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Mental Representation of Numbers and Arithmetical Competence in Early Primary School Age (MenZa)

Resource Type
Dataset : survey data, achievement test
  • Obersteiner, Andreas (Technical University Munich)
  • Reiss, Kristina
Publication Date
Free Keywords
Primary School; Students; Mathematics instruction; Schoolyear 01; Schoolyear 02; Number; Number comprehension; Promotion; Theory; Approximation; Precision; Mathematical achievement; Learning effect; Educational success; Problem solving; Arithmetical problem; Learning difficulty; Cognitive competence; Transfer; Experiment; Intervention; Survey; Testing methods; Pre-Test; Post-Test; Educational software; Computer assisted method; Germany
  • Abstract

    To support children`s development of mental number representations from a psychological and mathematics education perspective two approaches can be distinguished: On the one hand the use of structured quantity representation focusing on exact numerical processing (exact instructional approach) and on the other hand the use of linear number representations focusing on approximate number processing (approximate instructional approach). The project MenZa aimed at empirically testing the effectiveness of both theoretically reasonable approaches. (…) In Study 1 an experimental design with first graders was realized. The students were randomly assigned to one of the following conditions: approximate, exact, approximate and exact or neither approximate nor exact (= language training). All students received ten training sessions of 30 minutes each. To achieve maximal comparability, the intervention was implemented computer-based. (…) Before and after the intervention, the students completed achievement tests for basal numeric and arithmetic skills. In Study 2 a quasi-experimental design was applied. Second grade students with difficulties in mathematics attended ten training sessions (exact or approximate condition) in small group settings. First, mathematical exercises according to a set curriculum were discussed in the groups, then every student assembled the computer program also used in Study 1. Before and after the intervention the students performed the same achievement tests as in Study 1. Study 1 shows that both instructional approaches exert positive effects on those numerical skills that were directly supported (exact or approximate use of numbers).

Temporal Coverage
  • 2011-02-01 / 2011-04-30
Geographic Coverage
  • Bavaria
Sampled Universe

Students in grade 1 (N=204)


Probability Sample

Time Dimension
  • Cross-section
    Research Design: Experimental Design; Interventional Study with Prae-Post- and Follow-Up-Test in experimental 2x2-Design
Collection Mode
  • Self-administered questionnaire: Web-based
  • Educational measurements and tests
  • Measurements and Tests: Computer Assisted Test
application required:
CC0 1.0 Universal
Alternative Identifiers
  • 1 (Type: VerbundFDB)
  • Obersteiner, A. (2012). Mentale Repräsentationen von Zahlen und der Erwerb arithmetischer Fähigkeiten. Konzeptionierung und Evaluation einer Förderung mit psychologisch-didaktischer Grundlegung und Evaluation im ersten Schuljahr. Münster: Waxmann.

    • ID: 978-3-8309-2705-1 (ISBN)
    • ID: 1868-1441 (ISSN)
  • Obersteiner, A., Reiss, K., und Ufer, S. (2013). How training on exact or approximate mental representations of number can enhance first-grade students' basic number processing and arithmetic skills. Learning and Instruction, 23, 125–135.

    • ID: 0959-4752 (ISSN)
    • ID: 10.1016/j.learninstruc.2012.08.004 (DOI)
  • Obersteiner, A., Reiss, K., und Ufer, S. (2012). Reaktionszeitexperimente zur Messung von Lerneffekten im ersten Schuljahr. In M. Ludwig und M. Kleine (Hrsg.), Beiträge zum Mathematikunterricht 2012 (S. 633–636). Münster: WTM-Verlag.

    • ID: 978-3-942197-18-2 (ISBN)
  • Obersteiner, A., Ufer, S., und Reiss, K. (2010). Fostering the development of mental number representations and arithmetic competencies in the first school year. Frontiers in Neuroscience. Conference Abstract: EARLI SIG22 – Neuroscience and Education.

    • ID: 10.3389/conf.fnins.2010.11.00069 (DOI)
  • Obersteiner, A., Ufer, S., und Reiss, K. (2010). Förderung des Aufbaus mentaler Zahlrepräsentationen im Grundschulalter. In A. Lindmeier und S. Ufer (Hrsg.), Beiträge zum Mathematikunterricht 2010 (S. 649-652). Münster: WTM-Verlag.

    • ID: 978-3-942197-03-8 (ISBN)

Update Metadata: 2019-03-28 | Issue Number: 12 | Registration Date: 2016-06-27

Obersteiner, Andreas; Reiss, Kristina (2016): Mentale Repräsentation von Zahlen und arithmetische Kompetenz im frühen Grundschulalter (MenZa). Version: 1. IQB – Institut zur Qualitätsentwicklung im Bildungswesen. Dataset.