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Since the establishment of formal education in Iran, there has always been an emphasis on the application of mathematics in real life situation. To measure students’s competencies in applying mathematics in real life situations, there is a need to design a test with this purpose. During the current decade, PISA has been conducted in various countries to measure sudents’ competencies needed for solving real life problems in 15 years old. Because of the reliable systematic framework of PISA regarding mathematics literacy (ML) as a construct, agreed by mathematics experts, PISA framework has been chosen as a suitable framework to design a test to assess students’ competencies for ML. In this paper, we explain the stages of designing a similar test for the Iranian students of the same age. The approach to design the test is cognitive-diagnostic according to the framework of PISA and required modifications were made based on mathematics teachers’ viewpoints in Tehran. The final test items are based on three processes of mathematics literacy which consist of formulation employment and interpretation/ evaluation, and six cognitive competencies including communication, mathematising, representation, reasoning and argument, devising strategies for solving problems and using symbolic, formal and technical language and operations, in addition, four real context of personal societal occupational and scientific and finally four content area of quantity uncertainty and data change and relationships and space and shape.

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The aim of the present study was to investigate the educational activities of the preschool mathematics books regarding geometric shapes using documentary method. For the analysis, we used the document published in 1396 (2017) by the Ministry of Education in Iran for preschool level., as well as the zero, first and second level of the revised Van Hiele Model (Clementes and Batista, 1992) including Pre-recognition, Syncretic and analysis as the criteria. At first level, 10 criteria for analyzing activities of geometry shapes from the first three levels of the revised Van Hiele Model (Clementes and Batista, 1992) exteracted. Then five textbooks which were recommended by Education Growth Bibliography, Welfare Organization and several preschool centers selected and their geometric shapes content evaluated according to the 10 extracted criteria. Results showed the highest frequency of educational activities belonged to level one and the lowest frequency beloged to zero level of the revised Van Hiele model. The study concluded that the content of the preschool mathematics books needs to be revised and the educational activities of higher level than two recommended to be transferred to higher grade mathematics textbooks.

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The purpose of this research was to describe the perception of primary school teachers on how to help students in instructing of the volume, using the task-based interview method. For this purpose, some tasks was designed and implemented with two general question for six volunteer primary school teachers who had experience in teaching fifth and sixth grades. The answers were analyzed according to the instruction component of the cognitive activation model in the classroom (Kraus et al., 2008). The results showed the lecture method, the less use of concrete representations, different perceptions of the volume definition, spatial limitations and relying on arithmetic representation in solving the task. In total, the results of this research clarify the need of teachers to improve their knowledge in the field of instructing of the volume, and for this purpose, suggestions have been presented.