Undergraduate Mathematics Enhanced With Graphing Technology

2009

From preliminary analysis of teacher-nominated examples of successful technologysupported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater depth through case study of two teachers each teaching two lessons of this type. The practitioner model developed in earlier research provided a framework for synthesising teacher thinking about the contribution of graphing software. Further analysis highlighted the crucial part played by teacher prestructuring and shaping of technology-and-task-mediated student activity in realising the ideals of the practitioner model. Although teachers consider graphing software very accessible, successful classroom use still depends on their inducting students into using it for mathematical purposes, providing suitably prestructured lesson tasks, prompting strategic use of the software by students, and supporting mathematical interpretation of the results. Accordingly, this study has illustrated how, in the course of appropriating the technology, teachers adapt their classroom practice and develop their craft knowledge: particularly by establishing a coherent resource system that effectively incorporates the software; by adapting activity formats to exploit new interactive possibilities; by extending curriculum scripts to provide for proactive structuring and responsive shaping of activity; and by reworking lesson agendas to take advantage of the new time economy.

2004

This paper draws on research being developed within the teaching and learning strand of the Economic and Social Research Council InterActive Education Project, which is examining how new technologies can be used in educational settings to enhance learning. It focuses on the ways in which mathematics teachers can use digital tools for enhancing the learning of functions and graphs within a classroom setting.

2017

This paper was published in the Proceedings of the 13th International Congress on Mathematical Education held at Hamburg, Germany from 24 - 31 July 2016

Enhancing Mathematics Understanding through Visualization, 2013

This chapter outlines the structure of the initial module of a pilot project investigating the benefits of using dynamical mathematical software when teaching students about cross-curricular models of thinking. Focus is on the use of conceptual metaphors when teaching the concept of infinity in mathematics as well as in literature. The use of dynamical mathematics software facilitated constructions of multiple representations in problem solving in a series of carefully selected problems involving infinity. The pilot project is currently being evaluated, but preliminary findings indicate an increased student awareness of the usefulness of the software when learning how to use mathematical inscriptions for problem solving. The pilot project will be expanded in the Fall 2011 to include 6 classes across Denmark to test the applicability of the software, the teaching model and the teaching materials in a variety of classes to see if the initial successes of the project can be replicated.

Zentralblatt für Didaktik der Mathematik, 2003

In this paper we summarize our concepts and practice on computer-aided mathematical experimentation, and illustrate them by Mathematica projects that we have developed for our research and the courses "Computer-aided mathematical modelling" and "Computer Algebra I-II" held for students of life sciences at University of Szeged and computational engineering at TFH Berlin, University of Applied Sciences. Zusammenfassung: In diesem Artikel fassen wir unser Konzept und unsere Erfahrungen zu computergestützten mathematischen Experimenten zusammen. Wir illustrieren sie mit in Mathematica realisierten Beispielen. Diese wurden sowohl im Rahmen unserer Forschung als auch für die Kurse "Computergestützte mathematische Modellbildung" und "Computer Algebra I-II" entwickelt, die sich an Studenten der Universität Szeged bzw. an Studenten im Studiengang Computational Engineering der TFH Berlin richten.

2001

Computers in the Schools, 2013

2002

Over the past more than two decades, the population of students entering universities has significantly increased to the point where mass lectures have to be delivered to hundreds of students. More emphasis has been focused on teaching technical sciences and engineering in these days. The main prerequisite for all these scientific disciplines is Calculus. Many techniques have been developed at high school as well as tertiary level to teach calculus around the globe using various software with personal computer, because of low cost of quality software and hardware. One of the popular techniques, which are being used in teaching Calculus, is the Graphical Techniques. We argue that the technique can be used in the latest concept of 'Smart School', to teach Calculus and particularly the 'Additional Mathematics'. We put forward our argument that graphical techniques can change the traditional activities in teaching and learning of Additional Mathematics and particularly Calculus, trigonometry and geometry, because of visual concepts. This could lead to a smooth transition from manual to computer aided learning approaches.

2015

There is no doubt that technological tools have greatly impacted our mathematics teaching, learning and research in recent years. The exciting innovative ways of present-ing learning, teaching and research materials on the internet have prompted educators and researchers to rethink the importance of taking global views to solve local problems. In this paper, we use several examples to demonstrate how some abstract mathemati-cal concepts can be conveyed to students through graphical approach. The urgency of conducting collaborative research because of the existence of a solution is simply not ad-equate when computational tools are available nowadays. Furthermore, we emphasize that technology can be implemented e¤ectively to enhance pre-service teachers' content knowledge. Finally, we urge all software and hardware developers to work together to make the learning tools more uniformly accessible. After all, those starting to use techno-logical tools should be concentrating on how m...

Ensino e Tecnologia em Revista, 2017

Interactive Virtual Math (IVM) is a visualization tool to support secondary school students’ learning of graphs by dynamic events. In the prototype version students construct a graph and try to improve it themselves and with the feedback of the tool. In a small-scale experiment, which involved four classes at secondary and tertiary education and their mathematics teachers we investigated how the students used the tool in the classroom. In this study we focus on the students learning experience and the results are expected to provide knowledge and directions for further development of the tool. The corpus data consists of self-reported questionnaires and lessons observations. One main finding is that students, at different school levels, find the tool useful to construct or improve graphical representations and it can help to get a better understanding of the subject. The tool features that helped students most were the self-construction of the graphs and to get feedback about their ...

1992

The human brain is powerfully equipped to process visual information. By using computer graphics it is possible to tap this power to help students gain a greater understanding of many mathematical concepts. Furthermore, dynamic representations of mathematical processes furnish a degree of psychological reality that enables the mind to manipulate them in a far more fruitful way than could ever be achieved starting

Teaching Mathematics and Computer Science, 2004

The computer, if used more effectively, could bring advances that would improve mathematical education dramatically, not least with its ability to calculate quickly and display moving graphics. There is a gap between research results of the enthusiastic innovators in the field of information technology and the current weak integration of the use of computers into mathematics teaching. This paper examines what exactly the real potentials of using some mathematics computer software are to support mathematics teaching and learning in graph-oriented problems, more specifically we try to estimate the value added impact of computer use in the mathematics learning process. While electronic computation has been used by mathematicians for five decades, it has been in the hands of teachers and learners for at most three decades but the real breakthrough of decentralised and personalised microcomputer based computing has been widely available for less than two decades. And it is the latter facility that has brought the greatest promise for computers in mathematics education. That computational aids overall do a better job of holding students' mathematical interest and challenging them to use their intellectual power to mathematical achievement than do traditional static media is unquestionable. The real question needing investigation concerns the circumstances where each is appropriate. A case study enabled a specification of advantages and obstacles of using computers in graph-oriented questions. Individual students' interviews revealed two less able students' reactions, difficulties and misinterpretations while using computers in mathematics learning. Among research outcomes is that the mathematical achievement of the two students observed improved and this makes teaching with computers an overriding priority for each defined teaching method. This paper may not have been realised without the valuable help of the Hungarian Eötvös State Grant.

Procedia - Social and Behavioral Sciences

Technology can play an important role in mathematics education. It allows to better capture the attention of the students and enables them to better understand and master mathematical concepts. One of the most powerful computer programs that can assist us in the teaching of mathematics is Maple. Maple provides opportunities to explain classical mathematical concepts in a practical and effective way. Maple's effectiveness stems from its capacity to help visualize concepts and to solve complex problems which are difficult to be solved by hand. This effectiveness will be illustrated with three important topics in Calculus: Newton's Method, Riemann sum and the solid of revolution. The limitation of Technology is also discussed: while a program like Maple is very helpful, it cannot replace theory. Students must still understand all the theory behind the all pictures and must still practice all mathematics in traditional way.

The use of various types of technologies in the classroom and examinations is growing rapidly and is strongly influencing teaching and learning practices. In this paper, we will look at particular situations on how various technologies such as numerically capable calculators, graphics calculators, and technological tools that are CAS enabled or have CAS with Dynamic Geometry, impact students' learning. We also discuss briefly the educational opportunities that are made available by the emergence of graphics calculators with capabilities of handling electronic learning activities, such as Casio's Class Pad (see ) and Casio's 9860 graphics calculator.