In this paper, the widespread curricular aspiration to develop student facility with both content-specific and higher order thinking skills is investigated through a customised set of “hybrid tasks.” Gal (2004) included a “critical stance” among the key attributes for successful statistical thinking (ST). Critical thinking (CT) skills rely on self-regulation of the thinking processes and detection of patterns in supposedly disorganized structures (Ennis, 1989). Dealing critically with information – a crucial aspect for both domains – demands critical/evaluative thinking based on rational thinking processes and decisions (Aizikovitsh-Udi, 2012). In order to explore thinking processes related to tasks in the domains of both Statistical Thinking and Critical Thinking, individual semi-structured interviews were conducted with mathematics teachers. By using mathematics teachers as subjects, basic content competence can be assumed and it becomes possible to examine their content-related higher order thinking skills, both in terms of statistical thinking and critical thinking. The interviews focused on thinking-aloud when solving tasks and each lasted about 40–50 minutes. Figure 1 shows a sample task. Figure 1. Task “tablets” (Kuntze, Lindmeier & Reiss, 2008) The interviews demonstrated how elements of CT can contribute to ST, for example when evaluating data, its presentation and analysis, planning data collection, etc. Conversely, aspects of ST like dealing with statistical variation and uncertainty were shown to contribute to CT, especially for decisions in non-determinist situations, where full data is unavailable. This study has shown that both ST and CT skills can be evoked by the same task. We suggest that this models authentic and useful thinking practice more effectively than a more closed task that stimulated only statistical thinking and the application of taught procedures. An instructional program of hybrid tasks could provide the opportunity to employ content-specific (statistical) thinking, while simultaneously promoting and nurturing student use of higher order (critical) thinking.

Aizikovitsh-Udi, E. (2012). Developing critical thinking through probability models, intuitive judgments and decision-making under uncertainty. Published doctoral dissertation. Saarbrucken, Germany: LAP Lambert Academic Publishing. ISBN 978-3-8383-7240-2. Ennis, R. R. (1989). Critical thinking and subject specificity: Clarification and needed research. Educational Researcher, 18, 4–10. Gal, I. (2004). Statistical literacy, Meanings, Components, Responsibilities. In D. Ben-Zvi, & J. Garfield (Eds.), The Challenge of Developing Statistical Literacy, Reasoning and Thinking (pp. 47-78). Dordrecht: Kluwer. Kuntze, S., Lindmeier, A. & Reiss, K. (2008). “Using models and representations in statistical contexts” as a sub-competency of statistical literacy – Results from three empirical studies. Proceedings of ICME 11. [http://tsg.icme11.org/document/get/474].