Non-routine Problems Research Articles

Examination of Mathematics Teachers’ Strategic Flexibility in Solving Mathematical Problems

One of the fundamental skills teachers aim to impart in mathematics education is problem-solving. Developing and sustaining this skill is only possible if teachers possess strategic flexibility. Assessing the current level of teachers’ strategic flexibility is crucial, as it also plays a key role in their professional development. The research aims to explore the strategic flexibility of mathematics teachers in solving mathematical problems–both routine and non-routine problems. Using a qualitative research methodology, specifically the case study design, this study engaged a cohort of 12 mathematics teachers who were actively teaching during the autumn semester of the 2022-2023 academic year. These participants represented various educational levels, possessed different postgraduate qualifications, and had diverse years of professional experience. Data collection tools include a Problem Solving Flexibility Test with four math problems and semi-structured interviews to gather teachers’ perspectives on routine and non-routine problems. The semi-structured interviews aimed to reveal all the strategies that teachers use or can use when solving problems. In the initial stages of data analysis, the distinct strategies employed by each participating teacher in addressing the problems were classified. In the context of intra-task strategic flexibility, teachers often used different strategies simultaneously while solving a problem. Teachers were able to switch strategies or use a different strategy because they were able to tackle routine difficulties more readily. The most commonly favoured problem-solving approaches among participants was “Reasoning” and “Make a Drawing or Diagram”. Interestingly, strategies like “Look for a Pattern” and “Simplifying the Problem” were predominantly employed in non-routine scenarios, which is a significant finding of the research. It was found that teachers’ inter-tasks strategic flexibility paralleled their teaching experience and postgraduate education status. In summary, this study investigates how mathematics teachers adapt their problem-solving strategies when faced with different types of mathematical challenges, highlighting the prevalence of specific approaches in routine and non-routine contexts.

Reenvisioning adaptive expertise as a distributed phenomenon

ABSTRACT A critical strand of educational research examines how people, and youth in particular, make adaptations to overcome unexpected and non-routine problems. In this conceptual paper, the authors propose an expanded framework that reenvisions adaptive expertise as a distributed phenomenon, focusing on three interrelated aspects relevant to how people work toward adaptations: (1) recruitment and coordination of resources, (2) reframing of problems and goals, and (3) navigational foresight. The paper illustrates the framework through examples drawn from a study of youth participation in the maker movement.

ANALISIS LITERASI MATEMATIS SISWA SMP DALAM MENYELESAIKAN SOAL ALJABAR BERORIENTASI AKM NUMERASI DITINJAU DARI GAYA KOGNITIF

The aims in this research is to identify the mathematical literacy skill of student based on cognitive style, specifically field independent (FI) and field dependent (FD), in solving AKM numeracy oriented problems in algebra content on SPLDV material. Descriptive qualitative are applied as the method with data collected through written test, interview, and documentation, validated using triangulation technique. The study use three main stages in data analysis: reducing data, presenting data, and make conclusion. The findings show that field independent student excel in various mathematical literacy indicator compared to field dependent students, including communications skill, devising strategies for solving problems, reasoning and argument, using symbolic, operations, technical language and formal language. However, field independent student still face challenges in mathematization and representation, especially in non-routine problems. Meanwhile, field dependent student have advantages in mathematical literacy indicators such as communications skill, reasoning and argument, using symbolic, operations technical language and formal language, thus requiring more assistance and explanations to achieve the same result as field independent students.

Classification of students’ creative thinking for non-routine mathematical problems

Classification of students’ creative thinking for non-routine mathematical problems

Investigation of the Relationships between E-Learning Styles, Educational Technology Self-Efficacy Perceptions and Problem-Solving Skills of Pre-Service Elementary Mathematics Teachers'

This study aims to determine the relationship between pre-service elementary mathematics teachers' e-learning styles, educational technology self-efficacy perceptions, and problem-solving skills. The sample of the study, in which the relational screening model was used, consists of 150 pre-service teachers studying in a state university's elementary mathematics teaching department. Of the participants, 68% (n=102) were female and 32% (n=48) were male. Data collection tools, e-learning styles, education technology self-efficacy, and measurement tools consisting of non-routine problems were used to determine problem-solving skills and an information form. Pearson product-moment correlation technique and multiple linear regression analysis were used to analyze the data set. According to the study's findings, significant relationships were determined between the sub-dimensions of e-learning styles, education technology self-efficacy, and problem-solving skills. Predictive variables consisting of sub-dimensions of e-learning styles and education technology self-efficacy explained 36% of the variance of the problem-solving skill. At the same time, audio-visual learning, verbal learning, active learning, logical learning, modeling digital-age work and learning, designing and developing digital-age learning experiences and assessments, and engaging in professional growth and leadership variables were effective in problem-solving. Finally, according to the findings, some suggestions are presented.

Comparison of MAGIQ, MABAC, MARCOS, and MOORA Methods in Multi-Criteria Problems

Determining the best alternative from many criteria is one of the core problems in decision making, both routine and non-routine problems. One of them is in the problem of determining egg suppliers. Eggs are one of the basic needs of the community so that the demand for eggs is always increasing, this makes the emergence of many egg agents in distributing and fulfilling needs. Selective and careful selection is needed in order to get a supplier that meets the desired expectations. Problems then arise in the selection of egg suppliers that are not in accordance with the expectations of the manager. In determining egg suppliers that have been carried out by UD Taluh Subur, only by means of a simple comparison between several factors such as price, production quantity, and quality without considering other factors. In addition to this, business managers have limited knowledge in statistical and business decision making. To optimize the supplier selection process, a Decision Support System can be used to help provide recommendations for selecting prospective suppliers of fixed eggs. Based on the situation of decision makers who have limited knowledge in statistical decision making, the MAGIQ method is suitable for weighting. To provide a more accurate ranking, additional methods such as the MABAC, MARCOS, and MOORA methods are used. The purpose of this research is to focus on which method is most recommended for the case study faced in the research based on the analysis results of the sensitivity test. The results of the sensitivity test show that the MAGIQ-MABAC method has the highest value of 4.42737%, then the MAGIQ-MOORA method with a value of 2.34415% and the MAGIQ-MARCOS method with a value of 0.45729%.

Problem-Solving Skills and Difficulties of Pre-Service Mathematics Teachers in Non-Routine Problems

Problem-Solving Skills and Difficulties of Pre-Service Mathematics Teachers in Non-Routine Problems

How are the classification of students’ mathematical connections in solving non-routine problems?

How are the classification of students’ mathematical connections in solving non-routine problems?

Improving Students’ Creative Thinking Skills Assisted by GeoGebra Software

This study aims to improve students’ creative thinking skills in problem-based, ill-structured, open-ended learning through stimulus. This study used learning strategies that simultaneously develop problem-solving strategies and knowledge discipline. This learning can be achieved if educational activities are focused on authentic, contextual, and relevant tasks or problems so that students can gather the necessary information, evaluate alternative solutions, and present solutions they believe in. Moreover, the ability to generate uncommon or extraordinary ideas must be raised from the problems that exist in learning. The ability to think creatively in mathematics in education using the Problem-Based Learning (PBL) approach assisted by GeoGebra is expected to be a practical approach to educating students in increasing their intellectual potential and familiarizing them to deal with non-routine problems and applying it in their daily life to become a student who can think creatively. This study used a quasi-experimental research method with a quantitative approach conducted at SMA Negeri 2 Cimalaka. The instruments used in this study were questionnaires and tests. This study's approach, which was integrated with GeoGebra, can be used as an alternative to learning mathematics in schools. It can be developed with other approaches according to problems in mathematics.

Applıcatıon Desıgns to Measure the Mathematıcal Reasonıng Skılls of Teacher Candidates

Mathematical reasoning can be defined as the ability of individuals to approach situations they encounter from a mathematical perspective, to investigate the cause and effect, to make sense of the situation, and to make reasoning that will help reach a logical conclusion by using mathematical concepts and symbols. The purpose of the research is to evaluate the mathematical application designs of primary school teacher candidates studying at Khoja Akhmet Yassawi International Kazakh-Turkish University in order to measure the mathematical reasoning skills of primary school students. For this purpose, at the primary school level, teacher candidates will be asked to (a) identify and use appropriate reasoning, (b) recognize and use mathematical knowledge / patterns / structures / general properties, (c) recognize different representations of the same data, (d) predict, (e) Developing logical arguments regarding the solution, (f) Deciding on the correctness of the solution/result, (g) Making generalizations, and (h) Solving non-routine problems. In this respect, the research was designed in the case study pattern, one of the qualitative research methods. The study group of the research includes a total of 16 teacher candidates representing different grade levels. Typical case sampling method was used to select the teacher candidates in the study group. Pre-service teachers were asked to develop application designs in which they could evaluate the mathematical reasoning sub-dimensions mentioned above. In the research, the theoretical framework was scanned, and an application was carried out to 16 teacher candidates and at the end of the application, the teacher candidates were able to design questions for all their reasoning skills. When the questions they prepared were evaluated, it was seen that the question objectives met some of those stated in the literature.

MODUL KEMAHIRAN BERFIKIR ALGEBRA UNTUK PELAJAR TINGKATAN SATU

Algebraic Thinking Skills (KBA) is one aspect of skills that students need to master in order to solve non-routine problems. These skills are also needed as a basis for preparing students to enter university studies and job fields that require logical and analytical thinking. However, the performance of Malaysian students in solving algebraic problems has not yet reached a satisfactory level according to the TIMSS 2019 and PISA 2018 reports. Thus, the Algebraic Thinking Skills Module (MBA) was developed to foster KBA through three constructs namely i) arithmetic generalization, ii) functions, and iii) modeling. MBA is developed based on heuristic methods through Polya absorption Model and digital bar. A bar model is a rectangular illustration constructed to represent known and unknown quantities and relationships between quantities. The digital bar model refers to the free application of the bar model at the link https://mathsbot.com/manipulatives/bar. The KBA test was constructed and administered as a pre- and post-test to 120 Form One students from a rural school in Sabah. The results of the paired sample t-test showed that there was a significant difference in the mean score between the pre-test and the post-test (t(119) = -17.553, p < .05) after the intervention using MBA. This shows that MBA can improve KBA through heuristic methods. This innovation is expected to be developed in rural schools to form students who think algebraically and are literate in digital technology.

A Study of Grade Two Students Solving a Non-Routine Problem with Access to Manipulatives

A Study of Grade Two Students Solving a Non-Routine Problem with Access to Manipulatives

Research on Nonroutine Problems: A Hybrid Didactical Design for Overcoming Student Learning Obstacles

The multiplication of fractions was generally considered easy, but it became challenging when presented as a nonroutine problem. One solution to these challenges was integrating technology into learning. Therefore, the study is aimed at proposing a hybrid module as a solution. The design in this research was a didactical design research. The study involved 56 participants, aged 13–18 years, mainly female students from the Sasak tribe in an Indonesian junior high school. Researchers employed fraction comprehension tests, in-depth interviews, and a hybrid hypothesis module as primary instruments. For learning outcomes, NVivo-12-assisted thematic analysis was used, and for learning obstacles, retrospective-based qualitative analysis was used. The study findings revealed several factors that caused learning obstacles, including conceptual ontogenic, epistemological factors, and students’ restricted Internet access. The hybrid hypothesis module proved effective in assisting students by providing additional problem contexts and scaffolding, addressing previous learning obstacles. After implementation, there was a redesign of the hybrid module in the form of additional scaffolding to help students construct the concepts studied. This research concluded that the application of technology in the form of hybrid modules was able to minimize barriers to student learning.

On Cognitive Bias in the Legal Norm Interpretation in Relation to Linguistic Expertise

In the modern rule-making process conduction of several types of expertise is one of the significant and sometimes even mandatory stages of work on a draft law. In the subject of the Russian Federation, a city of federal significance – Sevastopol there is legal, anti-corruption, linguistic and legal-technical expertise carried out. Although the tasks assigned to legal experts and linguists are outlined both in the methodological recommendations of federal authorities and in the scientific-applied discourse, in practice the boundaries of these tasks are blurred. This article focuses on some theoretical and applied questions of linguistic expertise, the case study under discussion demonstrates the interrelation of linguistic expertise with other spheres of expertise and academic work; attention is drawn to the discussion on the boundaries of linguist’s competence and the tasks assigned to the subjects of linguistic expertise. The case-study of the legal norm of the Low of Sevastopol City 98-ZS, dated 26 Dec. 2014, «On some social support measures for multi-child families in Sevastopol» discusses a non-routine problem of the rule of law structure fault that causes cognitive bias in its interpretation. The conclusion summarizes the results of this research, raising some pressing questions, attention to which could contribute to improving the drafting law process, in particular within linguistic expertise.

An Application Based on the 5E Learning Cycle Model Supported by Concept Cartoon with Primary Pre-Service Teachers

The study aims to examine the effect of concept cartoon supported lesson plan development practices based on the 5E learning cycle model on the non-routine problem solving skills and attitudes towards mathematics teaching of primary pre-service teachers, to determine the level of problem construction, to evaluate the texts in the problems constructed with concept cartoons developed by primary pre-service teachers in terms of text writing success level and to reveal their opinions about the practices. The study utilized a nested design, which is a mixed-method research approach, and employed a convenient sampling method for participant selection. Data collection was carried out using the attitude towards mathematics teaching scale, problem solving scale, interview form, and lesson plans developed by primary pre-service teachers. The data were evaluated by content analysis, t-test for related samples, descriptive analysis, progressive scoring scale, problem posing skills scoring key, grading scale. Significant enhancements in attitudes toward mathematics teaching were observed in favor of the post-test, with opinions categorized into six distinct groups, highlighting challenges encountered during the evaluation phase and the process of problem posing. It was ascertained that the overall level of achievement in text creation was generally deemed satisfactory.

The link between teacher-student relationships and non-routine problem solving in ninth-grade mathematics: a moderated mediation model

In this study, we investigated the connections among teacher-student relationships (TSRs), intrinsic motivation, self-efficacy, and non-routine problem solving (NPS) in mathematics with a moderated mediation model. A sample of 3,101 Chinese ninth-graders (1,654 urban students and 1,447 rural students) participated in a large-scale survey. The results showed that intrinsic motivation and self-efficacy mediated the relation between TSRs and NPS, respectively, controlling for SES and gender. Moreover, the positive path coefficients from TSRs to self-efficacy, as well as from both intrinsic motivation and self-efficacy to NPS for rural students were significantly larger than those for urban students. The findings suggest that TSRs support students’ development in solving non-routine problems by boosting their intrinsic motivation and self-efficacy, especially for rural students. These findings extend the literature and provide some implications for educators and instructors.

ANALYSIS ON STUDENTS’ NUMERACY SKILLS IN SOLVING PROPORTION PROBLEMS IN THE CONTEXTS OF CANDI UMBUL TRADITIONAL MARKET

The weaknesses in students' abilities in applying mathematical concepts and rules to non-routine problems caused them difficulties in solving them. This study was aimed at analyzing students' numeracy skills in solving proportion problems with the contexts of Candi Umbul Traditional Market. The study was qualitative descriptive research involving two seventh-grade students in Indonesia as research subjects. The two student subjects were selected from 10 students who completed the numeracy task, one with the most correct answer and one with the most incorrect answer. The ten students who completed the numeracy task were the ones with the highest test scores among 32 students in the topics of proportion and social arithmetics. The research instruments used in the study were students' work sheets (in the form of essay tests) and interviews. The data analysis technique used was descriptive analysis. Findings show that not every student with high math scores had high numeracy skills. This is evident from the fact that students faced problems when completing proportion items in the context of Candi Umbul Traditional Market; they encountered difficulties in solving the problems. The results of this study are expected to serve as a reference for further research on students' numeracy skills.

KAJIAN MENDALAM TENTANG KEMAMPUAN PEMECAHAN MASALAH MATEMATIKA NON-RUTIN SISWA

This study aims to describe non-routine mathematics problem solving in relation to students' self-efficacy and math anxiety. We collect data from journal databases both national and international. The eligibility criteria are used with the keyword "non-routine mathematical problem solving" with intervals of the last 10 years. Based on the results of the synthesis, it was found that several important variables related to the topic were self-efficacy, reading comprehension, mathematic attitudes, think-aloud processes, mathematics anxiety, and truth-seeking. From these variables it was found that self-efficacy (self-confidence) and mathematics anxiety (anxiety mathematics) have an important role in solving non-routine mathematics problems

Ways of thinking siswa dalam menyelesaikan masalah pola bilangan non rutin: Suatu penelitian fenomenologi hermeneutik

This study was conducted with the aim of investigating and exploring students' ways of thinking (WoT) in solving non-routine number pattern problems. This study used a qualitative method with a hermeneutic phenomenological approach with grade 8 students at a junior high school in Banda Aceh. To achieve the research objectives, data collection was carried out using a written test instrument with a number pattern on a 4-digit palindrome, structured documentation, and clinical interviews. The results of the study show that students' WoT in solving non-routine number pattern problems is that there are four approaches used in solving non-routine problems, namely: first, determining the special case; second, determining the pattern; third, using a mathematical model; and fourth, using a similar problem. The subject of critical reflection uses the three WoTs above except for using similar problems. The subject of explicit reflection uses the three approaches above except for using a mathematical model. While Subjects who cannot solve the problem only use the strategy of identifying special cases. Another finding is that the subject of critical reflection tends to use different strategies from those given by the teacher, is unique, and gives reasons for algebraic forms. In contrast, explicit reflection subjects tend to be less flexible in using strategies and tend to use inductive or arithmetic reasons. To support students in their ability to pattern and think algebraically, teachers must accustom students to solving non-routine mathematical problems in various contexts of learning by using number patterns.

INFUSION OF POLYA AND DIGITAL BAR MODEL: AN ALGEBRAIC THINKING MODULE FOR SEVENTH GRADERS

Algebraic Thinking Skills (ATS) are one of the skills that students need to master in order to solve non-routine problems. These skills are also necessary as a foundation for students preparing to enter university studies and fields of work that require logical and analytical thinking. However, Malaysian students' performance in solving algebraic problems still needs to be satisfactory, according to the TIMSS 2019 and PISA 2018 reports. Therefore, the Algebraic Thinking Skills Module (ATSM) was developed to cultivate ATS through three constructs, namely i) arithmetic generalization, ii) functions, and iii) modelling. The ATSM was developed using the heuristic method by infusing the Polya and digital bars model. The bar model illustrates a rectangle representing known and unknown quantities and the relationship between quantities. The digital bar model refers to the free application of the bar model at https://mathsbot.com/manipulatives/bar. An ATS test was developed and administered as a pre-and post-test on 120 seventh graders from rural schools in Sabah. The paired sample t-test results showed a significant difference in the mean scores between the pre-test and post-test after the intervention using the ATSM. This shows that the ATSM can improve ATS through the infusion of the Polya and digital bars model. The ATSM is able to help rural schools to shape algebraic thinkers and digitally savvy students. Keywords: algebraic thinking skills, digital bar model, non-routine problem solving, Polya