Search

Background: Mastering fractions seems among the most critical mathematical skills for students to acquire in school as fraction understanding significantly predicts later mathematic achievements, but also broader academic and vocational prospects. As such, identifying longitudinal predictors of fraction understanding (e.g., mastery of numbers and operations) is highly relevant. However, almost all existing studies identifying more basic numerical skills as predictors of fraction understanding rest on data acquired in face-to-face testing--mostly in classrooms. Objectives: In this article, we evaluated whether results obtained in these previous studies generalized to data from the curriculum-based online learning environment Bettermarks for mathematics used in schools in the Netherlands. Methods: We considered data from more than 5000 students who solved over 1 million mathematical problem sets on basic mathematical skills, fractions, but also algebra. Results and Conclusions: In line with previous findings, we found that fraction understanding was predicted significantly by more basic mathematical skills. Our analyses also indicated that algebra achievement was predicted significantly by fraction understanding beyond influences of more basic mathematical skills. Implications: Together, these findings generalized previous results based on face-to-face testing to the context of data from online learning environments and thus, indicate that data from such large-scale online learning environments may well qualify to provide significant insights into the hierarchical development of mathematical skills.

Language and numerical development are associated in early childhood. In the present study, we focused on the association of the development of children's cardinality understanding of small numbers and their knowledge on unspecific quantifiers (i.e., many, a few). In a longitudinal study, we pursued the research question whether children's knowledge on quantifiers facilitated the acquisition of specific cardinality understanding. Therefore, we followed a total of 76 (34 boys and 42 girls) monolingual German-speaking children aged between 3;6 and 4;6 years at the first measurement time point for two more measurement time points 6 months and one year later. Children's cardinality understanding of small numbers and their quantifier knowledge were assessed using a give-N task. Results indicated a full mediation effect of children's quantifier knowledge at time point 2 on the development of their cardinality understanding from time point 2 to time point 3. This indicates a significant contribution of children's knowledge on unspecific quantifiers to the development of their specific cardinality understanding.

Research on instructional design provides inconsistent results on the use of game elements in cognitive tasks or learning. Cognitive load theory suggests that game elements increase extraneous cognitive load and, thus, may distract the users. In contrast, from an emotional design perspective, the use of game elements is argued to increase performance by providing a more interesting and motivating task environment. To contribute to this debate, the current study investigated the effect of game elements on behavioral performance, attention, and motivation. We designed two versions of the number line estimation task--one with game elements and one without. Participants completed both versions of the task while their eye-fixation behavior was recorded. Results indicated that participants paid attention to game elements, that is, they fixated them, although they were not necessary to complete the task. However, no difference in estimation accuracy was observed between the two task versions. Moreover, the task version with game elements was rated to be more attractive, stimulating, and novel, and participants reported experiencing greater flow. In sum, these data indicate that game elements seem to capture attention but also increase motivational aspects of learning tasks rather than decreasing performance.

Language-specific differences in number words influence number processing even in nonverbal numerical tasks. For instance, the unit-decade compatibility effect in two-digit number magnitude comparison (compatible number pairs [42_57: 4 < 5 and 2 < 7] are responded to faster than incompatible pairs [47_62: 4 < 6 but 7 > 2]) was shown to be influenced by the inversion of number words (e.g., in German the number word for 42 is "zweiundvierzig" [literally: "two-and-forty"]). In two studies, we used articulatory suppression to investigate whether previously observed cross-linguistic differences in two-digit number processing are indeed driven by differences in number word formation. In a two-digit number comparison task, German- and English-speaking participants had to identify the larger of two numbers presented in Arabic digits. In Study 1, participants performed the same task twice, with and without articulatory suppression. In Study 2, the percentage of within-decade filler items (36_39) was manipulated additionally. As expected, in both studies between-groups differences in the compatibility effect disappeared under articulatory suppression irrespective of the percentage of fillers included. Furthermore, paralleling results of previous studies including 33% or less filler items, we found that the compatibility effect was larger in German compared with English speakers in the 20% filler condition. However, this pattern was reversed in the 50% filler condition in both studies. Thus, results provide first direct evidence for influences of verbal number word formation on symbolic number processing. Moreover, these new findings suggest that linguistic influences and those of cognitive control processes associated with characteristics of the stimulus set interact in symbolic number processing.

The metaphor of the mental number line accounts for numerous empirical effects of spatial-numerical associations. In the present study, we aimed at investigating directional spatial-numerical associations reflected by SNARC-like digit-direction and sign-direction congruency effects as well as the sign-digit compatibility effect when 6th graders performed magnitude comparisons of multi-symbol numbers (i.e., positive and negative numbers). As spatial-numerical associations were associated with sensorimotor experiences, we used whole-body and finger tapping responses to manipulate the extent of motor responses. We only observed a SNARC-like digit-direction congruency effect, but neither a sign-direction congruency nor a sign-digit compatibility effect. This indicates that 6th graders may already have developed spatial-numerical associations for absolute number magnitude, but not yet for polarity signs. Furthermore, not observing a sign-digit compatibility effect seemed to suggest that 6th graders may not yet process multi-symbol numbers in the same parallel componential way as adults do. We argue that while 6th graders are able to process negative numbers, they are not yet automatically associated with space or integrated in the place-value structure of the Arabic number system like multi-digit numbers are at this age.

The aim of this study was to identify mathematical competencies in early childhood and cognitive correlates of those competencies in a prospective longitudinal sample of children (N = 1,292) in predominantly low-income and nonurban communities in the United States. General mental ability, processing speed, vocabulary, and the working memory (WM), inhibitory control (IC), and cognitive flexibility components of executive function (EF) were assessed when children were aged 4 and 5 years. Math ability was assessed prior to school entry using a norm-referenced assessment. Exploratory factor analysis indicated that items from the math assessment loaded onto factors representing conceptual and procedural skill. General mental ability, processing speed, vocabulary, and a unitary EF composite all related to both conceptual and procedural skill. When EF components were examined separately, however, only the IC aspect of EF was related to conceptual skill and only the WM aspect of EF was related to procedural skill.

Both adults and children are slower at judging the ordinality of non-consecutive sequences (e.g., 1-3-5) than consecutive sequences (e.g., 1-2-3). It has been suggested that the processing of non-consecutive sequences is slower because it conflicts with the intuition that only count-list sequences are correctly ordered. An alternative explanation, however, may be that people simply find it difficult to switch between consecutive and non-consecutive concepts of order during order judgement tasks. Therefore, in adult participants, we tested whether presenting consecutive and non-consecutive sequences separately would eliminate this switching demand and thus improve performance. In contrast with this prediction, however, we observed similar patterns of response times independent of whether sequences were presented separately or together (Experiment 1). Furthermore, this pattern of results remained even when we doubled the number of trials and made participants explicitly aware when consecutive and non-consecutive sequences were presented separately (Experiment 2). Overall, these results suggest slower response times for non-consecutive sequences do not result from a cognitive demand of switching between consecutive and non-consecutive concepts of order, at least not in adults. [ABSTRACT FROM AUTHOR]

In order processing, consecutive sequences (e.g., 1‐2‐3) are generally processed faster than nonconsecutive sequences (e.g., 1‐3‐5) (also referred to as the reverse distance effect). A common explanation for this effect is that order processing operates via a memory‐based associative mechanism whereby consecutive sequences are processed faster because they are more familiar and thus more easily retrieved from memory. Conflicting with this proposal, however, is the finding that this effect is often absent. A possible explanation for these absences is that familiarity may vary both within and across sequence types; therefore, not all consecutive sequences are necessarily more familiar than all nonconsecutive sequences. Accordingly, under this familiarity perspective, familiar sequences should always be processed faster than unfamiliar sequences, but consecutive sequences may not always be processed faster than nonconsecutive sequences. To test this hypothesis in an adult population, we used a comparative judgment approach to measure familiarity at the individual sequence level. Using this measure, we found that although not all participants showed a reverse distance effect, all participants displayed a familiarity effect. Notably, this familiarity effect appeared stronger than the reverse distance effect at both the group and individual level; thus, suggesting the reverse distance effect may be better conceptualized as a specific instance of a more general familiarity effect. [ABSTRACT FROM AUTHOR]