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Copyright of Gazi University Journal of Gazi Educational Faculty (GUJGEF) is the property of Gazi University Journal of Gazi Educational Faculty (GUJGEF) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Students' affective characteristics have been confirmed to shape their mathematics learning outcomes, including problem-solving performance and mathematics achievement. However, it remains unclear whether affect influences student mathematical problem posing - a process closely related to mathematical problem solving. Drawn from the expectancy-value theory (EVT), this study examined the relationship between students' affective factors (self-concept, intrinsic value, and test anxiety) and their mathematical problem posing performance (complexity, quantity, and accuracy). Structural equation models were employed to analyze the data of 302 Chinese Miao students. The results showed that self-concept had a positive association with the complexity and accuracy of the problems posed. Intrinsic value was positively related to the complexity and quantity of the problems posed. Conversely, test anxiety negatively predicted the complexity of the problems. Our findings provide quantitative evidence of the significant influence of students' affective characteristics on their problem posing performance and offer a better understanding of the problem-posing ability of Chinese minority students. Moreover, this study validates an instrument measuring student affect in mathematical problem posing based on EVT. [ABSTRACT FROM AUTHOR]

Educational literature indicates that solving open mathematical tasks (OTs) is a powerful creativity-directed activity. However, the use of these tasks with school students on an everyday basis is extremely limited. To promote implementation of OTs in middle school, we manage a large-scale R&D project, Math-Key, which makes open mathematical tasks available to teachers. Additionally, we encourage teachers to pose OTs by transforming textbook mathematical problems. In this paper, we analyze teachers' skills and affective conceptions related to posing OTs and using them in teaching. Forty-four teachers with different teaching experience (years of experience—YoE) and different levels of expertise participated in a 4-h workshop that introduced them to OTs and their categorization. They were also given a homework assignment: pose OTs and solve them to demonstrate their openness. This assignment was accompanied by a 5-point Likert scale questionnaire that examined teachers' affective conceptions about engaging and teaching with OTs. We drew distinctions between different types of OTs (TOTs) posed by the teachers and the problem posing strategies they used. We found that the types of tasks and strategies that teachers use are a function of teachers' experience in terms of both the level of mathematics taught and years of teaching. In the affective dimension, we found interesting connections between conceptions regarding the difficulty of posing OTs, conceptions regarding the suitability of OTs for teaching and learning, teachers' readiness to implement OTs in their classes, and their predictions regarding teachers' and students' problem-solving behaviors. [ABSTRACT FROM AUTHOR]

Educators in mathematics have long been concerned about students' motivation, anxiety, and other affective characteristics. Typically, research into affect focuses on one theoretical construct (e.g., emotion, motivation, beliefs, or interest). However, we introduce the term affective field to account for a person's various affective factors (emotions, attitudes, etc.) in their intraplay. In a case study, we use data from an extracurricular, inquiry-oriented collaborative problem posing and problem solving (PP&PS) program, which took place as a 1-year project with four upper secondary school students in Sweden (aged 16–18). We investigated the affective field of one student, Anna, in its social and dynamic nature. The question addressed in this context is: In what ways does an affective field of a student engaging in PP&PS evolve, and what may be explanations for this evolvement? Anna's affective field was dynamic over the course of the program. Her initial anxiety during the PP&PS program was rooted in her prior affective field about mathematics activities, but group collaboration, the feeling of safety and appreciation, together with an increased interest in within-solution PP and openness for trying new things went hand in hand with positive dynamics in her affective field. [ABSTRACT FROM AUTHOR]

The purpose of this study was to reveal both the effects of problem-posing interventions on the mathematical creative ability of students and how students' creative self-efficacy in mathematics was related to their mathematical creative ability. Elementary school students (n = 205) were randomly assigned to one of two groups: problem-posing or control. Results showed the mathematical creativity for the problem-posing group increased (p < 0.05) more than for students in the control group (d = 0.77). Results from the Confirmatory Factor Analysis showed that mathematical creativity was a higher order factor that included mathematical creative ability and mathematical creative self-efficacy as first-order factors. Among the implications for this is that integrating problem-posing activities into elementary school mathematics instruction can foster mathematical creativity. [ABSTRACT FROM AUTHOR]

This study explored 1634 Chinese eighth-grade students' domain- and task-specific self-efficacy and its relationship to their problem-posing performance. In particular, the linear regression model, generalized additive model (GAM), and piecewise regression model (PRM) were used to detail the linear and non-linear relationships between these variables. The findings indicate that most (92.5%) of the students could pose mathematical problems in all tasks, but the effect of their domain-specific self-efficacy on their problem-posing performance was lower than the effect of their task-specific self-efficacy. Students' problem-posing performance and their task-specific self-efficacy were not always matched when the requirements of the problem they posed varied in difficulty. As the level of difficulty increased, the correlation coefficient between task-specific self-efficacy and problem posing declined from 0.22 to 0.06. Furthermore, PRM confirmed that there were significant changes of the slope around the cut-point of the relationship between task-specific self-efficacy and students' problem-posing performance. Moreover, the relationship between task-specific self-efficacy and posing performance was different for easy and difficult problems, as the cut-point and slopes before and after the point varied. The findings of this study contribute both to understanding self-efficacy as well as advancing understanding about the characteristics of problem posing from a non-cognitive perspective. [ABSTRACT FROM AUTHOR]

The aim of the study was to analyze the mathematics exam anxiety and problem-posing self-efficacy of middle school students in terms of their school, gender, and grade levels, as well as the relationship among these parameters. The research was conducted with 37 fifth grade students, 53 sixth grade students, 72 seventh grade students, and 77 eight grade students; in total 239 students in two middle schools in Kayseri province, Turkey in 2019. The data collection tools comprised the "Mathematics Exam Anxiety Scale", developed by Şan (2014) and revised by Dulkadir (2017), and the "Problem Posing Self-Efficacy Scale", which was developed by Özgen (2019). For the analysis of the data the SPSS 25 package program was used. In the study, the reliability coefficient of the mathematics exam anxiety scale was found to be 0.486, and the reliability coefficient of the problem-posing self-efficacy scale was 0.942. Mathematics anxiety and problem posing self-efficacy did not differ significantly according to gender. A significant difference in mathematics exam anxiety was detected and the difference was between the fifth and seventh grades. No significant difference was found in the self-efficacy for problem posing at the grade levels. While mathematics examination anxiety showed a significant difference in terms of the schools, the self-efficacy for problem-posing did not differ significantly between schools. [ABSTRACT FROM AUTHOR]

Geometry subject that prosecute students to comprehend abstracts things is one of the causes of students' difficulties in mathematics learning. This study aims to determine the effect of Problem Posing and Problem Solving learning models with the Scientific Approach to students' adaptive reasoning on plane figure materials. It was conducted at the State Junior High School (SMPN) 4 Magetan, Indonesia. It employed quasi-experimental research methods. The populations were the seventh grade students with a total sample of 64 students who were divided into 34 students as experimental 1 class and the other as experimental 2 class. The simple random sampling method was chosen as the sampling technique. Moreover, normality test was the Lilliefors method; homogeneity was the Bartlett test; and t-test for research results analysis. The results revealed that the Problem Posing learning model with the Scientific Approach was better than Problem Solving with the Scientific Approach. It significantly enhanced students' adaptive reasoning on plane figure materials. The Problem Posing learning model with the Scientific Approach provided the needed skills to build knowledge, where students performed the process of observation, clarification, measurement, prediction, and hypotheses. Therefore, the model was appropriate for mathematics learning, especially on plane figure materials to increase students' adaptive reasoning and achievement. [ABSTRACT FROM AUTHOR]

In this study, we propose the notion of a socio-mathematical norm to explore the affective aspects of a classroom in the context of problem posing. Our case is a gifted and talented mathematics classroom with twelve students. The primary source of data consists of forty-three mathematics lessons. Our theoretical stance defines two dimensions of a socio-mathematical norm: student and teacher. The findings revealed three socio-mathematical norms (reformulations of problems, generating new problems, evaluation and correction based on the sufficiency of the information) that reflect the classroom's micro-culture, which involves problem posing. In addition to these basic norms, normative understanding related to "posing more challenging problems" allowed for challenging mathematical situations in the classroom, which is of particular importance for gifted and talented students. We discuss the teacher's and students' roles in problem posing activities. We also explore possible reasons for not observing socio-mathematical norms regarding the assessment of posed problems on a criterion that could support students for posing more original, more complex, and more realistic problems. The study suggests practical implications for the dynamics of a classroom where students engage in problem posing activities and theoretical implications regarding the two dimensions of a norm. [ABSTRACT FROM AUTHOR]

This is a review of experimental research in which students have been taught to pose mathematical problems as a means of developing their learning. Hence, the aim of the research is to combine the empirical evidence regarding the functionality of problem posing strategies and to explore the aspects which could influence the integration of problem posing in mathematical education. In this direction, a metaanalysis approach was utilized in this study. 20 experimental research published between years of 2000 and 2020 are contained in this research and 31 effect sizes were computed. According to random effects model, it was found that problem posing strategy has significant impact on learners’ problem-solving skills, mathematics achievement, level of problems posed, and attitudes towards mathematics (ES = 1.328; 1.142; 1.152; 0.643; p=0.05). These effects also were analyzed according to methodological and instructional variables. The findings obtained in the research was discussed in the light of the literature and suggestions were made for the future studies. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Kirsehir Education Faculty is the property of Journal of Kirsehir Education Faculty and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study aimed to expose pre-service elementary school teachers' awareness of selecting and using real-life context in the problems they posed. The participants of this study were asked to create mathematical problems. The findings showed that some of the participants were more focused on the mathematical concepts and procedures, but tended to ignore the contexts of the problems proposed. As a result, they created problems using numbers and stories that are not relevant to everyday life or are termed pseudo-problems. Some of the real-problems submitted by the participants were not based on an awareness of problem-context relevance. [ABSTRACT FROM AUTHOR]

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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. [ABSTRACT FROM AUTHOR]

Copyright of Erzincan University Journal of Education Faculty / Erzincan Üniversitesi Egitim Fakültesi Dergisi is the property of Erzincan University Faculty of Education Journal and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper focuses on problem solving and problem posing in mathematics education with 6-year-olds. After working on a problem-solving activity, the young students were asked to pose a similar task to a friend. This article explores how the students interpret the notion of similar. To be able to pose a problem-solving task themselves the students had to change perspective, from searching for information to providing information, and from searching for a solution to searching for a question. Also, to create a similar task the students had to reflect on the original problem-solving task. Thus, their posed tasks shed light on their interpretation of what the original problem-solving task was really about. The results show that the large majority of the students included some three-dimensional aspects from the original problem-solving task in their posed tasks. However, the questions they posed varied in terms of whether or not they included mathematical elements. [ABSTRACT FROM AUTHOR]

Teaching to develop creativity often requires a shift in instructional tasks. In this paper, we first summarize the body of research related to instructors facilitat- ing and recognizing mathematical creativity. We then provide details as to how one graduate course, designed to help mathematics educators develop a sense of school mathematics from an advanced standpoint, provided opportunities for students to: recognize the difference between problems and exercises, pose prob- lems, reect on the quality of the tasks they created and review tasks created by others. This series of activities were designed to help the graduate students rec- ognize and appreciate mathematical creativity. We then review the instructional activities in light of the five overarching principles to maximize creativity in K-12 mathematics classrooms suggested by Sriraman [36] and discuss how these might relate to the post-secondary and graduate education of mathematics educators. [ABSTRACT FROM AUTHOR]

The aim of this study was to examine the 5th grade students' problem-posing skills appropriate to the problem situations (unstructured, semi-structured and structured) about tables and graphs. The method of the present study was qualitative research method, because it enables to examine the problem-posing skills of the students in detail. In a public school, a total of 15 students, 5 of whom participated pilot study, were included to this study. In order to achieve the aim of the study, the students were given a scale of 9 problems, which was prepared in line with the pilot study and expert opinions. The students were asked to pose as much as problems related to scoreboard, frequency table and column graph. After the problems were posed, semi-structured interview form was applied to the students. Content analysis method was used for data analysis. When the findings gathered from the data collection tool were examined, it was seen that the students had difficulty in posing a problem sentence and a large part of the question sentences generated were related to the exercise category. With respect to data gathered, problem posing scale could be used in further studies that would study problem posing. Besides, instructional processes and including this topic in textbooks would be the suggestions of this study. [ABSTRACT FROM AUTHOR]

Textbooks are important for mathematics as they are for other courses. Problem posing is one of the important activities in mathematics education. In this manner, the goal of this study is to analyse the problem-posing activities in primary school mathematics textbooks offered by Ministry of National Education and used in 2017-2018 and 2018-2019 school years. For this purpose, 10 primary school mathematics textbooks were analysed with document analysis method according to their years, grade levels, learning domains, sub-learning domains and types of problem posing. We analyzed the number of problems posed, learning domains that it includes, the number of sub-learning, and problem types. Results showed that there are more activities in the textbooks in the school year of 2017-2018 than in the textbooks used in the school year of 2018-2019 in all grade levels except second grade level. In addition, no problem posing activity was found in any of the first-grade books. It is considered that increasing the number of problem-posing activities in the textbooks and diversifying the problem-posing type are necessary. [ABSTRACT FROM AUTHOR]

Writing and evaluating contextual problems is an important task in the work of teaching, and thus is part of the knowledge that prospective teachers must develop. In dealing with word problems posed both by children and themselves, prospective teachers will need to attend to the realism of the context and the consistency between the operation and context with integer operations. This study describes an examination of the ways in which 100 prospective teachers responded to a child's temperature story for an integer addition number sentence (i.e., − 9 + − 6 = ☐). The child's story, which was an actual story posed by a Grade 5 student, did not use temperature realistically (realism), nor was it consistent with the given number sentence (consistency). The results indicated that when prospective teachers evaluated the child's story, they tended to either focus on realism or consistency, but not both. If prospective teachers did not focus their response on realism or consistency, the response was much more likely to be unrealistic or inconsistent itself. Implications point to the importance of addressing both realism and consistency issues when examining integer word problems with prospective teachers. [ABSTRACT FROM AUTHOR]

In this article we present the conclusions drawn from our research on the subject of problem posing for mathematics competitions. We present the case study of a student who is familiar with problem solving, has understood what problem posing means and what is a mathematical problematic situation, has proven his mathematical skills, and is asked to create his own mathematical problem. The conclusions drawn from this research are, firstly, on the relation of mathematical creativity and mathematical problem posing, secondly, on the relation of mathematical education and self-education, and thirdly on the relationship between the creator of a problem and the potential solver of the problem. [ABSTRACT FROM AUTHOR]

The interrelationship between mathematics and science education has frequently been emphasized, and common goals and approaches have often been adopted between disciplines. Improving students' problem-solving skills in mathematics and science education has always been given special attention; however, the problem-posing approach which plays a key role in mathematics education has not been commonly utilized in science education. As a result, the purpose of this study was to better determine the effects of the problem-posing approach on students' problem-solving skills and metacognitive awareness in science education. This was a quasi-experimental based study conducted with 61 chemistry and 40 physics students; a problem-solving inventory and a metacognitive awareness inventory were administered to participants both as a pre-test and a post-test. During the 2017–2018 academic year, problem-solving activities based on the problem-posing approach were performed with the participating students during their senior year in various university chemistry and physics departments throughout the Republic of Turkey. The study results suggested that structured, semi-structured, and free problem-posing activities improve students' problem-solving skills and metacognitive awareness. These findings indicated not only the usefulness of integrating problem-posing activities into science education programs but also the need for further research into this question. [ABSTRACT FROM AUTHOR]

The purpose of the current study is to make inferences about pre-service teachers' levels of content and curriculum knowledge related to the concept of fraction through problem posing and problem solving processes. The study designed according to the case study design was conducted on senior pre-service classroom teachers attending a state university in Turkey. The data of the current study were collected through the problems posed and then solved by the pre-service teachers in the semistructured style on the basis of a visual presented to them. According to the findings obtained, it was seen that the content knowledge level of the pre-service classroom teachers about the concept of fraction; especially about the improper fraction, is not at the desired level. In addition, it was found that the pre-service teachers had problems in specifying for which grade level they posed and solved the fraction problems within the context of curriculum knowledge. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate the problem posing skills of prospective middle school mathematics teachers in the context of van Hiele levels of geometric thinking. Case study was used in this study. Participants were 65 third-year prospective middle school mathematics teachers. The data obtained from the prospective teachers' (PTs) written documents about the situation of a free problem posing. PTs were asked to pose problems in accordance with the first three van Hiele levels. At the same time, PTs were asked to explain the characteristics of the van Hiele level. Descriptive analysis was preferred in the study. The findings indicated that the problem posing rate of the PTs was low in the category "mathematical-appropriate for the level". It was found that more than half of the PTs' responses were not mathematical problems. The PTs posed mathematical problems in the category "appropriate for the level" mostly related to level 2. The number of PTs who correctly explained the characteristics of the level 3 is lower than the first two levels. According to findings, it can be said that PTs cannot transfer their knowledge about geometric thinking levels to problem posing. It is suggested that PTs' mathematics education courses should include problem posing experiences. The course contents to be designed for practice are thought to improve both the problem posing skills and the subject matter knowledge related to geometry. Future research should focus on multiple case studies integrating free, semi-structured, and structured problem posing situations. [ABSTRACT FROM AUTHOR]

We present in this paper a pair of approaches to support mathematics educators and learners in formulating original tasks. In particular, we facilitate the posing of rich mathematical problems by using two novel methods that were created by a mathematics department at a K-12 school in the United States, and further developed alongside our students as well as a wider professional learning team of master teachers. We situate our work within the broader literature on mathematical problem posing and describe our strategies by including examples of their use in generating problems and by providing examples of authentic student-assigned tasks that were created with our approaches. [ABSTRACT FROM AUTHOR]

Despite its almost four-decade history, research remains in the early stages of understanding the phenomenon of mathematical problem posing. In particular, the quality of problems created by beginning posers has been recognized as a persistent challenge. In this conceptual paper, I endorse an approach that identifies posing and solving as co-emergent components of steps learners take in a mathematically problematic situation. I further argue that some of the initial responses to the situation may constitute productive ingredients for creating problems that are personally meaningful and interesting to the learners. Drawing on the literature, I offer two principles through which the process of transitioning from initial responses to fully-fledged problems can be supported: making the didactical contract of the problem-posing activity transparent and immersing learners in socio-mathematical settings that are conducive to "good" problems. The approach is illustrated with fragments from a workshop for in-service teachers. The concluding discussion focuses on how the presented approach addresses some common issues in problem posing research. • Problem posing studies are subject to particular conventions. • Implicit problem posing is embedded in learners' mathematical activity. • Initial responses to a problematic situation can be useful to pose problems. • A problematic situation and a socio-mathematical setting are important. [ABSTRACT FROM AUTHOR]

This study contributes to understanding the influence of different problem posing tasks on the performance of in-service teachers in posing important and worthwhile mathematical problems. The problem posing tasks pertain to the part-whole concept of fraction which presents ongoing challenges for teachers and students. The study sample was comprised of 40 in-service primary school teachers who completed an electronic problem posing test. The problem posing tasks included different problem situations and prompts that addressed: (a) four types of problem posing processes (editing, selecting, comprehending, and translating), and (b) four levels of complexity (uni-structural, multi-structural, relational, extended abstract). The results suggested that in-service teachers' performance is mainly influenced by the process involved in a problem posing task, being higher in problem situations that are more closed structured compared to more open structured. The level of complexity was not found to influence in-service teachers' performance. • Different types of problem posing tasks were designed about the fraction part-whole concept. • Each problem posing task involved a different process of problem posing and a different complexity level. • The type of the problem posing task influences in-service teachers' performance. • Structured problem situations are associated with higher performance compared to open problem situations. • The level of complexity of the problem posing task does not influence in-service teachers' performance. [ABSTRACT FROM AUTHOR]

Current research and curriculum documents from several countries have highlighted the importance of problem posing. However, some elements of this activity in mathematics classes still need to be further explored and understood. The objective of this article is to investigate how situations and problem-posing prompts affect teaching through problem posing. Three teaching cases are presented and analyzed, including instructional techniques guiding teaching through problem posing. The results indicate that teachers must align the problem-posing task with the intended goals for the lesson, analyzing how the prompt can enhance or limit particular aspects of the problems posed by the students. • The role of the situations and prompt in problem posing. • The instructional goals of problem posing activities. • The relationship between problem posing and problem solving. • Instructional subsidies guiding teaching through problem posing. [ABSTRACT FROM AUTHOR]

In this study we address two issues related to problem-posing tasks in teacher education: (i) the characterization of the specialized knowledge mobilized by prospective teachers when carrying out these tasks and (ii) the identification of the prospective teachers' pedagogical intentions in making adaptations to textbook problems. We asked prospective teachers to outline their suggestions for transforming a multiplicative problem so as to "promote the understanding" of their potential pupils. We then carried out a content analysis of their responses using the Mathematics Teachers' Specialized Knowledge model of teachers' specialized knowledge and identified their pedagogical intentions by means of the constant comparison method. The results show that prospective primary teachers mobilized both mathematical and pedagogical content knowledge in their responses to the problem reformulation task. Further, four distinct pedagogical intentions emerged that drew on different interpretations of the task prompt, and this influenced the type of transformation the prospective primary teachers suggested and the knowledge they mobilized in their answers. • Problem posing can be studied from the perspective of teachers' professional activity. • Prospective teachers can be taught through and for problem posing. • Problem posing tasks can be studied in teacher education. • Teachers require professional knowledge to pose problem to their students. • Prospective teachers use both mathematical and pedagogical knowledge to pose problems. [ABSTRACT FROM AUTHOR]

This research focused on understanding the variables inherent in the design and implementation of a mathematical problem-posing task. We developed a single case study of a problem-posing lesson by an Early Childhood Education teacher in a classroom with 4- to 5-year-old children who were unfamiliar with such activities. The results of this study show the potential of considering five variables serving as critical points that pose dilemmas linked to the design and implementation of problem-posing tasks. We found that the task changed from its original design during implementation, implying that the choices the teacher made about the variables were not static and were strongly linked to the purpose of the problem-posing task as well as to the contextual characteristics of the early childhood classroom. This study provides a potentially useful framework for analyzing the design and implementation of problem-posing tasks as a dynamic process. • Theoretical framework for analysing the teaching of problem-posing. • A dynamic vision of problem posing tasks. • Teacher's dilemmas associated to design and implementation of problem posing task. • Example of teaching through problem-posing in early years education. [ABSTRACT FROM AUTHOR]

In problem-posing research, the influence of task variables on problem-posing outcomes is a relatively new endeavor. To systematically vary task variables, we designed eight problem-posing tasks by crossing two problem-posing situations (unstructured vs. structured) with two problem-posing prompts (open vs. closed) and two mathematical contexts (patterns vs. geometry). Using this design, we investigated the influence of these task variables on (1) creative problem-posing performance, (2) problem-posing self-efficacy, and (3) the relationship between self-efficacy and creative problem-posing performance in 187 pre-service teachers. The analyses show that (1) the influence of the situation and prompt is small and topic-specific, (2) that self-efficacy is significantly lower in unstructured situations with an open prompt than in the other tasks, and (3) that creative problem-posing performance and self-efficacy are correlated negatively. The findings imply a need for more detailed investigations regarding the influence on creative problem-posing performance and for which subjects it is relevant. [ABSTRACT FROM AUTHOR]

Problem posing—generating one's own problems—is considered a powerful teaching approach for fostering students' motivation such as their interest. However, research investigating the effects of task variables of self-generated problems on students' interest is largely missing. In this contribution, we present a study with 105 ninth- and tenth-graders to address the question of whether the task variables modelling potential, assessed by openness and authenticity, or complexity of self-generated problems have an impact on students' interest in solving them. Further, we investigated whether the effect of task variables of self-generated problems on students' interest differed among students with different levels of mathematical competence. High modelling potential had a positive effect on interest in solving the problem for students with low mathematical competence, whereas it had a negative effect for those with high mathematical competence. However, complexity of self-generated problems did not affect students' interest in solving problems. • Modelling potential and complexity of self-posed problems did not affect interest • Mathematical competence served as a moderator • High modelling potential had a positive effect for students with low competence • High modelling potential had a negative effect for students with high competence • Problem-posing experience promoted posing problems with high modelling potential [ABSTRACT FROM AUTHOR]

This study presents a specific case of how a teacher in China learned to teach with problem posing through a collaborative, iterative design process with a researcher. Supported by a networked improvement community, at every step of the journey that they undertook, they partnered to design, deliver, and revise a mathematics lesson that fostered students' learning through problem posing. A detailed travelogue of their journey serves to document what research on teaching through mathematical problem posing can look like and how the teacher learned to teach using this novel approach. We explore the utility of the 3H (head, heart, and hands) model as a powerful way to think about holistic, transformative teacher learning. In addition, we consider aspects of the networked improvement community in which the teacher–researcher partnership operated that enabled capacity for sustaining this kind of effort to change practice. • This study follows a journey of a teacher and a researcher designing, delivering, and revising a problem-posing-based lesson. • Shows how research on teaching through mathematical problem posing can look when conducted by a teacher–researcher partnership in an NIC. • Discusses utility of the 3H (head, heart, and hands) model as a holistic tool to describe teachers' transformative learning. [ABSTRACT FROM AUTHOR]

Problem posing (PP) has been found to contribute to teachers' mathematical pedagogical knowledge. However, little is known about what and how teachers learn when engaged in continuous iterative PP. We use the variation theory of learning to conceptualize what and how teachers learn during iterative PP, illustrating these processes via a case study. The main argument is that what teachers learn from engaging in iterative PP are different task variables we refer to as "dimensions of possible variation." Awareness of these dimensions allows teachers to skillfully generate new problems or re-formulate previously posed ones to achieve desired pedagogical goals. We show how, during a collaborative design process with the PD coordinator, a teacher-designer became aware of some new-to-her dimensions and developed corresponding techniques for diversifying tasks. These awarenesses were still evident in an interview six months after the end of the PD. Recommendations for teacher educators are suggested. • What teachers learn from engaging in iterative PP are different task variables we refer to as "dimensions of possible variation." • Awareness of these dimensions allows teachers to skillfully generate new problems or re-formulate previously posed ones to achieve desired pedagogical goals. • By suggesting specific task modifications, a tutor can boost teacher learning in iterative PP process. [ABSTRACT FROM AUTHOR]

This study aims to examine the improvement of students’ mathematical problem posing ability and mathematical disposition through the strategy of Formulate-Share-Listen-Create (FSLC) on probability concept. The method used in this research is the experimental method, with the design of pretest-posttest control group. The population is all students of the vocational high school in Cimahi, while the sample was selected two classes from one of the vocational high school selected at random. The instrument of a test in the form of description is used to measure students’ mathematical problem posing ability, while the non-test instrument is questionnaire of mathematical disposition scale. The results showed (1) The mathematical problems posing of the students who obtained FSLC learning strategy is better than that of those who obtained conventional one; (2) The improvement of mathematical problems posing of the students who obtained FSLC learning strategy is better than that of those who obtained conventional one; (3) The mathematical disposition of students who obtained FSLC learning strategy is better than that of those who obtained conventional learning.

In our contribution we focus on the possibility to use an educational tool called Concept Cartoons in future primary school teachers’ education, as an instrument for observing how future primary school teachers reason about fractions. In the introduction section we present Concept Cartoons, and also the primary school level of the fractions topic. In the first part of the research we analyse data obtained when future primary school teachers were solving a problem in the Concept Cartoon form. The task which we adapted to this form belongs to primary school mathematics, it focuses on the concept of a fraction per se (on the parts-and-whole decision and on comparison of two pre-partitioned models with diverse wholes). Using Concept Cartoons, we can observe which statements about the issue our respondents consider as correct, and which kinds of reasoning they use in their justifications. In the second part of the research we analyse problems that the respondents themselves posed in the Concept Cartoon form, with particular focus on tasks devoted to fractions.

The learning process is a process that contains reciprocal relationships between teachers and students, which takes place in an educational situation to achieve a particular goal. This interaction or mutual relationship between teachers and students is a key requirement for the process. What we are seeing in schools, teachers are too active in the learning process, while students are made passive, so the interaction between teachers and students in the learning process is not effective. To create effective mathematics learning requires appropriate learning models to solve and solve problems related to mathematics learning. Problem solving is one of the goals of learning mathematics. Learning math so that it can stimulate the development of ability. One strategy that can be used to create effective learning and. Problem posing decline on problem-making by students based on certain criteria, namely the solution of pre-suggestion (for question), in the solution pose (break the question), post a solution pose (similar problems)

This study aimed to describe about metacognitive process of student in geometry problem posing based cognitive style Field Dependent (FD) and Field Independent (FI). The subjects were four students of grade X. The result showed that metacognitive process of subjects FD and FI first category in posing geometry problem, doing activity of planning, monitoring and evaluating process and the result thinking about every step of problem posing. Metacognitive process of subject FD of second category in posing geometry problem, doing activity of planning, monitoring, and evaluating process and the result thinking about step understanding information, arranging the planning of problem posing and formulating problem. Furthermore, metacognitive process of subject FI second category in posing geometry problem, doing of planning activity, monitoring and evaluating process and the result thinking about step understanding information, arranging the planning of problem posing and controlling back of suitability problem made with first information

Meeting the needs of mathematically gifted and talented students is a challenge for educators. To support teachers of mathematically gifted and talented students to find appropriate solutions, several innovative projects were conducted in schools using funds provided by the New Brunswick, Canada, Department of Education. This article presents one such initiative: a collaborative project we developed with two middle school teachers to enrich the mathematical experience of their most advanced students. We worked with 40 students from both schools, involving them in creating mathematics problems using multimedia tools for the CAMI (Communauté d’apprentissages multidisciplinaires interactifs)1 website. We analyzed the richness of the problems created by the participants (Manuel, 2010), as well as students’ perceptions of their experiences, collected through semi-structured interviews. Students appreciated the experience, and recommended that the project be continued in following years. Most of the problems created by students were moderately rich, and included multiple steps, but were similar to those used in classrooms. Some students stated that they were more comfortable solving problems than creating new ones, which suggested that they found the task challenging. Our results showed that specific programs for students interested in mathematics could provide positive experiences and challenges. Our research also suggested that problem posing in mathematics classrooms needs to be investigated in more depth.

Problem Posing approach is necessary for teacher training students. Problem Posing can train students to create questions/problems and their solutions. Make problem then solve it is part of student’s creative thinking ability. Differential equations problem is one of the materials that learned in mathematics education courses. Every teacher training student of mathematics has diverse skills. This diversity certainly brings various creative thinking skills as well. The purpose of this study is to determine the ability of student’s creative thinking in mathematical education courses, differential equation problem posing. This study uses a qualitative approach with descriptive methods. Sources of data in this study are the students of mathematics education consist of one student of each with high, medium, and low begining math ability. The data collection was conducted by using observation, testing, and interviews. Technique authenticity of data using a triangulation method. Data analysis technique done in stages, data reduction, data presentation, drawing conclusions, and verification. The result of this study were (1) Students with high initial capability not have fluency and flexibility of thought, but it shows the novelty think that qualifies as a Creative Thinking Ability Level (CTAL) 2 is creative enough, (2) Students with prior knowledge currently have the fluency of thought, but do not have the flexibility and novelty think that qualifies as a Level capabilities creative thinking (CTAL) 1 is less creative, (3) Students with prior knowledge low yet has grace, eloquence, and the novelty of thought that goes into the criteria of creative thinking ability Level (CTAL) 0 is not creative.

Mathematical problem posing plays an important role in mathematics curriculum, since it encompasses the core of mathematics activities, among other things, with students’ activities to construct their own problems as the preliminary step to actual problem solving steps. This study aims at revealing the profile of students’ mathematical problem posing based on their cognitive styles in order to know and understand the learning of mathematics students. As a result of this study, students who have the cognitive style ‘field independent’ (FI) are able to propose a solvable mathematical problem and load new data, and also pose problems categorized as high-quality mathematical problems. Students who have the cognitive style of ‘field dependent’ (FD) are generally limited to solvable mathematical problems that do not contain new data, and mathematical problems of a moderate level. In this study, it is seen how student’s work mathematical problem posing using their cognitive style, resulting in a breakthrough in the process of learning to use students’ cognitive styles so as to increase the quality of learning outcomes.

Penelitian ini bertujuan untuk mengetahui pengaruh dan interaksi antara pembelajaran IPA menggunakan model Problem Solving dan Problem Posing dengan kreativitas verbal siswa terhadap kemampuan penyelesaian masalah IPA kelas VIII SMP Negeri 1 Pamekasan tahun ajaran 2017/2018. Penelitian ini merupakan penelitian eksperimen dengan menggunakan desain penelitian Factorial Experimental. Populasi pada penelitian ini adalah seluruh siswa kelas VIII SMP Negeri 1 Pamekasan. Sampel yang digunakan adalah kelas VIII I sebanyak 29 siswa sebagai kelas eksperimen 1 dan kelas VII J sebanyak 30 siswa sebagai kelas eksperimen 2. Teknik analisis data pengujian hipotesis kemampuan penyelesaian masalah IPA siswa menggunakan Uji anava dua jalan dengan desain 2×3 faktorial dilanjutkan dengan uji lanjut Scheffe dengan program SPSS versi 18.00. Berdasarkan hasil penelitian disimpulkan bahwa: (1) ada perbedaan pengaruh penggunaan model Problem Solving dan Problem Posing terhadap kemampuan penyelesaian masalah IPA siswa; (2) ada perbedaan pengaruh kreativitas verbal terhadap kemampuan penyelesaian masalah IPA siswa; (3) ada interaksi antara pembelajaran IPA menggunakan model Problem Solving dan Problem Posingdengan kreativitas verbal terhadap kemampuan penyelesaian masalah IPA siswa.

Abstract: This clasMeningkatkan Penalaran Matematis Siswa pada Materi Ukuran Pemussroom action research aims to describe learning by using the problem posing approach that can improve students’ mathemathical reasoning in central tendency material. There are 32 subjects from 12th accounting grade students of SMK Wiyata Mandala Kepung. Problem posing learning that can improve mathematical reasoning in this study is learning with the following stages: observing problem, arranging questions and solving them, and present it. The results showed that 81,25% of students have minimum reasoning qualifications “Good”. Abstrak: Penelitian tindakan kelas ini bertujuan untuk mendeskripsikan pembelajaran dengan menggunakan pendekatan problem posing yang dapat meningkatkan penalaran matematis siswa pada materi ukuran pemusatan data. Subjek penelitian terdiri dari 32 siswa kelas 12 Akuntansi SMK Wiyata Mandala Kepung. Pembelajaran problem posing yang dapat meningkatkan penalaran matematis siswa pada penelitian ini memiliki tahapan mengamati permasalahan, menyusun pertanyaan dan menyelesaikannya, serta mempresentasikannya. Hasil penelitian menunjukkan bahwa 81,25% siswa memiliki kualifikasi penalaran minimal “Baik”.