Mathematics Education in the Early Years by unknow

Author:unknow
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Assessment of Preschool Children’s Mathematical Competence

Meanwhile, a large variety of standardized assessments to measure quantity and number knowledge of young children exists. For example, in German-speaking countries, the Osnabrücker Test zur Zahlbegriffsentwicklung (OTZ) (Van Luit, van de Rijt, & Hasemann, 2001, German version of the Utrecht Early Numeracy Test), the Neuropsychologische Testbatterie für Zahlenverarbeitung und Rechnen bei Kindern (ZAREKI-K) (Von Aster, Bzufka, Horn, Weinhold Zulauf, & Schweiter, 2009), and the TEDI-MATH (Kaufmann et al., 2009) are popular to assess children’s quantity and number knowledge.

Although there are many tests addressing children’s competence in the content area of quantity, there are hardly any instruments addressing mathematical competence as a broad construct covering different content areas and different cognitive components. In the literature, we found a few examples of such assessment instruments which cover content areas beyond quantity: the item pool developed within the Early Numeracy Research Project (ENRP) (DEET, 2001), the Research-Based Early Math Assessment (REMA) (Clements, Sarama, & Liu, 2008; Weiland et al., 2012), and the Kieler Kindergartentest (KiKi) (Grüßing et al., 2013).

The ENRP is a one-to-one interview including items addressing the content areas number, measurement, and space. The interview is primarily developed as a diagnostic tool for primary school teachers in grade 1 and includes special parts for children before entering school. It can also be used as a research instrument. Because of its diagnostic focus, the ENRP interview also provides qualitative information about children’s knowledge, for example, the use of strategies for solving tasks.

The REMA focuses on number, geometry, measurement, patterns, and data analysis (classification) (Clements et al., 2008). As the authors used the instrument to evaluate a mathematics curriculum, they applied item response theory to estimate children’s competence on a unidimensional scale (ebd.). The authors reported that the Rasch model is an appropriate statistical tool to analyze the data collected by the REMA item pool and to describe children’s mathematical competence. Moreover, even a short version of the REMA was able to measure children’s mathematical competence with acceptable reliability and validity (Weiland et al., 2012).

The KiKi is also a one-to-one interview available in three different interlinked versions for children of age 4 (easy version), 5 (medium version), and 6 (difficult version) (more information below). The whole KiKi item pool (items from all test versions together) can be analyzed by the unidimensional Rasch model with acceptable item fit values (Grüßing et al., 2013, 76). Moreover, Jordan et al. (2015) analyzed data of 4-year-old children collected with the easy version of the KiKi with a confirmatory factor analysis (CFA) . They reported that it is possible to distinguish empirically three mathematical competence dimensions for this age cohort: quantity (Q), space and shape (S & S), and change and relationship (C & R). This result is represented in Fig. 8.1. Each ellipse represents a factor of preschool children’s mathematical competence. The curves and numbers label significant correlations between factors. As all three factors are assumed to be parts of mathematical competence, the correlations are expected to be high.

Fig. 8.1Structure of 4-year-old children’s mathematical competence (Jordan et al.

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