Function and Graph in DGS Environment

2016

Assuming that dynamic features of Dynamic Geometry Software may provide a basic representation of both variation and functional dependency, and taking Vygotskian perspective of semiotic mediation, a teaching experiment has been designed with the aim of introducing pupils to the idea of function. First data coming from the observations in Italian and French classrooms are presented.

1988

This report summarizes the work of a two-year project which focused primarily on the problems that students have with algebra in general, and graphs in particular. The first of two major sections in the document deals with the use of computer software to assist in the teaching of graphing. It concludes that thoughtful design and use of graphing software presents new opportunities for teaching about graphing. The next section of the report centers on the development of research instruments that are intended to study scale in the context of graphs of function. It includes a set of problem-based teaching materials that were used as research tools. The appendices contain descriptions of probes designed to see if students can interpret and create graphs of real-world phenomena, along with instruments dealing with mapping, scale, and computer explorations. (TW)

International Journal of Mathematical Education in Science and Technology, 2013

In a series of previous studies, the authors have described specific mental constructions that students need to develop, and which help explain widely observed difficulties in their graphical analysis of functions of two variables. This new study, which applies Action-Process-Object-Schema theory and Semiotic Representation Theory, is based on semi-structured interviews with 15 students. It results in new observations on student graphical understanding of two-variable functions. The effect of research findings in designing a set of activities to help students carry out the specific constructions found to be needed is briefly discussed.

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bsrlm.org.uk

In this paper, we contrast the mathematical simplicity of the function concept that is appreciated by some students and the spectrum of cognitive complications that most students have in coping with the function definition in its many representations. Our data is based on interviews with nine (17-year old) students selected as a crosssection from 114 responses to a questionnaire. We distinguish four categories in a spectrum from those who have a simple grasp of the core function concept applicable to the full range of representations to those who see only complicated details in different contexts without any overall grasp of the conceptual structure.

In the presentation we focused, from an enactivistic perspective, the effects that produce the uses of metaphors in the analytic study of graphical of functions in High Secondary School (16-17 years old students). The central metaphor "the graph of a function can be considered as the outline that leaves a point that moves subject to certain conditions" is speciffically observed.

2019

Value-thinking…………………………………………..28 Location-thinking……………………………………….29 Building on David et al.'s (2019a) Preliminary Framework ……………………………………………………………30 3 LITERATURE REVIEW……………………………………………………...32 Visualization in the Teaching and Learning of Calculus………………...33 Visualization As Instructional Interventions in Calculus……...34 Benefits of Visualization in the Learning of Calculus…………...39 Issues in Students' Understanding and Use of Graphs of Functions…….43 vii CHAPTER Page Issues in Students' Attention to Figural Aspects in Graphs……..44 Students' Tendencies When Reasoning From Graphical Examples..

International Journal of Mathematical Education in Science and Technology, 1992