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This study targeted various aptness considerations guiding preservice mathematics teachers' problem-posing in combinatorics, aiming at examining motivational and affective aspects in deciding the appropriateness of problems. To conduct this analysis, we established a theoretical framework that combines teacher-centred and student-centred considerations of aptness. Using mixed research methods, we explored the relationships between preservice mathematics teachers' performance in combinatorics and their considerations when suggesting problems. Forty-four preservice mathematics teachers were asked to (1) disclose considerations when proposing combinatorics problems and (2) participate in complimentary interviews. These findings suggest that preservice mathematics teachers' combinatorics achievements, ability to construct combinatorics problems, and tendency to take their peers' needs into account when considering aptness are related. However, most preservice mathematics teachers were concerned with teacher-centred considerations of aptness, focusing on their necessities. The connections between the various considerations of aptness delineate a theoretical model that may have implications for further research and teacher-training programmes. [ABSTRACT FROM AUTHOR]

The purpose of this study is to assess the fraction addition problems posed by pre-service teachers using digital storytelling and to identify their perspectives on this activity. 69 mathematics teacher candidates participated in the study. The research comprises two sections. Participants were expected to pose a problem via digital storytelling in the first round. After creating digital stories, participants were required to fill out an opinion survey. According to the study's findings, more than half of the participants correctly completed the problem-posing exercise. Additionally, pre-service teachers reported experiencing some difficulties when generating problems, despite their favorable opinions toward the use of digital storytelling to pose problems. Participants could pose problems involving the addition of two or three fractions. Participants encountered issues such as not being a problem or utilizing distinct operations. According to the participants' opinions, some of their skills had improved and they enjoyed the experience. [ABSTRACT FROM AUTHOR]

In the contemporary society, it is important to cultivate students' visual literacy. However, there has been a lack of sufficient training for students to improve their visual literacy in the classroom. A problem-posing approach (Visual Thinking Strategy, VTS, a learning strategy with question sequences to facilitate critical inquiry) has been proposed to achieve this objective. However, problem-posing should be supported with scaffolds to help learning deeply. And concept mapping is such a scaffold to aid problem-posing in visual literacy cultivation. In this study, a quasi-experiment was conducted on two classes of undergraduate students in Shanghai to evaluate the effects of the proposed approach. An online learning system was developed based on the proposed approach; moreover, a quasi-experiment was conducted on two classes of undergraduate students to evaluate the effects of the proposed approach. The experimental results show that the concept mapping-based online problem-posing approach improved the depth of students' visual analysis, which indicates sharpening of students' visual literacy and their critical thinking tendency. The interview results further showed that the students perceived the approach as being effective from the perspectives of "increasing visual analysis capability," "developing thinking capability," and "improving self-reflection in learning." [ABSTRACT FROM AUTHOR]

This research focused on the classroom management that a teacher performs during a problem formulation task with students in Early Childhood Education (4-5 years old). By means of a single case study, we focused on identifying the mathematical demands that the teacher establishes to favor progress in the formulation of a problem, the students' activity that triggers them and the relationships between both. The results indicate that most of the mathematical demands are oriented to favor the development of the context of the problem and reveal that the difficulties that trigger them are linked to the non-mathematical meaning of problem that prevails in the students. [ABSTRACT FROM AUTHOR]

AbstractIn this paper the potentiality of meaning generation in a constructionist environment through an interplay between problem solving and problem posing is examined. The meaning-making process is examined by following how a Grade-10 student is engaged in an iterative cycle of reformulating and solving the initial problem within a Logo-based microworld. The findings show that the contribution of this iterative cycle is in favor of the generation of mathematical meaning. The shift from reformulating to solving and vice versa supported the student to initially use his mathematical knowledge for achieving certain goals, then to discriminate and use parts of his Logo program through generalizing and debugging efforts to achieve new purposes. [ABSTRACT FROM AUTHOR]

Despite the increasing amount of research into mathematical problem posing, research shows that much is still unknown about students' cognitive processes when engaged in problem posing. In this study, 16 undergraduate students' problem-posing products and processes are examined in order to shed light on the forms of mathematical reasoning that the students engage in while posing their own problems. To better understand these products and processes, we compare them with the previously encountered problems during class (class problems). Using Lithner's framework (2008) alongside these comparisons, we were able to characterize the forms of reasoning that the students engaged in while posing their problems. Findings of the study indicate that while posing their own problems, most students relied on class problems and only made minor changes to these problems. As expected, their solutions to these problems were mostly similar to the class problem solutions. However, there were a few problems (28%), that were structurally different from class problems and whose solutions showed creative ways of thinking. The findings of this study provide useful insights into the cognitive processes that students engage in while posing problems. The insights can be used to better support students in posing better problems. [ABSTRACT FROM AUTHOR]

This article reports on a qualitative investigation into students' thinking about a differential equations problem posing task; i.e. an initial value problem. Analysis of written and verbal responses to the task indicate that only four of the 34 students who participated in the study were successful in posing problems. Furthermore, only one of the problems they posed is solvable. In general, findings of this study indicate that posing problems involving initial value problems is particularly challenging for students. In light of the multitude of benefits of problem posing in mathematics education, I recommend the inclusion of problem posing tasks in the teaching and learning of undergraduate mathematics courses, including ordinary differential equations. [ABSTRACT FROM AUTHOR]

The goal of this article is to examine and develop problem-posing case study teaching methods to promote business students' reflections on their premises around sustainability practices. Literature on transformative learning in sustainability informed our hypothesis that problem-posing instead of problem-solving case study teaching would yield greater incidences of students' premise reflections at the deepest level. For our quasi-experimental design, undergraduate students at a business school were presented with a teaching case of corporate sustainability then half were given problem-solving prompts for critical reflection while the other half were given problem-posing prompts. Resultant responses were classified to expose differences in the nature and levels of reflection between these two groups. This pedagogical research indicated that the problem-posing group reached deeper levels of reflections, though further research is needed to better understand this phenomenon. We advocate for the utility of a problem-posing approach in sustainability education. This study contributes a problem-posing protocol for business schools, curricula, and professors, as well as suggestions for further research for theoretical understanding of problem posing for transformative learning in sustainability. [ABSTRACT FROM AUTHOR]

The study investigates the integration of problem-posing techniques within mathematics pedagogy. The aim is to examine the competencies in posing problems by prospective fourth-grade classroom teachers during lesson preparation and figure out what changes need to be made. We designed this research as a quasi-experimental design involving 50 teacher candidates enrolled at a public university during the academic year of 2021-2022 in Turkey. We delved into the effects of problem-posing instruction by giving it to 25 prospective teachers who volunteered to be in the experimental group. We used the Problem-Posing Test as the data collection tool. The Problem-Posing Test consists of 12 distinct scenarios for posing problems, ranging from highly structured to semi-structures, and extending to open-ended problem posing situations. We collected the quantitative data using a rubric developed to evaluate the Problem Posing-Test. We employed the T-test and the Mann-Whitney U test for the analysis of quantitative data. Based on the pre-test results of problem posing, the prospective teachers’ problem-posing skills in the measurement and learning areas were insufficient. However, both groups were able to use the daily life contexts to address the problems they posed. The experimental group demonstrated a notable advantage in problem-posing skills on the post-test administered after receiving problem-posing instruction. We also concluded that problem-posing instruction positively affected the problems posed by prospective classroom teachers in the measurement and learning area. In this regard, offering an elective course on problem posing for the classroom teacher training program in education faculties would be beneficial. [ABSTRACT FROM AUTHOR]

Bu çalışmanın amacı, fen lisesi öğrencilerinin farklı tür problem kurma görevlerindeki başarı düzeylerinin ve görüşlerinin incelenmesidir. Çalışma grubunu bir fen lisesindeki 10.sınıf öğrencisi dokuz öğrenci oluşturmaktadır. Çalışmada nitel araştırma yöntemlerinden biri olan ‘durum çalışması’ deseni kullanılmıştır. Veri toplama aracı olarak öğrencilerin problem kurma etkinliklerindeki çalışmaları kullanılmıştır. Ayrıca çalışmanın sonunda yarı yapılandırılmış görüşme gerçekleştirilmiştir. Problem kurma etkinliklerinin tasarımında kavrama, aktarma, düzenleme ve seçme kategorilerinin yer aldığı Christou ve arkadaşlarına (2005) ait kuramsal çerçeveden yararlanılmıştır. Katılımcıların çalışmaları “Problem Kurma Beceri Testi Puanlama Cetveli” ile analiz edilmiştir. Çalışmadan elde edilen bulgulara göre öğrencilerin, problem kurarken başarılı olduğu ancak dil bilgisi ve ifade açısından eksikliklerinin bulunduğu görülmüştür. Ayrıca öğrencilerin problemleri daha önceki deneyimlerinden yola çıkarak kurdukları ve genellikle orijinal problem kurmadıkları görülmüştür. Öğrencilerin problem kurarken en zorlandıkları kategori, düzenleme görevi olmuştur ancak bu durum, problem kurma görevleri arasında hiyerarşi olduğunu göstermemektedir. Öğrencilerin görüşleri incelendiğinde problem kurmanın öğrencilerin bakış açısını değiştirmek, kendini ifade etmek, yaratıcılığını göstermek, eğlenceli vakit geçirmek gibi durumlarda katkı sağladığı saptanmıştır. Ayrıca grup çalışmasının iletişim ve karşısındaki insanın fikirlerini anlamada olumlu yönde etkilediği görülmüştür.

Background: Real‐world problems are important in math instruction, but they do not necessarily trigger students' task motivation. Personalizing real‐world problems by (1) matching problems to students' shared living environment (context personalization) and (2) asking students to pose their own problems (active personalization) might be two interventions to increase students' task motivation. Aim: In the current study, we investigated the effects of context personalization and active personalization on students' self‐efficacy expectations, intrinsic value, attainment value, utility value, and cost. Sample: The participants were 28 fifth‐ and sixth‐grade students who voluntarily took part in a six‐month afterschool program in which they posed problems with the aim of creating a math walk in their hometown. Method: Using a within‐subjects design, at the end of the afterschool program, the students rated their self‐efficacy expectations and task values for four self‐developed problems associated with their hometown, four peer‐developed problems associated with their hometown, and four instructor‐provided problems associated with unfamiliar locations. Results: Students reported higher self‐efficacy expectations, intrinsic value, attainment value, and utility value for active‐personalized than non‐personalized problems. To a lesser extent, context personalization promoted intrinsic value and attainment value. No effect was found for cost. Conclusions: Active personalization (i.e. asking students to pose their own real‐world problems) is suited to enhance students' task motivation, specifically their self‐efficacy expectations, intrinsic value, attainment value, and utility value. Context personalization still boosts students' intrinsic value and attainment value. Implementation in classroom instruction is discussed. [ABSTRACT FROM AUTHOR]

In this study, 176 Turkish seventh-grade students were asked to pose three problems for each of the swimming and purchasing tasks to examine how the solvability and complexity of the problems changed depending on the order of responses. The purchasing task required to pose a problem to derive a specific answer before posing new problems, whereas the swimming task required to pose problems based on existing data. The findings indicated that students performed poorly in terms of posing solvable problems in both tasks. The majority of solvable responses in the purchasing task were at the high complexity level, but most in the swimming task were at the low complexity level. No evidence of a relationship between the order of the responses and any of the analysis units (solvability and complexity) was found. Furthermore, when comparing the groups that posed and did not pose solvable problems for the specific answer in the purchasing task, the former group had a stronger tendency to maintain the complexity points in their other responses compared to their first response. [ABSTRACT FROM AUTHOR]

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Mathematics tasks situated in realistic situations play a central role in developing and applying mathematical knowledge. However, mathematics educators face difficulties in designing realistic mathematics tasks. This study was conducted to gain deeper insights into the characteristics of mathematical problems that underprepared preservice secondary mathematics teachers pose. This study examined 32 preservice secondary mathematics teachers' problem-posing skills based on three problem-posing situations: structured problem-posing, semi-structured problem-posing, and free problem-posing. As the context of the participants, they did not have learning experiences in designing realistic mathematics tasks. In evaluating the preservice teachers' works, the researchers used several evaluation criteria, namely the compatibility of the problem with the mathematical principles, plausibility and sufficiency of information, the problem text, level of context authenticity, cognitive demand, and the correctness of the solution. The results revealed that most preservice teachers posed problems with the first-order level of context use and low cognitive demand. Additionally, many of them encountered difficulties when attempting to solve the problem. The findings of this study were expected to serve as a basis for developing a curriculum for pedagogic and mathematics courses in teacher education.

This Classroom Action Research (CAR) is an effort to improve students' intrapersonal and interpersonal intelligence through the application of Problem Posing in mathematics learning in Junior High Schools on Constructed Spaces with Curved Sides. The research subjects were 64 students from the 9th grade of a Junior High School in Bandung. Data collection techniques include interviews, questionnaires, observations, and documentation. Intrapersonal and interpersonal intelligence in the experimental class using the Problem Posing learning model is relatively better than the control class using conventional learning models. The results of this study show that the application of the Problem Posing learning model can improve students' intrapersonal intelligence and interpersonal intelligence. There are several advantages that researchers get in implementing Problem Posing besides students become the center of learning and practice working in groups, students become much more enthusiastic so that the learning atmosphere is conducive and full of activity, and presentation activities can build courage and confidence in performance. Learning performance and building a positive attitude during learning. Suggestion: The problem-posing learning model can be an alternative to be applied in the classroom because it can foster self-confidence and make students more active, thereby increasing students' mathematical communication skills, which correlate with interpersonal intelligence. Penelitian ini sebagai upaya untuk meningkatkan kecerdasan intrapersonal dan interpersonal siswa melalui penerapan Problem Posing pada pembelajaran matematika di Sekolah Menengah Pertama (SMP) pada materi Bangun Ruang Sisi Lengkung. Jenis penelitian yaitu Penelitian Tindakan Kelas (PTK). Subyek penelitian sebanyak 64 orang siswa kelas 9 salah satu SMPN di Bandung. Teknik pengumpulan data meliputi: wawancara, angket, observasi, dan dokumentasi. Kecerdasan intrapersonal dan interpersonal pada kelas eksperimen dengan penggunaan model pembelajaran Problem Posing, relatif lebih baik dari kelas kontrol yang menggunakan model pembelajaran konvensional. Hasil dari penelitian ini bahwa penerapan model pembelajaran Problem Posing dapat meningkatkan kecerdasan intrapersonal dan kecerdasan interpersonal siswa, terbukti dari peningkatan rata-rata keduanya pada setiap siklus. Ada beberapa kelebihan yang didapat peneliti dalam menerapkan Problem Posing, selain siswa menjadi sentral pembelajaran dan melatih bekerja dalam kelompok, siswa menjadi jauh lebih semangat dan antusias sehingga suasana pembelajaran kondusif dan penuh aktifitas, selain itu kegiatan presentasi dapat membangun keberanian dan keyakinan dalam unjuk kinerja belajar dan membangun sikap positif selama pembelajaran. Oleh karena itu, model pembelajaran Problem Posing dapat menjadi alternatif untuk di-terapkan di dalam kelas karena dapat menumbuhkan percaya diri siswa untuk lebih aktif sehingga mampu meningkatkan kecerdasan intrapersonal dan kecerdasan interpersonal.

Prospective teachers often have difficulty in posing problems. This indicates unsuccessful analogical reasoning, so prospective teachers produce non-analog problems. Therefore, a study is needed to trace the process of unsuccessful analogical reasoning of prospective teachers so that they can produce non-analog problems. The research aims to describe the analogical reasoning process of prospective teachers that causes prospective teachers to produce non-analog problems. The research method used a case study with a qualitative approach. The participating research subjects were prospective teachers from one of the universities in Sidoarjo, East Java, Indonesia. The research subjects are prospective teachers who are asked to generate analog problems but produce non-analog problems. The research instruments included analog problem posing tasks and interviews. The analogical reasoning process of prospective teachers can be traced through process components or activities in terms of retrieval, structuring, representation, mapping, application, and verification. Prospective teachers generate non-analog problems, starting with inappropriate activities in object retrieval and source problem solving. The structuring and representation of analog source objects were not successfully done by prospective teachers, resulting in non-analog problems. This impacted the next activities, namely mapping, application, and verification which were unsuccessful in producing solutions to analog target problems. Calon guru seringkali mengalami kesulitan dalam mengajukan masalah. Hal ini menunjukkan penalaran analogi yang tidak berhasil, sehingga calon guru menghasilkan masalah non-analog. Oleh karena itu, dibutuhkan suatu penelitian untuk menelusuri proses ketidakberhasilan penalaran analogi calon guru sehingga dapat menghasilkan masalah non-analog. Tujuan peneltian adalah untuk mendeskripsikan proses penalaran analogi calon guru yang menjadi sebab calon guru menghasilkan masalah non-analog. Metode penelitian menggunakan studi kasus dengan pendekatan kualitatif. Subjek penelitian yang berpartisipasi merupakan calon guru dari salah satu Perguruan Tinggi di Sidoarjo, Jawa Timur, Indonesia. Dalam hal ini, subjek penelitian adalah calon guru yang diminta untuk menghasilkan masalah analog namun menghasilkan masalah non-analog. Instrumen penelitian meliputi tugas pengajuan masalah analog dan wawancara. Proses penalaran analogi calon guru dapat ditelusuri melalui komponen proses atau aktivitas dalam hal pemanggilan, penataan, representasi, pemetaan, penerapan, dan pemeriksaan. Calon guru menghasilkan masalah non-analog diawali dengan aktivitas tidak tepat pada pemanggilan objek-objek dan penyelesaian masalah sumber. Penataan dan representasi objek-objek sumber yang analog tidak berhasil dilakukan calon guru, sehingga menghasilkan masalah non-analog. Hal ini berdampak pada aktivitas berikutnya, yaitu pemetaan, penerapan, dan pemeriksaan yang tidak berhasil untuk menghasilkan solusi dari masalah target yang bersifat analog.

In mathematics teaching, problem posing is an expected outcome for students. It is important for future teachers to be able to pose problems effectively when implementing the mathematics curriculum. This study aimed to examine the problems posed by classroom teacher candidates based on their mathematical process skills. The Problem Posing Test, used as a data collection tool, was was developed based on four objectives within the domain of measurement learning. In this quasi-experimental study, both the experimental and control groups comprised 25 volunteer classroom teacher candidates each. Analysis of the problems posed by teacher candidates was carried out according to the conceptual framework created by the researchers. The analysis revealed that classroom teacher candidates struggled with mathematical communication, association, and reasoning skills. Specifically, it was observed that they often wrote mathematical units incorrectly or incompletely, overly relied on verbal representation, failed to make interdisciplinary connections, and frequently posed problems requiring analogy-based reasoning. After instruction in problem posing, teacher candidates in the experimental group demonstrated improved mathematical process skills. Future studies should examine the problems posed by teachers or teacher candidates across different grade levels to assess their mathematical process skills. [ABSTRACT FROM AUTHOR]

The effect of problem posing skills of fifth grade secondary school students in the context of creativity regarding patterns on their problem-solving skills was examined through mixed method with explanatory sequential design. This research was conducted with a total of 25 students, 2 of whom were in the pilot study. The problem posing test consists of a total of four different semi-structured problem situations related to two numbers and two shape patterns. The problem-solving test was created by selecting a total of 12 problems posed by participant students. In addition, interviews were held with 14 students to examine both the problem posing process and solving processes in more detail. The creativity scores of the students participating in the research were calculated with the problem posing test and their success scores with the problem-solving test. As a result of multiple regression analysis, it was determined that the fluency, flexibility and originality components of creativity regarding patterns did not predict problem-solving skills, but there was a significant relationship between the components and problem-solving skills. [ABSTRACT FROM AUTHOR]

This qualitative document analysis study reports on opportunities to learn provided by textbooks for mathematics content courses for pre-service elementary teachers. Specifically, the study examined opportunities to engage in problem posing and quantitative reasoning, in the context of fractions, provided by six textbooks commonly used in the teaching of content knowledge courses for pre-service elementary mathematics teachers in the United States. Among other things, this examination revealed two key findings. First, all the textbooks provide numerous opportunities that could potentially trigger students' quantitative reasoning. This is commendable, and a positive response to growing calls to increase such opportunities in mathematics education. Second, there is a paucity of opportunities to engage in problem posing in all the textbooks. Given the numerous benefits of using problem posing in the teaching and learning of mathematics, we recommend that authors of textbooks for mathematics content courses for pre-service elementary teachers provide more opportunities to engage in problem posing in their textbooks. We argue that the act of problem posing requires significant quantitative reasoning, and thus problem posing provides the opportunity for students to develop such reasoning. Implications for instruction and directions for future research are discussed. [ABSTRACT FROM AUTHOR]

The present study aimed to test the effect of the problem-posing instruction experimentally based on the extended active learning framework on the development of Turkish middle school sixth-grade students' (N = 19) problem-posing and -solving skills with whole-number operations. The training programme was completed in 13 lessons over a seven-week period. The posed problems were analysed based on their mathematical validity and semantic complexity, and their solutions were analysed using a four-phase rubric. The students significantly improved their problem-posing and -solving skills. Furthermore, students improved their skill to pose more complex problems in terms of number and type of semantic structures after the training programme. [ABSTRACT FROM AUTHOR]

Nutrition facts are the details on food packaging that describe its nutritional value, including serving size, calories, macronutrients like carbohydrates, protein, and fat, and micronutrients such as vitamins and minerals. These facts have mathematical concepts that can be utilized as a context for prospective teachers to create mathematical problems. By leveraging this real-world data, educators can contribute to multiple Sustainable Development Goals (SDGs), particularly SDG 3 (Good Health and Well-being), by promoting nutritional awareness, and SDG 4 (Quality Education) by enhancing student engagement and understanding through relatable examples. This study examines the profile of mathematical tasks created by prospective mathematics teachers using nutrition facts as a context that meets numeracy task criteria. Data were collected from 62 mathematical tasks created by 31 prospective teachers attending a realistic mathematics education course on numeracy based on a problem-posing task at a public university in Surabaya, Indonesia. The posed tasks were categorized into solvable or unsolvable tasks and the domains of the level of context use and the level of cognitive processes. Results revealed that the level of context use in the posed tasks varied from zero to second order. Surprisingly, most of the tasks were in the first-order level context. Most posed tasks reached the application level, with only a few identified as reasoning tasks. Interestingly, some tasks coded as second-order context were classified as reasoning tasks. The study provides implications for designing numeracy tasks using nutrition facts and interventions in teacher education related to numeracy task design.

This study tests a model that predicts the problem-posing performance of sixth-grade students (independent variable metacognition, mediator variables mathematics and native language course success scores at the end of the year). The research was conducted with the relational model. The results regarding the mediation effect indicated that the mathematics course success scores and the native language course success scores were separately full mediators in the effect metacognition has on problem-posing performance. The results regarding serial mediation effect revealed that the mathematics course success scores and native language course success scores had a full mediating effect on the effect of metacognition on problem-posing performance.

Penelitian ini bertujuan untuk medeskripsikan kemampuan literasi matematis calon guru dalam pengajuan masalah yang berorientasi data. Indikator kemampuan literasi matematis pada penelitian ini terdiri dari komunikasi, matematika, representasi, penalaran dan argumen, merancang strategi untuk memecahkan masalah, menggunakan bahasa simbol, fomal, teknis dan operasi, dan menggunakan alat matematika Jenis penelitian ini merupakan penelitian kualitatif dengan pendekatan deskriptif dengan desain penelitian fenomenologi. Subjek penelitian ini merupakan calon guru semester 3 dan 5 berdasarkan kemampuan matematika tinggi, sedang dan rendah. Instrumen penelitian yang digunakan adalah tes dan wawancara. Teknik analisis data terdiri dari reduksi data, kategorisasi data, pemaparan data dan penarikan simpulan. Hasil penelitian menunjukkan kemampuan literasi matematis calon guru berkemampuan rendah dan sedang dalam pengajuan masalah masih dapat dikatakan belum baik, karena hanya memenuhi beberapa indikator, masalah yang diajukan masih memuat sedikit informasi sehingga tidak memerlukan banyak tahapan serta strategi, masalah yang diajukan lebih bersifat informatif dalam bentuk cerita. Kemampuan literasi calon guru dengan kemampuan matematika tinggi dalam pengajuan masalah tergolong sudah baik, karena mampu memenuhi setiap indikator, mampu menyajikan masalah dalam berbagai bentuk representasi, mengaitkan berbagai konsep matematika berupa aljabar dan kombinatorik, memerlukan banyak strategi dan tahapan penyelesaian. Ketiga subjek belum mengajukan masalah yang menuntut jawaban argumentasi dalam penyelesaian This study aims to describe the mathematical literacy abilities of prospective teachers in data-oriented problem posing. The indicators of mathematical literacy ability in this study consist of communication, mathematics, representation, reasoning and arguments, devising strategies to solve problems, using symbolic, formal, technical and operational language, and using mathematical tools. This type of research is qualitative research with a descriptive approach to design phenomenological research. The subjects of this study were prospective teachers in semesters 3 and 5 based on high, medium and low mathematical abilities. The research instruments used were tests and interviews. Data analysis techniques consist of data reduction, data categorization, data exposure and drawing conclusions. The results of the study show that the mathematical literacy skills of prospective teachers have low ability and are still high. They are still not good, because they only fulfill a number of indicators, the problems posed still contain little information. The problems posed are more informative in the form of a story. The literacy skills of prospective teachers with high mathematical abilities at problem posing are considered good, because they are able to fulfill each indicator, are able to present problems in various forms of representation, link various mathematical concepts in the form of algebra and combinatorics, and require many strategies and stages of completion. The three subjects have not submitted a problem that demands an argumentative answer at completion

This paper examined the problem-solving and problem-posing skills of middle school students in terms of whether the factors of gender and school type have an impact, as well as to illustrate these skills with respect to grade levels. A total of 461 students from different middle school levels of both private and public schools participated in the study. The instrument and framework reported by Cai (2003) were applied in the data collection and analysis phases of the study. The results revealed no significant differences between private and public schools in terms of problem-solving and problem-posing skills. In terms of gender, similar characteristics were found in terms of problem-solving skills, while differences in problem-posing skills were noted. In addition, some differences were observed in terms of problem-solving and problem-posing skills according to grade level. These results are discussed in the context of the existing literature.

Matematika masih menjadi salah satu mata pelajaran yang dianggap sulit oleh siswa. Khususnya bagi siswa sekolah dasar yang masih terbatas pada tingkat abstraksi. Tingkat abstraksi siswa erat kaitannya dengan kemampuan penalaran matematis. Kemampuan penalaran matematis ini juga mempengaruhi prestasi belajar siswa secara keseluruhan. Salah satu pendekatan yang digunakan untuk meningkatkan kemampuan penalaran matematis dan juga prestasi belajar adalah dengan problem forming. Pendekatan ini memiliki tiga langkah utama yang dapat merangsang abstraksi siswa. Tiga langkah tersebut adalah menyajikan masalah, memecahkan masalah, dan membuat kesimpulan. Tujuan penelitian ini adalah untuk mendeskripsikan: 1. pengaruh pendekatan Problem Posing terhadap prestasi belajar siswa kelas V, 2. pengaruh Problem Posing terhadap kemampuan penalaran matematis siswa kelas V. Penelitian ini merupakan penelitian kuasi eksperimen yang menggunakan satu kelas eksperimen dan satu kelas kontrol. Kelas eksperimen menggunakan problem pose yaitu SDN Madusari I dan satu kelas kontrol tidak diberikan perlakuan yaitu SDN Potrojayan. Prestasi belajar dan kemampuan penalaran matematis diukur dengan menggunakan instrumen tes berupa soal jawaban singkat dan soal esai. Hipotesis yang digunakan adalah uji univariat dan uji multivariat. Hasil penelitian menunjukkan bahwa, 1. Pengajuan masalah tidak berpengaruh terhadap prestasi belajar dengan nilai signifikansi 0,067 (p < 0,05), 2. Pengajuan masalah tidak berpengaruh terhadap kemampuan penalaran matematis dengan nilai signifikansi 0,393 (p > 0,05).

This study proposes a model of several dimensions through which products of teachers' context-based mathematics problem posing (PP) can be modified. The dimensions are Correctness, Authenticity, Task Assortment (consisting of Mathematical Diversity, Multiple Data Representations, Question–Answer Format, Precision-Approximation, and Generalization), Task Flow, and Student Involvement. A study was conducted in the context of a professional development (PD) program in which eight secondary school teachers iteratively designed 22 context-based mathematics tasks. Using the variation theory of learning as a theoretical framework and qualitative content analysis methodology, we compared different versions of the same tasks, focusing on items participants added or revised. To demonstrate the usability of the resulting semi-hierarchical model, we apply it to characterize the teachers' final products of context-based PP. We found that most items teachers composed did not deviate from what we call the "common item form"—items that require numeric, exact, particular-case-related, and close-form answers without involving students in decision-making. Our findings may inform teacher educators and researchers on planning and implementing context-based mathematics task development by teachers in PD. [ABSTRACT FROM AUTHOR]

This study investigates 40 preservice middle school teachers' problems posed for two given fractions. Pre-service teachers were asked to pose three problems (farea, length and set model) for each of the operations of addition, subtraction, multiplication and division with these fractions. 12 problems posed by each pre-service teacher were examined in terms of their suitability for the given operation, the targeted model and real life relevance. Errors in the posed problems were also examined. As a result of the analysis, it was observed that the model in which pre-service teachers were the most unsuccessful in posing problems was the set model, and the model in which they were most successful was the length model. Many types of errors were encountered in the problems posed by the pre-service teachers. It has been observed that many errors exist together, especially in the problems posed for the set model. [ABSTRACT FROM AUTHOR]

Problem posing engages students in generating new problems based on given situations (including mathematical expressions or diagrams) or changing (i.e., reformulating) existing problems. Problem posing has been at the forefront of discussion over the past few decades. One of the important topics studied is the process of problem posing as experienced by students and teachers. This paper focuses on problem-posing processes and models thereof. We first provide an overview of previous research and then present the results of a scoping review regarding recent research on problem-posing processes. This review covers 75 papers published between 2017 and 2022 in top mathematics education research journals. We found that some of the prior research directly attempted to examine problem-posing processes, whereas others examined task variables related to problem-posing processes. We conclude this paper by proposing a model for problem-posing processes that encompasses four phases: orientation, connection, generation, and reflection. We also provide descriptions of the four phases of the model. The paper ends with suggestions for future research related to problem-posing processes in general and the problem-posing model proposed in particular. [ABSTRACT FROM AUTHOR]

This study aims to analyze the association between problem-solving and posing and its potential to promote learning and aid in understanding students' mathematical thinking. To this end, a qualitative case study was carried out involving elementary Grades 1-5' students in the solving of a problem that was adapted to generate different learning outcomes related to the division operation as well as associating the posing of problems with the request to add a question to the problem. The results confirm the importance of teachers' fostering of discussions and understanding students' mathematical thinking; they also reveal that difficulty in interpreting the problem statement may not always be the reason for students not providing a solution. In addition, the data shows the potential of problem posing to deepen or advance the learning that results from problem-solving. [ABSTRACT FROM AUTHOR]

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Copyright of Trakya Journal of Education is the property of Trakya Journal of Education 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 posing has long been recognized as a critically important teaching method and goal in the area of mathematics education. However, few studies have used problem posing to assess in-service teachers' mathematical understanding. The present study investigated in-service teachers' mathematical understanding of fraction division, which is often considered challenging content in elementary school, from three angles: computation, drawing, and problem posing. Two studies involving 66 and 193 primary and middle school teachers were conducted to reveal the in-service teachers' mathematical understanding and whether drawing and problem posing affected each other. Although the in-service teachers rarely had the opportunity to pose mathematical problems in their daily teaching, they were able to pose mathematical problems in this study. In addition, problem-posing tasks were more useful in diagnosing the in-service teachers' conceptual understanding than were computation or drawing. Thus, problem posing seems to have contributed to their conceptual understanding of fraction division on the drawing task. [ABSTRACT FROM AUTHOR]

To promote optimal learning in their students, mathematics teachers must be proficient in problem posing, making this skill a cornerstone in teacher training programs. This study presents a formative action in which pre-service teachers are required to create and analyze a problem involving proportional reasoning within a probabilistic context. For this problem, they must identify the objects and processes involved in its resolution, recognize the degree of algebraic reasoning implied and identify potential difficulties for students. Subsequently, they need to formulate and analyze a new problem with variation, which mobilizes higher-level algebraic activity. Results indicate that prospective teachers struggle to pose problems that engage proportional reasoning, as well as to identify in their analysis which elements of proportional and algebraic reasoning are present in their solutions. Despite this fact, a significant percentage of participants adequately modify the original problem to address higher levels of algebraic reasoning, identifying in these cases the new algebraic objects and potential difficulties that might arise as the degree of generalization required in the solution increases. The study concludes by underscoring the importance of training in problem posing to enhance the knowledge and competences of prospective teachers concerning proportional and algebraic reasoning. [ABSTRACT FROM AUTHOR]

This paper examined the problem-solving and problem-posing skills of middle school students in terms of whether the factors of gender and school type have an impact, as well as to illustrate these skills with respect to grade levels. A total of 461 students from different middle school levels of both private and public schools participated in the study. The instrument and framework reported by Cai (2003) were applied in the data collection and analysis phases of the study. The results revealed no significant differences between private and public schools in terms of problem-solving and problem-posing skills. In terms of gender, similar characteristics were found in terms of problem-solving skills, while differences in problem-posing skills were noted. In addition, some differences were observed in terms of problemsolving and problem-posing skills according to grade level. These results are discussed in the context of the existing literature. [ABSTRACT FROM AUTHOR]

This study tests a model that predicts the problem-posing performance of sixth-grade students (independent variable metacognition, mediator variables mathematics and native language course success scores at the end of the year). The research was conducted with the relational model. The results regarding the mediation effect indicated that the mathematics course success scores and the native language course success scores were separately full mediators in the effect metacognition has on problem-posing performance. The results regarding serial mediation effect revealed that the mathematics course success scores and native language course success scores had a full mediating effect on the effect of metacognition on problem-posing performance. [ABSTRACT FROM AUTHOR]