Visualisation and the Influence of Technology in ‘A’ Level Mathematics: A Classroom Investigation

Elliott, Sally; Hudson, Brian; O'Reilly, Declan

doi:10.1080/14794800008520074

Cited by 4 publications

(4 citation statements)

References 8 publications

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“…This is where the technology is powerful in facilitating the creation of many images rapidly in order to focus participants on the connections between them. Technology is also engaging and provides a change from the "normal" (forum Elliot (1998) [who] see visualisation as 'the relationship between images' to explain the boys' actions of using the software to sketch straight line graphs of equations inputted by them and improve their equations based on the feedback from the software (an indicator of his RiTPACK). He then explains how each time the feedback scaffolds the boys' learning in order to visualise there is a need to create many images to construct relationships that will facilitate visualisation and reasoning and concludes that the boys did benefit from the digital environment as in this thinking process another image is added to their visual understanding and they gain further clarity (End of Theme A task, week 4).…”

Section: The Case Of Markmentioning

confidence: 99%

Supporting Teachers in Developing Their RiTPACK Through Using Video Cases in an Online Course

Crisan

2018

Distance Learning, E-Learning and Blended Learning in Mathematics Education

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In order to help the participants on our online course engage critically with research to reflect on whether and how digital technology supports students' understanding and learning of mathematics, I proposed to trial the use of online video cases in the next presentation of this newly designed online course. In this chapter I will be reporting on trialling the use of video cases with the course participants and on the potential of using these videos with the aim of supporting the development of the participants' Research informed Teachers' Pedagogical Content Knowledge (RiTPACK) with a particular focus on how the digital environment supports students' mathematical work.

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Section: The Case Of Markmentioning

confidence: 99%

Supporting Teachers in Developing Their RiTPACK Through Using Video Cases in an Online Course

Crisan

2018

Distance Learning, E-Learning and Blended Learning in Mathematics Education

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“…Appropriate teaching approaches are thus crucial in GeoGebra-supported lessons to help students better manipulate digital tools and understand mathematical concepts. Therefore, in line with the framework of Technological Pedagogical Content Knowledge (TPACK), this paper aims to develop Previous studies have identified multiple difficulties in regard to quadratic functions, such as the misinterpretation of symmetrical lines and extreme points [5], sketching a quadratic function by looking at the difference in values of coefficients and solving simultaneous equations graphically. In accordance with my designed activity, this paper focuses on students' common difficulty in building the relationship between the algebraic equation of a quadratic function and a geometric graph [6].…”

Section: Introductionmentioning

confidence: 99%

Enhancing Teaching Quadratic Functions: The Benefits, Challenges, and Recommendations of Using GeoGebra

2023

AJMS

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This paper engages in an extensive literature review to discuss the existing research regarding using GeoGebra in teaching mathematics, specifically quadratic functions. After that, a description of the functionalities and features of GeoGebra and its potential for addressing the challenges of teaching and learning quadratic functions will be introduced. Based on my literature review, I designed an activity sequence designed to teach quadratic functions and explore how the activities align with learning objectives and the arrangement of tasks in line with the TPACK framework. The use of GeoGebra as a teaching tool has the potential to support students' reasoning and visualization skills and to assist teachers' demonstrations and explanations.

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“…They argue that computer based curriculum materials can give an "improved cognitive base" leading to a more powerful and flexible understanding of the mathematical concept. In a similar way, Carulla and Gomez (1997) note that technology can enable students to develop a greater "insight" into the relationship between graphs and functions and Elliott and Hudson (2000) suggest that a factor in allowing such insight to occur is that numerous functions and graphs can be demonstrated by a teacher in an effective manner that would not be possible with a whiteboard. Our study considers the way in which the computer enables the teacher, not to demonstrate numerous functions and graphs, but to allow the students to engage in exploring many different graphs and the outcome of such an approach.…”

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confidence: 99%

Making images and noticing properties: The role of graphing software in mathematical generalisation

Martin

Pirie

2003

Math Ed Res J

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This paper discusses the growth of mathematical understanding of two students, Graham and Don, as they use a computer graphing program to explore the properties of quadratic equations. Through analysing extracts of video data using the Pirie Kieren theoi T, we discuss the ways in which the mathematical understanding of the students grows and how their interactions occasion, facilitate, and restrict this. We consider four 'clips' of their mathematical working, highlighting different aspects of their developing understanding, and use of the graphing software. Although we are talking about a computer based graphing package, our conclusions are equally relevant to the use of graphing calculators.Penglase and Arnold (1996) provide a full and critical review of recent research into the use of the graphical calculator in mathematics teaching and learning. In considering the particular use of technology for exploring functions and graphs they note that: Some evidence suggests that use of the graphics calculator" aids the development of a more global understanding of the featm'es of functions, encore'aging conceptual images of functions, and understanding of the relationship between functions and graphs. Other" evidence appears to demonstrate that its use can result in incomplete understandings of function concepts. (p. 66) Interestingly, Penglase and Arnold (1996) note that many of these contradictory findings derive from the approaches which have been taken in looking at whether a graphing program leads to "a better understanding of the relationship between an algebraic function and its graph" (p. 67). They suggest that claims about the effectiveness of the software are often based on assessment procedures which equate understanding and learning with performance on traditional tests. Further, they suggest that much research is not actually concerned with the use of the tool in the process of teaching and learning, but instead a form of "program evaluation" (p. 58). In this paper we do not wish to equate mathematical understanding with test performance, and hence are not trying to evaluate the use of the computer in such terms. We are, however, seeking to offer an insight into the learning processes through which the computer might enable learners to work towards a better understanding of the relationship between a function and its graph.Hang and Thomas (1997), in investigating the effect of the use of computer based instruction, note that students who have used technology (in their case to work on calculus) developed a greater degree of "conceptual awareness" in comparison to those who were taught in a standard lecture form. Hang and Thomas (1997) suggest that without the computer the students had gaps in their conceptual understanding, and saw calculus as a "series of procedures and algorithms" with no "versatility of thought" (p. 87). They argue that computer based curriculum materials can give an "improved cognitive base" leading to a more powerful and flexible understanding of the mathematical concept. In a simila...

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Visualisation and the Influence of Technology in ‘A’ Level Mathematics: A Classroom Investigation

Cited by 4 publications

References 8 publications

Supporting Teachers in Developing Their RiTPACK Through Using Video Cases in an Online Course

Supporting Teachers in Developing Their RiTPACK Through Using Video Cases in an Online Course

Enhancing Teaching Quadratic Functions: The Benefits, Challenges, and Recommendations of Using GeoGebra

Making images and noticing properties: The role of graphing software in mathematical generalisation

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