Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-04T21:42:57.174Z Has data issue: false hasContentIssue false
  • English
  • Français

Teaching proofs without words using dynamic geometry

Published online by Cambridge University Press:  06 June 2019

Moshe Stupel ,
Avi Sigler  and
Jay Jahangiri
Moshe Stupel
Affiliation:
Gordon-Academic College of Education and Shaanan Religious, Academic College of Education, Haifa, Israel e-mail: [email protected]
Avi Sigler
Affiliation:
Shaanan Religious Academic College of Education, Haifa, Israel e-mail: [email protected]
Jay Jahangiri
Affiliation:
Mathematical Sciences, Kent State University, Kent, Ohio, U.S.A. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

A Proof Without Words (PWW) contains data, the claim that is to be proved, and one or more diagrams, sometimes without anything else and in other cases with a few mathematical expressions, without any verbal justifications [1]. It is assumed that students and researchers who possess the related appropriate mathematical knowledge will view the drawings and the expressions, will be able to follow and justify each step in the proof and develop their own visual proof abilities. PWW is very much like a cartoon which contains a drawing with sometimes only a few words or sometimes no words at all and the observers are expected to understand the context or the projected message.

Type
Articles
Information
The Mathematical Gazette , Volume 103 , Issue 557 , July 2019 , pp. 204 - 211
Copyright
© Mathematical Association 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brown, J. R., Philosophy of mathematics: an introduction to the world of proofs and pictures, Routledge (1999).Google Scholar
Nelsen, R. B., Proofs without words I: exercises in visual thinking, Vol. 1, The Mathematical Association of America (1993).Google Scholar
Nelsen, R. B., Proofs without words II: more exercises in visual thinking, Vol. 2, The Mathematical Association of America (2001).Google Scholar
Nelsen, R. B., Proofs without words III: further exercises in visual thinking, Vol. 3, The Mathematical Association of America (2015).CrossRefGoogle Scholar
Eves, H., Great moments in mathematics before 1650, The Mathematical Association of America (1983).Google Scholar
Vinner, S., The avoidance of visual consideration in calculus students, focus on learning problems in mathematics, 11(2) (1989), pp. 149-156.Google Scholar
De Villiers, M., An alternative approach to proof in dynamic geometry in Lehrer, R. and Chazan, D. (eds), Designing learning environments for developing understanding of geometry and space, Lawrence Erlbaum Associates, Hillsdale, N.J. (1998) pp. 369-394.Google Scholar
Stupel, M. and Ben-Chaim, D., One problem, multiple solutions: How multiple proofs can connect several areas of mathematics, Far East J. Math. Education, 11(2) (2013).Google Scholar
Geogebra, An equality between the half sum of two opposite side lengths of quadrilateral, accessed January 2019 at: https://www.geogebra.org/m/g6uTHHuRGoogle Scholar
Manfrino, R. B., Ortega, J. A. G., and Delgado, R. V., Inequalities: a Mathematical Olympiad approach, Birkhauser (2009) p. 67.CrossRefGoogle Scholar
Geogebra, Relationship among some elements of triangles, accessed January 2019 at: http://tube.geogebra.org/m/1993141Google Scholar
Geogebra, Relations between the radii of the inscribed circles of a triangle, accessed January 2019 at: https://www.geogebra.org/m/tdasPakJGoogle Scholar