How to Solve It: A New Aspect of Mathematical Method

By P. Campbell. 2005

1,812 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/500f684c4c3d48e86fda9248617e702a4c9f4cf8

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Citations in the corpus

Emotions and motivation in mathematics education: theoretical considerations and empirical contributions (2017, background): “…If he [the teacher] fills his allotted time with drilling his students in routine operations, he kills their interest… (Pólya 1945, p.”
Discipline-Based Education Research: Understanding and Improving Learning in Undergraduate Science and Engineering. (2012, methodology): “• using a specific problem-solving framework (Heller and Heller, 2000; Pólya, 1945; Reif, 1995; Van Heuvelen, 1991), • elucidating different problem types (Mestre, 2002; Van Heuvelen, 1995; Van Heuvelen and Maloney, 1999), • providing example solutions (Chi et al.”
Learning to think: The challenges of teaching thinking (2005, background): “Nesta situação, não é suficiente consumir simplesmente o conhecimento pré-digerido, deve-se também tornar-se um construtor do conhecimento (Scardamalia, Bereiter, & Lamon, 1994) e no solver do problema (Polya, 1957; Schoenfeld, 1982; Selz, 1935).”
Difficulties in initial algebra learning in Indonesia (2014, methodology): “This indicates that the student lacked understanding of the problem as a whole as the first problem solving heuristic (Polya 1973).”
Do Multiple Solutions Matter? Prompting Multiple Solutions, Interest, Competence, and Autonomy (2014, background): “Developing multiple solutions improves students’ creativity and fosters mathematical knowledge (Ervynck, 1991; Leikin, 2007; Pólya, 1945).”
Large Language Models as Analogical Reasoners (2023, background): “(Polya, 2004) and recall how they solved related problems in the past (e.g., finding the area of a square with a known side length) to derive insights for solving the new problem.”
Conceptualizing Perseverance in Problem Solving as Collective Enterprise (2017, background): “Problem solving is foundational tomathematical learning (English&Gainsburg, 2016; Pólya, 1981, 2014; Schoenfeld, 1985, 1992) such that the world over, children are expected to persist when they encounter challenging problems (CCSI, 2010; Department for Education and Employment [DfEE], 1999; Human…”
The Conjecturing Process: Perspectives in Theory and Implications in Practice (2007, background): “Polya (1954) pointed this out, and Banach (1932) wrote:”
Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics (2009, background): “An attribute which is considered integral to the problem solving process is strategic behavior (Polya 1957; Schoenfeld 1992).”
I Am, I Think I Can, and I Do: The Role of Personal Identity, Self-Efficacy, and Cross-Application of Experiences in Creativity at Work (2007, background): “Polya ( 1957 ) described in detail how applying a problem that is related in structure but that is from an unrelated domain can facilitate more effective problem solving.”
Modelling mathematics problem solving item responses using a multidimensional IRT model (2006, background): “The first part involved the development of a mathematics problem-solving framework that was theoretically grounded, drawing upon research in mathematics education and cognitive psychology.”
What kinds of perceptions and daily learning behaviors promote students' use of diagrams in mathematics problem solving? (2007, background): “In mathematics education, the development of students’ abilities in solving math word problems has been an important topic (see, e.g., Polya, 1945; Reed, 1999; Schoenfeld, 1985, 1992).”
Patterns of Metacognitive Behavior During Mathematics Problem-Solving in a Dynamic Geometry Environment (2013, background): “understanding episode were crucial in solving the problem, highlighting the importance of these preparatory behaviors also recognized by Pólya (1945/1973) and Zimmerman (2002).”
Minimax Estimation of Functionals of Discrete Distributions (2014, background): “[65] Y. Polyanskiy, H. V. Poor, and S. Verdú, “Channel coding rate in the finite blocklength regime,” Information Theory, IEEE Transactions on, vol. 56, no. 5, pp. 2307–2359, 2010.”