Victor Oxman
@wgalil.ac.il
School of Management
Western Galilee College
RESEARCH INTERESTS
Math & Math Education
Scopus Publications
Scopus Publications
Victor Oxman and Moshe Stupel
Cambridge University Press (CUP)
107.14 Does a trapezium exist whose side lengths form a geometric progression? It is known that there is no trapezium whose lengths of consecutive sides form an arithmetic progression [1]. Is this true also for a geometric progression? Let in trapezium with the lengths of consecutive sides form a geometric progression with common ratio . ABCD BC // AD q > 1 Obviously it is enough to consider two cases. In the first case the geometric progression starts at and in the second case it starts at . AB BC
Moshe Stupel and Victor Oxman
Cambridge University Press (CUP)
Victor Oxman and Moshe Stupel
Springer Science and Business Media LLC
Jay Jahangiri, Victor Oxman, and Moshe Stupel
Springer Science and Business Media LLC
Victor Oxman and Moshe Stupel
Cambridge University Press (CUP)
Victor Oxman and Moshe Stupel
Informa UK Limited
Victor Oxman
Informa UK Limited
In the article, we prove 18 inequalities involving inradius, a length of one side and one additional element of a given triangle. 14 of these inequalities are the necessary and sufficient conditions for the existence and uniqueness of such a triangle. All proofs are based on standard methods of calculus and can serve as a good demonstration of the relationship between different branches of mathematics (geometry, algebra, trigonometry, calculus). The article can be used by teachers and students in courses on advanced classical geometry.
Victor Oxman and Moshe Stupel
Informa UK Limited
ABSTRACT We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16–17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the danger of using a wrong converse, the problem was posed as field research to a group of pre-service teachers and training teachers in the ‘methods (of teaching mathematics)’ course, where similar failures were discovered. The conclusion is that a large part of the students was not aware that the converse is not always true, and its correctness is to be tested before it can be used. The investigation of the problem was accompanied by a dynamic geometry environment software that allowed us to examine the problem in the general case and so to make conclusions for particular cases.
Victor Oxman and Moshe Stupel
Cambridge University Press (CUP)
Victor Oxman, Ruti Segal, and Moshe Stupel
Modestum Publishing Ltd
The study aimed to expose how pre-service teachers perceived the value of an inquiry-based geometrical task with dynamic geometry software for increasing and deepening their understanding of the task itself, and for heightening their mathematical, pedagogical, and technological knowledge in the case of reflection and transformation. Twenty-seven pre-service teachers studying to become middle-school (junior high) mathematics teachers were assigned an inquiry-based geometrical task to explore – both by conventional, low-tech means (paper and pencil) and then in a dynamic geometry software (DGS) environment – the properties of objects formed by reflections in polygons (triangles and quadrilaterals) and to offer conjectures and proofs regarding the final polygon’s shape and area concerning the original. The results show that the majority of participants indicated that DGS provided a valuable instrument for revising and expanding their knowledge, that the assignment demonstrated the value that technological tools have in teaching and learning processes, and the importance of adapting learning tasks in geometry to a dynamic geometry environment for expanding and deepening geometrical and pedagogical knowledge and reasoning skills.
Victor Oxman and Moshe Stupel
Informa UK Limited
Summary We present a visual proof for an elegant property of three segments on the diagonal of a square.
Victor Oxman and Moshe Stupel
Informa UK Limited
The paper presents a problem that has all the components that make it usable as a research problem for both high school students and in training mathematics teachers at teacher training colleges and universities. The problem contains various geometric curves and shapes: squares, circles, sectors, segments, parabola. It can be developed in stages, asking additional questions that, on the one hand, increase the level of complexity, and on the other hand, reveal the beauty of mathematics.
Victor Oxman and Moshe Stupel
Informa UK Limited
ABSTRACT The present paper describes a dynamic investigation of polygons obtained by reflecting an arbitrary point located inside or outside a given polygon through the midpoints of its sides. The activity was based on hypothesizing on the shape of the reflection polygon that would be obtained, testing the hypotheses using dynamic software, and finding a justified mathematical proof. The activity was also applied to properties that are conserved or not conserved as a result of the reflection. Additionally, we find the mathematical relation for the ratio between the area of the reflection polygon and the area of the original polygon. The population of the study was pre-service teachers and experienced teachers who study in teaching college.
Victor Oxman, Moshe Stupel, and Shula Weissman
Informa UK Limited
The present paper describes beautiful conservation relations between areas formed by different geometrical shapes and area relations formed by algebraic functions. The conservation properties were investigated by students at an academic college of education using a computerized technological tool and were subsequently accompanied by justified proofs.
Victor Oxman and Avi Sigler
Informa UK Limited
ABSTRACT In this article we consider two triangles: one inscribed in another. We prove that the area of the central triangle is at least the harmonic mean of the areas of corner triangles. We give two proofs of this theorem. One is based on Rigby inequality and the other is based on the known algebraic inequality, to which we bring a new, geometric, proof. The article can be used by teachers and students in courses on advanced classical geometry.
Victor Oxman and Moshe Stupel
Cambridge University Press (CUP)
Victor Oxman, Avi Sigler, and Moshe Stupel
Springer International Publishing
Victor Oxman and Moshe Stupel
Informa UK Limited
Victor Oxman and Moshe Stupel
Informa UK Limited
ABSTRACT A geometrical task is presented with multiple solutions using different methods, in order to show the connection between various branches of mathematics and to highlight the importance of providing the students with an extensive ‘mathematical toolbox’. Investigation of the property that appears in the task was carried out using a computerized tool.
Shlomo Libeskind, Moshe Stupel, and Victor Oxman
Informa UK Limited
ABSTRACT 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 leaves some relationships or properties invariant, these properties prove to be inherently interesting to teachers and students.
Victor Oxman, Moshe Stupel, and Jay M. Jahangiri
Informa UK Limited
Abstract The article is dedicated to solving extrema problems in teaching mathematics, without using calculus. We present and discuss a wide variety of mathematical extrema tasks where the extrema are obtained and find their solutions without resorting to differential. Particular attention is paid to the role of arithmetic and geometric means inequality in solving these problems.
Victor Oxman and Moshe Stupel
Informa UK Limited
Summary In a triangle ABC in which angle A measures 60 degrees, the bisectors of angles B and C are used to construct a cyclic quadrilateral with two congruent sides.