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MATHEMATICAL PROBLEM  \nSOLVING COMPETENCY  \nIuliana Marchis  \nAbstract: Developing the problem solving competency is one of the main goals of school education, as it is a very important competency in someone’s everyday life and career as well.  \nMathematics is highly appropriate for developing this competence. This research studies future Primary and Preschool Pedagogy specialization students’mathematical problem solving and reasoning competency. These competencies are very important for a primary school teacher. The results show that most of the students easily can solve routine problems, but only half of them has adequate problem solving competency (i.e. they can successfully solve non-routine problems), and a quarter of them has good reasoning competency.  \nKeywords: Mathematical problem solving, Mathematical reasoning competency, primary schoolteacher  \nIntroduction  \nOne of the main goals of school education is developing pupils’ problem solving competency. This competency is “an individual’s capacity to use cognitive processes to confront and resolve real, cross ‐disciplinary situations where the solution path is not immediately obvious and where the literacy domains or curricula areas that might be applicable are not within a single domain of mathematics, science or reading.” (OECD, 2003, p. 156) Mathematics is one of the subjects highly appropriate for developing this competency.  \nThis research studies future Primary and Preschool Pedagogy specialization students’ Mathematical problem solving and reasoning competency. These two competencies are very important for a future primary school teacher.  \n1. Theoretical background  \nMathematics learning is based on problem solving. Mathematical tasks can be categorized in routine and non-routine tasks. Routine tasks are usually called exercises, as solving them is only required using already know methods. Non-routine tasks are called problems or, to be more specific, nonroutine problems. According to TIMSS 2011,“non-routine problems are problems that are very likely to be unfamiliar to students. They make cognitive demands over and above those needed for solution of routine problems, even when the knowledge and skills required for their solution have been learned.”(Mullis et al, 2009, p. 45) . So “a problem differs from an exercise in that the problem solver does not have an algorithm that, when applied, will certainly lead to a solution.”(Katowski, 1977, p. 163) Sometimes is difficult to decide if a Mathematical task is an exercise or a problem, because this depends on each student individually: the same task could be a problem for a student and an exercise for another student (Zhu & Fan, 2006) and it is not any more considered a problem if he/she solved it (Selden et al, 1999) .  \nMathematical problem solving needs application of multiple skills (De Corte, Verschaffel, & Op’t Eynde, 2000) . A successful problem solver needs to deeply understand Mathematical notions; to  \nmaster problem solving strategies and techniques; to have good decision making abilities and to have a positive attitude towards Mathematics (Schoenfeld, 1985) . We could observe that problem solving skills include domain specific knowledge, cognitive processes and motivational factors. Lester (1994) also includes the social-cultural context. Carlson and Bloom (2005) developed a taxonomy to characterize the attributes of problem solving, which has the following dimensions: resources, control, methods, heuristics, and affect. These dimensions are quite similar with those identified in previous research, for example of Schoenfeld (1985) . Mathematical reasoning competency is also important fora successful mathematical learning (Nunes et al., 2007) . Mathematical reasoning competency includes the following skills: understanding others’ explanations on their problem solving method; devising mathematical arguments to justif","cbCairSAY1PMQygQ","https://ap.wps.com/l/cbCairSAY1PMQygQ","pdf",106333,"English","# Introduction\n# 1. Theoretical background\n## 1.1 Routine vs non-routine tasks\n## 1.2 Problem solving and reasoning competencies\n# 2. Research\n## 2.1 Research design\n## 2.2 Research tool (problem sheet)","[{\"question\":\"What is the main educational goal addressed by the study?\",\"answer\":\"The study focuses on developing pupils’ mathematical problem solving competency, which is considered crucial in everyday life and future careers.\"},{\"question\":\"How do students perform on routine versus non-routine problems?\",\"answer\":\"Most students solve routine problems easily, but only about half have adequate problem solving competency for non-routine problems.\"},{\"question\":\"What does mathematical reasoning competency involve in the study?\",\"answer\":\"Mathematical reasoning competency includes understanding others’ explanations, devising arguments to justify claims or explain solutions, and knowing what a proof is.\"}]","Future Primary and Preschool Pedagogy Specialization Students’ Mathematical Problem Solving Competency - Volume 6 - Number 2 - 2013 Abstract | PDF",15]