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A common theme of models of conceptual growth is to establish the hierarchical structures of abilities that can be interpreted along developmental lines. Integrating the literature on the development of mathematical concepts and skills in children, a comprehensive 6 level model for describing, explaining and predicting the development of key numerical concepts and arithmetic skills from age 4 to 8, is proposed. Two studies will be presented. In the first study, 1095 preschool children completed a mathematics test (MARKO-D0) based on a 5-level model. The test fitted with a one-dimensional Rasch model. The extension of the model to a sixth level was verified in a new study: 312 first-graders took part in a mathematics test based on the six levels (MARKO-D1). In order to check whether the data of both samples adhered to the principle of unidimensionality, the data of MARKO-0 and MARKO-1 were used in a common analysis for comparative purposes. The applicability of these findings for a qualitative diagnostics and an adaptive training will be discussed.

A recently published interview-based test, known by its partly German acronym, MARKO-D SA, is introduced in this article by way of a narrative of its development through various cycles of research. The 48-item test, in 4 South African languages, captures number concept development of children in the 6 to 8-year age group. The authors present their argument for the South African versioning and translation of the test for this country, where there is a dearth of suitable assessment instruments for gauging young children’s mathematical concept development. We also present the findings of the research that was conducted to standardise and norm the local version of the test, along with our reasoning about the theoretical strength of the conceptual model that undergirds the test.

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Survey-based formats of assessing teaching quality in higher education are widely used and will likely continue to be used by higher education institutions around the world as various global trends contributing to their widespread use further evolve. Although the use of mobile devices for course evaluation continues to grow, there remain some unresolved aspects of the classic paper and web-based modes of evaluation. In the current study, the multigroup confirmatory factor analysis approach (MGCFA), an accepted methodological approach in general mixed-method survey research, was chosen to address some of the methodological issues when comparing these two evaluation modes. By randomly assigning one of the two modes to 33 continuing training courses at a Swiss higher education institution, this study tested whether the two different modes of assessing teaching quality yield the same results. The practical implications for course evaluation practice in institutions of higher education as well as the implications and limitations of the chosen methodological approach are discussed.