Go to...

Multinational | Belgium | Brazil | Chile | South Africa | Hungary | 


math and arithemtic concepts in preschoolers MARKO

MARKO-D is an individual test targeted at children that can be used to gain information about prerequisites for the future development in school regarding arithmetic competencies.

Process-oriented diagnostics require a theoretical framework which allows to describe and interpret individual competence changes. For MARKO-test, a corresponding dimension/scale of mathematical achievement in preschool age was developed on the basis of theoretical assumptions and empirical data. Five essential concepts are: numbers as counting sequence, ordinal number line, cardinal understanding, part – part – whole and concept of congruent intervals. There is empirical evidence for the validity of the model, using a unidimensional Rasch model. Therefore, a concept of testing is available which on the one hand allows to compare individual data with a social norm and on the other hand is usable to make valid statements about individual changes and the current development status of a child.

The MARKO test has been used in multiple countries and has bin validated in even more (see map).


University of Gent

  • Cooperation for the translation and validation of the "MARKO-D" test
    ("MARKO-S" will follow soon)
  • Since Fall 2018, Moritz Herzog (University of Duisburg Essen) is teaching in Gent as an ERASMUS-lecturer. 

Our Partners in Belgium


 Prof. Dr. Annemie Desoete

 University of Gent
 Department of Experimental Clinical and Health Psychology



  • Prof. Dr. Fritz-Stratmann will be a speaker at the Brazilian-German Winter School on Numerical Cognition 2019 in Belo Horizonte.
  • Cooperation in research on math anxiety

Our Partners in Brazil

Vitor G Haase

 Vitor G. Haase

 ehemals: Federal University of Minas Gerais


Pontifical Catholic University of Chile

  • For the Chilenian version of the "MARKO" test we cooperated with the Institute of Psychology at the Pontificial Catholic University of Chile (UC).

Our Partners in Chile

Ricardo Rosas


 Ricardo Rosas

 Pontificial Catholic University of Chile (UC)
 Escuela de Psicología


University of Johannesburg

  • Since January of 2015, Prof. Dr. Annemarie Fritz-Stratmann is a Distinguished Visiting Professor at the University of Johannesburg.
  • Since 2012, Prof. Dr. Annemarie Fritz-Stratmann is a Visiting Professor at the Institute for Childhood Education (Soweto Campus) of the University of Johannesburg.
  • We are cooperating with the Centre for Education Practice Research.

Our Partners in South Africa

Prof Elizabeth Henning

University of Johannesburg
Director: Centre for Education Practice Research and SARChI Chair

Prof Caroline Long

University of Johannesburg
Faculty of Education
Department of Childhood Education​

Recent Projects

Migration of math competency tests from Germany to South Africa

  • Standardization of the math tests "MARKO“ (Ricken, Fritz & Balzer, 2013) in four languages: English, Africaans, IsiZulu, SeSotho with the characters Lona und Jobo.
  • Translation, adaptation and expansion of the math training programms ng der Mathematik-Trainingsprogramme "Kalkulie" (Fritz, Gerlach, Ricken & Schmidt, 2007) and early support box for mathematics: Mina and the mole (Gerlach & Fritz, 2012) for the support program "Meerkat Maths
  • CFT-R (Culture Fair Intelligence Test, Cattell, 2013, 2nd edition): Adaptation, Standardization, and n of an intelligence test for South Africa in the languages: English, Africaans, IsiZulu, SeSotho



  • Testing the mathematical competence of young children In Germany and South Africa, EARLI conference, Munich, 26. - 31.08.2013
  • Support for children who struggle to build mathematical knowledge: – a development-oriented maths program SARAECE International Conference, Port Elizabeth, 04 - 07.02.2014
  • Iterations of translations from German to four South African languages in a mathematics competence test, EARLI Conference on SIG 5 Learning and Development in Early Childhood August 25-27, 2014 Jyväskylä, Finland

            Bild 1          Bild 2          Bild 3

Grafiken aus der südafrikanischen Version des MARKO.


University Szeged


We are cooperating with the Doctoral School of Education in the following fields:

  • Applications of diagnostic tests in educational practice
  • Modern educational paradigm in ICT
  • Tests for diagnosing math difficulties

Our Partners in Hungary


 Prof. Benő Csapó DSc

 Institute of Education
 H–6722 Szeged, Petőfi sgt. 30–34., Hungary




 Assoc. Prof. Gyöngyvér Molnár

 Institute of Education
 H–6722 Szeged, Petőfi sgt. 30-34., Hungary



Mojahed Mousa

(Doktorand bei Prof. Gyöngvér Molnár)


10th Conference on Educational Assessment Szeged, April 26-28, 2012


  • Annemarie Fritz, Gabi Ricken, Lars Balzer: A developmental model of arithmetic competencies in age 4 – 8
  • Antje Ehlert, Annemarie Fritz, Gabi Ricken & Lars Balzer: MARKO- 0 and 1. Diagnostic tests based on a developmental model
  • Petra Langhorst, Antje Ehlert, Annemarie Fritz: A math training for early mathematics instruction: Mina and the mole

13th Conference on Educational Assessment – April 23-25, 2015 Szeged, Hungary

Title: Assessment and instruction of early mathematics skills in international context
Chair: Annemarie Frizz-Stratmann


  • Annemarie Fritz, Antje Ehlert, Lars Balzer: Intercultural validation of a mathematics competence test for grade 1 children
  • Antje Ehlert, Annemarie Fritz: Validation of a grade 1 mathematics competence test for learning disabled children
  • Miriam Balt, Antje Ehlert, Annemarie Fritz: Early detection of mathematical learning difficulties in the context of internal school entry tests in German primary schools