Problem-posing Strategy Research Articles

Problem Posing in Prospective Primary School Teacher: Perspective Commognitive

This research explores the problem-posing abilities of students, especially prospective primary school teachers, which are demonstrated through problem-posing creativity produced through worksheets. In exploring students' problem-posing abilities, descriptive research with a qualitative approach was used. The subjects in the research were prospective primary school teacher students who had taken a number concept course which was chosen based on the problem-posing strategy that emerged after solving the given problem. Furthermore, subjects were interviewed in-depth to find out cognitive by looking at four indicators, namely word use, visual mediator, narrative and routine. The research results showed that there were no subjects with imitation strategies and subjects with reformulation strategies and reconstruction strategies did not give rise to problem-posing using visual mediators. This is because the subject is not used to problem-posing mathematical models in the form of diagrams or symbols.

The selections and differences in mathematical problem-posing strategies of junior high school students

To illustrate the selections and differences in mathematical problem-posing (MPP) strategies of junior high school students, this study constructs a theoretical framework for mathematical problem-posing strategies and then conducts an empirical study through a survey of 1653 Chinese junior high school students. The results show that students prioritize accepting the given information to pose mathematical problems, while few choose to change the given information. Most students used chaining, and very few students used symmetry to pose mathematical problems. From a developmental perspective, excluding the number of problems, there were grade differences in the selectivity of MPP strategies among students in grades 7, 8, and 9. Still, for each grade, accepting the given information and chaining were the most used strategies in the category therein. More than 77.56% (1282 students) chose category B to pose further mathematical problems after accepting or changing the given information to pose mathematical problems. The results of path analysis illustrate that there are two main routes of the evolution of the selections of the strategies of MPP of junior high school students: the first one is from category A to category B, and the second one is after the students use changing the given information, they are present with the selection of strategies, either use symmetry or chaining. The results may have important implications for the teaching and learning of problem-posing.

Effect of Real-World Problem-Posing Strategy on Engineering College Students’ Cognitive and Affective Skills

Effect of Real-World Problem-Posing Strategy on Engineering College Students’ Cognitive and Affective Skills

Effect of Teaching Mathematics Supported by Problem-posing Strategies on Problem-posing Skills

The present study aims to investigate the effects of teaching mathematics supported by problem posing strategies on 4th-grade students’ problem-posing skills. The study also seeks to determine students’ views about the process. To this end, the study employed the explanatory sequential design, one of the mixed methods that incorporate collecting quantitative data and qualitative data. The study group consisted of 4th-grade students studying in two different classrooms of a public school located in the west of Türkiye in the 2021-2022 academic year. The data were collected through a “Problem-Posing Skills Test” and a “Semi-Structured Interview Form.” The research concludes that teaching mathematics supported by problem posing strategies improves students’ problem-posing skills. In addition, this method was more effective than the one used in the control group in developing students' structured, semi-structured, and free problem-posing skills. At the end of the interviews, it was determined that teaching mathematics supported by problem posing strategies was an innovative, student-centered, and emotionally stimulating technique. It was also found that the students had more difficulty in semi-structured and free problem-posing tasks.

How to Pose Problems on Periodicity and Teaching with Problem Posing

Research on how to pose good problems in mathematical science is rarely touched. Inspired by Kilpatrick’s “Where do good problems come from?”, the current research investigates the problem of the specific problem posed by mathematicians in mathematical sciences. We select a recent mathematical conjecture of Yang related to periodic functions in the field of functions of one complex variable. These problems are extended to complex differential equations, difference equations, differential-difference equations, etc. Through mathematical analysis, we try to reproduce the effective strategies or techniques used by mathematicians in posing these new problems. The results show that mathematicians often use generalization, constraint manipulation, and specialization when they pose new mathematical problems. Conversely, goal manipulation and targeting a particular solution are rarely used. The results of the study may have a potential impact and promotion on implementing problem-posing teaching in primary and secondary schools. Accordingly, teachers and students can be encouraged to think like mathematicians, posing better problems and learning mathematics better. Then, we give some examples of mathematical teaching at the high school level using problem-posing strategies, which are frequently employed by mathematicians or mathematical researchers, and demonstrate how these strategies work. Therefore, this is a pioneering research that integrates the mathematical problem posing by mathematicians and the mathematical problem posing by elementary and secondary school math teachers and students. In addition, applying constraint manipulation and analogical reasoning, we present four unsolved mathematical problems, including three problems of complex difference-related periodic functions and one problem with complex difference equations.

Okuma Stratejilerine Yönelik Üst Bilişsel Farkındalığın Problem Kurma Becerisini Yordama Düzeyi

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

Opening mathematical problems for posing open mathematical tasks: what do teachers do and feel?

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.

A Meta-Analysis of the Impact of Problem Posing Strategies on Students’ Learning of Mathematics

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 meta-analysis 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.

IMPLEMENTATION OF TPS LEARNING MODELS WITH PROBLEM POSING TO TRAIN CREATIVE THINKING ON ACID-BASE

The research aims to be aware of the implementation of the TPS learning model with problem posing strategies on acid-base, student activity, creative thinking skills, completeness of learning outcomes, and responses of the learning model used. Use one group pretest-posttest research design and was applied to 54 high school students in class XI. The average percentage obtained by the feasibility of the learning model to 91.67% at the first meeting and to 98.60% at second meeting which both of them fall into the excellent category. The relevant activities result at the first meeting to 94,69% and irrelevant by 5,31% while activities of relevant at second meeting to 93,09% and irrelevant by 6,91%,, creative thinking skills increased by a percentage of 40.74% for the high category, 44.44% medium category, and 14.82% low category, for classical completeness learning outcomes by 88.89 %, and students' responses were 95.60% positive while 4.40% for negative responses.

Meningkatkan Kemampuan Kognitif Siswa melalui Strategi Problem Posing Di SMP Negeri 7 Padangsidimpuan

The purpose of this study was to improve students' cognitive abilities in the implementation of the mathematics learning process by using problem posing strategies. The type of research used is Classroom Action Research (CAR) in collaboration with teachers in Mathematics. This research was conducted at Padangsidimpuan Middle School 7. With research subjects class VII-1, amounting to 28 people. Data collection instruments used were tests. CAR procedures start from the planning, action, observation and reflection stages. This research was conducted in 2 cycles, each cycle having 2 meetings. The results of this study indicate that the cognitive abilities of students of class VII-1 SMP N 7 Padangsidimpuan increased by using the Problem Posing strategy. Because the increase in students' cognitive abilities through tests given during the learning process took place from the first cycle of the first meeting from 53.57% to 57.14% the first cycle of the second meeting and the second cycle of the first meeting from 75% to 85.14% the second cycle of the second meeting . In accordance with the indicators of the action of this study the results obtained have passed the predetermined average value of the average value of 75 until the second cycle of meeting 2 which is 77.92 with the percentage of students who complete 85.72.

Examining young children’s multiplication understanding through problem posing

ABSTRACT In the present study, researchers used problem-posing instruction to examine elementary students’ understanding of multiplication. Students in fourth and fifth grade classrooms (n = 24) from a rural school district participated in a semester-long study. The focus of this study was examining student solutions to two specific lessons with problems involving the use of multiplication. In each lesson, students were either asked to solve pre-written word problems that required the use of multiplication or to create original word problems that were solvable using multiplication. Qualitative analysis of student responses revealed six recurring themes about student comprehension of multiplication: a) incorrect operation, b) use of multiplication words, c) use of operational terminology, d) improper context, e) misunderstanding of units, and f) order of operations. Using problem-posing instruction as an assessment tool helped instructors gain a clearer understanding of students’ interpretations of multiplication compared to traditional problem-solving methods. Teachers can utilise problem-posing strategies as an opportunity to gain insight into how to help improve students’ understanding of given concepts.

Teachers' Views on the Problem-Solving & Problem-Posing Tasks in Primary School Mathematics Textbooks

This paper aims to reveal teachers' views on the problem-solving & problem-posing tasks of primary school mathematics textbooks. The study utilized the single-case embedded design. We examined the mathematics textbooks used in the Turkish public schools in the 2017-2018 academic year. Also, we interviewed twelve class teachers, who were determined by the criterion sampling method, to reveal their views on the textbooks. In order to collect data, we employed a "Data Coding Scheme" to determine the problem-solving & problem-posing tasks in the textbooks and a "Semi-Structured Interview Form" composed of two open-ended questions to find out about the teachers' views. Since the questions asked to the teachers were determined as themes in advance, the descriptive data analysis technique was used for data analysis. The study concludes that the examined mathematics textbooks contain a sufficient number of problem-solving tasks, which are equally distributed under each heading in the textbooks. On the other hand, it has been found that the textbooks contain a limited number of problem-posing tasks, which are not equally distributed under each heading. Furthermore, we determined that no textbook that we examined contains different types of problem-posing tasks. Also, according to the teachers whom we interviewed, although the number of problem-solving tasks in the textbooks is sufficient, the tasks should be more effective. They also stated that the textbooks contain very few problem-solving tasks requiring different problem-posing strategies.

A Systematic Literature Review on the Problem-Posing Strategies for Biology Problem-Posing Multimedia Module Design

Numerous research has documented the debate fuelled by scholars pertaining to problem-posing strategy in Mathematics. It has been argued that this strategy is capable of instilling student’s problem-solving skills. However, despite its popularity in Mathematics, the application on other subjects such as Biology particularly, via a media technology is still sparse. This study aims at identifying suitable strategies to be incorporated into a proposed multimedia module namely, Problem-Posing Multimedia Module (PPMM). To achieve the objective, a systematic literature review has been executed. This paper elaborates on the rigorous systematic literature review process done on the 289 selected journal articles and papers on problem-posing strategies topic. The analysis reveals that, while different field applies different strategies of problem-posing, most of them share similar themes in implementing problem-posing instructional strategies. These are communication, collaboration, creativity and critical thinking, which are part of the elements advocated in the 21st-century learning. These findings act as a heuristic device to propose a development of a problem-posing multimedia activity module.

Leading curriculum change: Reflections on how Abakhwezeli stoked the fire

Curriculum leadership is a complex and demanding practice, which goes beyond the research and disciplinary expertise of the curriculum leader. Engaging and leading educators in a process of curriculum change is not easy: it can be a difficult, and sometimes chaotic journey which is often characterised by philosophical debate, the calling into question of current practices, fear, and even openly acknowledged resistance. In order for change to succeed, leaders of curriculum change must facilitate a shared ownership of the change process. This will require the bringing together of individuals with different personal priorities and rallying them around a common goal, e.g. designing quality Bachelor of Education (B.Ed) programmes. Our curriculum renewal journey involved the use of problem-posing pedagogies and required us to employ transformative types of leadership strategies. In this paper, we reflect critically, on our roles, as members of the ‘ Abakhwezeli ’, in stoking the fires of curriculum change in the Nelson Mandela Metropolitan University (NMMU) Faculty of Education. Furthermore, this paper will highlight particular defining moments during the curriculum renewal journey, where stakeholder consultation and the use of transformative methodologies assisted in prompting deep, critical reflection on the (re)designing of our B.Ed programmes. Keywords: critical approach; critical pedagogy; curriculum renewal; dialogical spaces; problem-posing strategies; transformational leadership; transformative methodologies

중학생들의 수학적 문제제기 유형과 전략 분석

The purpose of this study was to analyze middle school students` problem posing types and strategies. we analyzed problems posed by 120 middle school students during mathematics class focused on problem posing activities in various aspects. Students` posed problems were classified into five types: not a problem(NP), non-math(NM), impossible(IM), insufficient(IN), sufficient(SU) and each of the posed problems. Students used three kinds of problem posing strategies such as goal manipulation(GM), assumption manipulation(AM), and condition manipulation(CM), and in posing one problem, one or more than two strategies were used. According to the prior studies, problem posing can contributes to the development of students` problem solving ability, creativity, mathematical aptitude, and a broader understanding of mathematical concepts. However, we found that some students had difficulties in posing problems or limited understandings of that. We hope the results of the study contribute to encouraging problem posing activities in mathematics instruction.

Development of a mobile learning system based on a collaborative problem-posing strategy

In this study, a problem-posing strategy is proposed for supporting collaborative mobile learning activities. Accordingly, a mobile learning environment has been developed, and an experiment on a local culture course has been conducted to evaluate the effectiveness of the proposed approach. Three classes of an elementary school in southern Taiwan participated in the experiment. One class was the experimental group who learned with the problem-posing-based mobile learning approach, while the other two classes were the control groups who learned with the conventional mobile learning approach and the traditional problem-posing approach, respectively. The experimental results show that the new approach not only improved the students' learning achievement, but also promoted their local culture identity and group learning self-efficacy.

See a Different Mathematics

Sporting News, a popular sports magazine, runs certain stories under the heading of “See a different game.” These stories are in-depth analyses of strategy. The slogan means that if you know more about the strategy of the game, you will see the game differently. If students are pushed to think about mathematics more deeply and flexibly, they will, in effect, “see a different mathematics.” We can change our game plans by strategically posing mathematics problems so that students get that chance. As we add to our playbook of problem-posing strategies, our students will come to “understand a different mathematics.”

Learning To Pose Mathematical Problems: Exploring Changes in Preservice Teachers' Practices.

Learning to pose mathematical tasks is one of the challenges of learning to teach mathematics. How and when preservice teachers may learn this essential practice,however, is not at all clear. This paper reports on a study that examined the changes in the problem posing strategies of a group of elementary preservice teachers as they posed problems to pupils. It reports that their later problem posing practices significantly differed from their earlier ones. Rather than posing traditional single steps and computational problems, these preservice teachers ventured into posing problems that had multiple approaches and solutions, were open-ended and exploratory, and were cognitively more complex. Their problem posing style also changed. Rather than making adaptations that made students' work easier or narrowed the mathematical scope of the problem, their adaptations became less leading and less focused on avoiding pupils' errors. Posing problems to an authentic audience, engaging in collaborative posing, and having access and opportunities to explore new kinds of problems are highlighted as important factors in promoting and supporting the reported changes.