Problem-posing Skills Research Articles

The Effect of Mathematics Instruction Integrated with Social Issues on Problem Posing Skill

This study investigated the effect of mathematics instruction integrated with social issues on developing secondary school seventh grade students’ problem posing skills. The study was carried out as an action research. Participants of the study were 17 seventh-grade students. In the study, a ten-week instruction was carried out. The quantitative data were collected with the Problem Posing Skill Test developed by the researchers. The qualitative data were collected by semi-structured interviews. Concerning data analysis, while the t-test was used for the dependent samples for quantitative data, inductive analysis was used for qualitative data. Results revealed significant differences between students’ pre-test and post-test scores in favor of post-test, and qualitative findings also supported these results.

THE OPINIONS OF PRIMARY SCHOOL TEACHERS ON GAINING PROBLEM POSING SKILL IN MATHEMATICS COURSE

The aim of this study is to determine the opinions of primary school teachers on gaining problem posing skill in mathematics course. The qualitative research method was used in this study. The participants of the study consist of fourteen primary school teachers working at different classroom grades at primary school. The semi-structured interview technique and the interview form prepared by the researchers were used to collect the data. The data of the study were analyzed with the NVIVO10 program and content analysis was used in the data analysis. As a result of the analysis performed, it was found out that primary school teachers expressed their opinions under the themes such as problem posing activities implemented in the mathematics course, the effects of problem posing on students, the knowledge and skills regarding problem posing, students’ problem posing skills, difficulties and problems experienced in problem posing activities and suggestions to develop problem posing skills and solution proposals.

Examination of Sixth Grade Students' Problem-Posing Skills: A Case study

The aim of this study is to examine the sixth grade students' skills in different problem situations requiring four operations in natural numbers and their views on problem posing. Participants of this study, where case study of qualitative research methods were preferred, consisted of 15 students studying at sixth grade level In the study, a problem-posing test including different problem-posing situations, and a semi-structured interview form related to basic operations in natural numbers, were used as data collection tools. Problem posing test consisted of 10 questions. The semi-structured interview form includes open-ended questions on students' mathematical problems and thoughts on problem solving.. The data obtained from the problem-posing test were analyzed with regard to the rubric of the test.. The answers were first classified as “empty”, “not a problem” and “problem”. Afterwards the answers determined to be a problem were evaluated and analyzed according to the criteria of “language”, “complexity of the problem” and “solvability” in the rubric put forward by Ada and Ozturk (2019). The data obtained from the interviews with the students were analyzed by descriptive analysis. According to the results of the study, while some of the students left the questions blank, a larger part of them could not form a problem sentence even though they answered the questions. In addition, a number of errors were identified in the students' perception of the problem concept. While students were able to pose problems in the most selection cases, they were able to pose very few problems in case of free problems. When the findings of the students' views are considered within the scope of the study, it is determined that problem-posing helps to understand the problem from a cognitive point of view and contributes to the meaning of procedural expression or mathematical subject. At the same time, it has been found that problem-posing creates positive attitudes in students by reducing prejudice against problems in terms of affective aspects and affects students' attitudes towards mathematics and brings them closer to the lesson. In line with the results of the study, some suggestions were made to the research and education stakeholders.

Examination of Sixth Grade Students' Problem-Posing Skills: A Case study

The aim of this study is to examine the sixth grade students' skills in different problem situations requiring four operations in natural numbers and their views on problem posing. Participants of this study, where case study of qualitative research methods were preferred, consisted of 15 students studying at sixth grade level In the study, a problem-posing test including different problem-posing situations, and a semi-structured interview form related to basic operations in natural numbers, were used as data collection tools. Problem posing test consisted of 10 questions. The semi-structured interview form includes open-ended questions on students' mathematical problems and thoughts on problem solving.. The data obtained from the problem-posing test were analyzed with regard to the rubric of the test.. The answers were first classified as “empty”, “not a problem” and “problem”. Afterwards the answers determined to be a problem were evaluated and analyzed according to the criteria of “language”, “complexity of the problem” and “solvability” in the rubric put forward by Ada and Öztürk (2019). The data obtained from the interviews with the students were analyzed by descriptive analysis. According to the results of the study, while some of the students left the questions blank, a larger part of them could not form a problem sentence even though they answered the questions. In addition, a number of errors were identified in the students' perception of the problem concept. While students were able to pose problems in the most selection cases, they were able to pose very few problems in case of free problems. When the findings of the students' views are considered within the scope of the study, it is determined that problem-posing helps to understand the problem from a cognitive point of view and contributes to the meaning of procedural expression or mathematical subject. At the same time, it has been found that problem-posing creates positive attitudes in students by reducing prejudice against problems in terms of affective aspects and affects students' attitudes towards mathematics and brings them closer to the lesson. In line with the results of the study, some suggestions were made to the research and education stakeholders.

Malaysian and American Preservice Teachers' Ability and Perspective on Mathematical Problem-Posing

Problem-posing has received considerable attention among the mathematics education community. In the present study, researchers explored preservice teachers in two countries in terms of their ability and perspectives on mathematical problem-posing. Twenty-four preservice teachers in a secondary school program in Malaysia and 26 preservice teachers in the middle school program in the United States participated in this study. The preservice teachers posed at least three mathematical block pattern problems and these were categorized according to structures, mathematical concepts, languages, and relevance elements. The results showed the American preservice teachers demonstrated better performance on the structure, mathematical concepts, and compatibility elements. The inferential analysis showed significant differences in problem-posing skills between these two groups of preservice teachers on structure (U = 149.5, p = .006) and relevance (U = 156.50, p =. 008) of the mathematical problems. Both groups had similar perspectives related to posing mathematical problems. Implications for classroom instruction were also discussed.

Problem-Posing Skills for Mathematical Literacy: The sample of Teachers and Pre-Service Teachers

Problem-Posing Skills for Mathematical Literacy: The sample of Teachers and Pre-Service Teachers

Okul Öncesi Öğretmenlerinin ve Öğretmen Adaylarının Toplama ve Çıkarmaya İlişkin Sözel Problem Kurma Becerileri

The aim of this study is to examine preschool teachers’ and pre-service teachers’ verbal problem-posing skills. The data of the study was gathered from 179 third and fourth year students studying in the preschool teaching department in a public university in Adana in the 2016-2017 academic year and 93 preschool teachers working in pre-school education institutions affiliated to Provincial Directorate of National Education in Adana. The data of the study was collected by using Verbal Problem Posing Form created by the researchers. Frequency and percentage techniques were used to analyze the data. As a result of the study, it was seen that teachers and pre-service teachers were able to pose some verbal problem types correctly while they could not pose other types. A majority of both teachers and pre-service teachers were largely successful in posing joining / result unknown; joining / change unknown; separating / result unknown and separating / change unknown problem types. Furthermore, both teachers and pre-service teachers had very little success in posing part-part-whole / whole unknown; part-part-whole / part unknown; comparison / smaller unknown; comparison / difference unknown problem types. Additionally, a majority of participants were found to be unsuccessful in posing the comparison/larger unknown type of problems.

Posing mathematically worthwhile problems: developing the problem-posing skills of prospective teachers

Problem solving is a key priority in school mathematics. Central to the valuable role played by problem solving is the quality of the problems posed. While we recognize the features of good problems and how to support learners in solving problems, less is known about the ways in which prospective teachers’ (PTs) conceptions of what constitutes a ‘good’ problem develop within the confines of an Initial Teacher Education program. This study explored the effect of engagement in a mathematics education course on the problem-posing skills of 415 prospective primary teachers. A 3-week instructional unit consisting of a series of lectures and tutorials on problem solving and problem posing was implemented. A questionnaire examining participants’ understandings of and ability to pose problems was administered prior to and following instruction. Results reveal that participation brought improvements in conceptions of what constituted a good problem and in the ability to pose good problems (targeted at grades 1–4). Initial problems generally were arithmetic, required one step to solve and had only one correct solution. Following the instructional unit, attention was paid to designing problems that had the potential of multiple strategy use, multiple possible correct solutions, multiple modes of representation and the incorporation of extraneous information. Despite these improvements, the complexities of problem posing and the challenges that persist for PTs in posing good problems are evidenced. Recommendations are made for the enhancement of problem-posing experiences, most notably developing skills in identifying mathematically worthwhile problems from a selection of problems or in reformulating given problems to make them better, that support PTs in developing the knowledge and understandings required to pose mathematically worthwhile problems.

Interés de los Futuros Maestros en Saber Crear Problemas de Matemáticas para Enseñar a Resolverlos

Skills of posing math problems are related to problem-solving skills. This research aims to know if pre-service teachers consider problem-posing skills are useful to teach problem-solving, starting from the hypothesis that there is little practice in problem-posing. The participants were 94 pre-service teachers of the University of Barcelona. This study points at the most important characteristics of mathematics problems for them, the relations between problem-posing and problem-solving, and which problem-posing skills they have developed. First findings they do not know relevant characteristics of mathematics problems, they do not consider posing and solving problems two different processes, and they think they are well prepared to pose problems. An educational tool is introduced to the usefulness of problem-posing to teach students problem-solving. Second findings a lack of practicing in problemposing and that teachers do not know how to pose problems for educational purposes. So, pre-service teachers do not consider problem posing a tool to teach problem-solving due to lack of practicing.

The effects of problem-posing intervention types on elementary students’ problem-solving

ABSTRACT Problem posing is the act of creating one’s own problems, unlike the traditional practice of solving problems posed by others. Problem posing is not a commonly taught topic. Though some students have difficulties acquiring problem-posing skills, the positive effects are far reaching. A quasi-experimental research design was used to determine the growth in problem-posing and -solving skills in a low socio-economic status rural elementary school. Teachers conducted mathematics learning centres daily while researchers conducted research-based intervention activities for 3 months. A short quiz was administered to students in grades 2-5 (N = 45) pre and post measuring problem-solving and problem-posing changes. A statistically significant difference (p < .05) was noted in both problem solving and problem posing. Results indicate that explicitly teaching problem posing in elementary classrooms is a worthwhile endeavour.

A study on the evaluation of problem posing skills in terms of academic success

The aim of this study is to examine problem posing skills of prospective teachers in terms of their academic success. To this end, 9 prospective physics teachers, who are sophomores, from the Department of Physics Teaching were included within the study taking into consideration their GPAs. These prospective teachers were grouped under three titles, namely, low, medium and high. When the total points of these prospective teachers related to problem posing skills were examined, it was seen that those who have high GPAs have higher problem posing skills than those with medium or lower GPAs, however, no significant difference was observed between those with medium or lower GPAs in terms of their problem solving skills.

Critical Inquiry Across the Disciplines: Strategies for Student-Generated Problem Posing

Problem posing is a higher-order, active-learning task that is important for students to develop. This article describes a series of interdisciplinary learning activities designed to help students strengthen their problem-posing skills, which requires that students become more responsible for their learning and that faculty move to a facilitator role. Developing students’ problem-posing skills and allowing them to grapple with course content can lead to deeper levels of understanding and improved critical thinking. In turn, students are more likely to be able to move their newfound knowledge beyond the classroom.