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The Concept of Invariance in School Mathematics
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Libeskind, Shlomo; Stupel, Moshe; Oxman, Victor – International Journal of Mathematical Education in Science and Technology, 2018
In this paper, we highlight examples from school mathematics in which invariance did not receive the attention it deserves. We describe how problems related to invariance stimulated the interest of both teachers and students. In school mathematics, invariance is of particular relevance in teaching and learning geometry. When permitted change…
Descriptors: Mathematics Instruction, Mathematical Concepts, Geometry, Teaching Methods
The Use of Transformations in Solving Equations
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Libeskind, Shlomo – International Journal of Mathematical Education in Science and Technology, 2010
Many workshops and meetings with the US high school mathematics teachers revealed a lack of familiarity with the use of transformations in solving equations and problems related to the roots of polynomials. This note describes two transformational approaches to the derivation of the quadratic formula as well as transformational approaches to…
Descriptors: Equations (Mathematics), Mathematics Teachers, Mathematics Instruction, Problem Solving
Some Ideas on How to Create Mathematical Problems.
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Avital, Shmuel; Libeskind, Shlomo – International Journal of Mathematical Education in Science and Technology, 1978
A major source of challenging problems for students is the use of higher mathematics to derive elementary problems. Several examples are given. (MP)
Descriptors: Calculus, College Mathematics, Higher Education, Inequalities