The concept of invariance in school mathematics

Libeskind, Shlomo; Stupel, Moshe; Oxman, Victor

doi:10.1080/0020739x.2017.1355992

Cited by 7 publications

(2 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Euclidean geometry, by nature, comprises a large set of conservation properties based on the results of a single change. In fact all geometrical theorems imply a certain axiom of conservation [2].…”

Section: Introductionmentioning

confidence: 99%

Geometrical theorems about conservation of area for use in classroom activities

Stupel¹,

Weissman

Tal

2021

Math. Gaz.

Self Cite

View full text Add to dashboard Cite

Five geometrical tasks demonstrating the interesting property of conservation of area that may be used in the mathematics classroom are presented. The initial premise is proved and then changes in attributes are investigated using dynamic geometric software to show that in the cases demonstrated there is conservation of area or specific ratios. These demonstrations illuminate the hidden beauty in mathematics and constitute an intellectual stimulus for discovering additional properties.

show abstract

Section: Introductionmentioning

confidence: 99%

Geometrical theorems about conservation of area for use in classroom activities

Stupel¹,

Weissman

Tal

2021

Math. Gaz.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The relationship between symmetry and invariance in mathematics and science has been symbiotic, each contributing to the other's development (Klein, 1990;Weyl, 1952, p.135). Indeed, invariance is very relevant in teaching and learning geometry, but it does not receive the attention it deserves in education (Libeskind, Stupel, & Oxman, 2018;Schuster, 1971). The activities described below are designed to achieve this topic in the teaching-learning process at primary school.…”

Section: Introductionmentioning

confidence: 99%

Nature of Science Interdisciplinary Teaching at Primary School Based on Symmetry and the Search of Invariants

Brasili¹,

Piergallini²

2021

Advances in Education and Educational Trends Series

View full text Add to dashboard Cite

The project is situated in the field of teaching physics, generally speaking, science education. It aims at studying the interplay between physics and mathematics, introducing an interdisciplinary approach based on the modern concept of symmetry or sameness within change (i.e., invariance). The interdisciplinary methods integrate the process skills common to discovery-based science and problem-based mathematics, typically of Nature of Science (NoS) modelling. We designed a teaching-learning sequence(TLS) and implemented it in an Italian primary school on a sample group (N = 96). Research conforms to pre-and post-test design with a control group. The resulting data were examined through a mixed method. We assess the effectiveness of the TLS by analysing the learning changes in the level of pupils’ knowledge of symmetry. The findings show that the pupils were in the regime of competence for grasping the changed view of symmetry. It also provides ideas that the concepts of symmetry and invariance will allow building the architecture of more extensive scientific knowledge. The study of transformations and invariants facilitates the acquisition of cognitive procedures fitting in many domains, modelling and generalization processes. This research contribution brings important suggestions for designs of successive steps in the learning path on symmetry.

show abstract