1 Teaching and learning elementary calculus concepts with a graphics calculator (original) (raw)
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Teaching and learning elementary calculus concepts with a graphics calculator
The availability of ICT offers opportunities to reconsider teaching and learning in the calculus curriculum. In this paper, some potential contributions of one form of ICT, the hand-held graphics calculator, are described and evaluated. Although algebraic calculators, graphics calculators with symbolic manipulation capabilities, have been available for some years now, attention in the paper is restricted to calculators without algebraic capabilities. These are more likely to be available on a wide scale in many East Asian countries than are algebraic calculators, and significant experience with them in schools has now accumulated. The paper will consider a number of key calculus concepts, such as the derivative of a function at a point, the derivative function, continuity, asymptotic behaviour, convergence, limits, integration and differential equations, to develop the argument that ICT offers an opportunity to help students understand the concepts behind the calculus, upon which st...
Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom
International Journal of Mathematical Education in Science and Technology, 2011
Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the mathematics classroom has not had the expected impact, as it has been its use in everyday life (f.e. cell phone). What about teachers' opinion? Mathematics teachers can be divided into three categories: Those with a boundless overflow (enthusiasm) that want to use the technology without worrying much about the construction of mathematical concepts, those who reject outright the use of technology because they think that their use inhibits the development of mathematical skills, and others that reflect on the balance that must exist between paper-pencil activities and use of technology. The mathematics teacher not having clear examples that support this last option about the balance of paper-pencil activities and technology, opt for one of the extreme positions outlined above. In this paper, we show the results of research on a methodology based on collaborative learning (ACODESA) in the training of mathematics teachers in secondary schools and implementation of activities in an environment of paper-pencil and CAS in the mathematics classroom. We note also that with the development of technology on the use of electronic tablets and interactive whiteboards, these activities will take on greater momentum in the near future. RESUMEN Los investigadores en educación matemática se preguntan por qué la tecnología ha impactado fuertemente en el medio social y no en el aula de matemáticas. El uso de la tecnología en el aula de matemáticas no ha tenido el impacto esperado como lo ha sido su uso en la vida corriente. ¿Cuál es la posición de los profesores? Los profesores de matemáticas se pueden dividir en tres tipos de categorías, aquellos que con un desbordamiento desmedido quieren utilizar la tecnología sin preocuparse mucho sobre la construcción de conceptos, aquellos que rechazan completamente el uso de tecnología porque piensan que su uso inhibe el desarrollo de habilidades matemáticas, y otros que reflexionan sobre el equilibrio que debe de haber entre actividades en papel-lápiz y uso de tecnología. El profesor de matemáticas al no contar con ejemplos claros que soporten esta última opción sobre el equilibrio en las actividades de papel-lápiz y tecnología, opta por alguno de los extremos antes señalados. En este documento, queremos mostrar los resultados de investigación sobre una metodología basada en el aprendizaje en colaboración (ACODESA) en la formación de profesores de matemáticas en la escuela secundaria e implementación de actividades en ambientes de papel-lápiz y calculadora (CAS) en el aula de matemáticas. Queremos señalar también, que con el desarrollo de la tecnología sobre el uso de tabletas electrónicas y pizarrones interactivos, este tipo de actividades cobrarán un impulso mayor en un futuro inmediato.
Assessment in calculus in the presence of graphics calculators
Mathematics Education Research Journal, 2002
In this paper we explore the extent and nature of students' calculator usage as determined from examination scripts in the Western Australian Calculus Tertiary Entrance Examination. Errors made and understanding called upon are discussed for seven questions. The inquiry highlights that skills associated with graphical interpretation need to be the subject of instruction, and that an awareness of the differing cognitive demands of graphical interpretation is needed when setting assessment items.
International Journal of Mathematical Education in Science and Technology, 2001
The paper describes an inquiry into students' uses of graphics calculators in the Tertiary Entrance Examination of Calculus in Western Australia for 1998, which was the rst year that calculators were allowed for the examination. The prevalence of calculator usage and marks allocated for six questions are considered, based on data collected from examination markers. The nature of calculator usage is described, including errors made, based on our perusal of examination scripts and interviews with students, teachers and markers. A comparative analysis of boys' and girls' performance, as measured by raw examination scores on the examination for 1995-1998 is given. The results suggest that the main areas of diYculty for students are interpreting graphics calculator outputs and knowing when use of graphics calculators is appropriate or possible. While initial indications are that the eVect of introducing the calculators is non-discriminatory between boys and girls, no claims can be made without longer-term analysis.
Although much has been written about technology in mathematics, much less has happened in schools. A major reason for this is the limited availability of com- puter hardware, not only in lesser-developed countries. Discussion among teachers both within and between countries is hampered by different metaphors for technology. These metaphors are described and their significance explained. It is suggested that regional use of technology is likely to be more effective if emphasis is placed upon graphics cal- culators rather than on microcomputers. The portability of graphics calculators is a key element. As well as economic and curriculum impediments to change, the central rôles of teachers and the need for effective support is acknowledged.
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.
Teaching elementary calculus with CAS calculators
2001
In this paper we present our experiences of introducing the CAS graphics calculator into a first year elementary calculus unit taught recently at Edith Cowan University in Perth. We used a Reform Calculus textbook and the fourfold analytic, geometric, numeric and word-description approach advocated in it. The students comprised a mixture of mature age students and school leavers, and they had a wide variety of mathematical and (non-CAS) calculator backgrounds. They were studying calculus as a service unit for a number of different major programs. A set of HP49G CAS graphics calculators was available for student use in class, in the tests and in the final examination. Some HP49G calculators were available in the library for out of class use. The essential difference between using standard graphics calculators for teaching/learning in the unit and using the CAS calculators is the ability to hand analytic procedures to the higher level technology, and associated with this are some new possibilities for learning. We give an overview of the approaches we took to teaching and then assessing with these calculators; and, in particular, we describe the approaches we took with limits, the problems encountered and our responses to the outcomes. We examine also aspects of the CAS use revealed by an analysis of selected test and assignment questions.