Directional Effects in Transformation Tasks

Schultz, Karen A.; Austin, Joe Dan

doi:10.2307/748577

Cited by 12 publications

(8 citation statements)

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“…Similar to the findings of other studies that have dealt with children (Cooper, 1992;Grenier, 1985;Hershkowitz et al, 1990;Schultz, 1978;Schultz & Austin, 1983;Thomas, 1978;Zaslavsky, 1994), the students did not exhibit any problems sketching a mirror image when the symmetry lines were vertical or horizontal. However, lines that were oblique often led them to distort the mirror image and create two parts which were congruent but not symmetrical.…”

Section: Discussionsupporting

confidence: 76%

“…Several studies in the period 1975-1985 investigated students' understanding of symmetry in the framework of courses on transformational geometry that were being introduced into experimental mathematics curricula at the time. These studies generally reported an association between students' cognitive development and their performance on symmetry-related tasks (Schultz, 1978;Schultz & Austin, 1983;Thomas, 1978;Thompson,1985).…”

Section: Teaching and Learning Symmetrymentioning

confidence: 99%

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Learning through teaching: The case of symmetry

2000

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A study was carried out within the framework of an undergraduate course in teaching skills and strategies. An experhnental part of the course was desigaled to provide an opportunity for the students to learn a mathematical topic through teaching it to eighth grade pupils in a Learning Through Teaching (LTT) enviromnent.Symmetry was chosen as file focal mathematical topic for the experiment. This paper focuses on the development of the students' understanding of line sy~mnetry. The findings show that the implemented LTT enviromnent served as a vehicle for the student teachers to learn mathematics. In spite of the difficulties they encountered during the study, the students expressed positive dispositions towards symmetry and its role in mathematics.Our study stems from the conviction that symmetry can be helpful both for understanding various mathematical concepts and for solving mathematical problems. We also beheve that symmetry has the potential to foster a rich and powerful learning, teaching, and learning-to-teach environment.The study reported in this paper is part of a larger research project aimed at exploring the concept of symmetry as a tool for the professional development of mathematics teachers (Leikin, 1997). The students who took part in the study were student teachers enrolled in an undergraduate course on general teaching skills and strategies. For the purpose of this study, students were required to learn the concept of symmetry in order to be able to teach it. The development of the students' content and pedago~cal knowledge (Shulman, 1986) was observed, documented, and analysed. This paper focuses on the development of students" knowledge of the concept of line symmetry and their dispositions towards symmetry.

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Section: Discussionsupporting

confidence: 76%

Section: Teaching and Learning Symmetrymentioning

confidence: 99%

Learning through teaching: The case of symmetry

2000

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“…Sebagai contoh siswa belum dapat megeneralisasikan bahwa refleksi titik A (x,y) ke sumbu X akan menghasilkan bayangan A'(x,-y). kesulitan lain yang dialami oleh siswa salah satunya dengan arah transformasi (Schultz & Austin, 1983 (Sembiring, Hoogland, & Dolk, 2010). PMRI menjadikan pengajaran matematika menjadi lebih bermakna.…”

Section: Sejak Tahun 2001 DI Indonesia Telah Berlangsung Suatu Pendekunclassified

Belajar Pencerminan dengan Menggunakan Permainan Bom-Boman di Kelas VII

2018

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This study produces a learning trajectory in transformation geometry, specifically on reflection using a game called “bom-boman”. This study using PMRI, the Indonesian version of realistic mathematics education. Subjects of this study are 36 seventh grade students of SMP Negeri 24 Palembang. This study using a design research approach with conducted in three stages: preliminary design, the design experiment (pilot experiment & teaching experiment), and retrospective analysis. Data were collected by observations, interviewing the student, collecting student worksheet, and documentation of classroom event and group works. Hypothetical Learning Trajectory (HLT) has been designed then compared to Actual Learning Trajectory (ALT) during the learning process. Retrospective analysis shows that student’s learning trajectories using the game help students to understand transformation geometry in reflection.

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“…The curriculum emphasizes helping students build relational understanding of the subject matter. Some research indicates that motion geometry tasks are tractable for elementary school students [6] and that such tasks may improve spatial abilities 171, although there is conflicting evidence suggesting that students this age can not effectively study geometric motions [8-lo]. These studies suggest that while rigorous mathematical transformations may be problematic for elementary age students, a less formal approach, including explicit attention to the transition from physical movements to more mathematically sophisticated representations, may be beneficial 11, 111.…”

mentioning

confidence: 98%

Effects of Computer and Noncomputer Environments on Students' Conceptualizations of Geometric Motions

Johnson-Gentile

Clements

Battista

1994

Journal of Educational Computing Research

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This study investigated the effects of computer and noncomputer environments on leaming of geometric motions. Two treatment groups, one of which used specially designed Logo computer environments, and one of which used manipulatives and paper and pencil, received eight lessons on geometric motions. Interviews revealed that both treatment groups, especially the Logo group, performed at a higher level of geometric thinking than did a control group. Both treatment groups outperformed the control group on immediate and delayed posttests; though the two treatment groups did not significantly differ on the immediate posttest, the Logo group outperformed the nonLogo group on the delayed posttest. Thus, there was support for the effectiveness of the curriculum and for the notion that the Logo-based version enhanced the construction of higher-level conceptualizations of motion geometry.The major focus of standard elementary school geometry curricula is on recognizing and naming geometric shapes, writing the proper symbolism for simple geometric concepts, and using formulas in geometric measurement. Too often

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Directional Effects in Transformation Tasks

Cited by 12 publications

References 0 publications

Learning through teaching: The case of symmetry

Learning through teaching: The case of symmetry

Belajar Pencerminan dengan Menggunakan Permainan Bom-Boman di Kelas VII

Effects of Computer and Noncomputer Environments on Students' Conceptualizations of Geometric Motions

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