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"Mathematical problem"
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The semantic system is involved in mathematical problem solving
Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving.
Journal Article
Problem solving : 50 math super puzzles
Presents fifty mathematical puzzles and problems, encouraging readers to think analytically about mathematical problems.
Book
Comparison of Mathematics Problem-Solving Abilities in Autistic and Non-autistic Children: the Influence of Cognitive Profile
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.
Journal Article
Problem solving in mathematics education: tracing its foundations and current research-practice trends
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.
Journal Article
Mathematical problems in and out of school: The impact of considering mathematical operations and reality on real-life solutions
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,
η
p
2
= 0.015), while being asked to consider appropriate mathematical operations significantly impaired realistic solutions (
F
(1, 161) = 8.54,
p
= 0.004,
η
p
2
= 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.
Journal Article
Algorithms to live by : the computer science of human decisions
Explores \"how the algorithms used by computers can also untangle very human questions. They explain how to have better hunches and when to leave things to chance, how to deal with overwhelming choices and how best to connect with others. From finding a spouse to finding a parking spot, from organizing one's inbox to understanding the workings of memory, [this book] transforms the wisdom of computer science into strategies for human living\"--Amazon.com.
Book
Teacher-student alignment to develop a valuing pedagogy: A case study of cultural dialogues for mathematical problem-solving
This study aims to develop effective pedagogies for addressing teacher and student values for mathematical problem-solving or valuing pedagogies (VPs) for mathematics. The aim is achieved by teacher-student alignment. The case study was conducted with a mathematician (the teacher) teaching an educational psychologist (the student) how to solve problems like a mathematician. The teacher taught the student by engaging in problem-solving activities like a one-to-one tutorial, immediately followed by their oral reflections. The formal teaching (including hand-writing) of teacher-student interaction was recorded. Follow-up oral and written dialogues continue between the teacher and the student in the later data analysis and paper process. Qualitative data analysis finds that the process generates three patterns of value alignment: teacher values transmission to students, teacher-student negotiations, and bridging teacher-student gaps by reform with teacher reflection and restructuring of pedagogies. The expert dialogues serve as an innovative methodology for identifying in-depth mechanisms for teacher-student value alignments and effective VPs.
Journal Article