Subtopic Deep Dive
Mathematical Problem Solving Frameworks
Research Guide
What is Mathematical Problem Solving Frameworks?
Mathematical Problem Solving Frameworks develop structured cognitive models and instructional strategies to teach problem-solving heuristics in mathematics education.
Frameworks like Polya's heuristics guide students through understanding, planning, executing, and reviewing problems (Lester, 2013). Research evaluates these across learner populations, integrating higher-order thinking skills (HOTS) and discovery learning (Retnawati et al., 2018; Simamora et al., 2018). Over 10 papers from 2008-2021, with 339 citations for top study on teachers' HOTS knowledge.
Why It Matters
These frameworks improve students' mathematical reasoning and self-efficacy via guided discovery in cultural contexts (Simamora et al., 2018, 324 citations). They enhance creative thinking and achievement through problem-based learning (Khoiriyah & Husamah, 2018, 200 citations) and digital tools like Math-Island (Yeh et al., 2019, 215 citations). Educators apply them to reform classrooms with Realistic Mathematics Education (RME), boosting problem-solving in primary schools (Sembiring et al., 2008, 167 citations).
Key Research Challenges
Teacher HOTS Knowledge Gaps
Teachers lack deep understanding of higher-order thinking skills for problem-solving instruction (Retnawati et al., 2018). This limits effective strategy implementation across diverse classrooms. Studies show need for targeted professional development (Sembiring et al., 2008).
Student Attitude Barriers
Negative attitudes toward mathematics hinder problem-solving engagement and performance (Mazana et al., 2018, 303 citations). Frameworks must address motivation alongside heuristics. Cultural and instructional contexts exacerbate this issue (Simamora et al., 2018).
Scalable Framework Adaptation
Adapting frameworks like RME or problem posing for varied learner populations remains challenging (Sembiring et al., 2008; Rosli et al., 2014, 92 citations). Digital integration adds complexity without guaranteed transferability (Yeh et al., 2019). Evaluation metrics for long-term efficacy are inconsistent.
Essential Papers
TEACHERS’ KNOWLEDGE ABOUT HIGHER-ORDER THINKING SKILLS AND ITS LEARNING STRATEGY
Heri Retnawati, Hasan Djidu, Kartianom Kartianom et al. · 2018 · Problems of Education in the 21st Century · 339 citations
Higher order thinking skill (HOTS) is one of the students’ abilities that should be developed through teaching and learning. Teachers’ knowledge about HOTS and its teaching and learning tactics is ...
Improving Students’ Mathematical Problem Solving Ability and Self-Efficacy through Guided Discovery Learning in Local Culture Context
Rustam Effendy Simamora, Sahat Saragih, Hasratuddin Hasratuddin · 2018 · International Electronic Journal of Mathematics Education · 324 citations
Qualified learning materials is needed in the efforts to improve the quality of teaching-learning mathematics. Qualified learning materials can be obtained through development research. Learning ma...
Investigating Students’ Attitude towards Learning Mathematics
Mzomwe Yahya Mazana, Calkin Suero Montero, Respickius Casmir · 2018 · International Electronic Journal of Mathematics Education · 303 citations
Students' learning of and performance in mathematics is affected by a number of factors, including students' attitude towards the subject, teachers instructional practices, and school environment. ...
Kemampuan Berpikir Tingkat Tinggi Dalam Menyelesaikan Soal HOTS Mata Pelajaran Matematika
Putu Manik Sugiari Saraswati, Gusti Ngurah Sastra Agustika · 2020 · Jurnal Ilmiah Sekolah Dasar · 229 citations
Pesatnya perkembangan pengetahuan dan teknologi abad 21, menuntut manusia memiliki kemampuan berpikir tingkat tinggi. Pada dunia pendidikan, HOTS merupakan kemampuan berpikir siswa yang tidak hanya...
Enhancing achievement and interest in mathematics learning through Math-Island
Charles Y.C. Yeh, Hercy N.H. Cheng, Zhi Hong Chen et al. · 2019 · Research and Practice in Technology Enhanced Learning · 215 citations
Abstract Conventional teacher-led instruction remains dominant in most elementary mathematics classrooms in Taiwan. Under such instruction, the teacher can rarely take care of all students. Many st...
Problem-based learning: Creative thinking skills, problem-solving skills, and learning outcome of seventh grade students
Anna Jarrotul Khoiriyah, Husamah Husamah · 2018 · JPBI (Jurnal Pendidikan Biologi Indonesia) · 200 citations
Creative thinking skills and problem-solving skills were among the competencies that must be possessed by students in the 21st-century, which need to be developed through the learning process, and ...
Teaching with digital technology
Alison Clark‐Wilson, Ornella Robutti, Mike Thomas · 2020 · ZDM · 197 citations
Abstract In this survey paper, we describe the state of the field of research on teaching mathematics with technology with an emphasis on the secondary school phase. We synthesize themes, questions...
Reading Guide
Foundational Papers
Start with Lester (2013) for problem-solving instruction thoughts and Sembiring et al. (2008) for RME implementation, as they establish core heuristics and reform strategies cited 167 times each.
Recent Advances
Study Retnawati et al. (2018, 339 citations) for HOTS teacher knowledge and Simamora et al. (2018, 324 citations) for discovery learning self-efficacy gains.
Core Methods
Polya's heuristics via noticing frameworks (Fernández et al., 2013); problem posing meta-analysis (Rosli et al., 2014); digital gamification (Yeh et al., 2019).
How PapersFlow Helps You Research Mathematical Problem Solving Frameworks
Discover & Search
Research Agent uses searchPapers and citationGraph to map frameworks from Retnawati et al. (2018) to Simamora et al. (2018), revealing HOTS clusters; exaSearch uncovers Indonesian RME adaptations; findSimilarPapers links Polya-inspired works to Lester (2013).
Analyze & Verify
Analysis Agent applies readPaperContent to extract HOTS strategies from Retnawati et al. (2018), verifies self-efficacy claims via verifyResponse (CoVe) against meta-analyses like Rosli et al. (2014), and uses runPythonAnalysis for GRADE grading of effect sizes in discovery learning studies; statistical verification confirms Simamora et al. (2018) outcomes.
Synthesize & Write
Synthesis Agent detects gaps in teacher training for HOTS frameworks and flags contradictions between attitude studies (Mazana et al., 2018); Writing Agent employs latexEditText for framework diagrams, latexSyncCitations for Polya references, and latexCompile for pedagogy reports; exportMermaid visualizes problem-solving workflow evolutions.
Use Cases
"Compare effect sizes of problem posing vs. guided discovery on math self-efficacy"
Research Agent → searchPapers + citationGraph → Analysis Agent → runPythonAnalysis (meta-analysis extraction with pandas) → GRADE grading + statistical output of Cohen's d from Rosli et al. (2014) and Simamora et al. (2018).
"Draft LaTeX lesson plan integrating Polya heuristics with RME"
Synthesis Agent → gap detection in Lester (2013) + Sembiring et al. (2008) → Writing Agent → latexEditText + latexSyncCitations + latexCompile → formatted PDF with embedded heuristics diagram.
"Find GitHub repos implementing Math-Island problem-solving tools"
Research Agent → paperExtractUrls on Yeh et al. (2019) → Code Discovery → paperFindGithubRepo + githubRepoInspect → list of educational game repos with Python analysis sandboxes.
Automated Workflows
Deep Research workflow conducts systematic review of 50+ HOTS papers: searchPapers → citationGraph → DeepScan checkpoints → structured report on framework efficacy (Retnawati et al., 2018). Theorizer generates new heuristic models from Polya (Lester, 2013) + RME (Sembiring et al., 2008) literature. DeepScan verifies attitude impacts via 7-step CoVe chain on Mazana et al. (2018).
Frequently Asked Questions
What defines Mathematical Problem Solving Frameworks?
Structured cognitive models and instructional strategies teaching heuristics like Polya's four steps, evaluated for HOTS development (Lester, 2013; Retnawati et al., 2018).
What are key methods in this subtopic?
Guided discovery learning (Simamora et al., 2018), problem-based learning (Khoiriyah & Husamah, 2018), and Realistic Mathematics Education (RME) (Sembiring et al., 2008).
What are prominent papers?
Retnawati et al. (2018, 339 citations) on teacher HOTS knowledge; Simamora et al. (2018, 324 citations) on discovery learning; Lester (2013, 167 citations) on problem-solving instruction.
What open problems exist?
Scaling frameworks digitally across cultures (Yeh et al., 2019; Bakker et al., 2021); long-term transfer of skills; teacher noticing of student thinking (Fernández et al., 2013).
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