Projects

Current situation

Low-threshold support diagnostics in the field of mathematics are based on highly varied default settings of the instruments themselves (Niedermann, Schweize, Steppacher, 2007): Instruments without norms, instruments with outdated norms, instruments with norms for Germany, instruments with special calibration samples, instruments with bias norms, time consuming instruments and instruments based on bias content exist in unison. There is often a lack of content analysis and theoretical referents for the single tasks. Furthermore, the instruments also vary with regard to cost and objectivity. Access to and availability of the instruments and the results of research is limited.

In their analysis, Hillenbrand, Hennemann and Pütz (2006) called for more specific and economical support planning. This recommendation will shape the strategy of this particular development project.

The design of this project calls on the experiences of canton Solothurn's school psychology services, which developed calculating sheets in 1990 (Meyer, 1996) and 2007 for the educational levels 1-5 resp. 1-6.
Kretz (1999) carried out a similar yet more comprehensive project in the canton of Luzern. It has been confirmed that such projects enable a fruitful, interdisciplinary approach to tackling those questions concerned with subject-specific didactics and diagnostic criteria.
Moser Opitz, Reusser and Berger (2008) provided instruments for levels 1-3 in the canton of Berne.

These standardised numeracy tests formed part of canton Solothurn's screening procedure and offered a proven, low-threshold, time-saving and cost-effective pedagogical-psychological diagnostic procedure (Leinert and Ratz, 1998). They contained processes that are still found in the current design.

Our project is aimed at creating and expanding a single element for the optimisation of subject-specific didactical support planning in the field of mathematics.

Project objective

The aim of this project was to create and evaluate mathematical short tests to be used as instruments in screening procedures at school levels 1-9. The test's well-balanced difficulty levels shall ensure not only the detection of children with learning difficulties, but also the detection of highly talented children.
A further component aim was to ensure that the whole procedure did not take longer than 20 minutes – creating a very fine line: The screening test must, on the one hand side, be an effective, empirical sieve-like instrument used to obtain current learning levels. On the other hand side, it must be as time-efficient and simple to use as possible.

Procedure

This project was anchored in the project methods, the classical test theory and the principles of empirical pedagogical diagnostics (Ingenkamp, Lissmann, 2005).

PSS year 1 (2008) students at the University of Applied Sciences of Special Needs Education were integrated into the project within the framework of the Cognition / Mathematics module, the aim of which was to equip them with example-based knowledge of qualitative and quantitative diagnostics in the field of mathematical performance.
They created nine group level tests. The tasks had to meet the indicative targets set by the supporting cantons, the HfH and the Principality of Liechtenstein in the following areas: Geometry, technical calculation (drawing, symbols, numbers, relations, mathematical operations), factual problems and problem solving. They also organised the empirical testing and electronic entry of data.

During the project period, they processed 240 content analyses and portraits of the selected mathematical tasks for the school levels 1-9. For the purpose of exploration, the tasks were presented to pupils in flexible interviews (Meyer, 2007). Guidelines regulated the organisation and progression of the whole project. All documents and data have been deposited in a project folder on the learning platform (BSCW).    

Evaluation and testing was carried out by HfH employees.

Results and outlook

The “General Guidance for the Implementation of Mathematical Short Tests 1-9 (MKT)” (Meyer, 2011) was drawn up parallel to this project. It contains a compilation of various considerations with regard to test didactics, test statistics, support planning and subject-specific didactics that highlights the versatility of MKT.

3600 children were tested using the beta version (the first version of a computer programme). Evaluation showed that eight of the nine tests are highly reliable. Eight of the nine tests also exhibited significant correlation with evaluations made by teaching staff. Seven of the nine tests classify the performance of the children satisfactorily (Lenhard and Max, 2010).

The existing standardised beta version is to be improved upon through the selection of items and the replacement of tasks with regard to their content and level of difficulty. This will allow an approximation to the normal distribution of test values. The capacity of existing tests to distinguish between children with good mathematical abilities is slight.
The resolution time of MKT 1-9 in the classroom trials was 32 minutes. There were several individual cases where the pupils completed the tasks much quicker. The reduction of items will lead to a reduction in resolution time.

Projectteam and contact

Stefan Meyer, lic.phil., Dozent HfH; e-mail:
Bortis Renate, Markus Steffen