Reconstructing Mathematics Pedagogy from a Constructivist Perspective

Simon, Martin

doi:10.2307/749205

Cited by 868 publications

(527 citation statements)

References 19 publications

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“…Upon engaging in a new experience, learners reorganise their conceptual framework to assimilate or accommodate this experience (von Glasersfeld, 1984). This is when learning takes place (Lerman, 1996), a process also captured by Piaget's notion of cognitive disequilibrium, where previous knowledge is challenged by unfamiliar or misunderstood experiences and moves towards cognitive equilibrium, as these experiences are reconceptualised and the knowledge has been constructed and accommodated (Simon, 1995).…”

Section: Constructivismmentioning

confidence: 99%

Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma

Bragg¹

2007

Math Ed Res J

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Mathematics games are widely employed in school classrooms for such reasons as a reward for early finishers or to enhance students' attitude towards mathematics. During a four week period, a total of 222 Grade 5 and 6 (9 to 12 years old) children from Melbourne, Australia, were taught multiplication and division of decimal numbers using calculator games or rich mathematical activities. Likert scale surveys of the children's attitudes towards games as a vehicle for learning mathematics revealed unexpectedly high proportions of negative attitudes at the conclusion of the research. In contrast, student interview data revealed positive associations between games and mathematical learning. This paper reports on the methodological dilemma of resultant conflicting attitudinal data related to game-playing. Concerns arising from the divergence in the results are raised in this paper. Implications based on the experience of this study may inform educational researchers about future methodological choices involving attitudinal research.Mathematical games are popular with teachers as alternatives to more traditional forms of repetitive practice, for many parts of the mathematics curriculum, and especially for arithmetical computation. The research literature, as well as popular commercial publishing, supports the idea that games can fire children's interest and motivation because students enjoy competition, challenge, and fun (Bragg, 2003;Bright, Harvey, & Wheeler, 1985;Ernest, 1986;Gough, 1999;Owens, 2005).This research began by assuming that a novel pedagogical approach, such as game-playing, might have a positive effect on students' classroom engagement and attitudes towards mathematics. What is reported here is based on a larger study which explored games as a pedagogical approach to enhance mathematical learning (see . Games were examined in that larger study for their potential to promote mathematical learning, but that aspect is not reported in this paper. Surprisingly, triangulation of the data revealed conflicting attitudinal responses from the students about games. These attitudinal data were collected via Likert scales and student interviews. This paper focuses on the methodological difficulty of interpreting conflicting results and raises some possible explanations as to the contradictory nature of these data. Background and Theoretical FrameworkAttitudes

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Section: Constructivismmentioning

confidence: 99%

Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma

Bragg¹

2007

Math Ed Res J

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“…This includes decisions on the way a task is introduced and worked through, on the possible roles of the artefacts to be played, and on the schemes and techniques to be developed and established by the students. Decisions on the exploitation mode can be seen as part of the design of a Hypothetical Learning Trajectory (Simon, 1995). In terms of the metaphor of orchestration, setting up the exploitation mode can be compared with determining the partition for each of the musical instruments involved, bearing in mind the anticipated harmonies that will emerge.…”

Section: Theoretical Framework and Research Questionsmentioning

confidence: 99%

The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom

et al. 2010

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The availability of technology in the mathematics classroom challenges the way teachers orchestrate student learning. Using the theory of instrumental orchestration as the main interpretative framework, this study investigates which types of orchestrations teachers develop when using technology and to what extent these are related to teachers' views on mathematics education and the role of technology therein. Data consisted of videotapes of 38 lessons taught by three teachers, who also provided information on their views through questionnaires and interviews. Qualitative analysis of these data led to the identification of orchestration types and teacher profiles. The orchestration preferences of the three teachers proved to be related to their views. A detailed analysis of one exemplary episode suggests how other theoretical perspectives might complement the theory of instrumental orchestration.

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“…Many researchers urge teachers to reflect upon their own teaching as a way of transforming their beliefs and making sound instructional decisions for their students (e.g., Cooney, 1999;Schön, 1983;Simon, 1995).One problem is that the prospective teachers' actual teaching practice is usually limited to only a few hours in a field experience setting while taking the mathematics me-thods course. With this in mind, more recent studies are geared toward creating explicit, task-oriented environments that provide more realistic classroom conditions.…”

Section: Supporting Prospective Teachers: Problems and Possibilitiesmentioning

confidence: 99%

Examination of Prospective Teachers' Perceptions on Mathematical Concepts and Their Potential Teaching Strategies

Lee¹

2014

Research in Mathematical Education

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This study examined the potential teaching strategies of prospective elementary teachers and their perceptions of the procedural/conceptual nature of examples. Fifty-four prospective teachers participated in this study, engaging in two-phase tasks. Analysis of data indicated that: (a) Overall, the participants' perceptions were geared toward putting emphasis on conceptual understanding rather than procedural understanding; but (b) Generally, procedure-oriented strategies were more frequently incorporated in participants' potential teaching plans. This implied that participants' preconceived ideas regarding math examples were not always reliable indicators of their potential teaching strategies. Implications and suggestions for mathematics teacher preparation are discussed.

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Reconstructing Mathematics Pedagogy from a Constructivist Perspective

Cited by 868 publications

References 19 publications

Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma

Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma

The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom

Examination of Prospective Teachers' Perceptions on Mathematical Concepts and Their Potential Teaching Strategies

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