Mathematical Thinking and Learning

Corte, Erik De; Verschaffel, Lieven

doi:10.1002/9780470147658.chpsy0404

Cited by 14 publications

(17 citation statements)

References 88 publications

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“…More specifically, she presents the research findings underlying the following 12 principles of learning and their relevance for education: (1) active involvement; (2) social participation; (3) meaningful activities; (4) relating new information to prior knowledge; (5) being strategic; (6) engaging in self-regulation and being reflective; (7) restructuring prior knowledge; (8) aiming toward understanding rather than memorization; (9) helping students learn to transfer; (10) taking time to practice; (11) developmental and individual differences; and (12) creating motivated learners. An important principle in this list that is not explicitly mentioned above is the emphasis on understanding; in other words, in learning and teaching domain-specific knowledge the focus should be on conceptual knowledge, but where relevant connected and integrated with procedural knowledge (De Corte & Verschaffel, 2006: see also Baroody & Dowker, 2003). Another principle in Vosniadou's list to which I will come back later is that students should learn to transfer.…”

Section: A Brief Analysis Of (Mathematical) Competencementioning

confidence: 99%

“…There is currently a broad consensus among scholars in the field of mathematics education (see e.g., De Corte & Verschaffel, 2006;National Research Council, 2001) that becoming competent in mathematics can be conceived of as acquiring a mathematical disposition. Building up and mastering such a disposition requires the acquisition of five categories of cognitive, affective, and cognitive components (for a more detailed discussion of some of these components see De Corte & Verschaffel, 2006):…”

Section: A Brief Analysis Of (Mathematical) Competencementioning

confidence: 99%

“…Building up and mastering such a disposition requires the acquisition of five categories of cognitive, affective, and cognitive components (for a more detailed discussion of some of these components see De Corte & Verschaffel, 2006):…”

Section: A Brief Analysis Of (Mathematical) Competencementioning

confidence: 99%

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Learning from instruction: the case of mathematics

Corte

2007

Learn Inq

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Starting from a brief analysis of adaptive competence in mathematics, this article describes a series of research-based characteristics of the kind of learning processes that should be elicited in students to facilitate and support in them the progressive acquisition of such competence. Four major characteristics are discussed in some detail: learning is constructive, self-regulated, situated or contextual, and collaborative. A rather new approach to transfer of learning is then presented in which transfer is conceived as the preparation for future learning. Throughout the article it is argued that, notwithstanding the progress made in research on learning from instruction, numerous and complex issues and problems remain for continued inquiry. (1) implicit learning and the brain; (2) informal learning; and (3) designs for formal learning and beyond. Learning from instruction which constitutes the core of instructional psychology converges largely with the third strand which involves according to Bransford et al. (2006) ''the use of knowledge about learning to create designs for formal learning and beyond (where 'beyond' includes ideas for school redesign and connections to informal learning activities), and to study of the effects of these designs to further inform theoretical development' ' (p. 221) Keywords

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Section: A Brief Analysis Of (Mathematical) Competencementioning

confidence: 99%

Section: A Brief Analysis Of (Mathematical) Competencementioning

confidence: 99%

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Learning from instruction: the case of mathematics

Corte

2007

Learn Inq

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“…Mathematical thinking involves the intricate relationship between mathematical sense making and knowledge and regulation of the problem-solving process (De Corte & Verschaffel, 2006;Lesh & Zawojewski, 2007). For example, Schoenfeld (1992, p. 345) described this intricate relationship as follows: 'Mathematics instruction … should give them [students] a sense of what mathematics is and how it is done'.…”

Section: Mathematical Thinkingmentioning

confidence: 99%

Evaluating the suitability of mathematical thinking problems for senior high‐school students by including mathematical sense making and global planning

Velzen

2016

The Curriculum Journal

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To cite this article: Joke H. van Velzen (2016) Evaluating the suitability of mathematical thinking problems for senior high-school students by including mathematical sense making and global planning, The Curriculum Journal, 27:3, 313-329, DOI: 10.1080/09585176.2016 ABSTRACTThe mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an evaluation method by including mathematical sense making and global planning. Eighteen 11th-grade high-school students, divided into three groups of three pairs, solved six mathematical thinking problems that included the finding of a numeric solution and the writing of mathematical texts and arguments. Content analysis of the students' solution procedures provided for three kinds of hierarchically ordered mathematical sense-making categories. The results showed the expected statistically significant difference between the kinds of problems, though only mathematical sense making enabled the exclusion of the routine problem. The implications for practice are discussed.

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“…6 ''Significance' here refers to statistical significance as presented by the official OECD PISA publications (OECD, 2010.). 7 Slovenia introduced reforms to primary education structure in the 1990s by extending general compulsory education to 9 years (with 6 years primary education) and outcome-oriented national curriculum. 8 In PISA 2003. results presentation there are significant differences presented including and excluding the Bonferroni adjustment.…”

Section: S O C I O L O G I J a I P R O S T O Rmentioning

confidence: 99%

Mathematics Competence and International Mathematics Testing: Croatian Starting Point

Domazet

Baranović

Matić

2013

Sip

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The article presents a review of the competence-framed concept of compulsory mathematics education and appropriate instruction methods, in light of the international influences on Croatia through comparative ranking in PISA mathematical literacy. We begin by reviewing the conceptual constructs behind social influences on the supra-national development of the literacy/competence concept in mathematics education and assessment, and briefly examine its components and instructional contributions. Within this context we proceed to map past and current, and extrapolate future, changes in the conceptualisation of school mathematics and mathematics teaching in Croatian compulsory education, including recent empirical findings on mathematics instruction in Croatian primary schools. The aim is to examine social and (comparative) political influences on subject-matter and teaching of 'hard' school subjects such as mathematics, chart Croatia's current position according to international assessment and instructional trends, and recommend possible steps in immediate development of educational policy.

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Mathematical Thinking and Learning

Cited by 14 publications

References 88 publications

Learning from instruction: the case of mathematics

Learning from instruction: the case of mathematics

Evaluating the suitability of mathematical thinking problems for senior high‐school students by including mathematical sense making and global planning

Mathematics Competence and International Mathematics Testing: Croatian Starting Point

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