Number processing: core deficits and recent developments in cognitive intervention.

Friday, September 30th, 2011 [08:30 - 10:30]

SY_04. Number processing: core deficits and recent developments in cognitive intervention

Goebel, S. M. ¹ & Kaufmann, L. ^2, ³

1 Department of Psychology, University of York, UK
2 Institute of Applied Psychology, UMIT-Private University for Health Sciences, Medical Informatics and Technology, Hall in Tyrol, Austria
3 Department of Pediatrics IV, Medical University Innsbruck, Innsbruck, Austria

Number processing is crucial for everyday life and professional endeavors. Our current understanding of the cognitive foundations of numerical and arithmetic difficulties, however, is scarce. So far, there are only very few empirically validated numeracy interventions. The aim of this symposium is to bring together researchers working on (i) cognitive foundations of numerical cognition and (ii) theoretically motivated interventions of numerical and arithmetic difficulties. Silke Goebel is going to present data on core cognitive deficits in adults with arithmetic difficulties of developmental origins, focusing on adaptive and non-adaptive strategy-use. The presentation by Bert Reynvoet will focus on the priming distance effect in children and adults with and without arithmetic difficulties. Furthermore he willl present findings on the individual differences in the priming distance effect and its relationship to math ability. Denes Scuzs will report behavioral and ERP findings related to the development of the magnitude representation and spatial-numerical associations in elementary school children. The last three talks will present novel intervention approaches for the remediation of numerical and arithmetic difficulties. First, Silvia Pixner will give an overview of intervention approaches for multiplication facts for primary and secondary school aged children. Their multimodal training establishing number-colour associations resulted in significant improvements in arithmetic. Second, promising findings of an embodied cognition approach for intervention of numerical and arithmetic difficulties in kindergarten children will be presented by Hans-Christoph Nuerk. Finally, Minna Hannula-Sormunen will present data of a one-year intervention program for 4-year-old children with numeracy difficulties.

TALKS

SY_04.1 - Finger counting, tally marks and adaptive strategy use in two adults with developmental arithmetic difficulties

Goebel, S. M. ¹ , Pixner, S. ² & Kaufmann, L. ^2, ³

In recent years the research into numerical and arithmetic difficulties in children has increased substantially. However, relatively little is still known about number processing and arithmetic performance patterns of adults with a life-long history of numerical and arithmetic difficulties. Clearly, longitudinal studies are needed to investigate the outcome of childhood numerical and arithmetic difficulties in adult life. Currently however, given the absence of those studies, investigating adults with pure numerical and arithmetic difficulties could also tell us more about developmental pathways. We will present data from two adults with severe arithmetic difficulties. Both adults are university students with above average cognitive skills who have experienced difficulties with number processing and arithmetic since childhood. RM is a pure case with no impairments in other cognitive domains. She uses tally marks and finger counting for simple addition and multiplication tasks. AC also uses elaborate strategies to solve arithmetic problems that are commonly used by fact retrieval. In contrast to RM, AC shows arithmetic difficulties in the context of developmental dyslexia. First we will compare and contrast in detail the strategies used by those two adults for single digit addition, subtraction and multiplication. Second we will then compare their performance on symbolic and non-symbolic number comparison tasks and spatial-numerical tasks to the performance of age and IQ-matched controls.

SY_04.2 - Magnitude representations in children and adults with and without arithmetic difficulties

Reynvoet, B. ¹ , Defever, E. ¹ & Goebel, S. M. ²

1 Department of Psychology, University of Leuven, Belgium
2 Department of Psychology, University of York, UK

Today, it is generally assumed that children and adults with arithmetic difficulties have a defected internal magnitude representation and/or have problems associating symbols to this internal magnitude representation. However, most of the evidence is obtained in comparison tasks and recently it has been argued that comparison data may reflect more general decisional mechanisms instead of representational characteristics. We re-evaluated these hypotheses underlying arithmetical difficulties with the priming paradigm. The priming distance effect is considered as a direct measure of the underlying magnitude representation. We will present data on individual differences in the priming distance effect in children and adults and their relation with mathematical ability. The results show relations between the size of the priming effect and mathematical ability. These results will be discussed against the hypotheses underlying arithmetic difficulties.

SY_04.3 - The development of the magnitude representation and spatial-numerical associations with symbolic number in 6 to 8 year-old children: behavioural and ERP evidence

Szucs, D. ¹ , White, S. ² & Soltesz, F. ¹

1 Department of Experimental Psychology, University of Cambridge, Cambridge, UK
2 Queensland University of Technology, Brisbane, Australia

Learning symbolic Arabic digits in early childhood requires the integration of both magnitude and spatial information with symbolic number notation. In two studies we investigated this integration process in detail during the first three years of primary school in 6, 7 and 8 year-old normally developing children. Study 1 used event-related brain potentials to determine the speed of access to magnitude information from Arabic digits in a situation when number meaning was not relevant; in the physical size judgment task of the numerical Stroop paradigm. ERPs provided a practically real-time index of the speed of access to magnitude information uncontaminated by response organization processes. This speed characterized the strength of association between magnitude information and symbolic digits. All age groups accessed magnitude information with similar speed. This suggests that access to basic magnitude information was mature very early during schooling. Study 2 took a step further and examined not only automatic access to magnitude but also automatic access to spatial information from symbolic digits within the same sample of children. Previous research has separately investigated the development of these components. However, developmental trajectories of symbolic number knowledge cannot be fully understood when considering components in isolation. Hence, we integrated these lines of research. The physical judgment task of the numerical Stroop paradigm demonstrated that automatic access to magnitude was present from Year 1 and an automatically evoked distance effect signaled that a refined processing of numerical information had developed. Additionally, a parity judgment task where number meaning was again, irrelevant, showed that the onset of the Spatial-Numerical Association of Response Codes (SNARC) effect occurs from 8 years of age (Year 2 of school). These findings uncover the developmental timeline of the integration of magnitude and spatial information during the early learning of Arabic digits in normally developing children.

SY_04.4 - Physical-spatial training of number magnitude representation: congruency of response and stimulus increases training effects

Nuerk, H. ^1, ² , Fischer, U. ¹ , Moeller, K. ^1, ² & Cress, U. ¹

1 Knowledge Media Research Center, Tuebingen, Germany
2 Institute of Psychology, Eberhard Karls University, Tuebingen, Germany

In recent years, the predictive value of children's early basic numerical competencies for their future arithmetic abilities has received growing interest. One of these basic numerical skills is the spatial representation of magnitude (mental number line representation). However, while correlative relationships are now well established, the causal links are weak, i.e., intervention studies training spatial-numerical relationships are still scarce. Therefore, we designed a new spatial-numerical training program that was supposed to increase accuracy of kindergarten children's mental number line representation. We tried to achieve this by associating both responses and presentation of the stimuli with the spatial orientation (left to right) of the mental number line representation. More precisely, children were trained in a magnitude comparison task employing an embodied cognition approach. They had to respond by a full-body spatial movement (i.e., step left or step right) on a digital dance mat while stimuli were presented along a left-to-right oriented number line in the experimental condition. This spatial-numerical training was more effective than a non-spatial control training (without a full-body response and without presentation of a number line) in enhancing children's performance in both a number line estimation task and a subtest of a standardized mathematical achievement battery (TEDI-MATH). These results suggest that training the mental number line by spatial congruency of a numerical stimulus and full-body response is successful and can increase numerical capabilities even in transfer tasks. Studies that are currently in progress will a) expand the current results to other new digital media (such as interactive whiteboards) and b) identify the specific constellations of response and presentation factors responsible for the greater effectiveness of the spatial-numerical training employing an embodied cognition approach.

SY_04.5 - A one-year intervention for 4-year-old children with low numerical skills

Hannula-Sormunen, M. ¹ , Rasanen, P. ² , Mattinen, A. ² , Kajamies, A. ¹ & Lehtinen, E. ¹

1 Department of Teacher Education, University of Turku, Finland
2 Niilo Maki Institute, Finland

Here we present a quasi-experimental intervention study on a new remedial program for four to five year-old children with difficulties in learning basic numerical skills. 'Teddy Bear Math' (TBM) program (Mattinen, Rasanen, Hannula & Lehtinen, 2008; 2010) is a systematically progressing one-year curriculum on basic number skills for children with difficulties in early numerical skills. The program is built on training of children's metacognitive skills contains weekly small group sessions at day-care settings, bridging numerical activities to daily life, as well as materials for cooperation with parents.TBM is based on general enrichment programs (Feuerstein et al., 1980; Greenberg, 2000; Haywood, Brooks & Burns, 1992) and to the ideas of socially constructed learning (e.g. Rogoff, 1990; Vygotsky, 1978) in which all activities were introduced to the children in variety of games and everyday contexts of a teddy bear family. Numerical training started from dealing with approximate numbers and very small exact numbers and progressed to counting up to ten items, adding, subtracting and comparing of exact numbers. Design of the one-year longitudinal study with pre-intermediate-post and delayed post-tests included an experimental group (n = 9) taking part in TBM and an age and skill matched control group (n=9) taking part in a listening comprehension program, which shared the same instructional structure and metacognitive training as TBM. Participants' (mean age 4 yrs 4 months) spontaneous focusing on numerosity, cardinality recognition and number sequence production skills were under the median of 4-year-old children's skills.Results show that the experimental group outperformed the control group in cardinality recognition skills. The TBM program, which is tightly integrated to everyday contexts, is effective in remediating young at-risk children's numerical skills, and thus show that there is a great deal of potential in developing programs that may help children early enough to prevent failure in later mathematics.