The Complex Process of Converting Tools into Mathematical Instruments. The Case of Calculators (original) (raw)

A model for the educational role of calculators

2014

Calculators can be used effectively for mathematics education in a number of ways, although frequently they are regarded merely as devices for undertaking computations. In this analytic paper, we describe and illustrate a four-part model to understand more fully the potential role of calculators for learning mathematics. The four elements of the model include representation, computation, exploration and affirmation. Effective use of a calculator by students learning mathematics will often involve more than one of these four components. The model has been derived from analysis of educational materials developed to support rich calculator use.

Calculators in mathematics education: A rapid evolution of tools, with differential effects

The Didactical Challenge of Symbolic Calculators Turning a Computational Device into a Mathematical Instrument, 9-40, 2005

The appearance of more and more complex tools in mathematics classes is not a response to an institutional need of school. It is, rather, the expression within this institution of a huge social phenomenon (the increase in the number of screens and machines) arising from the utilization of computerized tools by certain branches of mathematics and science.

From Artifact to Instrument: Mathematics Teaching Mediated by Symbolic Calculators

2003

The evolution of calculation tools available for the learning of mathematics has been quick and profound. After the first illusions on a naturally positive integration of these tools, new theoretical approaches have emerged. They take into account individual and social processes of the mathematical instrument construction from a given artifact. In this article we show how analyzing constraints of the tool allows the understanding of its influence on the knowledge construction. We propose the concept of instrumental orchestration to design different devices which may be built in class and thus strengthen the socialized part of the instrumental genesis: instrumental orchestration is defined by objectives, configuration and exploitation modes. It acts at the same time on the artifact, on the subject, on the relationship the subject has with the artifact and on the way the subject considers this relation

The Calculator as an Instrument of Validation of Mathematical Knowledge: A Case Study

2020

The discussions that arise when demonstration in mathematics is dealt with often cause opposing positions regarding the wisdom of its use. How can it be conducted in the classroom? How to discern which proofs enrich the academic formation of the students? If, in addition, we consider the contribution of new technology to teaching, it is necessary to reflect on how the form of validating mathematical knowledge is affected, if it is at all altered, in the classroom. In this paper several considerations on these ideas are discussed, and an experience with junior high school math teachers is described where mathematical reasoning is taught using a TI-92 calculator. A recent concern for including, in different present-day educational programs, a specific part related to demonstration. For example, in the Principles and Standards in School Mathematics: Discussion Draft (NCTM, 1998), one of the standards proposed is that of "Reasoning and Proof". Also, many recent studies focus o...

Learning and teaching mathematics with a graphic calculator

… Malaysian Math. Sc. …, 2002

The past three decades has seen many mathematics departments adopting plans for the appropriate use of instructional technology tools in the learning and teaching of mathematics, and in the assessment of mathematics learning.

Graphic calculators in the classroom: Students’ viewpoints

This paper presents the results of a study about the views and attitudes of students of a low achieving 11th grade class who were involved in an innovative experience with graphic calculators for all academic year. Contrasting the results obtained from a questionnaire and from interviews, it concludes that students tended to point some improvements in the mathematics class, but attributed their origin more to their teacher' style and personality than to the use of this technology. Graphic calculators are a quite powerful new technology for mathematics teaching (Demana & Waits, 1990). They have obvious curricular implications, especially at high school and college level. They point towards significant content changes, emphasizing graphical representations, stressing issues such as units and scale; and they may even favor a shift in learning styles, with more exploration and student activity. This paper presents a study that investigated students' views and attitudes towards graphic calculators as well as mathematics classes and its effects in their personal relation with this subject. Theoretical background The general conceptions, views and attitudes of the students regarding mathematics and mathematics classes are increasingly seen as crucial factors affecting their performance (Schoenfeld, 1989). It is of great interest to know how much can these be addressed by curriculum innovations. In a recent experience of a new national curriculum, 7th grade students' views and attitudes were found to improve significantly, in close relation with the introduced methodological changes. However, in the same experience, the views' and attitudes of college-bound 10th graders showed no positive change, but rather an increase in anxiety and distrust regarding the system (Ponte et al., 1992). Students' response to innovations in mathematics teaching is not always what the innovators seek. With powerful technologies, the students' approach to mathematics tasks may differ significantly, in an impoverished or even counterproductive way, from the original intentions (Hillel, 1992). And also, students' agendas and personal expectations regarding mathematics classes may resist to what they perceive as departures from the usual, and, on their view productive learning activities (Ponte & Carreira, 1992).

Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom

International Journal of Mathematical Education in Science and Technology, 2011

Our research project aimed at understanding the complexity of the construction of knowledge in a CAS environment. Basing our work on the French instrumental approach, in particular the Task-Technique-Theory (T-T-T) theoretical frame as adapted from Chevallard's Anthropological Theory of Didactics, we were mindful that a careful task design process was needed in order to promote in students rich and meaningful learning. In this paper, we explore further conjecture that the learning of techniques can foster conceptual understanding by investigating at close range the taskbased activity of a pair of 10th grade students-activity that illustrates the ways in which the use of symbolic calculators along with appropriate tasks can stimulate the emergence of epistemic actions within technique-oriented algebraic activity.

Using Symbolic Calculators to Study Mathematics

Mathematics Education Library, 2005

This chapter will consider in more depth the possible contribution of technology --especially CAS --to the study of mathematical domains. Using a theoretical approach to treat examples of classroom activities, we will show how a didactical reflection can help to understand this contribution. A variety of new techniques will be presented and related to paper-and-pencil techniques. Examining the pragmatic and epistemic value of both types of technique will help to make sense of classroom situations. It will also help to clarify the situation of teachers wanting to integrate new tools. Consideration of other approaches will show that educators emphasize the use of computer algebra to promote 'conceptual' mathematics. Nevertheless, they cannot ignore instrumented techniques when considering the real potentialities of new tools and the conditions for their integration.

An instrumental approach to mathematics learning in symbolic calculator environments

The Didactical Challenge of Symbolic Calculators Turning a Computational Device into a Mathematical Instrument, 145-168, 2005

A rapid technological evolution, linked to profound changes within the professional field of mathematics, brings into question the place of techniques in mathematics teaching. These changes have created serious difficulties for teachers; obliged to question their professional practices, they make different choices regarding integration of new technologies and techniques, choices that are linked to their mathematical conceptions and to their teaching styles.

Factors influencing students' interactions with advanced calculators

2017

There is an increasing use of and rapid advancements in technologies in education. In particular, there is a take-up of advanced calculators (graphing calculators and calculators with computer algebra system [CAS]) in senior secondary high-stakes examinations. Each year, tens of thousands of students in Australia, Singapore, and other regions, use advanced calculators in mathematics examinations that directly affect their entry into tertiary education. Thus, it was pertinent to investigate the ways in which students use these technologies when learning mathematics, and the factors that influenced them. This study was built upon a bricolage of theories from various fields such as mathematics education, educational technology, learning theories, learning styles, and gender studies. From a review of the literature in the different fields, it was hypothesised that factors such as students' gender, beliefs about and attitudes toward mathematics and technology, approaches to studying ...