Problem solving (Education)

Penelitian ini mengkaji permasalahan pemerataan pendidikan di Indonesia. Pemerataan pendidikan merupakan tantangan utama yang dihadapi Indonesia sebagai negara kepulauan dengan keragaman geografis, sosial, dan ekonomi yang tinggi. Kesenjangan akses dan kualitas pendidikan antara wilayah perkotaan dan pedesaan, serta antara kawasan barat dan timur Indonesia, masih menjadi isu yang belum terselesaikan secara optimal. Penelitian ini bertujuan untuk mengidentifikasi faktor-faktor penyebab ketimpangan pendidikan, menganalisis dampak yang ditimbulkan, serta menelaah berbagai kebijakan pemerintah dalam upaya mengatasinya. Penelitian ini menggunakan metode studi literatur melalui kajian terhadap berbagai sumber pustaka yang relevan. Hasil kajian menunjukkan bahwa ketimpangan pendidikan di Indonesia dipengaruhi oleh keterbatasan infrastruktur, distribusi tenaga pendidik yang tidak merata, kendala ekonomi keluarga, serta faktor geografis yang menyulitkan akses ke lembaga pendidikan. Berbagai program pemerintah seperti Program Indonesia Pintar dan Dana Bantuan Operasional Sekolah telah memberikan kontribusi positif, namun implementasinya masih memerlukan penguatan. Penelitian ini menyimpulkan bahwa diperlukan pendekatan kebijakan yang lebih komprehensif, berkelanjutan, dan berbasis kebutuhan lokal untuk mewujudkan pemerataan pendidikan yang berkeadilan di seluruh wilayah Indonesia.

This academic paper investigates the deep geometric properties, rigorous analytical proofs, and advanced structural applications of the Simson Line Theorem, a highly captivating topic in advanced Euclidean geometry that is unfortunately rarely covered within standard secondary school mathematics curricula. The fundamental essence of the theorem states that if perpendicular lines are dropped from any arbitrary point situated on the circumcircle of a given triangle to its three respective sides, the three resulting feet of these perpendiculars will always be strictly collinear. In this comprehensive study, we present a complete, highly structured, and elegant geometric proof of this unique collinearity property by utilizing the intrinsic cyclic properties of quadrilaterals and the sophisticated interplay of inscribed angles within a circle. Additionally, we actively explore the dynamic and fluid behavior of the Simson line using modern geometric visualization methodologies and explicitly demonstrate its high utility in solving some of the most challenging mathematical Olympiad problems across the globe. Through this multi-layered analysis, this independent research aims to foster higher-order analytical reasoning, advanced spatial awareness, and independent scientific research capabilities among high school students pursuing future STEM disciplines.

Anotacija. Visos kada nors susiformavusios žmonių grupės ar įvairių interesų vienijamos bendruomenės atsirado dėl žmonių kūrybos ir kūrybiškumo, dalijimosi informacija ir žiniomis, įvairiomis fizinėmis jausmų ir emocijų išraiškos formomis, žodiniais ir simboliniais kūriniais. Kita vertus, net ir mažiausios inovacijos visuomet duodavo akstiną socialinio gyvenimo kaitai. Bene didžiausias su naujosiomis technologijomis susijęs pokytis mokymo(si) kontekste yra naujos paradigmos, kurioje susiliejo du -mokymo ir mokymosi -procesai, atsiradimas. Kūrybiškumas neatsiejamas nuo žinių kūrimo proceso šiuolaikinėje visuomenėje. Šiame straipsnyje remiamasi trimis prieigomis prie kūrybiškumo įtinklinto mokymosi ir visapusiškesnių pažintinių gebėjimų ugdymo kontekste: Czikszentmihalyi sistemų teorija, Sternbergo ir Lubarto investavimo į kūrybiškumą teorija ir grupe požiūrių į kūrybiškumą, kurių dėmesio centre -problemų nustatymas ir sprendimas. Kalbant apie įtinklintą mokymą(si) ir visapusiškesnių pažintinių gebėjimų ugdymą universitetinėse studijose, svarbu pažvelgti į kūrybiškumą (i) kaip konceptą ir (ii) kūrybiškumą edukaciniame kontekste. Kūrybiškumas turi daug sąsajų su kritiniu raštingumu -kritiniu rašymu ir skaitymu, gebėjimu analizuoti, vertinti ir kurti

In the contemporary landscape of 2026, the dynamic of cognition for living freedom of belief is increasingly caught between the growing formalization of algorithmic education and the radical necessity for a pedagogy of choice. This essay explores how standardized machine-based routines risk modifying consciousness into “passive, dependent, filled” patterns, contrasting this with a “problem-posing” model that fosters a “free, active, creative, and investigative mind”. By synthesizing the educational theories of Paulo Freire and Ivan Illich with the philosophical “discipline of hope,” the study argues that true Freedom of Religion or Belief (FoRB) is not merely a legal status but a cognitive achievement rooted in “conscientization” and the “craftsmanship of the reflexive insider”. Ultimately, living freedom requires a pedagogy of contingency that enables individuals to navigate the “immanent frame” through a continuous “dialogue of myths” and ethical self-affirmation.

Omul luminat și omul iluminat O "lectură holografică" a conștiinței Majoritatea oamenilor au văzut cel puțin o dată o hologramă: o imagine care, privită din unghiuri diferite, dezvăluie profunzime și prezență-ca și cum un obiect tridimensional ar pluti în aer. Puțini, însă, s-au oprit să se întrebe de ce se întâmplă acest lucru. O hologramă nu este o fotografie. Pe placa fotografică nu există imaginea obiectului-ci doar o rețea densă de modele de interferență, urmele interacțiunii dintre două fascicule coerente de lumină: • unul de referință, pur și direct, • și unul reflectat, care a atins obiectul. Când aceste două unde se întâlnesc, suprapunerea lor înscrie pe placă un cod invizibil al diferențelor de fază. "Imaginea" este astfel stocată nu ca formă, ci ca relație. Ulterior, dacă aceeași placă este iluminată din nou cu fasciculul laser inițial-lumină cu aceeași frecvență și coerență-imaginea reapare, suspendată în spațiu. Pare vie, tangibilă. Fără această iluminare coerentă, holograma rămâne doar un model lipsit de sens, un labirint de lumină și umbră.

The review article analyses a new textbook dedicated to virtues and their role in the whole education written by Slovak authors (BLAŠČÍKOVÁ, Andrea, and NEMEC, Rastislav. Cnosti v celistvom vzdelávaní / Virtues in holistic education. Bratislava: Minor, 2025. ISBN 987-80-89888-55-9). The textbook introduces the cardinal virtues and their importance in personal education or development.  The authors have prepared didactic material intended primarily for future teachers.

This article comprehensively analyzes the current problems of teaching foreign languages in the process of preventing and eliminating emergencies. In particular, it highlights the role and importance of the language factor in ensuring effective communication in the context of natural and man-made disasters occurring globally. The study examines the main problems in this field, such as insufficient foreign language competence of specialists, the complexity of special terminology, difficulties in the process of rapid translation, and the lack of practical training. The article also scientifically proves the need to introduce innovative pedagogical technologies, use digital educational platforms, organize professionally oriented language courses, and strengthen training based on real situations as effective ways to eliminate these problems. The results of the study show that teaching foreign languages based on modern methods and technologies serves to ensure rapid and effective information exchange in emergencies.
Keywords: emergency, foreign language, communication, translation, problem, solution, innovation, terminology, international cooperation, digital education
In today's era of globalization, the number of emergency situations is increasing, and they often go beyond the borders of one country and require international cooperation. As a result of global climate change, accelerated urbanization processes, and technological development, the number and scale of natural and man-made disasters are increasing. In particular, in emergency situations such as earthquakes, floods, fires, pandemics, and man-made disasters, rescue services from different countries work together. In such conditions, effective communication is one of the main factors. Rapid and accurate exchange of information between representatives of different countries plays an important role in saving human lives. Especially in the early stages of emergencies, decisions made, orders given, and actions taken directly depend on the quality and accuracy of communication. Therefore, knowledge of foreign languages, especially English, has become a necessary competency for specialists working in the field of emergency situations [1]. As is known, English is widely used today as a means of international communication and plays an important role in ensuring cooperation between different countries. For example, specialists participating in international rescue operations communicate with each other in English. If the level of language proficiency is not sufficient, this can lead to misunderstandings, incorrect execution of orders, and even endanger human life.

A major limitation of fuzzy or neuro-fuzzy systems is their failure to deal with high-dimensional datasets. This happens primarily due to the use of T-norm, particularly, product or minimum (or a softer version of it). Thus, there are hardly any work dealing with datasets with dimensions more than hundred or so. Here, we propose a neuro-fuzzy framework that can handle datasets with dimensions even more than 7000! In this context, we propose an adaptive softmin (Ada-softmin) which effectively overcomes the drawbacks of "numeric underflow" and "fake minimum" that arise for existing fuzzy systems while dealing with high-dimensional problems. We call it an Adaptive Takagi-Sugeno-Kang (AdaTSK) fuzzy system. We then equip the AdaTSK system to perform feature selection and rule extraction in an integrated manner. In this context, a novel gate function is introduced and embedded only in the consequent parts, which can determine the useful features and rules, in two successive phases of learning. Unlike conventional fuzzy rule bases, we design an enhanced fuzzy rule base (En-FRB), which maintains adequate rules but does not grow the number of rules exponentially with dimension that typically happens for fuzzy neural networks. The integrated Feature Selection and Rule Extraction AdaTSK (FSRE-AdaTSK) system consists of three sequential phases: (i) feature selection, (ii) rule extraction, and (iii) fine tuning. The effectiveness of the FSRE-AdaTSK is demonstrated on 19 datasets of which five are in more than 2000 dimension including two with dimension greater than 7000. This may be the first time fuzzy systems are realized for classification involving more than 7000 input features.

Terms and conditions for use: By downloading this article from the EURASIA Journal website you agree that it can be used for the following purposes only: educational, instructional, scholarly research, personal use. You also agree that it cannot be redistributed (including emailing to a list-serve or such large groups), reproduced in any form, or published on a website for free or for a fee. Disclaimer: Publication of any material submitted by authors to the EURASIA Journal does not necessarily mean that the journal, publisher, editors, any of the editorial board members, or those who serve as reviewers approve, endorse or suggest the content. Publishing decisions are based and given only on scholarly evaluations. Apart from that, decisions and responsibility for adopting or using partly or in whole any of the methods, ideas or the like presented in EURASIA Journal pages solely depend on the readers' own judgment.

É atribuída a Neil Armstrong, o primeiro homem a pisar na Lua, a seguinte frase: “Subitamente, me dei conta de que aquela pequena ervilha, bela e azul, era a Terra. Estiquei meu polegar e fechei um olho. E o meu polegar tampou completamente o planeta Terra. Eu não me senti um gigante, mas muito, muito pequeno”. Assim somos diante da vastidão do tempo e espaço. Desta forma, nos resta o dever de procurar fazer o melhor com a dádiva que nos foi concedida – a capacidade de raciocínio e aprendizado. Essa é a tônica de mais este livro – inferir sobre um dos tópicos da matemática mais desafiadores e que mais causam espécie em muitos, a Trigonometria. Dividido em dois volumes, o desejo é de que tais notas de aula possam ser verdadeiramente úteis para diminuir a nossa “ignorância” e demonstrar que todo conhecimento é interconectado.

This article is about the systematization and representation young children spontaneously use when they are working on a combinatorial task. In this article, documentations from 123 children working on the same task are analysed. The question asked is if there are any connections between the systematizations and representations used in the documentations and how the children solve the task. The results indicate that there are some connections between systematization and representations and that both prepossess children's solutions. In this paper, we provide some possible reasons; however, we also state that more studies are needed to give deeper insights on these issues.

In mathematics education, digital tools have been used to enhance young children's understanding of specific subject matter. In such implementations, the digital tool can replace, amplify or transform 'ordinary' mathematics teaching. In an initial study, systematization and duplication were identified as critical when young children were to solve a combinatorial task. Therefore, a digital version of the task was developed and combined with a non-digital version, to introduce the use of dual artefacts. The digital version of the task enabled the children to visually explore systematization as well as the principle of completion. After using this digital version of the task, the children's written records became more systematic and included fewer duplications. We conclude that the digital version of the task reinforced young children's understanding of the combinatorial task and that the use of dual artefacts enhanced children's understanding of what a combinatorial problem encompasses.

In mathematics education, digital tools have been used to enhance young children's understanding of specific subject matter. In such implementations, the digital tool can replace, amplify or transform 'ordinary' mathematics teaching. In an initial study, systematization and duplication were identified as critical when young children were to solve a combinatorial task. Therefore, a digital version of the task was developed and combined with a non-digital version, to introduce the use of dual artefacts. The digital version of the task enabled the children to visually explore systematization as well as the principle of completion. After using this digital version of the task, the children's written records became more systematic and included fewer duplications. We conclude that the digital version of the task reinforced young children's understanding of the combinatorial task and that the use of dual artefacts enhanced children's understanding of what a combinatorial problem encompasses.

This article is about the systematization and representation young children spontaneously use when they are working on a combinatorial task. In this article, documentations from 123 children working on the same task are analysed. The question asked is if there are any connections between the systematizations and representations used in the documentations and how the children solve the task. The results indicate that there are some connections between systematization and representations and that both prepossess children's solutions. In this paper, we provide some possible reasons; however, we also state that more studies are needed to give deeper insights on these issues.

In mathematics education, digital tools have been used to enhance young children’s understanding of specific subject matter. In such implementations, the digital tool can replace, amplify or transform ‘ordinary’ mathematics teaching. In an initial study, systematization and duplication were identified as critical when young children were to solve a combinatorial task. Therefore, a digital version of the task was developed and combined with a non-digital version, to introduce the use of dual artefacts. The digital version of the task enabled the children to visually explore systematization as well as the principle of completion. After using this digital version of the task, the children’s written records became more systematic and included fewer duplications. We conclude that the digital version of the task reinforced young children’s understanding of the combinatorial task and that the use of dual artefacts enhanced children’s understanding of what a combinatorial problem encompasses.

This article is about the systematization and representation young children spontaneously use when they are working on a combinatorial task. In this article, documentations from 123 children working on the same task are analysed. The question asked is if there are any connections between the systematizations and representations used in the documentations and how the children solve the task. The results indicate that there are some connections between systematization and representations and that both prepossess children’s solutions. In this paper, we provide some possible reasons; however, we also state that more studies are needed to give deeper insights on these issues.

Inductive and deductive reasoning represent two foundational modes of human thought that significantly influence how individuals process information, draw conclusions, and make decisions in everyday life. This study examines the comparative efficacy of these two reasoning strategies when applied to real-world scenarios involving uncertainty, pattern recognition, and structured problem-solving. Inductive reasoning proceeds from specific observations to broader generalizations, making it a valuable tool for open-ended, data-driven tasks. Deductive reasoning, in contrast, starts from established premises and applies logical rules to derive precise conclusions, making it indispensable for contexts requiring accuracy, consistency, and formal logic. This research explores their theoretical distinctions while assessing their practical usefulness across academic, professional, and daily life settings. The abstract also highlights the need for a systematic understanding of how both reasoning modes interact with cognitive load, decision-making pressure, and the availability of information. Real-world environments rarely provide complete data or perfectly structured premises; thus, individuals must adapt by selecting the most effective reasoning approach based on situational demands. The analysis considers the cognitive processes that support these reasoning styles and investigates how individuals employ them when confronted with uncertainty, time constraints, or ambiguous data.

Fostering motivation and engagement in mathematics requires learning conditions that support students’ autonomy, competence, and relatedness. Self-Determination Theory [SDT] (Ryan & Deci, 2017) provides a valuable framework for understanding how these psychological needs shape students’ experiences of learning mathematics. This paper explores how SDT can inform the design of optimal learning conditions in primary school mathematics education, particularly in contexts where students engage with cognitively demanding tasks. We present a conceptual model for structuring learning experiences that enhance internalized motivation, persistence, and positive mathematical dispositions. To illustrate how instructional choices can shape students’ self-determined learning, we examine the Exploring Mathematical Sequences of Connected, Cumulative and Challenging Tasks [EMC3] project (Sullivan et al., 2020) as a case study of structured inquiry pedagogies aligned with SDT principles implemented within an early primary context (Foundation to Year 2). Our analysis highlights how specific instructional design choices—including scaffolding challenge, supporting autonomy, and fostering collaboration—can optimize learning conditions for primary school students. This paper contributes to both mathematics education and motivation research by offering a framework for designing instructional experiences that support self-determined learning in primary school mathematics.

Bu çalışmada, fen bilimleri dersinde ışığın yayılması ünitesinin öğretiminde STEM etkinliklerinin kullanılmasının 5. sınıf öğrencilerinin akademik başarılarına etkisinin belirlenmesi ve STEM etkinlikleri hakkında öğrenci görüşlerinin alınması amaçlanmıştır.

The adoption of robotics in education has increasingly gained attention. Robotics activities can be applied in any level of education since the early childhood up to, starting in primary schools until graduate schools. Besides, the concept of STEM learning is still a trending issue in the world of education. STEM-based learning with robotics can develop knowledge and the awareness of robotics for students. Notwithstanding the vast literature on adoption of robotics into the educational context activities, there is a possibility of a limited lack of explanation on how robotics contribute in the STEM learning environment at primary school. A systematic literature review was carried out to evaluate the latest developments of robotics topics in the literature. It is prominent in the literature that robotics contribute to teaching and learning in primary schools. Teachers indicated positive responses to robotics due to the ability to attract students’ attention and motivation. However, n...

Menggali beberapa informasi yang simpang siur (tidak jelas) diantaranya:

1. Menguraikan fondasi kontroversi melalui penelusuran
dokumen Komisi Pemilihan Umum (KPU) yang menampilkan riwayat
pendidikan Gibran. Dalam dokumen resmi itu, tercatat bahwa Gibran
menempuh pendidikan di SD Negeri Mangkubumen Kidul 16, SMP Negeri
1 Surakarta, lalu pindah ke Orchid Park Secondary School di Singapura pada 2002–2004, sebelum melanjutkan ke UTS Insearch Sydney pada 2004–2007. Susunan ini tampak sah di permukaan, namun ketika dikaitkan dengan sistem pendidikan Singapura dan Australia, muncul kejanggalan mengenai kesetaraan jenjang dan masa studi.

2. Menggali lebih dalam posisi Orchid Park Secondary School dalam kerangka pendidikan Singapura. Sekolah ini berada pada jenjang
Secondary 3–4, yang setara dengan kelas 9–10 dalam sistem Indonesia.
Setelah lulus, siswa seharusnya melanjutkan ke Junior College atau
Polytechnic Foundation Programme untuk menyelesaikan pendidikan  menengah atas. Fakta bahwa Gibran tidak tercatat menempuh dua tahun
lanjutan tersebut menjadi titik awal masalah akademik: bagaimana mungkin seseorang yang belum menyelesaikan pendidikan menengah penuh dapat diterima langsung di lembaga setara diploma Australia?

3. Menyoroti surat keterangan penyetaraan dari Direktorat Jenderal
Pendidikan Dasar dan Menengah (Ditjendikdasmen) Kementerian
Pendidikan dan Kebudayaan, yang dikeluarkan pada 6 Agustus 2019. Surat
ini menyatakan bahwa Gibran telah menempuh “Grade 12 di UTS Insearch,
Sydney” dan dinilai setara dengan lulusan SMK peminatan Akuntansi dan
Keuangan. Bab ini menegaskan bahwa frasa tersebut tidak didukung oleh
fakta akademik karena UTS Insearch bukan lembaga pendidikan menengah, melainkan institusi pathway atau transisi menuju universitas.

4. Menyajikan analisis struktural terhadap UTS Insearch berdasarkan arsip resmi tahun 2004 — termasuk brosur, handbook, dan dokumen kurikulum. Program Business & Commerce (Advanced Standing) dan Diploma of Business yang ditawarkan pada masa itu setara dengan tahun pertama kuliah sarjana (AQF Level 5), bukan pendidikan menengah (AQF Level 3). Dengan demikian, penyebutan “Grade 12 di UTS Insearch” adalah  kekeliruan konseptual yang memindahkan jenjang pendidikan tinggi ke
kategori menengah.

This is a survey paper submitted to the Design in Engineering Education Division (DEED). As a survey paper, it provides a comprehensive review of the literature on the topic of representations between engineering design and engineering analysis. This research aims to characterize the overlap as well as distinctness between engineering design thinking, on the one hand, and engineering model-based reasoning, on the other hand. The 1990s witnessed the rise of a transformative wave to the engineering curricula, where the "engineering science" model became dominant in engineering curricula. In this model, the focus in the first two years of the curriculum is placed on the "engineering sciences," or, alternatively, "analysis," with the expectation that students would apply the learned scientific principles to solve technical problems. However, a segregation problem between "design" and "analysis" started to emerge. The problem was caused not only by lack of appreciation for the complexities associated with design teaching and learning, but also by lack of students' fluency to apply their learned mathematical modeling skills in complex, open-ended design problems. In this paper, we develop a "representations framework" to study the relationship between engineering design thinking and engineering model-based reasoning. It is the focus of this study to understand the role of multiple representations in problem solving, in order to characterize the overlaps and the distinctiveness in the use of the term "representation" in the contexts of mathematical modeling and design processes. Engineering design is a systematic, intelligent process that aims to solve ambiguous problems. In the majority of current engineering education curricula, a major emphasis is placed on the traditional view where prerequisite ideas are taught in decontextualized situations. While students in their courses interact with models in varying contexts, teaching focuses on algorithmic steps to find a solution. In this paper, we develop a framework to understand how representation is described, taught and learned in analysis-focused classes and in design-focused classes.

The aim of the study is to discuss the relationship between leadership and creativity at a personal level, and to trace non-cognitive psychological factors which possibly determine creativity at work. The methods of scientific literature analysis and empirical qualitative research have been employed for the investigation. The richest 7 journals (diaries) of creative activity have been selected for empirical research from the total of 52 samples. The study presents empirical evidence of such factors of creativity and leadership as emotional involvement and the work - way of life connection. It also draws attention to the problem of creativity levels at an organization and stresses the connection between creativity and leadership. These problems still lack considerable attention of researchers, as the article shows. Main research implications for practice include the possibility to foresee high creativity and leadership at work by assessing the aforesaid individual characteristics. Fi...

Yes, video games are mainly for play and fun. But video games are educative as well as interesting and engaging—something that we all hope that more classrooms could be. Many of today's students spend more time playing video games than they do watching television, reading books, or ...

cnr.it 1. INTRODUZIONE Nel nostro lavoro di ricerca abbiamo compiuto varie sperimentazioni per studiare il ruolo che le tecnologie informatiche e telematiche possono svolgere nel superamento di difficoltà che emergono nell'apprendimento in campo aritmetico e nella soluzione di problemi aritmetici.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Bu araştırma, bilgisayarsız kodlama eğitiminin ilkokul öğrencilerinin dikkatlerini toplama düzeyi, problem çözme ve algoritmik düşünme becerileri üzerindeki etkisini belirlemek amacıyla gerçekleştirilmiştir. Çalışmada nicel araştırma modeli kapsamındaki ön test son test tek gruplu zayıf deneysel desen kullanılmıştır. Çalışma grubunu Mersin’in bir merkez ilçesinde bulunan bir devlet okulunda öğrenim gören 13 kız ve 10 erkek öğrenciden oluşan toplam 23 üçüncü sınıf öğrencileri oluşturmuştur. Veriler Burdon Dikkat Testi, Problem Çözme Becerisi Etkinlik Kâğıdı, Algoritmik Düşünme Becerisi Etkinlik Kâğıdı ve yarı yapılandırılmış görüşme formu kullanılarak toplanmıştır. Çalışma sonunda, uygulanan kodlama eğitiminin katılımcı ilkokul öğrencilerinin dikkatini toplama, problem çözme ve algoritmik düşünme becerileri üzerinde anlamlı düzeyde ve pozitif yönde bir etkisinin olduğu görülmüştür. Öğrenciler, kodlama etkinliklerinin hızlı düşünebilmelerini ve anlayabilmelerini sağladığını, doğru tah...

Background: Universities in Mogadishu within the Banadir Region have experienced a steady decline in new student enrollments, raising concerns about access, relevance, and sustainability of higher education in Somalia. Aim: This study aimed to examine the key socioeconomic, institutional, and structural factors contributing to the reduction of new student enrollments at universities in Mogadishu, Banadir Region. Methodology: A cross-sectional mixed-methods design was employed. Data were collected from a sample of 300 respondents, comprising 200 students (66.7%) and 100 academic and administrative staff (33.3%), using a structured questionnaire. Descriptive statistical analysis was used to summarize frequencies and percentages related to enrollment-influencing factors.

Lately, the research on 21st-century competencies has become the focus on research in the world of education. Critical thinking skills has become one of the competencies to face the challenges of the 21 st -century with learning model and media. This research aims to know the effect of implementing of Learning Cycle 7E Model (LCM-7E) assisted by mind map to students’ critical thinking skills. This research employs quasi-experimental design with two ways ANOVA analysis technique. The instrument used to measure the critical thinking skills was an essay test that consisted of 7 questions. The result of the hypothesis shows that there is an effect of the LCM-7E model assisted by mind map toward the students’ critical thinking skills. Yet, gender factors do not influence on the students’ critical thinking skills.

Problem posing is rarely seen in Spanish classrooms, least of all in preschool education. The lack of research, coupled with a lack of guidance, has resulted in teachers simply not considering the approach as something that could enrich their work. This study examines a problem-posing lesson given by a preschool teacher to a class of four-year-olds. It focuses in particular on the organisational principles and the factors to be taken into consideration in applying the strategy. Through the application of a bottom-up analysis, seven characterisers are identified, four associated with task design and planning: Characteristics of the resources, type of problem, expression of problem formulation, and type of problem formulation; and three associated with lesson management: Stages in task execution, degree of liberty, and role of the pupils’ drawings of the problem.

No ensino técnico, é importante que o conhecimento teórico esteja integrado ao conhecimento prático, para que o estudante possa conectar fundamentos ao exercício de atividades profissionais. No entanto, a formulação de aulas práticas pode ser uma atividade desafiadora ao docente, que precisa garantir condições de segurança, disponibilidade de equipamentos e materiais, espaço físico adequado, conexão entre teoria e prática, envolvimento e participação dos alunos, entre outros elementos. A proposta deste trabalho é compartilhar a experiência da formulação de uma aula prática de fundição, com uso de materiais alternativos e econômicos, da disciplina de Laboratório de Tecnologias Metalúrgicas do Curso Técnico em Metalurgia do CEFET-MG - campus Timóteo[1]. Como resultado, foi observado que a realização da simulação prática de fundição obteve maior participação dos estudantes e interesse no conteúdo associado ao processo industrial. Destaca-se a importância do planejamento e preparação an...

Me recordo como se fosse hoje da minha infância e do cotidiano como estudante da escola pública, em que sequer tinha noção da importância da educação. Nesta fase, sem dúvida, devo agradecer à minha família, principalmente, aos meus pais, Aparecida e Alcides, por demonstrarem que a educação seria o caminho. Agradeço à Jerusha, mãe do meu filho, por tudo que fez para que eu concluísse esta etapa, mais do que isso, para que eu buscasse ir além. Nesta trajetória, muita gente merece o agradecimento, mas este texto não comportaria o nome de cada professor/professora que tive, bem como daqueles amigos, irmã e familiares que se referem a mim como o "professor Herbert" com orgulho. Também não podem faltar meus alunos e ex-alunos, aqueles que me inspiram e também me enchem de orgulho, dando a certeza que pude ajudá-los por meio da educação. Neste trabalho, tive a colaboração de muitos destes alunos, Pedro, Nickolas, André, Vinícius e, especialmente nesta reta final, da Beatriz. Igualmente, devo muito à Diretoria de Ensino de São Carlos, com a parceria da Dirigente profa. Débora e com o suporte da profa. Silvana, que viabilizou a coleta de dados deste trabalho, bem como a todos os participantes da pesquisa. Aos colegas do Núcleo de Pesquisa em Inovação Curricular (Nupic), grupo do qual pertenço e com o qual aprendo muito, além de enriquecer a cada apresentação com as críticas carinhosas de cada um. Ao meu orientador, Dr. Maurício Pietrocola, que muito além de orientar, também apoiou cada passo e me ajudou a superar cada uma das dificuldades, seja com conselhos, seja com sua compreensão. À USP, a Alma mater que me acolheu e me mantenho conectado há 20 anos. A estes e todos os demais que aqui não nominei, sintam-se abraçados fortemente, e que um sorriso sem máscara possa ser a melhor forma de agradecimento. "Um dia escrevi que tudo é autobiografia; que a vida de cada um de nós está contando enquanto fazemos e dizemos; nos gestos, na maneira como andamos e olhamos, como viramos a cabeça ou apanhamos um objeto no chão. Queria eu dizer, então, que vivendo rodeado de sinais, nós próprios somos um sistema de sinais". [Trecho dos "cadernos de Lanzarote" uma autobiografia de José Saramago (1994)]. "Os professores têm muito o que ensinar pelo exemplo de combate em favor das mudanças fundamentais de que precisamos, de combate contra o autoritarismo e em favor da democracia. Nada disso é fácil, mas isso tudo constitui uma das frentes da luta maior de transformação profunda da sociedade brasileira. Os educadores progressistas precisam convencer-se de que não são puros ensinantesisso não existepuros especialistas da docência. Nós somos militantes políticos porque somos professores e professoras. Nossa tarefa não se esgota no ensino da matemática, da geografia, da sintaxe e da história. Implicando a seriedade e a competência com que ensinamos esses conteúdos, nossa tarefa exige o nosso compromisso e engajamento em favor da superação das injustiças sociais". (FREIRE, 1997, p. 54). JOÃO, Herbert Alexandre. O engajamento na formação continuada de professores: perspectiva dos rituais de interação e das emoções. 2022. 237f. Tese (Doutorado em Educação) -

Distribusi hipergeometrik merupakan salah satu distribusi probabilitas diskrit yang digunakan untuk memodelkan peluang keberhasilan dalam pengambilan sampel tanpa pengembalian dari suatu populasi berhingga. Distribusi ini memiliki peran penting dalam berbagai bidang seperti statistika kualitas, pendidikan, penelitian sosial, biologi, dan kedokteran. Artikel ini membahas secara komprehensif konsep distribusi hipergeometrik, karakteristiknya, perbedaannya dengan distribusi binomial, rumus matematis, serta contoh penerapan dalam kehidupan nyata. Dengan pemahaman yang baik terhadap distribusi ini, proses pengambilan keputusan berbasis data dapat dilakukan secara lebih akurat dan realistis.

Distribusi multinomial merupakan salah satu distribusi probabilitas diskrit yang digunakan untuk memodelkan kejadian dengan lebih dari dua kemungkinan hasil dalam suatu percobaan yang dilakukan secara berulang dan saling bebas. Distribusi ini merupakan pengembangan dari distribusi binomial, yang hanya menangani dua kategori hasil, sehingga distribusi multinomial lebih relevan untuk permasalahan nyata yang melibatkan banyak kategori. Makalah ini membahas konsep dasar distribusi multinomial meliputi definisi, asumsi-asumsi dasar, fungsi massa peluang, serta karakteristik statistik seperti nilai harapan, ragam, dan kovarians. Selain itu, disajikan beberapa contoh penerapan distribusi multinomial pada kasus pengambilan kelereng dan genetika untuk memperjelas pemahaman konsep dan perhitungan peluang. Melalui pembahasan ini, diharapkan pembaca mampu memahami prinsip kerja distribusi multinomial serta mengaplikasikannya dalam analisis probabilitas pada bidang teknik industri dan statistika terapan.

Kata kunci: distribusi multinomial, probabilitas, fungsi massa peluang, statistika diskrit, teknik industri.

Distribusi probabilitas merupakan salah satu konsep fundamental dalam teori probabilitas yang banyak digunakan dalam analisis pengambilan keputusan, khususnya pada bidang teknik industri. Penelitian ini bertujuan untuk membahas konsep, karakteristik, serta penerapan distribusi hipergeometrik dan distribusi multinomial dalam konteks bisnis dan industri. Distribusi hipergeometrik digunakan untuk memodelkan pengambilan sampel tanpa pengembalian dari populasi terbatas, sedangkan distribusi multinomial digunakan untuk menganalisis kejadian dengan lebih dari dua kategori hasil. Metode yang digunakan dalam penelitian ini adalah studi literatur dan analisis kuantitatif melalui penyelesaian contoh kasus yang relevan dengan kegiatan quality control, inspeksi produk, survei pelanggan, dan klasifikasi cacat pada proses manufaktur. Hasil pembahasan menunjukkan bahwa distribusi hipergeometrik sangat efektif dalam menggambarkan probabilitas kejadian pada sistem sampling terbatas tanpa pengembalian, sementara distribusi multinomial mampu memberikan gambaran distribusi probabilitas pada beberapa kategori secara simultan. Dengan pemahaman yang tepat terhadap kedua distribusi ini, pengambilan keputusan dalam bidang industri, khususnya terkait pengendalian kualitas dan evaluasi proses, dapat dilakukan secara lebih akurat dan sistematis.

Kata kunci: distribusi hipergeometrik, distribusi multinomial, teori probabilitas, quality control, teknik industri

Araştırmanın amacı sınıf öğretmeni adaylarının düşünme stilleri ile kontrol odağı durumları arasında ilişki olup olmadığını araştırmaktır. Bunun yanı sıra düşünme stilleri ve kontrol odağına göre adayların akademik başarılarında farklılaşma olup olmadığı incelenmiştir. Ayrıca sınıf öğretmeni adaylarının düşünme stilleri ve kontrol odağı durumlarındaki farklılaşmalar çeşitli bağımsız değişkenlere göre araştırılmıştır. Betimleyici ilişkisel tarama desenindeki araştırmanın çalışma evrenini 2006-2007 eğitim-öğretim yılında Gaziosmanpaşa Üniversitesi Eğitim Fakültesi Sınıf Öğretmenliği Bölümünde öğrenci olan 131 kişi oluşturmaktadır. Çalışmada veri toplama aracı olarak Dağ'ın (1991) Türkçeye uyarladığı "İç-Dış Kontrol Odağı Ölçeği" ile Sünbül (2004) tarafından Türkçeye uyarlanan "Düşünme Stilleri Ölçeği" kullanılmıştır. Verilerin analizinde Pearson Korelâsyon katsayısı, tek yönlü MANOVA, t-testi ve ANOVA testleri kullanılmıştır. Sonuçlar bireylerin düşünme stilleri ile kontrol odağı durumlarıyla yakından ilişkili olduğunu göstermesi ve çeşitli faktörlerin bireylerin kontrol merkezi ve dolayısıyla düşünme stilleri üzerinde etkili olabileceğine dikkat çekmesi yönünden önemlidir.

Indonesia has many gifted young scientists, who need to get support and good opportunities to work. Numerical ability is one of element that must be mastered in mathematics. This study aims to determine the effect of numerical ability of students who take part in learning using the Team Assisted Individualization (TAI) learning model with those who follow conventional learning models. The type of research is quasi experimental design. The instrument used was a numerical ability test on sequence topic and a series of essay tests. Data were analyzed from the results of the posttest using t-test. Based on the calculation results obtained tcount of 3,977 and ttable of 2,005, it can be concluded that ttable = table means that the Team Assisted Individualization (TAI) learning model has a good impact on the numerical ability of students.

In this Note two problems of geometric minima are solved. The first is: given a propel angie:,-{.7 and a fixed point P in its interior'. constnrct a.straight line BC t}rrough P rvlt}r B e (-1.r and C e (.1y such that the pcrirneter of the tria,ngle -1BC to be minirnal. The seconcl one is related to the first: Let z,{y be:r proper angle arxl C i./) be:r circle tangent to its si(le-q. Con.ctnrct a tangent BC to this cilclo lbr B € (--h ancl C f (-1u such tl.rat the circle to be insclibecl in the triarrgle ,{BC and the perimeter of the triangle ABC to be ntinimal.

Background: The advent of new and emerging technologies and industries has highlighted the need to equip youth with a unique skillset necessary to cope with a rapidly changing and complex digital era and adapt to modern societies' demands. This need has led to the development of teaching approaches to equip students with creative and innovative skills to help prevent any future skills gap. This shift has fuelled the growth of STEAM (Science, Technology, Engineering, Arts and Mathematics) Education worldwide. Objectives: Our goal was to engage in a systematic review of the literature to identify the application and prevalence of emerging technologies within the landscape of STEAM Education. We engaged in a systematic review of the literature. Following the application of exclusion criteria to 461 studies, 43 studies were extracted and analysed. Findings and Conclusions: Analysis of these studies provides evidence of the fastgrowing use of innovative emerging technologies within the STEAM landscape across all levels of education, from early childhood to college-level settings. Our analysis reveals an emphasis on developing STEAM-related disciplinary knowledge and the desire to develop students' 21st-century skills with a notable lack of targeted emphasis on developing understandings in the arts disciplines. We identify the need for carefully designed intervention studies involving collaboration between multidisciplinary STEAM experts that use high-quality measures which support the development of inferences relating to learning outcomes arising from such interventions.

This paper traces the historical development of perspectives on specific learning disabilities in the Czech Republic, from the earliest insights in antiquity to the contemporary inclusive trends in education. It captures the evolution from the medical model to the psychological approach and, more recently, to pedagogical interpretations. The paper highlights key figures, legislative milestones, and institutional changes that have influenced the approach to educating pupils with specific learning disabilities. Attention is also given to educational support systems, remedial care, and current challenges in the fields of diagnosis and education. The text demonstrates how societal views on these pupils have evolved and how the system of care has shifted towards individualization, respect, and interdisciplinary collaboration.