MenZa – Mental representations on numbers and arithmetic competencies in the first school years

Investigators

Description of the Project

A major goal of early mathematics instruction is to enhance students' arithmetic competencies. These competencies comprise exact mental calculation as well as approximate calculation and number estimation. Various manipulative materials are used in primary schools in order to support students' development of mental number representations. These materials can represent either exact numerosities (e.g., a pegboard with two rows of ten pegs each) or analogue quantities (e.g., empty number line). While theoretical considerations support their use, the empirical foundation of effects on students' learning is scarce. Cognitive and neuropsychological findings suggest that there are distinct cognitive systems for exact and approximate number processing. While the exact number system allows the rapid understanding of small numbers (subitizing), the approximate system represents quantities on an analogue way. It is not fully understood how these cognitive systems contribute to arithmetic development, if they can be trained separately, and how they are related to other cognitive abilities, e.g., spatial abilites.

This project addresses the effect of specific training programs on the development of students' mental number representations and on their arithmetic competencies. In a first experimental study in grade 1, modified versions of the learning software The Number Race will be used. While one version requires exact number processing, the other one requires approximate number processing. In a second study, training effects of normally developed students will be compared to those of students with specific mathematical deficits in grade 2.

The results of this project can help to better understand influential factors on childrens' early arithmetic development.

Publications and Presentations

  • Obersteiner, A., Reiss, K., & Ufer, S. (2013). Short-term effects of exact or approximate number training on arithmetical achievement in low-achieving children. Poster presented at the 2013 Annual Meeting of the American Educational Research Association. San Francisco (CA).
  • Obersteiner, A., Reiss, K., & 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.
  • 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.
  • Obersteiner, A., Reiss, K., & Ufer, S. (2012). Reaktionszeitexperimente zur Messung von Lerneffekten im ersten Schuljahr. In M. Ludwig & M. Kleine (Hrsg.), Beiträge zum Mathematikunterricht 2012 (S. 633–636). Münster: WTM-Verlag.
  • Obersteiner, A. (2012). Was bringen computerbasierte Interventionen zur Förderung basaler numerischer Fähigkeiten? Tagung des Arbeitskreises Grundschule der GDM. Tabarz.
  • Obersteiner, A., Reiss, K., & Ufer, S. (2012). Effects of exact or approximate training on arithmetical achievement in low achieving children. Poster presented at the Meeting of the EARLI SIG "Neuroscience and Education". London (UK).
  • Obersteiner, A. (2011). Förderung des Aufbaus mentaler Repräsentationen von Zahlen und arithmetischer Kompetenz im frühen Grundschulalter. Meeting of the Interest Group Psychologie und Mathematikdidaktik of the GDM. Rauischholzhausen.
  • Obersteiner, A., Ufer, S., & Reiss, K. (2011). Effects of computer-based interventions to enhance the development of mental number representations. 14th Biennial Conference of the European Association for Research on Learning and Instruction (EARLI). Exeter (UK).
  • Obersteiner, A., Reiss, K., & Ufer, S. (2011). Effekte einer Förderung basaler Zahlverarbeitung im ersten Schuljahr. 37th Conference Psychologie und Gehirn (pp. 93-94). Heidelberg.
  • Obersteiner, A., Ufer, S., & Reiss, K. (2010). Eine Interventionsstudie zur Förderung mentaler Zahlrepräsentationen im Grundschulalter. 74th Conference of Arbeitsgruppe für Empirische Pädagogische Forschung (AEPF). Jena.
  • Obersteiner, A., Ufer, S., & 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. doi: 10.3389/conf.fnins.2010.11.00069.
  • Obersteiner, A., Ufer, S., & Reiss, K. (2010). Förderung des Aufbaus mentaler Zahlrepräsentationen im Grundschulalter. In A. Lindmeier & S. Ufer (Eds.), Beiträge zum Mathematikunterricht 2010 (pp. 649–652). Münster: WTM-Verlag.

Funding

This project was funded by the German Federal Ministry of Education and Research.