Theoritical Famework New.docx3333.docx

THEORITICAL FAMEWORK NEW

There have been many research studies discussing the problem solving teaching and its results. Verschaffel et al (1999) wrote that the problem solving instruction given to the fourth and fifth grade students helped them solve mathematical application problems and that the students could learn problem solving strategies. Folmer (2000) wrote that in the fourth grade, the instruction on nonroutine problems improved the students’ use of cognitive strategies and their awareness of how they solved the problems. Pugale (2001) suggested that successful high school students could be distinguished from others in terms of Murat ALTUN Egitimde Kuram ve Uygulama Dilek Sezgin MEMNUN Journal of Theory and Practice in Education 2008, 4 (2):213-238 © Çanakkale Onsekiz Mart University, Faculty of Education. All rights reserved. © Çanakkale Onsekiz Mart Üniversitesi, Eğitim Fakültesi. Bütün hakları saklıdır. 217 the ways they focus on problems, organize data, make calculations and give meaning to the results. Krutetski reported that in the sixth grade, the students who succeed in solving non-routine problems are the ones who can analyze problems from different perspectives before solving, make syntheses, generalize the solution

methods and benefit from solutions to similar problems (Niederer and Irwin, 2001). Pape and Wang (2003) had the result that successful secondary school students are those who are able to determine their goals, make plans, control their own behaviors, organize the places where they study and evaluate themselves with the help of others. De Hoys, Gray and Simpson (2004) analyzed the non-routine problem solving processes of two undergraduate students and reported that the more successful student was the one who focused on developing a method himself according to the qualities of the problem while the other sought for a method to work in the solution only. Nancarrow (2004) examined how the students solved the non-routine algebra problems in a lesson based on a problem solving method designed to sustain the students’ heuristics to solve the problems and their creativity. The study, which was conducted with a control group, showed that there is a correlation between the success in solving a problem and the knowledge of the basic concepts and methods about the problem, and that the experimental instruction was useful for improving the students’ cognitive strategies.

A. Cognitive Process Cognition is the study of how the mind works [15]. Cognitive processes are the mental processes of an individual. Many theories based on cognitive development or processes were developed; the most cited being those of Piaget and Vygostky. Research evidences suggested that the mind has internal mental states such as beliefs, desires and intentions. Cognitive processes may be understood in terms of information processing, especially when a lot of abstraction or processes are involved. Several frameworks of problem solving have been created. [16] four phase (understanding, planning, carrying out the plan and looking back) description of problem solving procedures is a prototype on which recent mathematical problem solving research has been based. [11] argued that four factors (knowledge base; problem solving strategies - heuristics; Control - monitoring and self-regulation; belief) are necessary and sufficient for understanding the quality and success of the problem solving attempts. Many other similar frameworks were generated [17][19]. In this study, the framework proposed by [19] will be used to explore the

cognitive processes associated with problem solving and which she established as follows: Reading: To understand each part of the problem to establish relationships among the parts. Paraphrasing: To translate the linguistic information in the problem by rephrasing or restating the problem. International Journal of Learning and Teaching Vol. 3, No. 1, March 2017 © 2017 International Journal of Learning and Teaching 46 doi: 10.18178/ijlt.3.1.46-50 Visualizing: to process the linguistic and numerical information in a mathematical problem and form internal representations in memory. Hypothesizing: to develop a solution plan that is linked to the comprehension of the problem and the integration of the problem information. Reading and representation strategies assist problem solvers in deciding on a solution path. Estimating: to accurately predict an outcome based on the question and the goal that was set. Computing: to perform the correct operations and also recall the necessary mathematics fact for accuracy. Checking: to verify both the process and the product.