In Turkey, there have been some curriculum reforms in Turkish education system in last ten years one of which is mathematics curriculum. It emphasizes largely on conceptual understanding of children from their concrete experiences in order to enhance their mathematical understanding and abstraction, therefore teachers should bring well-structured tasks into their classrooms (MNE, 2005). It is also one of the standards for teaching mathematics of NCTM that the teacher of mathematics should design learning experiences and pose tasks that are based on sound and significant mathematics (Van De Walle, Karp, & Bay-Williams, 2010). On the other hand, the general aim of the design and implementation of tasks for mathematics teacher education is to enable mathematics teachers to construct the knowledge of teaching school mathematics (Zaslavsky, 2007). Watson and Mason (2007) reviewed 111 papers of working on mathematical tasks with teachers and they found little said about mathematical task design for teacher education. It makes sense, therefore, to work with teachers on task design rather than only on task implementation (Watson, 2008). In Turkey, the great emphasis on mathematical tasks for teaching mathematics by new curriculum has also drawn researchers’ attention to different aspects of mathematical tasks. In those studies, mathematical tasks are commonly investigated as part of the new mathematics curriculum and there are very few researches directly on mathematical tasks. Among those researches some of them have examined pre-service and in-service teachers’ perceptions of mathematical tasks (Bozkurt, 2012; Eraslan, 2011; Kaya, 2008; Ozmantar, et al., 2010; Ugurel, Bukova-Guzel, & Kula, 2010) and others have examined solely mathematical task and its features (Kerpic, 2011; Ugurel & Bukova-Guzel, 2010; Usun & Gokcen, 2010).  For this reason, it is crucial to study pre-service teachers on task design in the context of teacher education.

This study aims to answer the following question:

What is the nature of mathematical tasks that pre-service primary teachers have designed in terms of task design principles?

Tasks, particularly academic ones, are defined as the products that students are expected to formulate and generate, and the resources available to students while they are generating the product (Doyle, 1983). There are various frameworks developed for analyzing structures of mathematical tasks. Among these, the conceptual framework based on the construct of mathematical instructional task (Stein, Grover, & Henningsen, 1996) has been used widely to analyze mathematical tasks. Stein, et al. have defined task features referring to “aspects of tasks that mathematics educators have identified as important considerations for the engagement of student thinking, reasoning, and sense making” (p.461). These features include multiple solution strategies, multiple representations, and mathematical communication.  Although much has been written about types of mathematical tasks to encourage high-level mathematical thinking, there have been very few investigations of the mathematical tasks design principles other than the mathematical task types. In this study, the task design principles developed by Bingolbali, Ozmantar, Saglam, Demir and Bozkurt (2012) is used in order to investigate pre-service primary teachers’ designs of mathematical tasks. As part of their project they trained in-service primary, elementary mathematics and science teachers in six specific areas one of which was task design. They set up fifteen task design principles elicited from the results of national and international studies: purpose, use of time, classroom organization, student’s prior knowledge, multiple start point, comprehensiveness, suitability of material, supply of material, instruction for using material, teacher role, student role, student’s misconception, student’s difficulty, measurement and evaluation, and flexibility.

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