vocabulary, and executive function)? Longitudinal data generated from a new spatial skill test for 3‐year‐old children, called the TOSA (Test of Spatial Assembly), show that it is a reliable and valid measure of early spatial skills that provides strong prediction to spatial skills measured with established tests at age 5. New data using this measure finds links between early spatial skill and mathematics, language, and executive function skills. Analyses suggest that preschool spatial experiences may play a central role in children's mathematical skills around the time of school entry. Executive function skills provide an additional unique contribution to predicting mathematical performance. In addition, individual differences, specifically socioeconomic status, are related to spatial and mathematical skill. We conclude by exploring ways of providing rich early spatial experiences to children. [ABSTRACT FROM AUTHOR]

Abstract: Experiences with spatial toys such as blocks, puzzles, and shape games, and the spatial words and gestures they evoke from adults, have a significant influence on the early development of spatial skills. Spatial skills are important for success in science, technology, engineering, and mathematics (STEM) fields [77] (e.g., Wai, Lubinski, Benbow and Steiger, 2010), and are related to early mathematics performance [48] (Mix and Cheng, 2012), as early as age 3 [73] (Verdine, Golinkoff et al., in press). This paper focuses on the effects of early spatial experiences and their impacts on school readiness, discusses factors that influence the amount and quality of spatial play, and suggests methods for providing a “spatial education” prior to school entry. [Copyright &y& Elsevier]

Parents provide motivational and cognitive support within the same interaction, yet researchers have investigated these separately. We examined two key aspects of parental support, praise (motivational support) and spatial language (cognitive support), from fathers and mothers during three tasks with their first-grade children (6-7-year-olds; N = 107; 56 girls; 72.0% White, 23.4% Black). Parents' praise and spatial language varied by task but not child sex: Both parents produced more praise in the Etch-a-Sketch and block tasks than the card game and produced more spatial language in the Etch-a-Sketch task than other tasks. We further examined whether praise and spatial language in the two spatial tasks (Etch-a-Sketch and block construction) were related to children's later math and spatial skills. We found neither additive nor multiplicative effects of parents' praise or spatial language. We also did not see additive or multiplicative effects of fathers' and mothers' support. However, fathers' greater spatial language at first grade was negatively associated with boys' (but not girls') math achievement in third grade, with greater father spatial tokens related to their sons' lower math achievement. This suggests that boys may perceive fathers' support more negatively than girls do or that fathers may offer additional support for boys with lower abilities. Taken together, this study emphasizes the importance of considering contexts in examining parental support. The correlational nature of the study warrants future research to establish causal relations and to enhance our understanding of multifaceted parent-child interactions. [ABSTRACT FROM AUTHOR]