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## A General Analytical Model for Problem Solving Teaching: BoS

#### Ali Kürşat Erümit [1] , Vasif Nabiyev [2] , Temel Kösa [3] , Mehmet Kokoç [4] , Ayşegül Aksoy [5]

In this study, a general analytical model called Bag of Solution (BOS) was developed to help students understand and solve mathematical problems. The model is based on graph theory, a topic under discrete mathematics. The types of problems to be modelled for BoS were determined by looking at densities of the problems in the central placement examinations and exam preparation books. As a result, three types of problems were selected; namely Mixture, Worker and Motion problems. In order to develop a common model for solution of the three types of problems, a total of 1509 mixture, worker and movement problems were examined. After the analysis, the problem types were taken together, and variable relations were determined, and a common graph model was created. Since it is an algorithmic model, it allows solving problems both by paper and pencil and computer. This study proves that different types of problems (with different scenarios, objects and object relations) can be solved using a single model. It is expected that the BoS developed in this study will offer two benefits. It is hoped to both provide an algorithmic basis for computer-aided instructional materials, adaptive systems and intelligent tutoring systems to be developed for problem solving and also help students to develop a new understanding of the problem-solving process. A common graph structure that can covers the entirety of a problem can allow students to construct their own learning while solving the problem step by step.

Graph theory, problem modeling, problem solving, bag of solution
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Primary Language en Social, Education and Educational Research Research Articles Orcid: 0000-0003-4910-4989Author: Ali Kürşat Erümit (Primary Author)Institution: TRABZON ÜNİVERSİTESİ, FATİH EĞİTİM FAKÜLTESİCountry: Turkey Author: Vasif NabiyevInstitution: Karadeniz Technical UniversityCountry: Turkey Author: Temel KösaInstitution: TRABZON ÜNİVERSİTESİ Author: Mehmet KokoçInstitution: TRABZON ÜNİVERSİTESİ Author: Ayşegül AksoyInstitution: TRABZON ÜNİVERSİTESİ Publication Date : September 10, 2019
 Bibtex @research article { turkbilmat486084, journal = {Turkish Journal of Computer and Mathematics Education (TURCOMAT)}, issn = {}, eissn = {1309-4653}, address = {}, publisher = {Türkbilmat Eğitim Hizmetleri}, year = {2019}, volume = {10}, pages = {476 - 500}, doi = {10.16949/turkbilmat.486084}, title = {A General Analytical Model for Problem Solving Teaching: BoS}, key = {cite}, author = {Erümit, Ali Kürşat and Nabiyev, Vasif and Kösa, Temel and Kokoç, Mehmet and Aksoy, Ayşegül} } APA Erümit, A , Nabiyev, V , Kösa, T , Kokoç, M , Aksoy, A . (2019). A General Analytical Model for Problem Solving Teaching: BoS. Turkish Journal of Computer and Mathematics Education (TURCOMAT) , 10 (2) , 476-500 . DOI: 10.16949/turkbilmat.486084 MLA Erümit, A , Nabiyev, V , Kösa, T , Kokoç, M , Aksoy, A . "A General Analytical Model for Problem Solving Teaching: BoS". Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10 (2019 ): 476-500 Chicago Erümit, A , Nabiyev, V , Kösa, T , Kokoç, M , Aksoy, A . "A General Analytical Model for Problem Solving Teaching: BoS". Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10 (2019 ): 476-500 RIS TY - JOUR T1 - A General Analytical Model for Problem Solving Teaching: BoS AU - Ali Kürşat Erümit , Vasif Nabiyev , Temel Kösa , Mehmet Kokoç , Ayşegül Aksoy Y1 - 2019 PY - 2019 N1 - doi: 10.16949/turkbilmat.486084 DO - 10.16949/turkbilmat.486084 T2 - Turkish Journal of Computer and Mathematics Education (TURCOMAT) JF - Journal JO - JOR SP - 476 EP - 500 VL - 10 IS - 2 SN - -1309-4653 M3 - doi: 10.16949/turkbilmat.486084 UR - https://doi.org/10.16949/turkbilmat.486084 Y2 - 2019 ER - EndNote %0 Türk Bilgisayar ve Matematik Eğitimi Dergisi A General Analytical Model for Problem Solving Teaching: BoS %A Ali Kürşat Erümit , Vasif Nabiyev , Temel Kösa , Mehmet Kokoç , Ayşegül Aksoy %T A General Analytical Model for Problem Solving Teaching: BoS %D 2019 %J Turkish Journal of Computer and Mathematics Education (TURCOMAT) %P -1309-4653 %V 10 %N 2 %R doi: 10.16949/turkbilmat.486084 %U 10.16949/turkbilmat.486084 ISNAD Erümit, Ali Kürşat , Nabiyev, Vasif , Kösa, Temel , Kokoç, Mehmet , Aksoy, Ayşegül . "A General Analytical Model for Problem Solving Teaching: BoS". Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10 / 2 (September 2019): 476-500 . https://doi.org/10.16949/turkbilmat.486084 AMA Erümit A , Nabiyev V , Kösa T , Kokoç M , Aksoy A . A General Analytical Model for Problem Solving Teaching: BoS. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2019; 10(2): 476-500. Vancouver Erümit A , Nabiyev V , Kösa T , Kokoç M , Aksoy A . A General Analytical Model for Problem Solving Teaching: BoS. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2019; 10(2): 500-476.