Research has demonstrated strong relations between spatial skill and mathematics across ages and in both typical and atypical populations, suggesting that a significant proportion of variance in ...mathematics performance can be explained by variance in spatial skill. Why do these relations exist and how do they develop? Studies of dimensionality in the two domains suggest the relation holds across tasks and is not limited to specific spatial or mathematics subskills. Spatial skills might perform several functions in real‐time problem solving, but these have not been differentiated empirically. The relation appears to be based on automatic shared processing, as well as strategic recruitment of spatial processes. Developmentally, the relation is consistent in its strength, but may change qualitatively, particularly in response to novel mathematics content.
We tested whether mental rotation training improved math performance in 6- to 8-year-olds. Children were pretested on a range of number and math skills. Then one group received a single session of ...mental rotation training using an object completion task that had previously improved spatial ability in children this age (Ehrlich, Levine, & Goldin-Meadow,
2006
). The remaining children completed crossword puzzles instead. Children's posttest scores revealed that those in the spatial training group improved significantly on calculation problems. In contrast, children in the control group did not improve on any math tasks. Further analyses revealed that the spatial training group's improvement was largely due to better performance on missing term problems (e.g., 4 + ____ = 11).
Celotno besedilo
Dostopno za:
BFBNIB, DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
The gut of healthy human neonates is usually devoid of viruses at birth, but quickly becomes colonized, which-in some cases-leads to gastrointestinal disorders
. Here we show that the assembly of the ...viral community in neonates takes place in distinct steps. Fluorescent staining of virus-like particles purified from infant meconium or early stool samples shows few or no particles, but by one month of life particle numbers increase to 10
per gram, and these numbers seem to persist throughout life
. We investigated the origin of these viral populations using shotgun metagenomic sequencing of virus-enriched preparations and whole microbial communities, followed by targeted microbiological analyses. Results indicate that, early after birth, pioneer bacteria colonize the infant gut and by one month prophages induced from these bacteria provide the predominant population of virus-like particles. By four months of life, identifiable viruses that replicate in human cells become more prominent. Multiple human viruses were more abundant in stool samples from babies who were exclusively fed on formula milk compared with those fed partially or fully on breast milk, paralleling reports that breast milk can be protective against viral infections
. Bacteriophage populations also differed depending on whether or not the infant was breastfed. We show that the colonization of the infant gut is stepwise, first mainly by temperate bacteriophages induced from pioneer bacteria, and later by viruses that replicate in human cells; this second phase is modulated by breastfeeding.
The relations among various spatial and mathematics skills were assessed in a cross-sectional study of 854 children from kindergarten, third, and sixth grades (i.e., 5 to 13 years of age). Children ...completed a battery of spatial mathematics tests and their scores were submitted to exploratory factor analyses both within and across domains. In the within domain analyses, all of the measures formed single factors at each age, suggesting consistent, unitary structures across this age range. Yet, as in previous work, the 2 domains were highly correlated, both in terms of overall composite score and pairwise comparisons of individual tasks. When both spatial and mathematics scores were submitted to the same factor analysis, the 2 domain specific factors again emerged, but there also were significant cross-domain factor loadings that varied with age. Multivariate regressions replicated the factor analysis and further revealed that mental rotation was the best predictor of mathematical performance in kindergarten, and visual-spatial working memory was the best predictor of mathematical performance in sixth grade. The mathematical tasks that predicted the most variance in spatial skill were place value (K, 3rd, 6th), word problems (3rd, 6th), calculation (K), fraction concepts (3rd), and algebra (6th). Thus, although spatial skill and mathematics each have strong internal structures, they also share significant overlap, and have particularly strong cross-domain relations for certain tasks.
Prior research has revealed robust and consistent relations between spatial and mathematical skills. Yet, establishing a causal relation has been met with mixed effects. To better understand whether, ...to what extent, and under what conditions mathematics performance can be improved through spatial training, we conducted a systematic meta-analysis of the extant literature. Our analysis included 29 studies that used controlled pre-post study designs to test the effects of spatial training on mathematics (N = 3,765; k = 89). The average effect size (Hedges's g) of training relative to control conditions was .28 (SE = .07). Critically, there was also evidence that spatial training improved individuals' spatial thinking (g = .49, SE = .09). Follow-up analyses revealed that age, use of concrete manipulatives, and type of transfer ("near" vs. "far") moderated the effects of spatial training on mathematics. As the age of participants increased from 3 to 20 years, the effects of spatial training also increased in size. Spatial training paradigms that used concrete materials (e.g., manipulatives) were more effective than those that did not (e.g., computerized training). Larger transfer effects were observed for mathematics outcomes more closely aligned to the spatial training delivered compared to outcomes more distally related. None of the other variables examined (training dosage, spatial gains, posttest timing, type of control group, experimental design, publication status) moderated the effects. Additionally, analyses of publication bias and selective outcome reporting were nonsignificant. Overall, our results support prior research and theoretical claims that spatial training is an effective means for enhancing mathematical understanding and performance. However, our meta-analysis also highlights a poor understanding of the mechanisms that support transfer. To fully realize the potential benefits of spatial training on mathematics achievement, more theoretically guided studies are needed.
The number‐line task has been extensively used to study the mental representation of numbers in children. However, studies suggest that proportional reasoning provides a better account of children’s ...performance. Ninety 4‐ to 6‐year‐olds were given a number‐line task with symbolic numbers, with clustered dot arrays that resembled a perceptual scaling task, or with spread‐out dot arrays that involved numerical estimation. Children performed well with clustered dot arrays, but poorly with symbolic numbers and spread‐out dot arrays. Performances with symbolic numbers and spread‐out dot arrays were highly correlated and were related to counting skill; neither was true for clustered dot arrays. Overall, results provide evidence for the role of mental representation of numbers in the symbolic number‐line task.
In this article, we review approaches to modeling a connection between spatial and mathematical thinking across development. We critically evaluate the strengths and weaknesses of factor analyses, ...meta-analyses, and experimental literatures. We examine those studies that set out to describe the nature and number of spatial and mathematical skills and specific connections between these abilities, especially those that included children as participants. We also find evidence of strong spatial-mathematical connections and transfer from spatial interventions to mathematical understanding. Finally, we map out the kinds of studies that could enhance our understanding of the mechanisms by which spatial and mathematical processing are connected and the principles by which mathematical outcomes could be enhanced through spatial training in educational settings.
A pretest-training-posttest design assessed whether training to improve spatial skills also improved mathematics performance in elementary-aged children. First grade students (mean age = 7 years, n = ...134) and sixth grade students (mean age = 12 years, n = 124) completed training in 1 of 2 spatial skills-spatial visualization or form perception/VSWM-or in a nonspatial control condition that featured language arts training. Spatial training led to better overall mathematics performance in both grades, and the gains were significantly greater than for language arts training. The same effects were found regardless of spatial training type, or the type of mathematics tested.
Educational Impact and Implications Statement
We tested whether children's mathematics scores could be improved with training in spatial skills (like, imagining objects rotating or remembering locations), based on previous research showing a connection between math and spatial skill. We found that spatial training improved math scores for children in first and sixth grade, and it did not seem to matter what kind of spatial practice we used or what specific math problems we tested. Our findings suggest that when children solve mathematics problems, they may recruit spatial thinking to help them, so teachers might use spatial tasks as a warm-up before mathematics instruction, or provide extra spatial practice to students who show weak spatial skills.
There is a well-known relation between spatial ability and mathematics dating back to the work of early twentieth century factor analysts. This connection is a ripe opportunity for educators, who ...might use spatial training to improve math learning. However, a closer look at the literature reveals gaps that impede direct application. The primary problem is that although this relation is well established in older children and adults, its emergence in early development and subsequent developmental interactions are not well documented. Moreover, there is a need for more mechanistic explanations that might be leveraged to improve math education. In this chapter, we attempt to address these issues by reviewing the existing literature to identify instances where answers are available and others where further research is needed.
Numerous studies from developmental psychology have suggested that human symbolic representation of numbers is built upon the evolutionally old capacity for representing quantities that is shared ...with other species. Substantial research from mathematics education also supports the idea that mathematical concepts are best learned through their corresponding physical representations. We argue for an independent pathway to learning “big” multi-digit symbolic numbers that focuses on the symbol system itself. Across five experiments using both between- and within-subject designs, we asked preschoolers to identify written multi-digit numbers with their spoken names in a two-alternative-choice-test or to indicate the larger quantity between two written numbers. Results showed that preschoolers could reliably map spoken number names to written forms and compare the magnitudes of two written multi-digit numbers. Importantly, these abilities were not related to their non-symbolic representation of quantities. These findings have important implications for numerical cognition, symbolic development, teaching, and education.
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