Deutsches Institut für Internationale Pädagogische Forschung (DIPF)
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The approximate number system (ANS) has been consistently found to be associated with math achievement. However, little is known about the interactions between the different instantiations of the ANS and in how many ways they are related to exact calculation. In a cross-sectional design, we investigated the relationship between three measures of ANS acuity (non-symbolic comparison, non-symbolic estimation and non-symbolic addition), their cross-sectional trajectories and specific contributions to exact calculation. Children with mathematical difficulties (MD) and typically achieving (TA) controls attending the first six years of formal schooling participated in the study. The MD group exhibited impairments in multiple instantiations of the ANS compared to their TA peers. The ANS acuity measured by all three tasks positively correlated with age in TA children, while no correlation was found between non-symbolic comparison and age in the MD group. The measures of ANS acuity significantly correlated with each other, reflecting at least in part a common numerosity code. Crucially, we found that non-symbolic estimation partially and non-symbolic addition fully mediated the effects of non-symbolic comparison in exact calculation.
The approximate number system (ANS) is assumingly related to mathematical learning but evidence supporting this assumption is mixed. The inconsistent findings might be attributed to the fact that different measures have been used to assess the ANS and mathematical skills. Moreover, associations between the performance on a measure of the ANS and mathematical skills may be discontinuous, i.e., stronger for children with lower math scores than for children with higher math scores, and may change with age. The aim of the present study was to examine the development of the ANS and arithmetic skills in elementary school children and to investigate how the relationship between the ANS and arithmetic skills develops. Individual markers of children's ANS (internal Weber fractions and mean reaction times in a non-symbolic numerical comparison task) and addition skills were assessed in their first year of school and 1 year later. Children showed improvements in addition performance and in the internal Weber fractions, whereas mean reaction times in the non-symbolic numerical comparison task did not change significantly. While children's addition performance was associated with the internal Weber fractions in the first year, it was associated with mean reaction times in the non-symbolic numerical comparison task in the second year. These associations were not found to be discontinuous and could not be explained by individual differences in reasoning, processing speed, or inhibitory control. The present study extends previous findings by demonstrating that addition performance is associated with different markers of the ANS in the course of development.
Lernverhalten und Lehrorganisation werden als komplementäre Komponenten einer Lernkultur betrachtet. Auf der Grundlage eines Modells der Lernmotivation wurde das Lernverhalten Studierender mit einer Latenten Klassenanalyse untersucht. Die Gruppenprofile wurden zu Noten und Workload-Daten einer Zeitbudget-Erhebung in Bezug gesetzt. Es zeigte sich, dass nur eine Gruppe Studierender ihren Lernprozess unter herkömmlichen Bedingungen selbstbestimmt erfolgreich gestaltet. Eine andere Lehrorganisation könnte Lernende anderer Typen der Motivationsregulation besser unterstützen.
Different lines of evidence suggest that children's mental representations of numbers are spatially organized in form of a mental number line. It is, however, still unclear whether a spatial organization is specific for the numerical domain or also applies to other ordinal sequences in children. In the present study, children (n = 129) aged 8–9 years were asked to indicate the midpoint of lines flanked by task-irrelevant digits or letters. We found that the localization of the midpoint was systematically biased toward the larger digit. A similar, but less pronounced, effect was detected for letters with spatial biases toward the letter succeeding in the alphabet. Instead of assuming domain-specific forms of spatial representations, we suggest that ordinal information expressing relations between different items of a sequence might be spatially coded in children, whereby numbers seem to convey this kind of information in the most salient way.
As demonstrated by the Overlapping Waves Model (Siegler, 1996), children’s strategy use in arithmetic tasks is variable, adaptive, and changes gradually with age and experience. In this study, first grade elementary school children (n = 73), who scored high, middle, or low in a standardized scholastic mathematic achievement test, were confronted with different arithmetic tasks (simple addition, e.g., 3 + 2, simple subtraction, e.g., 7 – 2, and more advanced addition, e.g., 7 + 9) to evoke different calculation strategies. Video analysis and children’s self-report were used to identify individual strategy behavior. In accordance with the Overlapping Waves Model, children in all achievement groups showed variable and multiple strategy usage and adapted their behavior to the tasks of the different categories. We demonstrated that not only low achievers differed from normal achievers but also that high achievers exhibited a unique pattern of strategy behavior in early mathematics.
In the course of elementary school children start to develop an academic self-concept reflecting their motivation, thoughts, and feelings about a specific domain. For the domain of mathematics, gender differences can emerge which are characterized by a less pronounced math self-concept for girls. However, studies are rather sparse regarding the early years of elementary school education, hence, the point in time when such gender differences emerge yet remains a matter of debate. In our study, we found that the math self-concept of elementary school children (n = 81) declined from first to second grade. While no differences in math achievement were observed between girls and boys, it became apparent that girls’ math self-concept was already less pronounced than the math self-concept of boys in the first years of elementary school. Our findings emphasize the importance of considering such gender differences even at the beginning of school education.
We introduce a computational model of the negative priming (NP) effect that includes perception, memory, attention, decision making, and action. The model is designed to provide a coherent picture across competing theories of NP. The model is formulated in terms of abstract dynamics for the activations of features, their binding into object entities, their semantic categorization as well as related memories and appropriate reactions. The dynamic variables interact in a connectionist network which is shown to be adaptable to a variety of experimental paradigms. We find that selective attention can be modeled by means of inhibitory processes and by a threshold dynamics. From the necessity of quantifying the experimental paradigms, we conclude that the specificity of the experimental paradigm must be taken into account when predicting the nature of the NP effect.
The purpose of the present study was to examine the effects of cooperative training strategies to enhance students' socioscientific decision making as well as their metacognitive skills in the science classroom. Socioscientific decision making refers to both “describing socioscientific issues” as well as “developing and evaluating solutions” to socioscientific issues. We investigated two cooperative training strategies which differed with respect to embedded metacognitive instructions that were developed on the basis of the IMPROVE method. Participants were 360 senior high school students who studied either in a cooperative learning setting (COOP), a cooperative learning setting with embedded metacognitive questions (COOP+META), or a nontreatment control group. Results indicate that students in the two training conditions outperformed students in the control group on both processes of socioscientific decision making. However, students in the COOP+META condition did not outperform students in the COOP condition. With respect to students' learning outcomes on the regulation facet of metacognition, results indicate that all conditions improved over time. Students in the COOP+META condition exhibited highest mean scores at posttest measures, but again, results were not significant. Implications for integrating metacognitive instructions into science classrooms are discussed.
The neural correlates of developmental dyslexia have been investigated intensively over the last two decades and reliable evidence for a dysfunction of left-hemispheric reading systems in dyslexic readers has been found in functional neuroimaging studies. In addition, structural imaging studies using voxel-based morphometry (VBM) demonstrated grey matter reductions in dyslexics in several brain regions. To objectively assess the consistency of these findings, we performed activation likelihood estimation (ALE) meta-analysis on nine published VBM studies reporting 62 foci of grey matter reduction in dyslexic readers. We found six significant clusters of convergence in bilateral temporo-parietal and left occipito-temporal cortical regions and in the cerebellum bilaterally. To identify possible overlaps between structural and functional deviations in dyslexic readers, we conducted additional ALE meta-analyses of imaging studies reporting functional underactivations (125 foci from 24 studies) or overactivations (95 foci from 11 studies ) in dyslexics. Subsequent conjunction analyses revealed overlaps between the results of the VBM meta-analysis and the meta-analysis of functional underactivations in the fusiform and supramarginal gyri of the left hemisphere. An overlap between VBM results and the meta-analysis of functional overactivations was found in the left cerebellum. The results of our study provide evidence for consistent grey matter variations bilaterally in the dyslexic brain and substantial overlap of these structural variations with functional abnormalities in left hemispheric regions.
We examined whether positive transfer of cognitive training, which so far has been observed for individual tests only, also generalizes to cognitive abilities, thereby carrying greater promise for improving everyday intellectual competence in adulthood and old age. In the COGITO Study, 101 younger and 103 older adults practiced six tests of perceptual speed (PS), three tests of working memory (WM), and three tests of episodic memory (EM) for over 100 daily 1-h sessions. Transfer assessment included multiple tests of PS, WM, EM, and reasoning. In both age groups, reliable positive transfer was found not only for individual tests but also for cognitive abilities, represented as latent factors. Furthermore, the pattern of correlations between latent change factors of practiced and latent change factors of transfer tasks indicates systematic relations at the level of broad abilities, making the interpretation of effects as resulting from unspecific increases in motivation or self-concept less likely. Keywords: cognitive training, cognitive abilities, transfer, latent factors, working memory