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Tips for calculating smartly

Adaptive choice of computational strategies when adding and subtracting in the number space up to 1000: Individual and educational determining factors for the acquisition of competences



Deutsche Forschungsgemeinschaft (DFG) 2010 - 2012
(HE 4561/3‑3 und LI 1639/1-3)

Persons involved
Prof. Dr. Aiso Heinze, IPN, Kiel
Prof. Dr. Frank Lipowsky, Department of Educational Science, Kassel
Prof. Dr. Meike Grüßing, University of Vechta
Dr. Julia Arend, Department of Educational Science, Kassel

The adaptive choice of computational strategies is an important competence that can be regarded as a prerequisite for efficient and flexible calculations and estimations in everyday life and at work. An open question is how to design and structure lessons in order to promote this competence efficiently. Accordingly, this project investigates the effects of two instructional approaches on third graders’ competence acquisition to adaptively choose semi-written strategies when adding and subtracting in the number space up to 1,000.

In the explicative approach, there is a repertoire of computational strategies that are discovered first and trained afterwards. Once different strategies have been learned, the class discusses the adaptive use of strategies. The problem-solving approach is characterized by the fact that there is no intended repertoire of strategies to be learned. Instead, they should be developed individually through problem-solving activities and discussed by comparing the solution strategies. Knowledge of task-related criteria for the selection of efficient strategies is built up step by step through continuous problem solving and subsequent reflection.

Research questions
The aim of the project is to investigate the effectiveness of the two instructional approaches in terms of the individual competence to adaptively choose addition and subtraction strategies. In particular, it will be investigated whether the instructional strategies show different effects with respect to

  1. the individual acquisition of competences by high-performing and low-performing      students
  2. the subjective criteria for the adaptive choice of computational strategies
  3. the stability of the acquired competence of adaptive strategy choice


Heinze, A., Arend, J., Grüßing, M., & Lipowsky, F. (2020). Systematisch einführen oder selbst entdecken lassen? Eine experimentelle Studie zur Förderung der adaptiven Nutzung von Rechenstrategien bei Grundschulkindern. Unterrichtswissenschaft, 48(1), 11-34.

Heinze, A., Arend, J., Grüßing, M., & Lipowsky, F. (2018). Instructional approaches to foster third graders’ adaptive use of strategies: an experimental study on the effects of two learning environments on multi-digit addition and subtraction. Instructional Science, 46(6), 869-891.

Heinze, A. (2018). Halbschriftliches Rechnen: Geht es sicher und geschickt? Wie Kinder einen flexiblen Einsatz von Rechenstrategien lernen können. Mathematik differenziert, (1), 6- 9