Mathematical Problem Solving

By Manuel Santos-Trigo, Z. Gooya. 2015

1,068 citations recorded by the source corpus.

The program was designed to set up to organize, structure, and discuss the academic agenda of mathematical problem solving and its developments. The program included an open invitation to the mathematics education community to contribute and reflect on research and practicing issues that involve: (a) Addressing the origin, characterization, and foundation of mathematical problem solving, (b) discussing problem solving frameworks used to support research and curricula reforms in mathematical problem solving; (c) analyzing local and international research programs in mathematical problem solving; (d) discussing curriculum proposals that support the development of mathematical problem solving; (e) analyzing different ways to assess mathematical problem solving performances; (f) discussing the role played by the use of different digital tools in students’ development of mathematical problem solving proficiency; (g) addressing programs that foster learners’ development of problem solving approaches beyond school; and (h) identifying future developments of the field.

Subfields: Education

View Paper: https://www.semanticscholar.org/paper/c7802cc953a14172f45c41ff89dcca3e069ae972

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Citations in the corpus

Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof (2015, positive): “Beliefs are extracted from one’s experiences and from the culture in which one is embedded^ (p. 360).”
Reflections on Problem Solving Theory and Practice (2013, background): “Introduction My book Mathematical Problem Solving (Schoenfeld, 1985), which I shall refer to as MPS) was published more than 25 years ago.”
Engineering Students' Perceptions of Problem Solving and Their Future (2018, background): “The researchers’ preconceived notions of problem solving from existing literature (Jonassen, 2000, 2004, 2010; Schoenfeld, 1985, 1992, 2008) and the dominant cultural trends around problem solving in engineering (Litzinger et al., 2010) were bracketed prior to our interactions with the participants.”
Roles and characteristics of problem solving in the mathematics curriculum: a review (2020, background): “Finally, affective aspects are one of the weightiest factors, and the most difficult to change (Chapman, 2015; Schoenfeld, 1985).”
A metacognitive-based instruction for Primary Four students to approach non-routine mathematical word problems (2014, background): “1.2 Metacognition and attitudes Schoenfeld (1985), however, noted that successful problem solving required more than a direct application of Pòlya’s approach in the classroom.”
Hidden Assumptions and Unaddressed Questions in Mathematics for All Rhetoric (2015, neutral): “The last several years have seen the rise of cognitive and decontextualized analyses (e.g., Davis, 1986; Schoenfeld, 1985, 1987) followed by a transition to situated analyses (e.g., Anderson, Reder, & Simon, 1996; Brown, Collins, & Duguid, 1989; Cobb, 2000; Cobb & Bowers, 1999; Cobb, Yackel, &…”
The assessment cycle: a model for learning through peer assessment (2016, background): “This interplay is evident in complex activities such as mathematical problemsolving (Schoenfeld 1985).”
The Examining Mathematical Word Problems Solving Ability under Efficient Representation Aspect (2013, background): “Mayer (2003) divided mathematical word problem solving into four "cognitive phases": translating, integrating, planning and execution [13, 18, 10].”
Principles for designing mathematical tasks that enhance imitative and creative reasoning (2017, background): “There is little or no transfer to such competencies from easier learning processes, such as imitation of given solution templates (Schoenfeld 1985; Brousseau 1997; Niss 2007).”
Patterns of Metacognitive Behavior During Mathematics Problem-Solving in a Dynamic Geometry Environment (2013, methodology): “With respect to problem solving in DGEs, the software provides students with a genuine problem solving activity (Fey et al., 2010; Olive et al., 2010; Wilson et al., 1993).”
Metacognitive Skills and Problem-Solving (2021, background): “The students who have high metacognitive skills are more successful in problem-solving (Desoete, 2008; Hollingworth & McLoughlin, 2005; Schoenfeld, 1985).”
Conceptualizations of Students With and Without Disabilities in Educational Research in Mathematics; A Critical Review (2017, background): “Confrey and Kazak [23] described several strands of constructivism: research on problem solving [24, 25], research on student misconceptions [26], and theories of cognitive development in mathematics [27].”
The reflective diary as a method for the formative assessment of self-regulated learning (2018, background): “The way students think about knowledge and knowing will affect their approach to learning (Schoenfeld 1985), problem-solving (Schommer 1990), and SRL in general (Muis 2007).”
Promoting Access to Common Core Mathematics for Students with Severe Disabilities Through Mathematical Problem Solving (2017, background): “…the problem text, creating a mathematical representation of the problem, developing a plan to solve, executing the plan, and interpreting the solution, which present challenges for students with disabilities who have executive functioning and self-regulation difficulties (Fuchs & Fuchs, 2007).”
How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, background): “…some researchers have outlined the heuristics and processes that experts use to successfully write proofs (e.g., Koedinger & Anderson, 1990; Schoenfeld, 1985; Weber, 2001), and instruction designed to explicitly teach students these heuristics and processes have substantially increased…”
Conceptualizing Perseverance in Problem Solving as Collective Enterprise (2017, background): “…refers to students grappling with important mathematical ideas that are just beyond reach (Hiebert & Grouws, 2007), while “effort” refers to children modeling or representing ideas to their peers, considering others’ explanations, or monitoring their problem solving (CCSI, 2010; Schoenfeld, 1985).”
The characteristics of mathematical creativity (2015, neutral): “It should be noted that the Gestalt model has served as the kindling for many contemporary problem-solving models (Polya, 1945; Schoenfeld, 1985; Lester, 1985).”