On Assessment of Problem Solving

Training towards the development of the capacity of learners has become an inevitable trend of world education. Vietnamese education also emphasizes the comprehensive development of the capacity and the quality of students. In mathematics teaching, there are some notable capacities such as problem-solving capacity, cooperation capacity, capacity for using mathematical language, computing capacity and so on. In particular, the problem-solving capacity is very important to students because it helps them to solve problems not only in mathematics but also in practice. In this paper, we want to investigate the problem-solving capacity of students in primary schools through a problem required to solve in different ways. The results of the study showed that students had enough the problem-solving capacity to find out various solutions to the given problem.

ITM Web of Conferences, 2017

This study was conducted to determine the problem solving skills of the third grade students studying at the department of elementary school mathematics teaching. The study was conducted in the second semester of the academic year of 2015-2016. The study group consists of 47 third year student who study at Ondokuz Mayıs University, Faculty of Education Elementary School Mathematics Teaching ad take the selective course of Problem Solving in Mathematics. Within the scope of this course, the researchers explained subjects related to problem and problem solving, problem solving skills and solved problems during the first 4 weeks of the course. For the rest of the weeks, the students were divided into groups. They have solved two non-routine problems each week for 8 weeks. The method of study is the interview method, which is one of the qualitative research methods. In light of the retrieved findings, the answers given by the students have been thematized as the stages of problem solving, understanding the problem, implementing the problem, evaluation of the problem, reasons for taking the courses, association problems, ways of finding different solutions, development of procedural skills, creating formulas, mathematical thinking, use of mathematical language, suitability of the course, views on problem solving, and the contribution of the course.

Turkish Journal of Computer and Mathematics Education (TURCOMAT)

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.

The Journal of Problem Solving, 2013

Problem solving has received broad public interest as an important competency in modern societies. In educational large-scale assessments paper-pencil based analytical problem solving was included first (e.g., Programme for International Student Assessment, PISA 2003). With growing interest in more complex situations, the focus has shifted to interactive problem solving (e.g., PISA 2012) requiring identification and control of complex systems. In the future, collaborative problem solving represents the next step in assessing problem solving ability (e.g., PISA 2015). This paper describes these different approaches to assessing problem solving ability in large-scale assessments considering theoretical questions as well as assessment issues. For each of the three types of problem solving, the definition and understanding of the construct is explained, items examples are shown together with some empirical results, and limitations of the respective approach are discussed. A final discussion centers on the connection of cognitive and differential psychology within educational research and assessment.

2016

Purpose of this study is to determine problem solving skills of primary mathematics preservice teachers in mathematics teaching. This research was carried out with the 3rd year students studying in the department of elementary mathematics teaching at Samsun Ondokuz Mayıs University. Research method was determined as case study, one of the qualitative methods. In the study, the students were taught for 13 weeks (39 hours) Polya’s (1945) problem solving stages that are composed of 4 stages and the problem solving stages were introduced in order to improve their problem solving skills. In the research, two problems developed by Posamentier and Krulik (1998) and semi-structured interview form developed by the researcher were used as data collection tools. In the analysis of the data, solutions of the problems applied were examined considering Polya’s (1945) problem solving steps. The findings obtained via the solutions of applied problems and via the semi-structured interview form were ...

Journal of Education and Practice, 2019

Student problem solving abilities are still low because of the lack of response of students' feedback to the teacher's questions and explanations, and the lack of concentration on mathematics. The cause of the problem is the lack of problem solving abilities of students in mathematics learning, and variations in the application of learning models. This study aims to analyze the effect of the application of problem-based learning models on mathematical problem solving abilities of students at SMAN 7 Padangsidimpuan. The type of experimental research consisted of case groups (problem based learning methods) and controls (question and answer method), with a 2x3 factorial design. The population in the study is the student at class X SMAN 7 as many as three classes with a total of as many as 34 students / class. The research samples were class X-2 and X-3, with random sampling techniques. Techniques in collecting data through tests, observations, and interviews. Statistical analysis was performed using t test analysis. The results showed that the problem-based learning model was better than through the application of direct learning, with the average results of the experimental class students being 80.74 and the control class 68.24. The application of problem-based learning to improve students' problem solving skills can be carried out by teachers in the dual improvement of the quality of education in schools.

Proceedings of the Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018), 2018

Problem solving is the ability which can be used not only to solve a simple problem but also a complicated problem. It is a skill which can be trained in every level of education. Therefore, teachers are required to be able to trill this ability and an obligation for mathematics teacher to have an excellent problem solving skills. This research aimed to explore the ability of postgraduate students to solve mathematics problems. Mathematics postgraduate student at Universitas Negeri Surabaya had been chosen as a subject. The instrument was developed based on Polya (1973). Firstly, we did literature reviews in order to explore what kind of problem solving test which could be used to mapping student ability. Moreover, we constructed a student's worksheet with high order thinking problem. It had been analysed to find out the student's ability. The result showed that students' ability in solving mathematics problem is bad. Almost 100% subjects understand about the problem, unfortunately only 50% of students are able to use the data. It is about 50% of students are able to connect their knowledge with the problem and only 60% subjects are able to make a plan and able to implement it.

American Journal of Educational Research

This study aims to analyze: (1) The level of students' mathematical problem-solving ability, (2) Mistakes made by students in solving mathematical problem-solving problems. This type of research is qualitative research. The subjects of this study were students of class VII-A at Tunas Baru Jin Seung Middle School, Batam City. The results showed that: (1) High-ability students were able to carry out the stages of understanding the problem, devise a plan, carry out a plan and look back. Moderate-ability students are being able to carry out the stages of understanding the problem, devising a plan, and carry out a plan. While low-ability students can carry out the stage of understanding the problem. (2) Students can understand the problem by writing down what is known and asked, but unable to explain in their sentences. Students are not able to devise a plan because of the inability to associate information with one another. Students are not able to carry out a plan, this is due to the inability of students to make plans so they do not understand how to solve problems and calculation errors occur in the completion process. Students are not able to look back obtained and give their arguments.

Advances in Social Science, Education and Humanities Research

This research aims to test the problem-solving abilities of students who were taught in different ways, through problemsolving learning and group discussion models. The research design used a quasi-experimental design with a Nonequivalent Control Group Design (NCGD). The research subjects were students of class XI at MA Badrul Arifin Situbondo, who were determined by purposive sampling and obtained two research classes. The experimental group learned with a problem-solving learning model, while the control group learned using a group discussion model. The results showed that those who studied with the problem-solving model had better problem-solving ability than those with the group discussion model.

AKSIOMA: Jurnal Program Studi Pendidikan Matematika

Students' ability to solve mathematical problems is the most important part of learning mathematics. Therefore, assessing students' ability to solve mathematical problems is one of the tasks of mathematics teachers that must be done. This study aims to develop a test instrument to assess students' ability to solve mathematical problems. The research method used Systematic Literature Review (SLR) by analyzing primary sources from books and articles. Before developing an instrument to assess students' ability to solve mathematical problems, the variables involved in mathematical problem solving were first analyzed. Furthermore, there are four domains involved in the instrument development framework carried out. They are resources, heuristics, control, and belief system. Based on this study, it was found that: (1) the aspects correlated with mathematical problem solving are reasoning, decision making, critical thinking, and creative thinking; (2) the types of tasks rela...