Visualization of Functional Dependences in Dynamic Geometry Systems

We describe various methods of visualization of functions and geometric transformations encountered in school mathematics by means of the dynamic geometry systems such as MathKit, The Geometer’s Sketchpad, and GeoGebra and their usage scenarios in the spirit of modern trends in education. Novel opportunities for teaching and learning functions and their properties based on computer models are discussed. The focus is on specifically computerized interpretations of functions, in particular, the so-called dynagraphs, in which parallel axes of arguments and values are used, and the correspondence given by the function is found when the argument-point moves along its axis.

Dynamic Geometry Systems in Mathematics Education: Attitudes of Teachers

At present, the innovative trends in education are also often associated with the integration of ICT into the teaching process. The relationship between mathematics, teaching and computers are long-standing and complex. The actual practice of mathematics has changed its nature considerably because of the availability of powerful computers, both in the workplace and on researches’ desks. Several software systems are available for mathematics teachers, among which have dynamic geometry systems a significant presence. Although various forms of education for teachers are currently organized and teachers have at their disposal a variety of learning materials and ideas for teaching, it is questionable to what extent these factors are reflected in school practice. The article describes a survey which was aimed to assess the state of the use of dynamic geometry systems in mathematics teaching at elementary and secondary schools and to find out teachers’ views about suitability and possibilities of using it to improve mathematics education. The survey was conducted by questionnaire and subsequently also by interviews with teachers.

Reasoning by contradiction in dynamic geometry

This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students’ work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we support the claim that a DGS can offer guidance in the solver’s development of an indirect argument thanks to the potential it offers of both constructing certain properties robustly, and of helping the solver perceive pseudo objects.Razonamiento por contradicción en geometría dinámicaEste artículo aborda las contribuciones que los sistemas de geometría dinámica (DGSs) pueden dar al razonamiento por contradicción en geometría. Presentamos un análisis de tres extractos del trabajo de estudiantes y el uso de la noción de pseudo-objeto, elaborado a partir de investigaciones anteriores, para mostrar algunas especificidades del DGS en la construcción de pruebas por contradicción. En particular, afirmamos que un DGS puede orientar en el desarrollo de un argumento indirecto gracias a las posibilidades que ofrece tanto para construir sólidamente algunas propiedades como para ayudar a percibir los pseudoobjetos.Handle: http://hdl.handle.net/10481/22368Nº de citas en WOS (2017): 2 (Citas de 2º orden, 4)Nº de citas en SCOPUS (2017): 1 (Citas de 2º orden, 5)