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The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look for possible ways for students to develop a way of reasoning to work on problems that involve variational phenomena. Thus, we identified tasks in which calculus students exhibit limited understanding of essential concepts to approach and solve those tasks. The purpose is to illustrate and discuss how the systematic use of a Dynamic Geometry System (DGS) could provide a set of affordances for students to develop ways of thinking to grasp calculus foundational ideas and to study the derivative concept. Here, we relied on Thurston's seminal work that emphasizes the relevance for learners to identify, connect, and coordinate different dimensions and meanings (intuitive, symbolic, algorithmic, geometric, physical, and formal) to construct, understand, and apply the concept of derivative. [ABSTRACT FROM AUTHOR]

How can students effectively learn and transfer mathematical procedures to solve new problems? Here, we tested the effects of deliberately committing and correcting errors during mathematical problem-solving practice on transfer of the learned procedures. In two experiments, university students were instructed on mathematical algorithms (synthetic division and matrix multiplication) and solved practice problems during open-book study. Learners were then tested on flexibly adapting the algorithms to solve novel problems that were structurally more complex or embedded in "real-life" scenarios (i.e., mathematical word problems). Deliberately committing and correcting procedural errors during problem-solving practice yielded better transfer than errorless repeated practice (Experiment 1) or studying incorrect worked examples by finding, explaining, and correcting the errors that one's peers had made (Experiment 2). Yet, most learners failed to accurately predict or recognize the advantage of deliberate erring even after the test, instead misjudging this technique as less effective. This suggests that experiencing the benefit of deliberate erring is insufficient to dispel learners' metacognitive illusion that generating errors is not helpful for their learning. Overall, our results point to the critical role of first-hand errors in mathematical learning. Relative to avoiding errors or even studying others' errors and juxtaposing them with the correct solutions, guiding learners to deliberately commit and correct their own errors after instruction improves mathematical problem solving and transfer. Educational Impact and Implications Statement: Transfer of learning lies at the heart of education, but is often difficult to achieve. Here, we show in the domain of mathematics that deliberately committing and correcting procedural errors during problem-solving practice enhances students' transfer of the learned procedures to solve novel, more challenging problems. Deliberate erring was not only more effective than errorless repeated practice, but also finding, explaining, and correcting others' errors in incorrect worked examples. These results expand our repertoire of approaches to harness the power of errors for improving mathematical problem solving and transfer in education. [ABSTRACT FROM AUTHOR]

Self-regulation in mathematical problem solving is of particular importance in the initial training of Primary Education teachers as it can contribute to improving their own competence in mathematics and at the same time enable them to teach effectively and in a personalized way. With this idea in mind, this study identifies self-regulation profiles present in university students in mathematical problem-solving contexts based on data from the application of a validated scale on a sample of 402 pre-service teachers of primary education at University of the Basque Country. The cluster analysis carried out made it possible to identify and characterize three profiles, labelled according to the level of self-regulation represented by each of them (low, medium, high). In view of the results obtained, we perceive a need to design didactic proposals that allow these profiles to evolve from the lowest to the highest levels. [ABSTRACT FROM AUTHOR]

The teaching of Mathematics is present in the most diverse training programs. Its teaching cannot be seen as a simple activity, but it requires methods and strategies that facilitate its teaching and understanding of the contents by students, the game, without a doubt, constitutes an important strategy. The objective of this study was to implement didactic strategies based on games to improve the ability to solve mathematical problems in third grade students of Basic General Education Dr. Carlos Manuel Espinoza Educational Unit. The use of different methods and techniques, used from a mixed approach, allowed us to know the main difficulties present in the resolution of mathematical problems and the possibility of applying the game as a didactic strategy. The organization of the research in two phases guaranteed a better execution of the same, allowing the results to be achieved in an orderly manner, as well as to use at all times the necessary didactic actions based on the game. The consultation with experts, carried out as part of the validation of the didactic strategy, offered favorable criteria in all the aspects consulted for the study. This evidenced coherence and effectiveness in the main aspects analyzed in the research, as well as an important positive transformation in the improvement of the performance and performance of students in relation to the resolution of mathematical problems. [ABSTRACT FROM AUTHOR]

The implementation of ludic approaches in the teaching of mathematics has generated a growing interest due to its potential to improve learning and academic performance in this discipline. The objective of this study was to design a system of ludic tasks for the development of mathematical problem-solving skills in sixth grade elementary school students. The sample consisted of 43 sixthgrade students of the Luis Alfredo Noboa Icaza Educational Unit during the 2023-2024 school year, divided into an experimental group (n=22) and a control group (n=21). A combination of classroom observation, pre-and post-tests, validation by expert criteria and statistical analysis was used, including the Mann-Whitney U test. The results revealed that the experimental group experienced significant improvements compared to the control group in terms of cognitive, procedural, and attitudinal skills related to mathematical problem-solving. The implementation of playful activities such as the "Math Treasure Hunt" and the "Math Problem Challenge" fostered a stimulating educational environment that promoted active participation, collaboration among students, and the practical application of mathematical concepts. These findings suggest that the integration of playful tasks in the curriculum can be an effective strategy to improve mathematics learning at the elementary school level. [ABSTRACT FROM AUTHOR]

The development of skills and abilities to solve mathematical problems is essential for 4th year students of Basic General Education (EGB). Effective methodological strategies can significantly improve mathematics learning and prepare students to successfully face academic and real-life challenges. The objective of this research is to design a teaching guide to improve the development of skills and abilities in solving mathematical problems in 4th EGB students in the “Julio Peña Bermeo” Private Educational Unit. The research employs a mixed approach, combining qualitative and quantitative methods to collect and analyze data. Interviews were conducted with teachers and education experts about the development of skills and abilities for solving mathematical problems. The research provided teachers with a teaching guide that allowed them to improve the didactic way of teaching content. The experimental results show a significant increase in the development of skills and abilities for solving mathematical problems after the research was implemented. [ABSTRACT FROM AUTHOR]

In this study, effects of asking participants to make different types of considerations when solving a realistic word problem were investigated. A two-factorial experiment with the factors "addressing realistic considerations" (with vs. without) and "addressing mathematical operations" (with vs. without) was conducted. It was assumed that reality-based considerations would lead to reality-based problem-solving strategies, thus fostering real-life solutions, while considering mathematical operations would lead to problem-solving strategies usually promoted in school, which were expected to impair realistic solutions. Analyses are based on N = 165 participants. The results showed that being asked to make reality-based considerations did not significantly affect realistic solutions (F(1, 161) = 2.43, p = 0.121, ηp2 = 0.015), while being asked to consider appropriate mathematical operations significantly impaired realistic solutions (F(1, 161) = 8.54, p = 0.004, ηp2 = 0.050). These findings suggest that inducing typical school problem-solving strategies may be detrimental when it comes to solving mathematical problems in a realistic way. [ABSTRACT FROM AUTHOR]

Mathematics in SMK is a general subject that must be understood, in fact many students avoid mathematics, one of the reasons is because the teaching materials have not facilitated the characteristics of students. The purpose of this study is to evaluate the validity, application, and effectiveness of digital entrepreneurship-based mathematics modules in improving students' problem-solving abilities. With students from class XI vocational courses, this research applies the ADDIE paradigm. Data were obtained using Entremath validation questionnaires, student and teacher response questionnaires, and post-test scores. The results show that mathematics is entrepreneur-based. Entremath is considered to fall under the very valid criteria. It is declared practical, with 86.9% of students and 96% of teachers belonging to the very practical category, and effectively denoted by a sig value greater than table t. The results of entrepreneurial mathematics research contain qualities that can be used for mathematics education Matematika di SMK merupakan mata pelajaran umum yang harus dipahami, nyatanya banyak siswa yang menghindari matematika, salah satu penyebabnya adalah karena bahan ajar yang belum memfasilitasi karakteristik siswa. Tujuan penelitian ini adalah untuk mengevaluasi validitas, penerapan, dan efektivitas modul digital matematika berbasis kewirausahaan dalam meningkatkan kemampuan pemecahan masalah siswa. Dengan peserta didik kelas XI program studi SMK, penelitian ini menerapkan paradigma ADDIE. Data diperoleh dengan menggunakan angket validasi Entremath, angket respon siswa dan guru, serta nilai post-test. Hasilnya menunjukkan bahwa modul digital matematika berbasis wirausaha dianggap masuk dalam kriteria yang sangat valid. Dinyatakan praktis, dengan respon positif 86,9% dari siswa dan 96% dari guru termasuk dalam kategori sangat praktis, dan efektif ditunjukkan dengan nilai sig lebih besar dari t tabel. Hasil penelitian matematika kewirausahaan mengandung kualitas yang dapat digunakan untuk pendidikan matematika.

Self-proficiency, distinct from self-efficacy, is a more comprehensive dimension in assessing students’ abilities. Moreover, the TAI cooperative learning model is believed to be relevant in enhancing self-proficiency, as well as other mathematical ability dimensions, particularly in Statistics course. Therefore, this study aimed to assess the enhancement of self-proficiency, mathematical problem-solving and mathematical communication by implementing the TAI (Team-Assisted Individualization) Cooperative Learning Model in the context of Non-Parametric Statistics, which is a core undergraduate statistics course. A quasi-experimental approach with purposive sampling, which comprised 72 observation samples divided into control and experimental groups, was used to conduct this study. Evaluation instruments consisted of mathematical problem-solving test, mathematical communication test, and self-proficiency test, along with observation sheets. Furthermore, these statistical analysis tools were used included the Paired Sample t-test, the Independent Sample t-test, as well as the ANCOVA (Analysis of Covariance). The results, obtained through various assessments that examined mean differences and comprehensive statistical analyses, comprised both independent and dependent sample evaluations. The evaluations consistently showed substantial increase in problem-solving ability, communication skills, and self-proficiency in the cohort subjected to the experimental conditions, surpassing those observed in the control group. The ANCOVA estimations further validated the meaningful effect of the teaching strategy on the enhancement of the tested aspects. In conclusion, this study implied that the implementation of TAI learning model effectively enhanced all three objectively and measurably assessed aspects, particularly in the context of non-parametric statistics course.

In tracing recent research trends and directions in mathematical problem-solving, it is argued that advances in mathematics practices occur and take place around two intertwined activities, mathematics problem formulation and ways to approach and solve those problems. In this context, a problematizing principle emerges as central activity to organize mathematics curriculum proposals and ways to structure problem-solving learning environments. Subjects' use of concrete, abstract, symbolic, or digital tools not only influences the ways to pose and pursue mathematical problems; but also shapes the type of representation, exploration, and reasoning they engage to work and solve problems. Problem-solving foundations that privilege learners' development of habits of mathematical practices that involve an inquiry method to formulate conjectures, to look for different ways to represent and approach problems, and to support and communicate results shed light on directions of current research trends and the relevance of rethinking curriculum proposals and extending problem-solving environments in terms of teachers/students' consistent use of digital tools and online developments. [ABSTRACT FROM AUTHOR]

Self-regulation in mathematical problem solving is of particular importance in the initial training of Primary Education teachers as it can contribute to improving their own competence in mathematics and at the same time enable them to teach effectively and in a personalized way. With this idea in mind, this study identifies self-regulation profiles present in university students in mathematical problem-solving contexts based on data from the application of a validated scale on a sample of 402 pre-service teachers of primary education at University of the Basque Country. The cluster analysis carried out made it possible to identify and characterize three profiles, labelled according to the level of self-regulation represented by each of them (low, medium, high). In view of the results obtained, we perceive a need to design didactic proposals that allow these profiles to evolve from the lowest to the highest levels.

Consider a 1 x 3 grid whose top-left vertex is connected to the bottom-right vertex of each of the unit squares. What is the sum of the three acute angles formed by the connecting segments with the unit squares' bases? This is the so-called three-squares problem, often attributed to Gardner. In a recent academic year, the author used a video on this problem, produced by the YouTube channel Numberphile, for a group project in a first-semester undergraduate module: Mathematical Problem Solving. The project involved collaborative writing on the problem and individual completion of a peer-assessment form. We report the outcomes of this project, which give rise to both theoretical and pedagogical discussions. The theoretical discussion comprises seven alternative solutions to the problem, as well as a generalisation to the case of identical parallelograms forming an arbitrary-sized grid whose top-left vertex is connected to the bottom-right vertex of each parallelogram. The pedagogical discussion highlights the peer-assessment form's effectiveness in detecting unequal group members' contribution, as well as the students' inadequate communication skills. The latter, which has consistently raised concerns, subsequently led to the module being developed and renamed as Mathematical Writing and Reasoning, whose realisation commenced the following academic year. [ABSTRACT FROM AUTHOR]

The William Lowell Putnam Mathematical Competition is an intercollegiate mathematics competition for students in the United States and Canada and is regarded as the most prestigious and challenging mathematics competition in North America (Alexanderson, 2004; AMS, 2020; Grossman, 2002; Reznick, 1994; Schoenfeld, 1985). Students who earn the five highest scores on the examination are named Putnam Fellows. Since its inception in 1938, only 306 individuals have won the competition and a select few have won multiple times. Clearly, being named a Putnam Fellow is a remarkable achievement and therefore, understanding the factors and characteristics that contribute to their success is important for students interested in mathematics and STEM-related fields. Twenty-five males who were named Putnam Fellows either four, three, or two times were recruited for the study. A 17-item questionnaire was created from various research sources (Campbell, 1996a, 1996b; Campbell & Wu, 1996; DeFranco, 1996), and used to collect information around four broad areas--personal experiences, formal educational experiences, the affective domain and the cognitive domain. Qualitative research techniques were used to analyze the data. The results indicated that four subcategories of personal experiences, five subcategories of formal educational experiences, seven subcategories involving the affective domain, and three subcategories of the cognitive domain all played an important role in the development of Putnam Fellows. Future research recommendations should examine the factors and characteristics of female Putnam winners and ways to promote and support them as well as the role that Pólya-like heuristics play in the development of Putnam winners. [ABSTRACT FROM AUTHOR]

This research aims to examine the use of learning media that is good, effective and appropriate to the needs and characteristics of students through YouTube media and Learning Blogs and its relationship with mathematical problemsolving abilities and learning achievement. The method used was quantitative quasi-experiment with correlation tests on mathematical problem solving abilities and learning achievement for classes VIII C and VIII D at SMP Tarakanita 2 Jakarta with 58 respondents. The Cronbach's Alpha test on the YouTube media test instruments (0.83), Blog (0.82), Problem Solving (Pretest 0.92 and Posttest 0.86), and Achievement (0.90) shows high validity and reliability. Based on non-parametric hypothesis testing using the Spearman Test method, it is known that there is a correlation between the use of YouTube media and Problem Solving (R-count 0.37), YouTube and Achievement (R-count 0.41), Blogs and Problem Solving (R-count 0. .42), and Blog with Achievement (R-count .39). The non-parametric Mann Whitney test in the control class and experimental class regarding achievement was stated to be identical with the same mean and variance so that there was no difference in the increase in NGain in the two classes. [ABSTRACT FROM AUTHOR]

The current study investigated how and when two different aspects of teacher-student relationship (TSR; closeness and conflict) influence students' mathematical problem solving ability. Participants were 9163 eighth-grade Chinese adolescents (53.5% male) nested in 908 schools, who took part in a standard mathematics assessment and survey using student questionnaires that were all developed by the Collaborative Innovation Center of Assessment toward Basic Education Quality (CICA-BEQ) in China in 2015. The results indicated that (a) after controlling the factors of gender and SES, teacher-student closeness had a significant and positive effect on mathematical problem solving, while teacher-student conflict did not, (b) the mediating role of mathematical self-efficacy in the relationships of TSRs and mathematical problem solving was confirmed, and (c) school climate negatively moderated the indirect relationships between TSRs and mathematical problem solving. [ABSTRACT FROM AUTHOR]

This study examines relationships between mathematical problem-solving performance (in terms of strategies used and accuracy) and the main cognitive domains associated with mathematical learning (i.e. executive functions, verbal comprehension and social perception) of children with and without autism spectrum disorder (ASD and non-ASD resp.). The study involved 26 ASD and 26 non-ASD children without intellectual disabilities, between 6 and 12 years old, matched by sex, age and school (grade and classroom). The results show a higher percentage of ASD children with problem solving difficulties than non-ASD (57% vs. 23% resp.). Poor performing ASD children showed comparatively lower scores in inhibition, theory of mind and verbal comprehension. Implications for the design of mathematical interventions for ASD students are discussed. [ABSTRACT FROM AUTHOR]

In task-based mathematics classes, where several solution approaches may be valid, diagnosing students’ solution processes and adaptively supporting them is a significant challenge for teachers. The question arises as to how mathematics teachers can successfully support students in solving these mathematical tasks and which aspects constitute adaptive teaching interventions. However, few studies have analyzed adaptive teaching interventions in the context of mathematics didactics. This paper first presents a detailed model of adaptive teaching interventions. Based on this model, the interventions of four secondary school mathematics teachers were analyzed using two methodological approaches. The applicability of the model was analyzed, and factors that hinder the adaptivity of teachers’ interventions were identified. The results show that 41–63 % of all identified teaching interventions were adaptive. Up to 55 % of the teachers’ interventions took place even though the students were not facing barriers within their learning processes. The sampled teachers faced major difficulties in diagnosing and in addressing the barriers in students’ solution processes. Furthermore, up to 65 % of all teaching interventions analyzed did not enable students to overcome barriers in their solution processes.

Bu çalışmanın amacı; TR Dizin’de yayımlanan Türkiye’deki eğitim fakülteleri dergilerine ait matematiksel problem çözme ile ilgili makalelerin betimsel içerik analizinin yapılıp genel eğiliminin belirlenmesidir. TR Dizin’de yayımlanan eğitim fakülteleri dergilerine ait matematiksel problem çözme çalışma alanını konu edinmiş ilk makalenin yayım yılı olan 2004 yılından 2022 yılının sonuna kadar yayımlanan tüm makaleler incelenmiş ve 110 makale çalışmaya dâhil edilmiştir. Araştırma kapsamında hazırlanan araştırma kapsamında hazırlanan "TR Dizin’de Yayımlanan Matematiksel Problem Çözme Temalı Makaleleri İnceleme Formu" çerçevesinde makaleler incelenmiştir. İlgili makaleler alt problemler çerçevesinde belirlenen kategoriler kapsamında analiz edilmiştir. Oluşturulan kategorilere ait frekans ve yüzde dağılımları Microsoft Excel programı yardımıyla hesaplanmış ve ulaşılan veriler ise tablolar yardımı ile detaylı bir şekilde sunulmuştur. Araştırmanın sonuçlarına göre; matematiksel problem çözmeyle ilgili en çok 7.sınıf öğrencileriyle çalışmalar yapıldığı, nicel araştırma yöntemlerinin seçildiği, nicel analizlerin yapıldığı ve veri toplama aracı olarak anket ve ölçeklerin daha çok tercih edildiği sonuçlarına ulaşılmıştır. Çalışmadan elde edilen sonuçların bu konu alanında gerçekleştirilen çalışmaların güçlü ve eksik yönlerini görme açısından yararlı olacağı ve matematiksel problem çözmeye yönelik çalışmaların eğiliminin bütüncül bir bakış açısıyla görülebilmesi açısından gelecek çalışmalara rehber olabileceği düşünülmektedir.

Students' ability to solve mathematical problems is the most important part of learning mathematics. Therefore, assessing students' ability to solve mathematical problems is one of the tasks of mathematics teachers that must be done. This study aims to develop a test instrument to assess students' ability to solve mathematical problems. The research method used Systematic Literature Review (SLR) by analyzing primary sources from books and articles. Before developing an instrument to assess students' ability to solve mathematical problems, the variables involved in mathematical problem solving were first analyzed. Furthermore, there are four domains involved in the instrument development framework carried out. They are resources, heuristics, control, and belief system. Based on this study, it was found that: (1) the aspects correlated with mathematical problem solving are reasoning, decision making, critical thinking, and creative thinking; (2) the types of tasks related to mathematical problem solving can be viewed from the structure, the number of essential steps needed to reach the solution, its orientation, and its presentation.

Metacognition-related studies often focus on the knowledge, regulation, and experience components but little on the instructional strategies used. In particular and especially within the Indian context, not much focus is given regard to a clear and coherent academic framework that reinforces the use of metacognitive instructional strategies in mathematical problem solving amongst undergraduate students. Using a quasi-experimental method, the purpose of this study is to look closely into the use of metacognitive instructional strategies by undergraduate students. Eighty-four students participated and initial data were collected using the prepared mathematical problem-solving test based on competitive examinations. Single group pre-test and post-test focus group design and the test comparison method were used to analyze the data collected. Findings revealed undergraduate students in the focus group do differ significantly in their mathematical problem solving competence and use of metacognitive instructional strategies between the pre-test and the post-test. The findings shed some light on the distinct role of metacognitive instructional strategy and some ensuing factors during mathematical problem solving in competitive examinations.

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Adversity Qoutient (AQ) is a person's intelligence in dealing with difficulties or problems. Each student has a different AQ which has implications for the process of solving different mathematical problems. This study aims to analyze mathematical problem solving ability in terms of adversity quotient through guided inquiry assisted by GeoGebra. This research was conducted during one semester of the 2019/2020 academic year. The population in the study were all students of grade XI of the Shipping Vocational School in the Technika Expertise Program. The research sample selected one class as an experimental class totaling 45 students and one class as a control class totaling 34 students. The data sources in this study are problem solving ability test answer sheets, AQ questionnaires and interviews. The results of the study showed that students' mathematical problem solving ability through guided inquiry learning assisted by GeoGebra achieved learning completeness with several categories, including: quitters category students in solving problems are able to understand the problem by writing what is known and what is asked and explaining the problem in their own sentences but sometimes these students are still in doubt in answering; camper category students are able to understand the information contained in each item, able to state the problem using their own language, able to write and explain the problem solving plan coherently, able to plan problem solving properly and correctly, but some students with this category are less careful and rarely double-check how they solve problems according to what is expected in the problem and the steps of mathematical problem solving skills; Students with the climber category are able to plan problems well, able to write and explain problem solving plans coherently and correctly and include formulas that are relevant to the plans written down, carry out calculations in accordance with the plans that have been made so that the answers obtained are right in accordance with the objectives in the problem, able to write and explain other ways to solve the problems contained in the problem. [ABSTRACT FROM AUTHOR]

Abstrak Pelaksanaan pembelajaran matematika memiliki tujuan utama yaitu memperkuat kemampuan peserta didik dalam memecahkan masalah. Namun, Kemampuan peserta didik dalam memecahkan masalah masih terbilang minim. Untuk mengetahui seberapa baik siswa dapat memecahkan masalah adalah tujuan dari penelitian ini dan mencari tahu efek serta korelasi antara tingkat resiliensi matematis yang dimiliki peserta didik dengan kemampuan mereka dalam pemecahan masalah matematis. Penelitian ini menggunakan metode penelitian kuantitatif dengan pendekatan berbasis survei. Penelitian ini dilakukan dengan menggunakan sampel dari peserta didik kelas XI IPS SMA Negeri 106 Jakarta sebanyak 67 peserta didik kelas XI IPS SMA Negeri 106 Jakarta yang dipilih menggunakan teknik simple random sampling. Penelitian dimulai dengan menyebarkan angket kepada peserta didik untuk mengukur resiliensi matematis mereka serta menyebarkan soal tes matematika untuk mengetahui ukuran kapasitas seseorang untuk memecahkan permasalahan matematis. Berlandaskan hasil pengujian analisis regresi linier sederhana menggunakan aplikasi IBM SPSS yakni menunjukkan besar nilai koefisien korelasinya R yaitu 0,577 dengan R2 = 33,30%. Dari hasil pengujian tersebut mengindikasikan besar efek resiliensi matematis mencapai 33,30% pada kemampuan pemecahan masalah matematis peserta didik. Abstract The primary objective of implementing mathematics instruction is to improve students' problem-solving skills. Nonetheless, the problem-solving skills of students remain limited. The purpose of this research is to determine how effectively students can solve issues, as well as the influence and association between their degree of mathematical resilience and their capacity to solve mathematical difficulties. This research utilizes a survey-based quantitative research methodology. This research was conducted using a sample of students from class XI IPS SMA Negeri 106 Jakarta. 67 students from class XI IPS SMA Negeri 106 Jakarta were recruited using a technique of simple random sampling. The project was initiated by providing questionnaires to students to gauge their mathematical resilience and math exam questions to determine a person's capacity to solve mathematical difficulties. Based on the findings of a basic linear regression analysis using the IBM SPSS program, the correlation coefficient R is calculated to be 0.577, with R2=33.30 %. The test findings suggested that mathematical resilience has a 33.30 % impact on pupils' arithmetic problem-solving skills.

Abstract: Today's educational requirements for entering society 5.0 include requirements for being able to change with the times. The availability of technology plays a significant role and can act as a bridge for educators and students to develop cognitive abilities including conceptual understanding and quantitative problem-solving in the classroom. The study's objectives are to evaluate (1) the ADDIE model's application to the development of animated video media, and (2) the impact of this media on students' conceptual comprehension and capacity for mathematical problem-solving. The method used in the form of Research and Development (R&D) with data collection techniques in the form of observations, interviews, tests and questionnaires with the research population is class VIII-A students with a total of 24 students. Meanwhile, the analysis used inferential statistics in the form of t-test and NGain and descriptive statistics in the form of percentages. Meanwhile, the population of VIII MTs Negeri 6 Mandailing Natal school for the 2020/2021 school year in class VIII-A is 24 students. (1) The study's invention, an ADDIE model with reliable and applicable test results, is one of its findings;(2) The effectiveness of anismation video media may be said to be effective (70.32) for resolving student issues and has a significant impact with a value of (0.00 0.05). However, it can be argued that it is effective (78.4) for helping students learn concepts. The findings of the research and development study on animated videos are significant for enhancing concept comprehension and helping students in the classroom solve mathematical issues. Abstrak: Dewasa ini, memasuki society 5.0 dunia pendidikan memiliki tuntutan berderet untuk dapat beradaptasi perkembangan zaman. Eksistensi teknologi menjadi peranan penting dan dapat menjadi perantara pendidik dan terdidik untuk meningkatkan keterampilan berpikir seperti pemahaman konsep dan pemecahan masalah matematis di kelas. Tujuan penelitian untuk menganalisis (1) Pengembangan media video animasi dengan model ADDIE; (2) Efektivitas media video anismasi terhadap pemahaman konsep dan pemecahan masalah matematis peserta didik. Metode yang digunakan berupa Research and Development (R&D) dengan teknik pengumpulan data berupa observasi, wawancara, tes dan angket dengan populasi penelitian adalah siswa kelas VIII-A dengan jumlah 24 siswa. Adapun, analisis yang digunakan statistik inferensial berupa t-test dan NGain serta statistik deskriptif berupa persentase. Adapun, populasi VIII MTs Negeri 6 Mandailing Natal school tahun ajaran 2020/2021 pada kelas VIII-A yang berjumlah 24 siswa. Hasil penelitian meliputi (1) Pengembangan yang digunakan berupa model ADDIE dengan hasil pengujian valid dan praktis; (2) Efektivitas media video anismasi dapat dikatakan efektif (78,4)untuk pemahaman konsep peserta didik dan berpengaruh secara signifikan dengan nilai (0,00

This study seeks to determine the impact of the Problem-Based Learning (PBL) model supplemented with higher-order thinking skills (HOTS) problems on the mathematical problem-solving skills of high school students. The research employs a quantitative approach, specifically through adopting a quasi-experimental method with a post-test-only non-equivalent control group design. The participants consist of 72 tenth-grade students, with half (36 students) exposed to the PBL model enriched with HOTS problems, and the other half exposed to the standard PBL model without HOTS problems. A descriptive test comprising five mathematical problem-solving items was administered to measure the impact. This test was rigorously validated by two professors from UHAMKA and further validated by students from another tenth-grade class. The data analysis was conducted using the Non-Parametric Mann-Whitney test. The findings suggest a noteworthy difference in mathematical problem-solving abilities between students instructed using the PBL model integrated with HOTS problems and those who did not.

Mathematical problem solving is a process involving metacognitive (e.g., judging progress), cognitive (e.g., working memory), and affective (e.g., math anxiety) factors. Recent research encourages researchers who study math cognition to consider the role that the interaction between metacognition and math anxiety plays in mathematical problem solving. Problem solvers can make many metacognitive judgments during a math problem, ranging from global judgments such as, "Do I care to solve this problem?" to minor cue-based judgments such as, "Is my current strategy successful in making progress toward the correct solution?" Metacognitive monitoring can hinder accurate mathematical problem solving when the monitoring is task-irrelevant; however, task-relevant metacognitive experiences can lead to helpful control decisions in mathematical problem solving such as checking work, considering plausibility of an answer, and considering alternate strategies. Worry and negative thoughts (i.e., math anxiety) can both interfere with the accuracy of metacognitive experiences as cues in mathematical problem solving and lead to avoidance of metacognitive control decisions that could otherwise improve performance. The current paper briefly reviews and incorporates prior literature with current qualitative reports (n = 673) to establish a novel framework of regulated attention in mathematical problem solving (RAMPS). [ABSTRACT FROM AUTHOR]

This study was conducted to examine peer tutoring models in collaborative learning of mathematical problem solving (MPS) in flipped classrooms and their effect on group achievement. Quantitative data collected include 32 videos of eight groups of students in four MPS periods that were designed based on a simplified version of Polya's four-stage model, and their worksheets completed in each period. The video data were coded based on a framework with low-level and high-level cognitive behaviors as well as management behaviors and were analyzed using lag sequence analysis from which three types of peer tutoring models were determined: organization-oriented, cognitive-supported, and cognitive-guided. ANOVA analysis showed that the groups with cognitive-guided tutors performed significantly better than the groups guided by cognitive-supported and organization-oriented tutors, between which the performance difference did not reach a significant level. The results of this study suggest that training provided to peer tutors should focus more on how to stimulate high-level cognitive thinking skills than on organization skills. [ABSTRACT FROM AUTHOR]

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The ability to solve problems is one of the cognitive abilities in mathematics that need to be mastered by students. In supporting mastery to solve problems, it is necessary to have the motivation to learn for students. This study aims to determine the relationship between learning motivation to students' mathematical problem-solving. The research method used is the correlation method with a quantitative approach. The population of this study was all students of class XI at Toma Nasional high school 2 and the sample selected was class XI science majors which collected 15 students. The instrument used in this research is a test to measure the ability to solve problems in the form of an explanation of 3 questions, while the non-test instrument to measure the level of learning motivation is in the form of a scale in the questionnaire. Data were analyzed using Pearson's product-moment correlation test. The results of this study indicate that at a significance level of 0.05 there is a relationship between learning motivation and students' problem-solving abilities. In addition, the linear regression equation Y = 12.964+0.422X is obtained, which means that for every additional 1 value of learning motivation, the mathematical problem-solving ability increases by 0.422.

There are many studies that examine students' abilities, but there are still few that examine students' ability to solve PISA problems with konten space and shape. This research uses Polya indicators, namely understanding problems, planning for problem solving, implementation of planning, and re-checking. Describing students' ability to solve problems with PISA questions reviewed from gender differences is the goal of this study. The method used is qualitative with a data triangulation technique that takes data by the test method and interviews involving 6 subjects consisting of 3 male subjects and 3 female subjects. The result of this study is that female students are superior to male students in problem-solving ability. Lack of scrupulousness makes male students in problem-solving ability under female students. Mistakes in male students that often occur are at the stage of carrying out problem-solving planning and re-checking the results of the answers obtained, while female students only occur during the re-checking process.

Research has revealed that both cognitive factors, such as knowledge, problem solving strategies and affective factors, such as motivation and emotions, strongly influence mathematical problem solving. However, few studies have examined the content specificity and generality of the relationship between mathematical problem solving and affective factors. This study examines the content specificity and generality of the relationship between mathematical problem solving, task value, math anxiety and engagement among high school students. Japanese second-year high school students (n = 240) completed questionnaires. The multilevel structural equation modelling revealed that utility value for entrance examinations and emotional engagement positively affected mathematical problem solving via cognitive engagement between various contents level. Emotional engagement positively affected mathematical problem solving via cognitive engagement within a certain content level. The results suggest that promoting the perception that learning mathematics has high utility value for university entrance examinations across various contents can increase students’ cognitive engagement and, therefore, improve mathematical problem solving. Furthermore, both increasing students’ emotional engagement only when they learn certain content and consistently increasing it may improve cognitive engagement and, therefore, allow learners to better solve mathematical problems. The study’s findings have significant implications for educational practice and mathematical problem-solving research.

Although working memory (WM) is an important factor in mathematical problem solving (MPS), it remains unclear how well WM relates to MPS. Thus, we aimed to determine this relationship by using a meta-analysis. We searched electronic databases for studies published between 2000 and 2020 and established operational criteria. We conducted Egger's regression tests and created funnel plots to test for publication bias. Finally, a three-level meta-analytic model analysis of data from 130 studies involving 43,938 participants and 1,355 effect sizes revealed a moderate relationship between WM and MPS (r = 0.280, 95% CI = [0.263, 0.314]). Moreover, moderator analyses showed that: (1) dressed-up word problems were more strongly tied to WM than to intra-mathematical problems; (2) the central executive function showed the strongest relation with MPS, whereas the phonological loop had the weakest; (3) gender ratio had significant moderating effects; and (4) some of the above-mentioned significant moderating effects were unique after controlling for other factors. Implications for research and practice were also discussed. [ABSTRACT FROM AUTHOR]

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The COVID-19 pandemic and the requirement for social distancing led to the closure of extracurricular activities that usually involve teamwork and collaboration, such as math clubs. Research on the design and effectiveness of extracurricular mathematical activities that aim to promote student interest and improve mathematical skills is limited, particularly in these challenging times. This exploratory case study examines an online after-school program, the Tecn@Mat Club, aimed at promoting middle grade students' ability in solving mathematical problems with digital technologies during the pandemic. Based on document analysis, observation of the club sessions, questionnaires, and interviews with the participants (students and a mathematics education expert), this research documents the design and implementation of the Tecn@Mat Club, as well as its participants' experiences and perspectives regarding the activity in which they engaged. The main results show the feasibility of adapting in-person, after-school math activities for an online setting, engaging middle grade students in mathematical problem-solving with technology by providing moderate mathematical challenges and promoting collaborative work. Results of a SWOT analysis (the acronym for strengths, weaknesses, opportunities, threats) allow for the identification of the key features to preserve and challenges to overcome in future replications of the club. Limitations of this study and future research directions are discussed. [ABSTRACT FROM AUTHOR]

Learning mathematics is considered a difficult subject for students. Learning difficulties experienced by students often have an impact on the lack of awareness of the importance of mathematics in students' daily life. Optimization of learning mathematics with problem-based learning can be applied using the 3N teachings of Tamansiswa concepts, namely Niteni, Nirokke, Nambahi. This research is qualitative in the form of a literature review. This article describes how teachers can optimize PBL with Tamansiswa teachings in learning mathematics so that students become enjoy, more effortless, and responsive in applying mathematical concepts in daily life.

This study was motiviated by a situation where grade 2 elementary students studying mathematics were not demonstrating responsibility in daily tasks, were challenged in mastering mathematical concepts, and were lacking optimal problem-solving skills. The purpose of this study was to analyze the increased responsibility, improved conceptual understanding, and improved mathematical problem-solving skills of grade 2 elementary students using the Concrete-Pictorial-Abstract (CPA) approach with multiplication and division concepts. This study adopted class action research consisting of three cycles. Each cycle consisted of four stages, namely planning, action, observation, and reflection. The research subjects were 15 grade 2 elementary school students. This research was conducted at SDS XYZ, Jakarta. The data was collected through observations, tests, and documentation. The instruments used in this study were assessment rubrics and test questions. The results of this study have revealed that the application of the Concrete-Pictorial-Abstract (CPA) approach can improve responsibility with scores of 53.2, 54.9, and 62.6 respectively from cycle I to cycle III although the specified standard score was not reached. There was also evidence of improved conceptual understanding with scores of 73.3, 74.5, and 80.2 and mathematical problem-solving skills with scores of 72.1, 78.8, and 85.8 respectively from cycle I to III. BAHASA INDONESIA ABSTRACT: Dilatarbelakangi oleh kondisi kurangnya sikap tanggung jawab siswa dalam mengembangkan tugas dikehidupan sehari-hari, rendahnya kemampuan penguasaan konsep Matematika, serta belum optimalnya kemampuan pemecahan masalah siswa kelas II SD dalam pembelajaran Matematika, dan kurang bervariasinya metode yang digunakan, sehinggga pembelajaran tidak kondusif menjadi bahan penelitian tesis ini. Tujuan Penelitian adalah untuk menganalisis peningkatan tanggung jawab, kemampuan penguasaan konsep, dan kemampuan pemecahan masalah siswa kelas II SD melalui pendekatan Concrete-Pictorial-Abstract (CPA) pada pokok bahasan perkalian dan pembagian. Penelitian ini merupakan penelitian tindakan kelas yang terdiri dari tiga siklus. Di mana setiap siklus terdiri dari empat tahap yaitu perencanaan, tindakan, observasi, dan refleksi. Mengambil tempat penelitian di SDS XYZ, Jakarta, subjek penelitian melibatkan 15 siswa kelas II SD. Pengumpulan data dalam penelitian ini dilakukan dengan menggunakan observasi, tes, dan dokumentasi. Sedangkan instrumen yang digunakan adalah rubrik penilaian dan soal tes. Hasil penelitian menunjukkan bahwa penerapan pendekatan Concrete-Pictorial-Abstract (CPA) dapat meningkatkan sikap tanggung jawab dengan nilai rata-rata siklus I 53.2, siklus II 54.9, dan siklus III 62.6, namun begitu, angka tersebut belum berhasil mencapai standar nilai yang ditentukan. Dengan CPA, siswa dapat meningkatkan kemampuan penguasaan konsep matematika dengan nilai siklus I 73.3, siklus II 74.5, dan siklus III 80.2. Tidak hanya itu, pendekatan ini juga dapat meningkatkan kemampuan pemecahan masalah matematika siswa dengan nilai siklus I 72.1, siklus II 78.8, dan siklus III 85.8.

In the classrooms, teachers faced the dilemma of whether or not to use virtual environments to continue teaching, because students were able to pose and solve mathematical problems with the help of ICT. The objective is to analyze the student's perspectives when applying real situations, remote real situations and situations from the mathematical poem to solve the posing and solving of mathematical problems. The methodology is descriptive, quantitative, exploratory and observational, with a sample of 72 elementary school students. Resulting significant effects and positive acceptance of the methodology. In Conclusion students no longer used virtual environments and ICT to pose and solve mathematical problems. [ABSTRACT FROM AUTHOR]

Problem-posing is an essential component of mathematics education because, among other reasons, when students are given the opportunity to pose their problems, they can take ownership of their learning and become more engaged in the given subject. Thus, problem-posing can lead to a deeper understanding of the studied mathematical concepts. In a collaborative action research study, the authors explored whether well-structured problem-posing activities could be incorporated into classes with students of mixed ability in mathematics. This question is addressed by examining the correlation between students' mathematics grades and problem-posing success. The problem-posing approach used in this paper relies on problem solving as a parallel activity. Hence, the study also focuses on the relationship between problem posing and problem solving. The paper presents the results of a classroom experiment with 86 sixth-grade students and their teachers from Hungary and Romania. After evaluating the students' problem-posing products and problem-solving performances, the results show that problem posing, based on a worked-out model problem, is a feasible challenge for most students. Moreover, this experiment identified a direct relationship between successful problem posing and problem solving. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Advanced Education Studies is the property of Journal of Advanced Education Studies 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.)

Our study aims to determine how Habermas' construct of rationality can serve to identify and interpret the difficulties experienced by university students in the mathematical problem-solving process. To this end, a problem which required modelling and solving a differential equation was used. The problem-solving processes of university students were analysed based on rationality components. The findings demonstrated that the problems in epistemic rationality such as predominance of the figure over the definition and/or theorems, use of dogmatic knowledge, intuitive generalizations, lack of prior knowledge, incorrect recognition of the differential equation prevented the choosing and using of an appropriate problem-solving method, leading to problems in teleological rationality. It was determined that the student performance in communicative rationality was negatively affected by problems in epistemic rationality such as using of knowledge acquired by rote and predominance of figure prototype on the definitions and/or theorems. Throughout the analysis, it is required to define two new sub-components, named "geometric" and "algebraic" representation under the modelling requirements of epistemic rationality. It is advised to use the extended version of Habermas' construct of rationality to examine the performance of students in mathematical activities to get more detailed and accurate results. [ABSTRACT FROM AUTHOR]