Fostering Early Numerical Skills at School Start in Children at Risk for Mathematical Achievement Problems: A Small Sample Size Training Study

By Hasselhorn, Marcus; Linke-Hasselhorn, Kathrin | International Education Studies, March 2013 | Go to article overview

Fostering Early Numerical Skills at School Start in Children at Risk for Mathematical Achievement Problems: A Small Sample Size Training Study


Hasselhorn, Marcus, Linke-Hasselhorn, Kathrin, International Education Studies


Abstract

Eight six-year old German children with development disabilities regarding such number competencies as have been demonstrated to be among the most relevant precursor skills for the acquisition of elementary mathematics received intensive training with the program "Mengen, zählen, Zahlen" ["quantities, counting, numbers"] (MZZ, Krajewski, Nieding, & Schneider, 2007). In 24 30-minute training sessions administered across an interval of eight weeks, four children received the full program. Using a pretest-posttest control group design, the effectiveness of the training was demonstrated with a large effect size (d = 4.6). In addition, a shortened training of the waiting control group (n = 4) after finishing the principal evaluation replicated the appropriateness of the MZZ program (d = 2.5) as a means of remediating early number competence deficiencies at the onset of formal schooling.

Keywords: early education, poor early number competencies, cognitive training

1. Introduction

Societal and educational political expectations regarding pre-primary education and care have changed in a fundamental way in recent years. While attending kindergarten was for a long time predominantly attributed to socialisation, fostering the emotional, social, motor-related and moral development of children, recently many federal states in Germany presented orientation plans for pre-primary education and care that also target the preparation of specialized skills such as language competence, mathematics, and natural and life sciences. Furthermore, a significant change in guiding principles can be observed throughout the past decades: While until the 1960s, the prevailing opinion was to attribute learning achievement mainly to innate skills, this view has been substituted by the idea that school-based offerings can compensate for social disparities and provide for equal learning opportunities.

Findings from the first PISA study (Baumert et al., 2001) were interpreted as evidence for that this demand for compensation has so far been inadequately fulfilled by the German education system, or at least to a far less extent than this has been realized by other OECD countries. There is reason to believe that the comparatively poor outcomes of German secondary school students in PISA studies may not least be due to a neglect of pre-primary education: If it were possible to make disadvantaged children sufficiently "fit" at an early stage of the education process, this should also affect the later acquisition of competencies in a positive way.

Findings from the Munich SCHOLASTIK study (Weinert & Helmke, 1997) in particular indicate that children starting primary education with a low level of achievement maintain their relative position until the end of their primary education, i.e. weaker/poorer pupils hardly seem to catch up on their peers. This also applies to the domain of mathematics. According to primary educational standards in mathematics issued by the German Standing Conference of Ministers of Cultural Affairs these standards are mainly concerned with developing skills in the following domains:

* constructing an idea of numbers and understanding of operations,

* developing spatial competencies and distinguishing shapes,

* recognizing patterns and structures,

* developing concepts of size and competencies for measuring and comparing

* assessing data and frequency and developing elementary concepts of probability.

Early numerical skills that are relevant for later school learning processes are developed even at kindergarten age (e.g., Jordan, Kaplan, Locuniak, & Ramineni, 2007; Krajewski & Schneider, 2009: LeFevre, Fast, Swarchuk, Smith-Chant, Bisanz, Kamawar, & Penner-Wilger, 2010). The development of a concept of numbers rests on the integration of different concepts, skills and abilities. In this context, special significance is at first sight attributed to "number skills" such as counting and grasping structured and unstructured quantities (cf. …

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