Posing mathematical literacy problems is one of the challenging issues in literacy studies. The present study focused on how to develop the ability to pose mathematical literacy problems. Within the context of the training given to middle school mathematics teachers on how to pose mathematical literacy problems, literacy problems were introduced. Each of the problems was discussed and evaluated regarding the structural characteristics and differences from the routine problems. Respectively, the steps of (i) completing an incomplete problem with a context as a mathematical literacy problem; (ii) evaluating the problems in the textbooks in terms of realistic problems and converting them into mathematical literacy problems; and (iii) conducting exercises for writing original mathematical literacy problems. It was concluded that teachers were more successful in creating contexts, that they tended to write operation-oriented problems, that they often used sentences ending with the words "please calculate" and "find" by being influenced by the traditional word-problem sentences contained in the textbooks, and that they had more difficulty in developing problems which should bring forward a mathematical suggestion than other problem types.

Abstract:This study attempts to reveal pre-service teachers' conceptions, definitions, and understanding of quadrilaterals and their internal relationships in terms of personal and formal figural concepts via case of the parallelograms. To collect data, an open-ended question was addressed to 27 pre-service mathematics teachers, and clinical interviews were conducted with them. The factors influential on pre-service teachers' definitions of parallelograms and conceptions regarding internal relationships between quadrilaterals were analyzed. The strongest result involved definitions based on prototype figures and partially seeing internal relationships between quadrilaterals via these definitions. As a different result from what is reported in the literature, it was found that the fact that rectangle remains as a special case of parallelogram in pre-service teachers' figural concepts leads them not to adopt the hierarchical relationship. The findings suggested that learners were likely to recognize quadrilaterals by a special case of them and prototypical figures, even though they knew the formal definition in general. This led learners to have difficulty in understanding the inclusion relations of quadrilaterals.

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The need to transfer the mathematics learned at school to real-life and use mathematical knowledge in life has brought the expression of mathematical literacy to the fore. Meeting this need is possible by raising mathematically literate students in schools and planning education to achieve this. From this starting point, this study aims to introduce a teaching model called Dual-Focused Teaching, which is designed to develop mathematical literacy during mathematics instruction. Constructed based on data from a design-based research project, this model focuses on reaching, deepening, and reinforcing mathematical concepts and generalizations. The model's content includes learning theories on which it is based, its application in the lesson, and its reflection on the lesson on a sample lesson plan are explained in all aspects of this study. The need for this model, its applicability, and potential are discussed in light of the literature.

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