Finger counting, finger number gesturing, and basic numerical skills: A cross-sectional study in 3- to 5-year-olds.

Recent evidence suggests that using finger-based strategies is beneficial for the acquisition of basic numerical skills. There are basically two finger-based strategies to be distinguished: (a) finger counting (i.e., extending single fingers successively) and (b) finger number gesturing (i.e., extending fingers simultaneously to represent magnitudes). In this study, we investigated both spontaneous and prompted finger counting and finger number gesturing as well as their contribution to basic numerical skills in 3- to 5-year-olds (N = 156). Results revealed that only 6% of children spontaneously used their fingers for counting when asked to name a specific number of animals, whereas 59% applied finger number gesturing to show their age. This indicates that the spontaneous use of finger-based strategies depends heavily on the specific context. Moreover, children performed significantly better in prompted finger counting than in finger number gesturing, suggesting that both strategies build on each other. Finally, both prompted finger counting and finger number gesturing significantly and individually predicted counting, cardinal number knowledge, and basic arithmetic. These results indicate that finger counting and finger number gesturing follow and positively relate to numerical development.

You can count on your fingers: Finger-based intervention improves first-graders' arithmetic learning.

The question of whether finger use should be encouraged or discouraged in early mathematics instruction remains a topic of debate. Scientific evidence on this matter is scarce due to the limited number of systematic intervention studies. Accordingly, we conducted an intervention study in which first-graders (Mage = 6.48 years, SD = 0.35) completed a finger-based training (18 sessions of âˆ¼ 30 min each) over the course of the first school year. The training was integrated into standard mathematics instruction in schools and compared with business-as-usual curriculum teaching. At the end of first grade and in a follow-up test 9 months later in second grade, children who received the finger training (n = 119) outperformed the control group (n = 123) in written addition and subtraction. No group differences were observed for number line estimation tasks. These results suggest that finger-based numerical strategies can enhance arithmetic learning, supporting the idea of an embodied representation of numbers, and challenge the prevailing skepticism about finger use in primary mathematics education.

Grounding (fairly) complex numerical knowledge: an educational example.

In this article, we contextualize and discuss an on-line contribution to this special issue in which a video-recorded lecture demonstrates the teaching of an abstract mathematical concept, namely regression to the mean. We first motivate the pertinence of this example from the perspective of embodied cognition. Then, we identify mechanisms of teaching that reflect embodied cognitive practices, such as the concreteness fading approach. Rather than a comprehensive review of multiple extensive literatures, this article provides the interested reader with several sources or entries into those literatures.

Fostering early numerical competencies by playing conventional board games.

Recent evidence indicates that playing numerical board games is beneficial for the numerical development of preschoolers. However, board games used in these studies were often specifically developed for training numerical skills. Therefore, we examined whether similar beneficial effects could be observed for playing conventional board games such as Parcheesi. In an intervention study with seven 30-min training sessions over a period of 4 weeks, we observed that 4- to 6-year-old children (Mage = 4 years 11 months) who played conventional board games with traditional number dice (with dot faces numbered from one to six) benefitted more from the board games than children who played board games with color or non-numerical symbol dice. Pretest-posttest comparisons indicated differential effects on counting skills and the ability to recognize and use structures. Beyond these immediate training effects observed in posttest, the differential beneficial effects of playing board games using traditional dot dice on recognizing and using structures was still present in a follow-up test 1 year after the intervention. Thus, playing conventional board games using traditional number dice seems to be an effective low-threshold intervention to foster early numerical competencies.

Mode effect: An issue of perspective? Writing mode differences in a spelling assessment in German children with and without developmental dyslexia.

Digital technology has an increasing influence on writing processes. In this context, the question arises whether changes in writing mode (i.e., handwriting vs. computer-keyboard typing) also require changes in writing assessments. However, data directly comparing writing mode influences in children with and without developmental writing deficits are scarce. This study investigated the influence of writing mode in German-speaking, typically developing children and children with developmental dyslexia (DD) from two different levels. Results showed on a general level that writing mode influenced overall spelling accuracy, writing time, and self-corrections comparably in children with and without DD. On a rule-specific level, outcomes for writing time and self-corrections substantiated these findings. However, as regards spelling accuracy, a mode effect was only apparent for capitalization, whereas other spelling rules were resistant to writing mode influences. Present findings suggest that a mode effect is present only for typing specific aspects (e.g., capitalization) rather than reflecting a general influence on orthographic principles (e.g., grapheme-phoneme assignment, morphologic principles). These mode-specific aspects seem to comparably affect the writing performance of typically developing children and children with DD. We recommend writing assessments to consider that different writing modes may influence individual spelling rules differently.

Mastery of structured quantities like finger or dice patterns predict arithmetic performance.

In the present study, we investigated whether structured quantities like finger or dice patterns are enumerated better than unstructured quantities because they may not require counting. Moreover, we hypothesized children's mastery of structured quantities to predict their later arithmetic performance longitudinally. In particular, we expected that children more proficient in enumerating structured quantities early in their numerical development, should develop more effective calculation strategies later because they may rely on counting less. Therefore, we conducted a longitudinal study (including 116 children, 58 girls) over the course of about 7 months from preschool (at about 6 years of age) to the middle of first grade. Results showed that structured quantities were indeed enumerated more accurately and faster than unstructured quantities in preschool. Additionally, we observed significant associations of enumeration of structured and unstructured with children's addition performance in first grade. However, regression analysis indicated only enumeration of structured but not unstructured quantities to significantly predict later addition performance. In sum, this longitudinal study clearly indicates that mastery of structured quantities seems to be beneficial for children's development of basic arithmetic abilities.

More than simple facts: cross-linguistic differences in place-value processing in arithmetic fact retrieval.

Linguistic specificities such as the inversion property of number words (e.g., in German 43 is spoken dreiundvierzig, literally three and  forty) moderate Arabic number processing. So far, cross-linguistic studies have mostly focused on inversion-related effects on simple (e.g., number comparison) and calculation-based (e.g., multi-digit addition) magnitude processing of numerical information. Despite the assumption that multiplication facts are represented in verbal format, not much attention has been paid to inversion-related influences on multiplication fact retrieval. Accordingly, the current study evaluated inversion-related effects on the processing of place-value information in multiplication. In a verification paradigm, the decade consistency effect (i.e., more errors when the decade of a solution probe shares the decade digit with the correct solution) was larger for English- than German-speaking participants for table-related probes. Processing of decade digits might be prioritised in English-speaking participants because the decade digit is named first in English number words, whereas in German number words the unit digit is named first. Our results indicate that (1) the influence of specificities of a verbal number word formation on place-value processing generalise to arithmetic fact retrieval and (2) inversion of number words might even be advantageous in specific cases.

Embodied numerical representations and their association with multi-digit arithmetic performance.

There is a well-documented association between fingers and numbers, which was claimed to stem from the use of finger-based strategies for counting and calculating during childhood. Recently, it has been argued that this may lead to a concomitant activation of finger-based alongside other numerical representations when encountering single-digit numbers. Indeed, the occurrence of such a co-activation is supported by observed influences of finger counting habits on different numerical tasks, including single-digit arithmetic problem solving. In this study, we pursued the question whether the influence of finger-based representations on arithmetic generalizes to multi-digit arithmetic by investigating the association between the recognition of canonical and non-canonical finger patterns and multi-digit arithmetic in adults. Results indicated that canonical finger-based numerical representations were significantly associated with addition performance only, whereas non-canonical finger-based representations were associated significantly with all four arithmetic operations. We argue that, because non-canonical patterns do not benefit from the iconicity of canonical patterns, their magnitude may need to be constructed through magnitude manipulation which may in turn increase associations with mental arithmetic. In sum, our findings provide converging evidence for a functional association between finger-based representations and arithmetic performance.

Anticipation of difficult tasks: neural correlates of negative emotions and emotion regulation.

BACKGROUND: Difficult cognitive tasks are often associated with negative feelings. This can be already the case for the mere anticipation of having to do a difficult task. For the case of difficult math tasks, it was recently suggested that such a negative emotional response may be exclusive to highly math-anxious individuals. However, it is also conceivable that negative emotional responses simply reflect that math is perceived as difficult. Here we investigated whether non-math-anxious individuals also experience negative emotional responses when anticipating to do difficult math tasks. METHODS: We compared brain activation following the presentation of a numerical cue indicating either difficult or easy upcoming proportion magnitude comparison tasks. RESULTS: Comparable to previous results for highly math-anxious individuals we observed a network associated with negative emotions to be activated in non-math-anxious individuals when facing cues indicating a difficult upcoming task. Importantly, however, math anxiety scores did not predict the neural response. Furthermore, we observed activation in areas associated with processes of cognitive control areas such as anterior cingulate cortex, which were suggested to play a key role in emotion regulation. CONCLUSION: Activation in the emotion processing network was observed when anticipating an upcoming difficult (math) task. However, this activation was not predicted by individual' degree of math anxiety. Therefore, we suggest that negative emotional responses to difficult math tasks might be a rather common reaction not specific to math-anxious individuals. Whether or not this initial negative response impairs math performance, however, might depend on the ability to regulate those emotions effectively.

Place-value computation in children with mathematics difficulties.

Recent research has provided initial evidence that children with math difficulties (MD) experience problems in processing place-value information in basic numerical tasks. However, it remains unclear whether these problems generalize to basic arithmetic operations. For instance, multi-digit addition problems with carryover specifically require the computation of place-value information. Yet little is known about the carry effect in children with MD. Therefore, the current study investigated whether problems in processing place-value information among third-grade children with MD (n = 29 9-year-olds) compared with an age-matched control group (n = 50) generalize to two-digit addition. The results indicate an increased carry effect for response latencies and error rates in children with MD. These findings suggest that deficits in processing place-value information among children with MD generalize to place-value computations in multi-digit arithmetic. Potential contributions of strategy use and working memory for difficulties in processing place-value information are discussed.

Set size influences the relationship between ANS acuity and math performance: a result of different strategies?

Previous research has proposed that the approximate number system (ANS) constitutes a building block for later mathematical abilities. Therefore, numerous studies investigated the relationship between ANS acuity and mathematical performance, but results are inconsistent. Properties of the experimental design have been discussed as a potential explanation of these inconsistencies. In the present study, we investigated the influence of set size and presentation duration on the association between non-symbolic magnitude comparison and math performance. Moreover, we focused on strategies reported as an explanation for these inconsistencies. In particular, we employed a non-symbolic magnitude comparison task and asked participants how they solved the task. We observed that set size was a significant moderator of the relationship between non-symbolic magnitude comparison and math performance, whereas presentation duration of the stimuli did not moderate this relationship. This supports the notion that specific design characteristics contribute to the inconsistent results. Moreover, participants reported different strategies including numerosity-based, visual, counting, calculation-based, and subitizing strategies. Frequencies of these strategies differed between different set sizes and presentation durations. However, we found no specific strategy, which alone predicted arithmetic performance, but when considering the frequency of all reported strategies, arithmetic performance could be predicted. Visual strategies made the largest contribution to this prediction. To conclude, the present findings suggest that different design characteristics contribute to the inconsistent findings regarding the relationship between non-symbolic magnitude comparison and mathematical performance by inducing different strategies and additional processes.

Neuro-cognitive mechanisms of global Gestalt perception in visual quantification.

Recent neuroimaging studies identified posterior regions in the temporal and parietal lobes as neuro-functional correlates of subitizing and global Gestalt perception. Beyond notable overlap on a neuronal level both mechanisms are remarkably similar on a behavioral level representing both a specific form of visual top-down processing where single elements are integrated into a superordinate entity. In the present study, we investigated whether subitizing draws on principles of global Gestalt perception enabling rapid top-down processes of visual quantification. We designed two functional neuroimaging experiments: a task identifying voxels responding to global Gestalt stimuli in posterior temporo-parietal brain regions and a visual quantification task on dot patterns with magnitudes within and outside the subitizing range. We hypothesized that voxels activated in global Gestalt perception should respond stronger to dot patterns within than those outside the subitizing range. The results confirmed this prediction for left-hemispheric posterior temporo-parietal brain areas. Additionally, we trained a classifier with response patterns from global Gestalt perception to predict neural responses of visual quantification. With this approach we were able to classify from TPJ Gestalt ROIs of both hemispheres whether a trial requiring subitizing was processed. The present study demonstrates that mechanisms of subitizing seem to build on processes of high-level visual perception.

Magnitude processing of symbolic and non-symbolic proportions: an fMRI study.

BACKGROUND: Recent research indicates that processing proportion magnitude is associated with activation in the intraparietal sulcus. Thus, brain areas associated with the processing of numbers (i.e., absolute magnitude) were activated during processing symbolic fractions as well as non-symbolic proportions. Here, we investigated systematically the cognitive processing of symbolic (e.g., fractions and decimals) and non-symbolic proportions (e.g., dot patterns and pie charts) in a two-stage procedure. First, we investigated relative magnitude-related activations of proportion processing. Second, we evaluated whether symbolic and non-symbolic proportions share common neural substrates. METHODS: We conducted an fMRI study using magnitude comparison tasks with symbolic and non-symbolic proportions, respectively. As an indicator for magnitude-related processing of proportions, the distance effect was evaluated. RESULTS: A conjunction analysis indicated joint activation of specific occipito-parietal areas including right intraparietal sulcus (IPS) during proportion magnitude processing. More specifically, results indicate that the IPS, which is commonly associated with absolute magnitude processing, is involved in processing relative magnitude information as well, irrespective of symbolic or non-symbolic presentation format. However, we also found distinct activation patterns for the magnitude processing of the different presentation formats. CONCLUSION: Our findings suggest that processing for the separate presentation formats is not only associated with magnitude manipulations in the IPS, but also increasing demands on executive functions and strategy use associated with frontal brain regions as well as visual attention and encoding in occipital regions. Thus, the magnitude processing of proportions may not exclusively reflect processing of number magnitude information but also rather domain-general processes.

The CERAD Neuropsychological Assessment Battery Is Sensitive to Alcohol-Related Cognitive Deficiencies in Elderly Patients: A Retrospective Matched Case-Control Study.

OBJECTIVES: Adverse effects of heavy drinking on cognition have frequently been reported. In the present study, we systematically examined for the first time whether clinical neuropsychological assessments may be sensitive to alcohol abuse in elderly patients with suspected minor neurocognitive disorder. METHODS: A total of 144 elderly with and without alcohol abuse (each group n=72; mean age 66.7 years) were selected from a patient pool of n=738 by applying propensity score matching (a statistical method allowing to match participants in experimental and control group by balancing various covariates to reduce selection bias). Accordingly, study groups were almost perfectly matched regarding age, education, gender, and Mini Mental State Examination score. Neuropsychological performance was measured using the CERAD (Consortium to Establish a Registry for Alzheimer's Disease). Classification analyses (i.e., decision tree and boosted trees models) were conducted to examine whether CERAD variables or total score contributed to group classification. RESULTS: Decision tree models disclosed that groups could be reliably classified based on the CERAD variables "Word List Discriminability" (tapping verbal recognition memory, 64% classification accuracy) and "Trail Making Test A" (measuring visuo-motor speed, 59% classification accuracy). Boosted tree analyses further indicated the sensitivity of "Word List Recall" (measuring free verbal recall) for discriminating elderly with versus without a history of alcohol abuse. CONCLUSIONS: This indicates that specific CERAD variables seem to be sensitive to alcohol-related cognitive dysfunctions in elderly patients with suspected minor neurocognitive disorder. (JINS, 2018, 24, 360-371).

Basic numerical competences in large-scale assessment data: Structure and long-term relevance.

Basic numerical competences are seen as building blocks for later numerical and mathematical achievement. The current study aimed at investigating the structure of early numeracy reflected by different basic numerical competences in kindergarten and its predictive value for mathematical achievement 6 years later using data from large-scale assessment. This allowed analyses based on considerably large sample sizes (N > 1700). A confirmatory factor analysis indicated that a model differentiating five basic numerical competences at the end of kindergarten fitted the data better than a one-factor model of early numeracy representing a comprehensive number sense. In addition, these basic numerical competences were observed to reliably predict performance in a curricular mathematics test in Grade 6 even after controlling for influences of general cognitive ability. Thus, our results indicated a differentiated view on early numeracy considering basic numerical competences in kindergarten reflected in large-scale assessment data. Consideration of different basic numerical competences allows for evaluating their specific predictive value for later mathematical achievement but also mathematical learning difficulties.

Physiological threat responses predict number processing.

Being able to adequately process numbers is a key competency in everyday life. Yet, self-reported negative affective responses towards numbers are known to deteriorate numerical performance. Here, we investigated how physiological threat responses predict numerical performance. Physiological responses reflect whether individuals evaluate a task as exceeding or matching their resources and in turn experience either threat or challenge, which influences subsequent performance. We hypothesized that, the more individuals respond to a numerical task with physiological threat, the worse they would perform. Results of an experiment with cardiovascular indicators of threat/challenge corroborated this expectation. The findings thereby contribute to our understanding of the physiological mechanism underlying the influence of negative affective responses towards numbers on numerical performance.

Using propensity score matching to construct experimental stimuli.

Propensity score matching is widely used in various fields of research, including psychology, medicine, education, and sociology. It is usually applied to find a matched control group for a treatment group. In the present article, we suggest that propensity score matching might also be used to construct item sets matched for different parameters. We constructed stimuli to illustrate the use of propensity score matching in item construction for the exemplary cases of numerical cognition research and reading research. In particular, we provide a step-by-step approach, using the statistics software R, for how to apply propensity score matching for constructing matched stimuli. This approach involves deciding on a population of stimuli, determining and calculating the covariates, and finally applying the propensity-matching method to find a set of items matched to another predefined set. Thereby, we were able to construct well-matched item sets for both examples. Hence, we conclude that the propensity-score-matching method is useful for constructing matched stimuli. Further cases of application are discussed.

Fact learning in complex arithmetic-the role of the angular gyrus revisited.

In recent theoretical considerations as well as in neuroimaging findings the left angular gyrus (AG) has been associated with the retrieval of arithmetic facts. This interpretation was corroborated by higher AG activity when processing trained as compared with untrained multiplication problems. However, so far neural correlates of processing trained versus untrained problems were only compared after training. We employed an established learning paradigm (i.e., extensive training of multiplication problems) but measured brain activation before and afte training to evaluate neural correlates of arithmetic fact acquisition more specifically. When comparing activation patterns for trained and untrained problems of the post-training session, higher AG activation for trained problems was replicated. However, when activation for trained problems was compared to activation for the same problems in the pre-training session, no signal change in the AG was observed. Instead, our results point toward a central role of hippocampal, para-hippocampal, and retrosplenial structures in arithmetic fact retrieval. We suggest that the AG might not be associated with the actual retrieval of arithmetic facts, and outline an attentional account of the role of the AG in arithmetic fact retrieval that is compatible with recent attention to memory hypotheses. Hum Brain Mapp 37:3061-3079, 2016. © 2016 Wiley Periodicals, Inc.

Finger gnosis predicts a unique but small part of variance in initial arithmetic performance.

Recent studies indicated that finger gnosis (i.e., the ability to perceive and differentiate one's own fingers) is associated reliably with basic numerical competencies. In this study, we aimed at examining whether finger gnosis is also a unique predictor for initial arithmetic competencies at the beginning of first grade-and thus before formal math instruction starts. Therefore, we controlled for influences of domain-specific numerical precursor competencies, domain-general cognitive ability, and natural variables such as gender and age. Results from 321 German first-graders revealed that finger gnosis indeed predicted a unique and relevant but nevertheless only small part of the variance in initial arithmetic performance (∼1%-2%) as compared with influences of general cognitive ability and numerical precursor competencies. Taken together, these results substantiated the notion of a unique association between finger gnosis and arithmetic and further corroborate the theoretical idea of finger-based representations contributing to numerical cognition. However, the only small part of variance explained by finger gnosis seems to limit its relevance for diagnostic purposes.

Processing multi-digit numbers: a translingual eye-tracking study.

The present study aimed at investigating the underlying cognitive processes and language specificities of three-digit number processing. More specifically, it was intended to clarify whether the single digits of three-digit numbers are processed in parallel and/or sequentially and whether processing strategies are influenced by the inversion of number words with respect to the Arabic digits [e.g., 43: dreiundvierzig ("three and forty")] and/or by differences in reading behavior of the respective first language. Therefore, English- and German-speaking adults had to complete a three-digit number comparison task while their eye-fixation behavior was recorded. Replicating previous results, reliable hundred-decade-compatibility effects (e.g., 742_896: hundred-decade compatible because 7 < 8 and 4 < 9; 362_517: hundred-decade incompatible because 3 < 5 but 6 > 1) for English- as well as hundred-unit-compatibility effects for English- and German-speaking participants were observed, indicating parallel processing strategies. While no indices of partial sequential processing were found for the English-speaking group, about half of the German-speaking participants showed an inverse hundred-decade-compatibility effect accompanied by longer inspection time on the hundred digit indicating additional sequential processes. Thereby, the present data revealed that in transition from two- to higher multi-digit numbers, the homogeneity of underlying processing strategies varies between language groups. The regular German orthography (allowing for letter-by-letter reading) and its associated more sequential reading behavior may have promoted sequential processing strategies in multi-digit number processing. Furthermore, these results indicated that the inversion of number words alone is not sufficient to explain all observed language differences in three-digit number processing.