Recognising equivalent algebraic expressions : An important component of algebraic expectation for working with CAS
- Authors: Ball, Lynda , Pierce, Robyn , Stacey, Kaye
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at the 2003 joint meeting of PME and PMENA, Hawaii, USA : 13th July, 2003
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003000365
Teaching linear functions in context with graphics calculators : Students' responses and the impact of the approach on their use of algebraic symbols
- Authors: Bardini, Caroline , Pierce, Robyn , Stacey, Kaye
- Date: 2004
- Type: Text , Journal article
- Relation: The International Journal of Science and Mathematics Education Vol. 2, no. 3 (2004), p. 353-376
- Full Text:
- Reviewed:
- Description: This study analyses some of the consequences of adopting a functional/modelling approach to the teaching of algebra. The teaching of one class of 17 students was observed over five weeks, with 15 students undertaking both pre- and post-tests and 6 students and the teacher being interviewed individually. Use of graphics calculators made the predominantly graphical approach feasible. Students made considerable progress in describing linear relationships algebraically. They commented favourably on several aspects of learning concepts through problems in real contexts and were able to set up equations to solve contextualised problems. Three features of the program exerted a triple influence on students use and understanding of algebraic symbols. Students concern to express features of the context was evident in some responses, as was the influence of particular contexts selected. Use of graphics calculators affected some students choice of letters. The functional approach was evident in the meanings ascribed to letters and rules. Students were very positively disposed to the calculators, and interesting differences were observed between the confidence with which they asked questions about the technology and the diffidence with which they asked mathematical questions.
- Description: 2003000925
Teaching with CAS in a time of transition
- Authors: Kendal, Margaret , Stacey, Kaye , Pierce, Robyn
- Date: 2002
- Type: Text , Journal article
- Relation: International Journal of Computer Algebra in Mathematics Education Vol. 9, no. 2 (2002), p. 113-128
- Full Text:
- Reviewed:
- Description: Integrating a powerful instrument such as CAS into teaching and learning mathematics requires changes to many aspects of the classroom, which teachers will make from the base of their prior teaching styles and their beliefs about mathematics and how it should be taught. The paper describes the different ways in which two pioneering Australian teachers adapted their teaching to use CAS. One teacher used CAS with the primary goal of increasing understanding but restricted students’ use. The other teacher adopted CAS as an extra technique for solving standard problems, emphasising timesaving routines by hand and with CAS. Through these case studies we comment on the following issues related to teaching with CAS: different ways of organising the classroom, variety in approaches to teaching the use of CAS, the increased range of methods for solving problems and for teaching, the contrast between using of graphics calculators and CAS, the challenge of finding the place of by-hand skills and CAS use, and the curriculum and assessment changes required in schools.
- Description: C1
- Description: 2003000120
Algebraic insight : The algebra needed to use CAS
- Authors: Pierce, Robyn , Stacey, Kaye
- Date: 2002
- Type: Text , Journal article
- Relation: Mathematics Teacher Vol. 95, no. 8 (2002), p. 622-627
- Full Text: false
- Reviewed:
- Description: C1
- Description: 2003000145
A scale for monitoring students' attitudes to learning mathematics with technology
- Authors: Pierce, Robyn , Stacey, Kaye , Barkatsas, Anastasios
- Date: 2007
- Type: Text , Journal article
- Relation: Computers and Education Vol. 48, no. 2 (2007), p. 285-300
- Full Text:
- Reviewed:
- Description: The Mathematics and Technology Attitudes Scale (MTAS) is a simple scale for middle secondary years students that monitors five affective variables relevant to learning mathematics with technology. The subscales measure mathematics confidence, confidence with technology, attitude to learning mathematics with technology and two aspects of engagement in learning mathematics. The paper presents a model of how technology use can enhance mathematics achievement, a review of other instruments and a psychometric analysis of the MTAS. It also reports the responses of 350 students from 6 schools to demonstrate the power of the MTAS to provide useful insights for teachers and researchers. 'Attitude to learning mathematics with technology' had a wider range of scores than other variables studied. For boys, this attitude is correlated only with confidence in using technology, but for girls the only relationship found was a negative correlation with mathematics confidence. These differences need to be taken into account when planning instruction. © 2005 Elsevier Ltd. All rights reserved.
- Description: C1
- Description: 2003004898
Learning to use CAS: Voices from a classroom
- Authors: Pierce, Robyn , Stacey, Kaye
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at the 28th conference of the International Group for the Psychology of Matematics Education, PME 28, Bergen, Norway : 14th July, 2004
- Full Text:
- Reviewed:
- Description: This paper reports on the experiences of students who were learning mathematics with CAS for a second consecutive school year. Evidence presented shows that nearly all students managed the challenging task of mastering the technical aspects of using CAS well. It also shows that the level of technical difficulty and the degree to which it presents an obstacle to mathematical learning is not predictable from conventional mathematical ability. There is a complex interaction between cognitive and affective factors. Planning appropriate teaching for developing the effective use of CAS will require awareness and understanding of these individual differences.
- Description: E1
- Description: 2003000920
Enhancing the image of mathematics by association with simple pleasures from real world contexts
- Authors: Pierce, Robyn , Stacey, Kaye
- Date: 2006
- Type: Text , Journal article
- Relation: ZDM Zentralblatt fur Didaktik der Mathematik Vol. 38, no. 3 (2006), p. 214-225
- Full Text:
- Reviewed:
- Description: Those who market people or products choose their images very carefully. They create positive associations in the public's mind by photographing their clients with sporting heroes or national icons. In this paper we present a variety of evidence to show that a major and overlooked reason for teachers' use and choice of real world problems is to take advantage of this ‘halo effect’ to improve studients' attitude towards learning mathematics. Analysis of interviews, reports, and results of a brief survey from teachers of middle secondary school classes indicate that they place a very high priority on positive attitudes and hence both choose and enhance real world problems to promote studients' affective engagement through simple pleasures. Pleasant sensory stimuli, generally non-cognitive and peripheral to the situation to be modelled, are used to promote a positive view of mathematics. This is a good strategy for creating enjoyable and memorable lessons, but there is a danger that it may override more substantive learning goals.
- Description: C1
- Description: 2003001563
Monitoring effective use of computer algebra systems
- Authors: Pierce, Robyn , Stacey, Kaye
- Date: 2002
- Type: Text , Conference paper
- Relation: Paper presented at Mathematics Education in the South Pacific Proceedings of the 25th Annual Conference of the Mathematics Education Research Groups of Australasia, Auckland, New Zealand : 7th July, 2002
- Full Text:
- Reviewed:
- Description: Computer Algebra Systems (CAS) potentially offer students a powerful tool. However the mere availability of CAS does not enhance teaching and learning; students (and teachers) need to use it effectively. This paper presents a framework for components of Effective Use of CAS and illustrates its use as a guide for monitoring the progress of students. The results presented highlight the importance of considering the interaction between technical and personal aspects of Effective Use of CAS.
- Description: E1
- Description: 2003000121
Monitoring progress in algebra in a CAS active context: Symbol sense, algebraic insight and algebraic expectation
- Authors: Pierce, Robyn , Stacey, Kaye
- Date: 2004
- Type: Text , Journal article
- Relation: The International Journal for Technology in Mathematics Education Vol. 11, no. 1 (2004), p. 1-11
- Full Text:
- Reviewed:
- Description: The purpose of this paper is to provide researchers with a shared framework, terminology and tool to improve the coherence of research into learning mathematics with CAS and to assist its findings to accumulate into a significant body of knowledge. Experience with calculators in arithmetic led to a framework for number sense. There is an obvious parallel for algebra, where the development of algebraic insight to monitor symbolic work will assume high importance. We present a framework for algebraic insight then explore one aspect, algebraic expectation, in detail. Just as estimation is a valued skill for monitoring arithmetic calculations, we suggest that expectation should be a focus in teaching algebra, especially when symbolic technology is available. Through typical examples, we demonstrate the value of the algebraic insight framework for monitoring students’ work with CAS.
- Description: C1
- Description: 2003000924
A framework for monitoring progress and planning teaching towards the effective use of computer algebra systems
- Authors: Pierce, Robyn , Stacey, Kaye
- Date: 2004
- Type: Text , Journal article
- Relation: International Journal of Computers for Mathematical Learning Vol. 9, no. 1 (2004), p. 59-93
- Full Text:
- Reviewed:
- Description: This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS technology and how these may be used to monitor students' developing use of CAS; from this, the framework may be used to plan teaching in order to gain greater benefit from the availability of CAS. Four case studies describing students' development over a semester are reported. These demonstrate a variety of combinations of technical competencies and personal attributes. They indicate the importance of both the technical and personal aspects but suggest that negative attitudes rather than technical difficulties can limit the effective use of CAS. Finally practical suggestions are given for teaching strategies which may promote effective use of CAS.
- Description: C1
- Description: 2003000923
Mathematics from still and moving images
- Authors: Pierce, Robyn , Stacey, Kaye , Ball, Lynda
- Date: 2005
- Type: Text , Journal article
- Relation: AMT: The Australian Mathematics Teacher Vol. 61, no. 3 (2005), p. 26-31
- Full Text:
- Reviewed:
- Description: Digital photos and digital movies offer an excellent way of bringing real world situations into the mathematics classroom. The technologies surveyed here are feasible for everyday classroom use and inexpensive. Examples are drawn from the teaching of Cartesian coordinates, linear functions, ratio and Pythagoras' theorem using still images, and quadratic functions using moving images. Resources and tips for creating suitable images for analysis are given. (Contains 6 figures.)
- Description: C1
- Description: 2003001446