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  • 1.
    Andersson, Ulf
    et al.
    Linköping University, Department of Behavioural Sciences and Learning, Psychology. Linköping University, Faculty of Arts and Sciences.
    Skagerlund, Kenny
    Linköping University, Department of Behavioural Sciences and Learning, Psychology. Linköping University, Faculty of Arts and Sciences.
    Olsson, Linda
    Linköping University, Department of Behavioural Sciences and Learning, Psychology. Linköping University, Faculty of Arts and Sciences.
    Östergren, Rickard
    Linköping University, Department of Behavioural Sciences and Learning, Education, Teaching and Learning. Linköping University, Faculty of Educational Sciences.
    Pathways to arithmetic fact retrieval and percentage calculation in adolescents2017In: British Journal of Educational Psychology, ISSN 0007-0998, E-ISSN 2044-8279, Vol. 87, no 4, p. 647-663Article in journal (Refereed)
    Abstract [en]

    Background

    Developing sufficient mathematical skills is a prerequisite to function adequately in society today. Given this, an important task is to increase our understanding regarding the cognitive mechanisms underlying young people's acquisition of early number skills and formal mathematical knowledge.

    Aims

    The purpose was to examine whether the pathways to mathematics model provides a valid account of the cognitive mechanisms underlying symbolic-number processing and mathematics in adolescents. The pathways model states that the three pathways should provide independent support to symbolic-number skill. Each pathway's unique contribution to formal mathematics varies depending on the complexity and demand of the tasks.

    Sample

    The study used a sample of 114 adolescents (71 girls). Their mean age was 14.60 years (SD = 1.00).

    Methods

    The adolescents were assessed on tests tapping the three pathways and general cognitive abilities (e.g., working memory). A structural equation path analysis was computed.

    Results

    Symbolic-number comparison was predicted by the linguistic pathway, the quantitative pathway, and processing speed. The linguistic pathway, quantitative pathways, and symbolic-number comparison predicted arithmetic fact retrieval. The linguistic pathway, working memory, visual analogies, and symbolic-number comparison predicted percentage calculation.

    Conclusions

    There are both similarities and differences in the cognitive mechanisms underlying arithmetic fact retrieval and percentage calculation in adolescents. Adolescents’ symbolic-number processing, arithmetic fact retrieval, and percentage calculation continue to rely on the linguistic pathways, whereas the reliance upon the spatial pathway has ceased. The reliance upon the quantitative pathway varies depending on the task.

  • 2.
    Olsson, Linda
    Linköping University, Department of Behavioural Sciences and Learning, Psychology. Linköping University, Faculty of Arts and Sciences.
    “Count on me!”: Mathematical development, developmental dyscalculia and computer-based intervention2018Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    A “sense” of number can be found across species, yet only humans supplement it with exact and symbolic number, such as number words and digits. However, what abilities leads to successful or unsuccessful arithmetic proficiency is still debated. Furthermore, as the predictability between early understanding of math and later achievement is stronger than for other subjects, early deficits can cause significant later deficits. The purpose of the current thesis was to contribute to the description of what aspects of non-symbolic and symbolic processing leads to later successful or unsuccessful arithmetic proficiency, and to study the effects of different designs of computer-programs on pre-school class aged children. The cognitive mechanisms underlying symbolic number processing and different arithmetic skills were mapped to discover their contributions to children’s proficiency. Findings show that the non-symbolic system continues to contribute to arithmetic performance, and that the general cognitive abilities’ contributions might vary with development. Moreover, more advanced mathematical skills were supported by less advanced. In order to investigate the underlying core deficit in DD, performance was contrasted with an individually matched control group on general cognitive abilities. Findings indicate that DD children are impaired on both nonsymbolic and symbolic processing, the most impairment on the symbolic measures. Furthermore, the results indicated subgroups. In order to investigate the effects of early intervention, three theoretically different designs of computer programs, designed in accordance to hypotheses of number processing were compared to a passive control group. Results revealed that even brief, daily arithmetic training utilizing theoretically different designs impacted different aspects of symbolic processing. The presented findings indicate that the non-symbolic system is the foundation for the symbolic system, and that DD is caused by a non-symbolic deficit. The present thesis also adds evidence that formal arithmetic is founded on precise representations, rather than approximate.

    List of papers
    1. Cognitive mechanisms underlying third graders' arithmetic skills: Expanding the pathways to mathematics model.
    Open this publication in new window or tab >>Cognitive mechanisms underlying third graders' arithmetic skills: Expanding the pathways to mathematics model.
    2018 (English)In: Journal of experimental child psychology (Print), ISSN 0022-0965, E-ISSN 1096-0457, Vol. 167, p. 369-387Article in journal (Refereed) Published
    Abstract [en]

    A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills.

    Place, publisher, year, edition, pages
    Elsevier, 2018
    Keywords
    Approximate quantitative pathway, Arithmetic, Linguistic pathway, Spatial processing pathway, Symbolic number processing, Verbal working memory pathway
    National Category
    Psychology
    Identifiers
    urn:nbn:se:liu:diva-144197 (URN)10.1016/j.jecp.2017.11.010 (DOI)000423652300024 ()29232622 (PubMedID)
    Note

    Funding agencies: Swedish Council for Working Life and Social Research [2008-0238]

    Available from: 2018-01-10 Created: 2018-01-10 Last updated: 2018-02-21
    2. Developmental dyscalculia: A deficit in the approximate number system or an access deficit?
    Open this publication in new window or tab >>Developmental dyscalculia: A deficit in the approximate number system or an access deficit?
    2016 (English)In: Cognitive development, ISSN 0885-2014, E-ISSN 1879-226X, Vol. 39, p. 154-167Article in journal (Refereed) Published
    Abstract [en]

    Developmental dyscalculia (DD), a pervasive learning difficulty, affects 5-6% of the population. The current study sought to identify the underlying deficits by contrasting third graders (10-year old) performance against predictions made by two main hypotheses; the preverbal ANS and/or OTS and the access deficit. Through a mathematical and general cognitive screening, identified DD children were compared to individually matched controls on experimental tasks containing non-symbolic and symbolic tasks. DD children showed impairment on almost all symbolic tasks. Results on the non-symbolic tasks showed that DD children had poorer ANS acuity and reduced subitizing range. Most of the results were in support of the defective preverbal ANS and OTS hypothesis. However, as the effect sizes for the symbolic tasks were greater than for the non-symbolic, results indicate that the DD group was more impaired on the symbolic tasks. (C) 2016 Elsevier Inc. All rights reserved.

    Place, publisher, year, edition, pages
    ELSEVIER SCIENCE INC, 2016
    Keywords
    Dyscalculia; Approximate number system (ANS); Object tracking system (OTS); Access deficit; Non-symbolic and symbolic processing; Subitizing
    National Category
    Psychology (excluding Applied Psychology)
    Identifiers
    urn:nbn:se:liu:diva-131713 (URN)10.1016/j.cogdev.2016.04.006 (DOI)000381955000014 ()
    Note

    Funding Agencies|Swedish Council for Working Life and Social Research [Dnr 721-2011-2872]; Swedish Research Council [421-2007-1881]

    Available from: 2016-10-03 Created: 2016-09-30 Last updated: 2018-01-10
  • 3.
    Träff, Ulf
    et al.
    Linköping University, Department of Behavioural Sciences and Learning, Psychology. Linköping University, Faculty of Arts and Sciences.
    Olsson, Linda
    Linköping University, Department of Behavioural Sciences and Learning, Psychology. Linköping University, Faculty of Arts and Sciences.
    Skagerlund, Kenny
    Linköping University, Department of Behavioural Sciences and Learning, Psychology. Linköping University, Faculty of Arts and Sciences.
    Östergren, Rickard
    Linköping University, Department of Behavioural Sciences and Learning, Education, Teaching and Learning. Linköping University, Faculty of Educational Sciences.
    Cognitive mechanisms underlying third graders' arithmetic skills: Expanding the pathways to mathematics model.2018In: Journal of experimental child psychology (Print), ISSN 0022-0965, E-ISSN 1096-0457, Vol. 167, p. 369-387Article in journal (Refereed)
    Abstract [en]

    A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills.

  • 4.
    Träff, Ulf
    et al.
    Linköping University, Department of Behavioural Sciences and Learning, Psychology. Linköping University, Faculty of Arts and Sciences.
    Olsson, Linda
    Linköping University, Department of Behavioural Sciences and Learning, Psychology. Linköping University, Faculty of Arts and Sciences.
    Östergren, Rickard
    Linköping University, Department of Behavioural Sciences and Learning, Education, Teaching and Learning. Linköping University, Faculty of Educational Sciences.
    Skagerlund, Kenny
    Linköping University, Department of Behavioural Sciences and Learning, Psychology. Linköping University, Faculty of Arts and Sciences.
    Heterogeneity of developmental dyscalculia: Cases with different deficit profiles2017In: Frontiers in Psychology, ISSN 1664-1078, E-ISSN 1664-1078Article in journal (Refereed)
    Abstract [en]

    Context: The aim was to further understand the heterogeneity of  developmental dyscalculia (DD). Utilizing four children (8-9 year-old) performance was contrasted against predominant hypotheses of DD.

    Case report: Despite showing similar mathematical deficits, these children showed remarkable interindividual variability regarding cognitive profile and deficits. Two cases were consistent with the approximate number system deficit account, and the general magnitude-processing deficit account. One case had an access deficit in combination with a general cognitive deficit. One cases suffered from general cognitive deficits only.

    Conclusions: The results showed that DD cannot be attributed to a single explanatory factor. These findings support a multiple deficits account of DD and suggest that some cases have multiple deficits, whereas other cases have a single deficit. We discuss a previously proposed distinction between primary DD and secondary DD, and suggest hypotheses of dysfunctional neurocognitive correlates responsible for the displayed deficits.

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