İlköğretim 7. ve 8. Sınıf Öğrencilerinin Gerçek-Yaşam Problemlerini Çözerken Sergiledikleri Yaklaşımlar ve Kullandıkları Strateji ve Modellerin İncelenmesi

Abstract

AbstractThis study scrutinises approaches and thinking processes displayed by the elementary school students when solving real-world problems. It employed a qualitative inquiry to produce rich and realistic data about the case at hand. The research sample included 116 students. The data were obtained from written exam and semi-structured interviews, and they were analysed using content and discourse analysis methods. The results indicated that most of the students disregarded the real-life situations that the problems are related to. They displayed non-realistic approaches that included application of rules, procedures, and factual knowledge in a straightforward and uncritical way. Most of the students lacked the ability to use alternative approaches and appropriate strategies. Some constructed models of the problem situations, yet most of these students were not able to utilise these instruments as a conceptual tool to gain insight into the situations. Rather, models were used as part of the routine - rules, procedures and factual knowledge - that the students applied uncritically.Key WordsReal-World Problems, Problem Solving Approaches, Student Thinking, Problem Solving Strategies, Mathematical Models.Problem solving is considered the most significant cognitive activity in professional and everyday life (Jonassen, 2000). International documents suggest that problem solving should be used as an integrating theme in the mathematics curricula assuming that this could increase students' achievements in mathematics (Cockroft, 1982; National Council of Teachers of Mathematics [NCTM], 1989). It is indicated that students who followed problem-based mathematics curricula outperformed their counterparts both in mathematics achievement and in problem solving (Cai, 2003; Cai & Nie, 2007; Clarke, Breed, & Fraser, 2004). Problem refers to a situation in which the desired goal has to be attained but direct path towards the goal is blocked. It refers to a situation that requires resolution, but an individual sees no apparent path to the solution (Krulik & Rudnick, 1985; Orton & Wain, 1994). Briefly, if a situation causes cognitive conflicts in the minds of individuals it can be considered as a problem (Baki, 2006). Problem solving is a dynamic process in which students try to understand the situation, make a plan for the solution, select or develop methods and strategies, apply all these heuristics to get the solutions; and finally they check out the answers obtained (Barnet, Sowder, & Vos, 1980; Mayer, 1985; Polya, 1973; Schoenfeld, 1992; Suydam, 1980). In this process one may use various strategies (e.g., making a list, looking for patterns, working backwards) and different kinds of models (see Bayazit & Aksoy, 2008; Baykul, 2000; LeBlanc, 1977; Posamentier & Krulik, 1998). Mathematical problems are classified into two major categories: routine and non-routine problems. Routine problems can be resolved by the application of rules, procedures and basic operations that the problem solvers already know (Arslan & Altun, 2007; Mahlios, 1988). Non-routine problems causes great difficulties for students (Elia, Heuvel-Panhuizen, & Kolovou, 2009); this is because they do not have a straightforward solution; rather they request creative and critical thinking, employing alternative approaches and using various strategies and mathematical models (Altun, 2005; Inoue, 2005). In order to solve such problems one may need to use metacognitive skills including self-monitoring and self-regulations (Hartman, 1998; Mayer, Sims, & Tajika, 1995; Nancarrow, 2004).One type of non-routine problem includes real-world problems (Verschaffel, De Corte, & Vierstraete, 1999). Their solution requests giving particular attention to real-life contexts that the problems are related to. Students need to utilise their intuitive knowledge and daily-life experiences to resolve real-world problems (Nesher & Hershkovitz, 1997). …