Calculators and Computer Algebra Systems: Their Use in Mathematics Examinations
About: This article is published in The Mathematical Gazette.The article was published on 1995-03-01. It has received 20 citations till now. The article focuses on the topics: Calculator input methods & Symbolic computation.
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TL;DR: In this paper, a survey of mathematics teachers' use of computers, graphics calculators, and the Internet in Queensland secondary schools, and examines relationships between use and teachers' pedagogical knowledge and beliefs, access to technology, and professional development opportunities.
Abstract: For many years, education researchers excited by the potential for digital technologies to transform mathematics teaching and learning have predicted that these technologies would become rapidly integrated into every level of education. However, recent international research shows that technology still plays a marginal role in mathematics classrooms. These trends deserve investigation in the Australian context, where over the past 10 years secondary school mathematics curricula have been revised to allow or require use of digital technologies in learning and assessment tasks. This paper reports on a survey of mathematics teachers’ use of computers, graphics calculators, and the Internet in Queensland secondary schools, and examines relationships between use and teachers’ pedagogical knowledge and beliefs, access to technology, and professional development opportunities. Although access to all forms of technology was a significant factor related to use, teacher beliefs and participation in professional development were also influential. Teachers wanted professional development that modelled planning and pedagogy so they could meaningfully integrate technology into their lessons in ways that help students learn mathematical concepts. The findings have implications not only for resourcing of schools, but also for designing professional development that engages teachers with technology in their local professional contexts.
92 citations
Journal Article•
TL;DR: The authors describe and exemplify a typology of use of graphics calculators in mathematics examinations, from the perspective of people designing examinations, together with some principles for the awarding of partial credit to student responses.
Abstract: As graphics calculators become more available, interest will focus on how to incorporate them appropriately into curriculum structures, and particularly into examinations. We describe and exemplify a typology of use of graphics calculators in mathematics examinations, from the perspective of people designing examinations, together with some principles for the awarding of partial credit to student responses. This typology can be used to help design examinations in which students are permitted to use graphics calculators as well as to interrogate existing examination practice.
21 citations
TL;DR: In this paper, a small group of students were provided with specially adapted graphics calculators, which were virtually identical to the students' own calculators but contained speci cally different features.
Abstract: In many British schools, A-level Mathematics students are advised to purchase graphics calculators at the start of their Mathematics course, and there has been considerable research into the effectiveness of the use of graphics calculators in developing mathematical understanding. Recent UK examination regulations have prohibited the use of graphics calculators in certain module examinations but allowed them to be used in others. This study set out to investigate how a small group of students actually used their graphics calculators under examination conditions. The students sat an externally set practice examination paper for a statistics module. The examination paper was analysed by the research team in order to identify the potential use that the students could have made of the graphics calculators in each question. When they took the examination the students were provided with specially adapted calculators; these calculators were virtually identical to the students' own calculators but contained speci...
18 citations
01 Jan 2007
TL;DR: In this paper, the authors investigate how and why secondary school mathematics teachers use digital technologies to help their students learn and identify critical factors that support or hinder innovative teaching and learning, with the aid of Valsiner's zone theory.
Abstract: This paper reports on the initial phase of a research study that is investigating how and why secondary school mathematics teachers use digital technologies to help their students learn Case studies of a beginning teacher and an experienced teacher, both of whom are regarded as effective users of technology, aim to identify critical factors that support or hinder innovative teaching and learning The findings are analysed with the aid of Valsiner’s (1997) zone theory to study interactions between teachers’ knowledge and beliefs, their professional contexts, and their formal and informal professional development experiences
18 citations
11 Jun 2008
TL;DR: Observations validate aspects of the current design of MathBrush, suggest areas for refinement, and inform the design of future pen-math systems.
Abstract: Current generations of computer algebra systems require users to transform two dimensional math expressions into one dimensional strings, to master complex sets of commands, and to analyze lengthy output strings for relevant information. MathBrush is a system, designed based on research in education pedagogy, that provides a pen-based interface to many of the features of computer algebra systems. We describe relevant work in education pedagogy as a motivation for MathBrush's design. We highlight aspects of MathBrush that are unique from other contemporary pen-math systems. Finally, we present the results of a thinkaloud evaluation of the MathBrush system. Together, these observations validate aspects of the current design of MathBrush, suggest areas for refinement, and inform the design of future pen-math systems.
17 citations
References
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Book•
01 Jan 1988
TL;DR: The Methods of Educational Inquiry General Humanistic Research Methods Scientific Research Methods Critical Theory, Policy Research, and Evaluation Issues in Educational Research Research Methodology Humanistic Analysis Procedures Scientific Analysis Procedures Measurement in educational research.
Abstract: The Methods of Educational Inquiry General Humanistic Research Methods Scientific Research Methods Critical Theory, Policy Research, and Evaluation Issues in Educational Research Research Methodology Humanistic Analysis Procedures Scientific Analysis Procedures Measurement in Educational Research Introduction to Measurement Item Response Methods Applications of Measurement in Research
727 citations
TL;DR: In this paper, the authors compared the mathematical performance of upper secondary school mathematics students for whom a graphic calculator is a standard mathematical tool, with that of students of similar background without regular access to graphing technology.
Abstract: This article reports a study comparing the mathematical performance of upper secondary school mathematics students for whom a graphic calculator is a standard mathematical tool, with that of students of similar background without regular access to graphing technology. Students were tested on two types of item: symbolisation items, calling for an algebraic description of some cartesian graph; and interpretation items, calling for the extraction of information from some verbally contextualised graph. The findings illustrate that, under appropriate conditions, access to information technology can have an important influence both on the mathematical approaches employed by students and on their mathematical attainment. On the symbolisation items, use of graphic calculators was associated not only with markedly superior attainment by all students, but with greatly enhanced relative attainment on the part of female students.
144 citations
TL;DR: A oveview and analysis of recent progress in applying electronic information technology to creation of new environments for intellectual work in mathematics is given.
Abstract: This paper, prepared for the survey lecture of theme group T2 at the Sixth International Congress on Mathematical Education in Budapest, gives an oveview and analysis of recent progress in applying electronic information technology to creation of new environments for intellectual work in mathematics. The paper is divided into six major sections considering the impact of: 1. Numerical computation; 2. Graphic computation; 3. Symbolic computation; 4. Multiple Representations of Information; 5. Programming and Connections of Computer Science and Mathematics Curricula; 6. Artificial Intelligence and Machine Tutors.
127 citations
TL;DR: In this paper, an investigation into the effect of using open books in an ‘A' level GCE examination in English Literature showed that because the examination was intentionally designed to use texts and notes in the examination, students acquired higher levels of attainment than their peers who took a traditional examination.
Abstract: Abstarct Investigations into the effectiveness of open‐book examinations have shown that they reduce students’ test anxiety and need to memorise factual material. An investigation into the effect of using open‐books in an ‘A’ level GCE examination in English Literature showed that because the examination was intentionally designed to use texts and notes in the examination, students acquired higher levels of attainment than their peers who took a traditional examination.
37 citations
3 citations