Small-group searches for mathematical proofs and individual reconstructions of mathematical concepts

Vidakovic, Draga; Martin, William O.

doi:10.1016/j.jmathb.2004.09.006

Cited by 8 publications

(9 citation statements)

References 26 publications

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“…Vidakovic and Martin (2004) provide transcripts and analysis of student interaction while devising proofs in geometry. Strober, Cook, and Fuller (1997) used videotapes to examine the interactions among introductory economics students working on a problem.…”

Section: Related Literaturementioning

confidence: 99%

An Empirical Examination of the Roles of Ability and Gender in Collaborative Homework Assignments

Parker¹

2010

The Journal of Economic Education

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This paper investigates how ability and gender affect grades on homework projects performed by assigned pairs of students in an undergraduate macroeconomics course. The assignment grade is found to depend on the ability of both students, and the relative importance of the stronger and weaker student differs in predictable ways depending on the kind of assignment. Male-male pairs earn lower grades than male-female or female-female pairs, conditional on the measured ability of the students.

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Section: Related Literaturementioning

confidence: 99%

An Empirical Examination of the Roles of Ability and Gender in Collaborative Homework Assignments

Parker¹

2010

The Journal of Economic Education

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“…In "Small-group Searches for Mathematical Proofs and Individual Reconstructions of Mathematical Concepts", Vidakovick and Martin agreed that constructivist theory provides the basis for co-operative and collaborative learning (Vidakovic & Martin, 2004). Discussion, they claimed, leads to deeper understanding.…”

Section: Introductionmentioning

confidence: 99%

“…By missing an opportunity for externalization, we limit internalization; that is to say, if we do not have a chance to explain our thought to someone else we fail to solidify learning (Vidakovic & Martin, 2004). They emphasized that in the mid-20 th century two theories have dominated mathematics education research, Piaget's information processing model and Vygosky's social-constructivism.…”

Section: Introductionmentioning

confidence: 99%

“…They emphasized that in the mid-20 th century two theories have dominated mathematics education research, Piaget's information processing model and Vygosky's social-constructivism. Vidakovic and Martin advocated co-constructivism that reconciles both the individual and social aspects of Piaget and Vygotsky (Vidakovic & Martin, 2004). Viadaok and Martin concluded that mathematics learning can be enhanced by peer-collaboration in small groups, provided there are some common understandings of what counts as a proof.…”

Section: Introductionmentioning

confidence: 99%

“…There must be exposure to a higher level of reasoning, active participation (active reasoning and the exchange of ideas), and communication (Fawcett & Gourton, 2005;Vidakovic & Martin, 2004). Different skill levels lead to the conflict necessary for conflict (in ZPD and for Piaget).…”

Section: Introductionmentioning

confidence: 99%

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Constructivism and Peer Collaboration in Elementary Mathematics Education: The Connection to Epistemology

Gupta

2008

EURASIA J MATH SCI T

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In this paper, an attempt is made to determine if peer collaboration increases student achievement in teaching elementary mathematics. Empirical evidence and philosophical problems with constructivist epistemology are considered. Two things are argued: first, it is reasonable to think, for elementary mathematics, peers collaboration is useful (especially in heterogeneous groups). Peer collaboration is an appendage to instruction, not a replacement for the didactics of an expert, or individual problem solving (which occurs both at its inception, when mathematics is discovered as well as advanced levels). There is reciprocity between individual and social settings in learning mathematics. Second, for the teaching of mathematics an adequate epistemology will guide, to some extent, a successful pedagogy.

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Teaching a new conceptual framework of weight and gravitation in middle school

2015

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Empirical studies have reported difficulties, confusion, and lack of understanding among students at all levels of instruction regarding the issue of weight-gravitation-weighing relationships. This study examined the impact of a new conceptual framework of weight, on a small group of 7th-grade students (N ¼ 14) in a middle school in Israel. This conceptual framework, which defined weight operationally as weighing results, implied a natural distinction between weight and gravitational force, in contrast to the gravitational definition of weight, which identifies these two concepts. The new framework not only better fits modern scientific epistemology but also matches the common intuitive conception of weight as representing the heaviness of objects. This coherence promises innovative teaching leading to easier and more meaningful learning. The applied pedagogical method included a historical excurse and knowledge mediation through a discursive mode of teaching using images of different environments (Thinking Journey). The collected data of students' knowledge were structured in terms of scheme-facets of knowledge, which allowed qualitative evaluation of knowledge changes due to the instruction. We found that discussion of the lunar environment led students to appreciate the universality of gravitational attraction and to develop operational meaning for the up-down direction. Considering the environment of a coasting satellite encouraged students to distinguish between the gravitational force causing the orbiting around the Earth, and weight as the force that objects naturally exert on their support. It appeared that falling served as an anchoring concept leading students to the operational definition of weight. #

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Small-group searches for mathematical proofs and individual reconstructions of mathematical concepts

Cited by 8 publications

References 26 publications

An Empirical Examination of the Roles of Ability and Gender in Collaborative Homework Assignments

An Empirical Examination of the Roles of Ability and Gender in Collaborative Homework Assignments

Constructivism and Peer Collaboration in Elementary Mathematics Education: The Connection to Epistemology

Teaching a new conceptual framework of weight and gravitation in middle school

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