Problem Posing Research Articles

Toward Inquiry and Problem Posing in Teacher Education

Toward Inquiry and Problem Posing in Teacher Education

A General Description of Mathematics Problem Posing

A General Description of Mathematics Problem Posing

Implementation of Learning with the Problem Posing Method to Increase Activeness and Learning Outcomes of Physics in the Material of Temperature and Heat

Purpose of the study: This research aims to find out how physics learning using the Problem posing Method is implemented in high school and to find out whether learning physics using the Problem posing Method can increase the activeness and learning outcomes of high school students in physics.
 Methodology: This type of research is classroom action research carried out in 2 cycles. This research was conducted in high school. The subjects of this research were 31 students of class X high school. The research data is in the form of student activity and learning outcomes. Students' learning activity is known from the results of observation sheets, while students' learning outcomes are known from the results of evaluations carried out at the end of each cycle.
 Main Findings: The results showed that the active learning of students in cycle II showed an increase when compared to cycle I. The results showed learning with the Problem Posing model was preferred by students so that it was hoped that the teacher could apply the Problem Posing model as a variation in learning Physics. The limitation of the research which only applies the Problem Posing model to the material Temperature and Heat with a relatively short research time, it is hoped that further research can be carried out on other materials.
 Novelty/Originality of this study: The novelty of this research is that classroom action research was carried out to determine students' activeness in the learning process using a problem posing model specifically for learning physics on temperature and heat.

What is the area of a pig? Problem posing and problem solving in early childhood education

Problem posing and problem solving serve as a crucial element of classroom instruction in early mathematics education, and have long been a topic of study of many practitioners and researchers. Used as a powerful tool for differentiation, they affect the ways in which the practice of mathematics is perceived by students and also help teachers gauge children’s understanding of concepts. In the student-centered approach, problem posing and problem solving can successfully engage students in creative educational situations. This research has been part of a broader design research project, the aim of which was to investigate the relationship between a classroom environment that allows for dialogue and young children’s propensity to design and solve their own tasks. Methodology included taking field notes and photographs, followed by reflection sessions. Turning young mathematicians into independent inquirers helped them gain authentic ownership of their knowledge. Additionally, it aided in the development of the young children’s competencies in effective engagement in problem posing activities. The toolbox of instructional techniques for problem posing in the classroom evolved, transforming mathematical classrooms into inquiry polygons for all learners.

Impact of prompts on students’ mathematical problem posing

This study used three pairs of problem-posing tasks to examine the impact of different prompts on students’ problem posing. Two kinds of prompts were involved. The first asked students to pose 2–3 different mathematical problems without specifying other requirements for the problems, whereas the second kind of prompt did specify additional requirements. A total of 2124 students’ responses were analyzed to examine the impact of the prompts along multiple dimensions. In response to problem-posing prompts with more specific requirements, students tended to engage in more in-depth mathematical thinking and posed much more linguistically and semantically complex problems with more relationships or steps required to solve them. The findings from this study not only contribute to our understanding of problem-posing processes but also have direct implications for teaching mathematics through problem posing.

Investigation of Mathematics Teachers’ Views on Teaching Integers and Problem Posing Skills

Investigation of Mathematics Teachers’ Views on Teaching Integers and Problem Posing Skills

A Systematic Review of Literature on Mathematical Problem Posing in Korea

In this systematic literature review, we reviewed 48 original empirical papers focusing on Korean students’ and teachers’ mathematical problem-posing (MPP) in classrooms. All the included papers were published in peer-reviewed mathematics education research journals and located through comprehensive database searches and individual journal searches involving Korean students and teachers. We categorized the papers into two main groups based on the type of participants: 34 students’ MPP papers and 14 teachers’ MPP papers. We further categorized the papers based on the characterization of MPP used: MPP as a construct, intervention, or variable. For students’ MPP papers, most were identified as intervention papers that examined the impacts of MPP interventions on students’ cognitive domains (e.g., problem posing, creativity, problem solving) or affective domains (e.g., attitude, interest). For teachers’ MPP papers, more than half of the papers were identified as documenting teachers’ various types of knowledge related to MPP. This systematic literature review will shed light on the research evidence found by these Korean researchers and how their empirical studies were conducted. It will also help disseminate research evidence regarding Korean students’ and teachers’ MPP internationally.

Ortaokul matematik öğretmen adaylarının model oluşturma etkinliği tasarlama yeterlikleri, problem çözmeye yönelik inançları, problem kurmaya yönelik öz-yeterlik inançları ve aralarındaki ilişki

This study aimed to determine the change and the relationship between elementary school mathematics teacher candidates' competence to design model-eliciting activities, their beliefs towards problem-solving, and their self-efficacy beliefs towards problem posing according to gender and overall academic grade point average (GPA). Modeling activities designed by 64 elementary school mathematics teacher candidates in Turkey were evaluated by means of a grading key created in the context of "compliance with MEA design principles". In addition, a scale consisting of 24 items was applied to determine the beliefs of the teacher candidates towards problem-solving, and a 26-imoetem scale was applied to determine their self-efficacy beliefs towards problem-posing, and the responses were analyzed by quantitative methods (one-way multiple variance analysis, correlation analysis, multiple regression test). The findings reveal that elementary school mathematics teacher candidates' proficiency in designing model-eliciting activities is generally at a high level, while their belief in problem-solving and self-efficacy beliefs in problem posing is generally at a moderate level. Based on the studies that concluded that modeling competencies develop as they work on modeling problems and that the experience of mathematical modeling affects their mathematical modeling competencies, it was concluded that modeling problems were used to solve mathematical problems and teach these solutions in the mathematical modeling course they took. It was determined that the linear combinations of teacher candidates' proficiency in designing model-eliciting activities, beliefs in problem-solving, and self-efficacy beliefs in problem-posing did not show a significant difference. The fact that pre-service teachers' beliefs about problem solving and posing are not related to their MEA design competencies is thought to be due to their previous routine mathematical problem solving experiences being more dominant. On the other hand, since the mathematical modeling process is basically considered as a problem-solving process, it was expected that these beliefs of pre-service teachers would be related to MEA design proficiency. It is important to conduct qualitative research with teacher candidates in order to examine this situation in more detail and to reveal the underlying causes.

Creative Problem Posing: Analysis of the Problems Posed Towards Different Strategies by Prospective Mathematics Teachers

The purpose of this study is to analyze problems posed by prospective elementary mathematics teachers of towards different strategies in scope of creativity. Participants of the study are 36 prospective teachers, who take the course of “Problem Solving Strategies”. In this course they study problem-solving strategies. At the end of the course, they were asked to pose three problems suitable for the strategies. Each participant posed a total of 27 problems with three problems for each 9 problem-solving strategies. Problems posed by participants were analyzed in terms of the indicators of fluency, flexibility and originality and chi-square independence test was applied so as to determine whether the creativity of problem posing depends on the strategies. It was seen that fluency had the highest average among all strategies excluding the conscious guessing and control strategy. It was seen that the drawing strategy had the highest average among the strategies in scope of flexibility and the conscious guess and control strategy had the highest average among the strategies in scope of originality. Also it as seen that participants’ creativity levels for various strategies are usually high, and in some cases in the higher echelons of the medium category. This small variation is found to be statistically significant.

Current Research On Problem Posing : A Review

Teachers and students must learn how to pose problems effectively, hence there is a need for ongoing research on this topic. In order to identify the next topic that can be explored in the field of problem posing, this study aims to capture the latest research trends regarding problem posing over the last five years, starting from 2018-2023. The method used is Systematic Literature Review (SLR). The results of this study are research on problem posing widely spread in various topics, including a) theoretical considerations of problem posing, b) the relationship between problem posing and other abilities, c) analysis of teacher problem posing abilities, d) analysis of students' problem posing abilities and e) learning design to improve problem posing skills. These findings indicate that the problem posing has been extensively researched by scholars. The development of teaching materials that involve problem posing and learning design to enhance prospective teacher problem posing skill are two potential area of future research.

Posing and Solving Modelling Problems—Extending the Modelling Process from a Problem Posing Perspective

In mathematics education, pre-formulated modelling problems are used to teach mathematical modelling. However, in out-of-school scenarios problems have to be identified and posed often first before they can be solved. Despite the ongoing emphasis on the activities involved in solving given modelling problems, little is known about the activities involved in developing and solving own modelling problems and the connection between these activities. To help fill this gap, we explored the modelling process from a problem posing perspective by asking the questions: (1) What activities are involved in developing modelling problems? and (2) What activities are involved in solving self-generated modelling problems? To answer these research questions, we conducted a qualitative study with seven pre-service teachers. The pre-service teachers were asked to pose problems that were based on given real-world situations and to solve their self-generated problems while thinking aloud. We analyzed pre-service teachers’ developing and subsequent solving phases with respect to the problem posing and modelling activities they were engaged in. Based on theories of problem posing and modelling, we developed an integrated process-model of posing and solving own modelling problems and validated it in the present study. The results indicate that posing own modelling problems might foster important modelling activities. The integrated process-model of developing and solving own modelling problems provides the basis for future research on modelling problems from a problem posing perspective.

Non-routine problem posing and prospective middle school mathematics teachers: an emotional perspective

Problem posing is an indispensable constituent of mathematical thinking, which makes it a requisite ability for students of all grades. Therefore, pre- and in-service teachers should carry out problem posing activities of high quality, and having them pose non-routine problems may be a good way to make this happen. In this context, this study intends to examine prospective middle-school math teachers’ performances and emotions in non-routine problem posing, as well as to investigate whether there is any relationship between these two variables. The study was carried out with 64 prospective teachers in the scope of an elective course about problem solving. Data sources were created problems and questionnaires collected from the participants. The former was used to evaluate success while the latter was employed for describing emotions. According to the results, the participants were moderately successful in designing non-routine problems. As for emotions, although the participants mostly acknowledged the merit of posing non-routine problems, they found it very demanding as well. Besides, the interplay between performance and emotions in non-routine problem posing was low. The results indicate that prospective teachers have the potential to generate non-routine problems, and are predominantly positive toward this skill.

Implementing a pedagogical cycle to support data modelling and statistical reasoning in years 1 and 2 through the Interdisciplinary Mathematics and Science (IMS) project

This paper illustrates how years 1 and 2 students were guided to engage in data modelling and statistical reasoning through interdisciplinary mathematics and science investigations drawn from an Australian 3-year longitudinal study: Interdisciplinary Mathematics and Science Learning (https://imslearning.org/). The project developed learning sequences for 12 inquiry-based investigations involving 35 teachers and cohorts of between 25 and 70 students across years 1 through 6. The research used a design-based methodology to develop, implement, and refine a 4-stage pedagogical cycle based on students’ problem posing, data generation, organisation, interpretation, and reasoning about data. Across the stages of the IMS cycle, students generated increasingly sophisticated representations of data and made decisions about whether these supported their explanations, claims about, and solutions to scientific problems. The teacher’s role in supporting students’ statistical reasoning was analysed across two learning sequences: Ecology in year 1 and Paper Helicopters in year 2 involving the same cohort of students. An explicit focus on data modelling and meta-representational practices enabled the year 1 students to form statistical ideas, such as distribution, sampling, and aggregation, and to construct a range of data representations. In year 2, students engaged in tasks that focused on ordering and aggregating data, measures of central tendency, inferential reasoning, and, in some cases, informal ideas of variability. The study explores how a representation-focused interdisciplinary pedagogy can support the development of data modelling and statistical thinking from an early age.

Effectiveness of problem posing and investigation in terms of problem solving abilities, motivation and achievement in mathematics

The study aims at describing the comparison between the Problem-Posing Approach and the Investigation Approach in terms of effectiveness from the perspective of Mathematical Problem-Solving Skills, mathematical motivation and Mathematical Learning Achievements. The nature of the study is a quasi-experimental research. During the conduct of the study, the overall number of populations was 206 students from Grade VII of the State 2 Junior High School Gamping. The samples within the study were selected randomly from the population namely 32 students from Grade VII A and 34 students from Grade VII B. Then, the instrument that had been administered within the conduct of the study was the Mathematical Problem-Solving Skills Test, the Mathematical Learning Achievement Test and the Mathematical Learning Motivation Questionnaire. After the data had been gathered, the overall data were analysed by using the one-sample t-test, the T2 Hotteling’s Test and the independent sample t-test. The results of the study show that the learning process by means of Investigation Approach has been more effective in comparison to Problem-Posing Approach from the perspective of Mathematical Problem-Solving Skills and Mathematical Learning Achievement but, on the other hand, the results of the study also show that the learning process by means of Problem-Posing Approach has been more effective in comparison to Investigation Approach from the perspective of Mathematical Learning Motivation for the Grade VII students of the State 2 Junior High School Gamping.

Okuma Stratejilerine Yönelik Üst Bilişsel Farkındalığın Problem Kurma Becerisini Yordama Düzeyi

The aim of the study was analyzing the predictive relations between reading strategies metacognitive awareness and problem posing skills of seventh grade students. Within the study, 373 seventh grade students participated. The data of the study was collected using “Metacognitive Awareness of Reading Strategies Inventory” and “Problem Posing Skills Test”. Through the analysis of the data, simple linear regression analysis was used. As a result of the study, it was determined that reading strategies metacognitive awareness levels of seventh grade students significantly predicted problem posing skills and explained 42% of the change in problem posing skills. In line with these results; it is recommended that teachers plan and implement interdisciplinary problem posing activities that include the use of different reading and problem posing strategies for the development of reading comprehension and cognitive awareness.

ANALOGY PROBLEM POSING FOR ELEMENTARY SCHOOL STUDENTS ON WORD PROBLEMS

This study aims to determine the analogy characteristics of elementary school students in proposing word problems. Analogical reasoning is a complex process that involves retrieving structured knowledge from long-term memory, representing and manipulating role-filling ties in working memory, identifying elements that play appropriate roles, generating new conclusions, and learning abstract schemes. The characteristics of analogy are categorized into four: (1) reformulation, rearrangement of information by changing the order of numbers but still paying attention to the order of mathematical operations. (2) reconstruction, Students rearrange information in the initial problem so that the problem appears different but is identical to the initial problem. (3) reproduction, the resulting product creates a new problem that is different by changing the structure of the initial problem. (4) imitation, changing the structure of the given problem by expanding the goal statement so that the initial problem becomes a step of the solution process of the new problem. Students' failure in making problem posing is included in non-reformulation, where students cannot make problem posing on word problems according to the problem structure

The interplay of critical language pedagogy and young Arabic EFL learners

This paper is based on the first author’s experience of experimenting with critical language pedagogy (CLP) when she was teaching in the UAE. While prior research focuses mainly on the theoretical aspects of CLP, empirical studies on the effectiveness of implementing critical approaches and developing related teaching materials in Arab EFL contexts with young learners are underrepresented. Informed by Paulo Freire’s formulation of ‘culture circles’, this case study reports on the problem-posing literacy practice in a class of Grade 4 female Arabic students in an Abu Dhabi government school—a sample unique to both CLP and case study research. Results indicate EFL learners’ increased capacity for problem posing and motivation for writing, metacognition, and application of prior knowledge during the pre-writing discussion. Findings of this study add evidence-based, practical dimensions to existing critical research, paving the way for like-minded language educators to trial CLP with young learners.

Comparison of Problem-Posing Skills of Gifted and Non-Gifted Primary School Students

The purpose of this study was to compare the problem posing skills of gifted and non-gifted primary school students. In this study, the case study method was used. The participants who were selected by convenient sampling consisted of 24 gifted and 24 non-gifted students attending from the East of Black Sea region of Turkey. The data in the study were collected with an open-ended problem posing test that was developed by the researchers. This test consists of three situations requiring free, semi-structured and structured, problem posing. The data were evaluated according to the problem posing test evaluation form that was developed by the researchers. At the end of the study, while there was no statistical significance between gifted and non-gifted primary school students in free and semi-structured problem posing, it was found that non-gifted primary school students were statistically significantly better than gifted primary school students in structured problem posing.

The Potential of the Problem Posing Method on Mathematics Learning Outcomes: A Study in Grade IX-G Students of SMPN 244 Jakarta, Indonesia

Mathematics is still one of the subjects that is less attractive to students. Students often think that mathematics is difficult or even boring. The posing method is one of the efforts that can be developed in order to be a solution in the process of teaching mathematics so that mathematics is no longer something difficult and frightening. A posing method is an approach to learning mathematics where students are not only oriented to solving a problem. However, students participate in making questions. This study aimed to determine the potential of the posing method in improving mathematics learning outcomes in grade IX-G students of SMPN 244 Jakarta, Indonesia. This study is an experimental study with a pre-post test design approach. A total of 36 research subjects participated in this study. The posing method intervention in this study consisted of 2 cycles, with 2 meetings in each cycle. Furthermore, re-intervention and evaluation of the implementation of cycle II as in cycle I. The success of the posing method is carried out by assessing student learning outcomes. Data analysis was carried out in a univariate manner by comparing the average and frequency of student learning outcomes. The results of the study showed that there was a shift in learning outcomes from those that were initially at a score of 5 and then experienced improvement after the posing method was applied to the majority of scores 8 and 9. In conclusion, the posing method has the potential to improve mathematics learning outcomes in grade IX-G students of SMPN 244 Jakarta, Indonesia.

Problem Posing: images as a trigger element of the activity

This article aims to analyze the possibilities of problem posing activities by students when images are provided as a trigger element. To do so, in the theoretical discussion related to problem posing, we present understandings assumed by us and in the literature related to the theme, and different possibilities of didactic activities, especially in association with Problem Solving. Qualitative research is portrayed, regarding Problem Posing, implemented by teachers who teach Mathematics, participants of a continuing education course, and developed with masters and doctoral students in a postgraduate course. The results indicate the potential of this type of activity for the development of creativity, mathematical learning, and also as a tool to evaluate the understanding of students, especially when associated with problem solving.