Revealing conceptions of rate of change
- Authors: Herbert, Sandra , Pierce, Robyn
- Date: 2009
- Type: Text , Conference paper
- Relation: Paper presented at MERGA32 Conference, Massey University, Wellington, New Zealand : 5th-9th July 2009
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- Description: Rate of change is an important mathematical concept. Research referring to students’ difficulties with this concept spans more than twenty years. Research suggests that problems experienced by some calculus students are likely a result of pre-existing limited or incorrect conceptions of rate of change. This study investigated 23 Victorian Year 10 students’ understanding of rate as revealed by phenomenographic analysis of interviews. Eight conceptions of rate of change emerged. Four important aspects of the concept were identified and gaps in students’ thinking defined. In addition, the employment of phenomenography, to reveal conceptions of rate, is described in detail.
- Description: 2003007238
An 'Emergent Model' for rate of change
- Authors: Herbert, Elizabeth , Pierce, Robyn
- Date: 2008
- Type: Text , Journal article
- Relation: International Journal of Computers for Mathematical Learning Vol. 13, no. 3 (2008), p. 231-249
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- Description: Does speed provide a ‘model for’ rate of change in other contexts? Does JavaMathWorlds (JMW), animated simulation software, assist in the development of the ‘model for’ rate of change? This project investigates the transference of understandings of rate gained in a motion context to a non-motion context. Students were 27 14–15 year old students at an Australian secondary school. The instructional sequence, utilising JMW, provided rich learning experiences of rate of change in the context of a moving elevator. This context connects to students’ prior knowledge. The data taken from pre- and post-tests and student interviews revealed a wide variation in students’ understanding of rate of change. The variation was mapped on a hypothetical learning trajectory and interpreted in the terms of the ‘emergent models’ theory (Gravemeijer, Math Think Learn 1(2):155–177, 1999) and illustrated by specific examples from the data. The results demonstrate that most students were able to use the ‘model of’ rate of change developed in a vertical motion context as a ‘model for’ rate of change in a horizontal motion context. A smaller majority of students were able to use their, often incomplete, ‘model of’ rate of change as a ‘model for’ reasoning about rate of change in a non-motion context.
- Description: C1
Massively multiplayer online role-playing games : The past, present, and future
- Authors: Achterbosch, Leigh , Pierce, Robyn , Simmons, Gregory
- Date: 2008
- Type: Text , Journal article
- Relation: Computers in Entertainment Vol. 5, no. 4 (2008), p. 1-33
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- Description: Massively multiplayer online role-playing games (MMORPGs) are emerging in the computer game industry as a very popular genre. These games have existed since the late 1990s, but in the last few years the market has become increasingly strong. This relatively new genre is attracting a widespread audience, bringing together those who previously enjoyed both pen and paper and computer role-playing games, as well as those who enjoy socializing with other players in a virtual environment. Game developers see MMORPGs as a potentially profitable business due to its widespread appeal, but the reality is that only a small percentage of MMORPGs that are released become a success [Kosak 2006]. This article attempts to determine the many aspects that make a successful MMORPG; it also attempts to ascertain what new and innovative features are expected by the users from the next generation of MMORPGs. This is achieved by looking at and discussing past literature and surveying the MMORPG community's perception of previous and current MMORPGs, as well as their expectations of the next generation. An online survey attracted 122 participants to provide their perceptions of current and past MMORPGs. This article determines and outlines the respondents' preferences in the MMORPG genre, discussing what implications these could have on its future. The survey also gave insight into the respondents' expectations of the future of MMORPGs. We conclude this article with a discussion of aspects of current MMORPGs that the participants would like improved, as well as new features they would like incorporated into the next generation of games. © 2008 ACM.
- Description: C1
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
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- 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
Video evidence : What gestures tell us about students' understanding of rate of change
- Authors: Herbert, Sandra , Pierce, Robyn
- Date: 2007
- Type: Text , Conference paper
- Relation: Paper presented at 30th Annual Conference of the Mathematics Education Research Group Of Australasia: Mathematics: Essential Research, Essential Practice, Wrest Point Hotel Casino, Hobart, Tasmania : 2nd-6th July 2007 p. 362-371
- Full Text: false
- Description: This paper reports on insights into students' understanding of the concept of rate of change, provided by examining the gestures made, by 25 Year 10 students, in video-recorded interviews. Detailed analysis, of both the sounds and images, illuminates the meaning of rate-related gestures. Findings indicate that students often use the symbols and metaphors of gesture to complement, supplement, or even contradict verbal descriptions. Many students demonstrated, by the combination of their words and gestures, a sound qualitative understanding of constant rate, with a few attempting to quantify rate. This interpretation of gestures may provide teachers with a better understanding of the progress in their students' thinking.
- Description: 2003002300
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
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- 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
Incomplete or incorrect understanding of decimals: An important deficit for student nurses
- Authors: Pierce, Robyn , Steinle, Vicki
- Date: 2006
- Type: Text , Conference paper
- Relation: Paper presented at the 30th Conference of the International Group for the Psychology of Mathematics Education, PME30, Mathematics in the Centre, Prague, Czech Republic : 16th - 21st July, 2006 p. 161-169
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- Description: In this study more than 40% of the 355 student nurses who completed a pre-test, involving comparisons of decimal numbers, made errors that indicate an incomplete or incorrect conceptual understanding. This includes students who are sometimes able to achieve 100% on drug calculations tests. Seven test items with error rates of between 10% and 26% form the focus of our discussion. A sub-group of the students attended a one-hour remedial intervention using various physical materials to give conceptual meaning to decimal numbers. A matched post-test three months after the intervention, detected a statistically significant improvement for the intervention students but not for those who only practiced drug calculation procedures. Conceptual teaching for number sense is needed to underpin procedures.
- Description: E1
- Description: 2003001562
Algebraic insight underpins the use of CAS for modelling
- Authors: Pierce, Robyn
- Date: 2005
- Type: Text , Journal article
- Relation: The Montana Mathematics Enthusiast Vol. 2, no. 2 (2005), p. 107-117
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- Description: Computer Algebra Systems (CAS) performs algorithmic processes quickly and correctly. Concern is commonly expressed that students using CAS will merely be pushing buttons but this paper indicates that, while CAS may assist students, this facility impacts on only one section of the mathematical modeling process: CAS may be used to help find mathematical solutions to mathematically formulated problems. Controlling and monitoring the use of CAS to perform the necessary routine processes requires the mathematical thinking referred to as algebraic insight. This paper sets out a framework of the aspects, and elements of algebraic insight and illustrates the importance of students developing each of the two key aspects: algebraic expectation and ability to link representations. This framework may be used for both planning teaching and monitoring students’ progress.
- Description: C1
- Description: 2003001447
Gifted are lifted higher: an exploration of the development of the higher order thinking skills of gifted playing strategy games
- Authors: Herbert, Sandra , Pierce, Robyn
- Date: 2005
- Type: Text , Journal article
- Relation: TalentEd Vol. 22, no. 1 (2005), p. 22-30
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- Description: Strategy games can provide an opportunity to develop higher order thinking skills in students gifted in mathematics. Extending and engaging gifted students is a demanding task. This paper reports on a twelve-week project undertaken with a group of nine gifted lower secondary school students. These students played and analysed five traditional strategy games. Following this experience, they were asked to create a challenging strategy game of their own. This paper discusses the rationale for the use of traditional strategy games, outlines the methodology employed, explains the selection of specific games and describes the observed improvement in students' higher order thinking skills.
- Description: C1
- Description: 2003001374
Linear functions and a triple influence of teaching on the development of students' algebraic expectation
- Authors: Pierce, Robyn
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper presented at the 29th Conference of the International Group for the Psychology of Mathematics Education, PME29, Melbourne : 10th - 15th July, 2005
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- Description: The study of linear functions is important as it provides students with their first experience of identifying and interpreting the relationship between two dependent variables. This paper, which builds on previous research, reports a study undertaken with 64, year 9 students from two Australian schools. Linear functions were introduced to these students through a graphics calculator supported, functional approach to modelling contextual problems. The teaching was generally successful. Scrutiny of pre- and post-tests highlights the triple influence of the teaching on their progress in each element of Algebraic Expectation relevant to this stage.
- Description: E1
- Description: 2003001444
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
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- 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
Potential of technology and a familiar context to enhance students’ concept of rate of change
- Authors: Herbert, Sandra , Pierce, Robyn
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper presented at 28th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA), Sydney : 7th July, 2005 Vol. 2, p. 435-442
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- Description: Students’ concept image of rate of change may be incomplete or erroneous This paper reports a pilot study, with secondary school students, which explores the potential of technology (JavaMathWorlds), depicting a familiar context of motion, to develop students’ existing schema of informal understandings of rate of change to more formal mathematical representations Students developed numerous ‘models of’ rate of change in a motion context which then transferred to serve as a ‘model for’ rate of change in other contexts
- Description: E1
- Description: 2003001373
Using CAS to enrich the teaching and learning of mathematics
- Authors: Pierce, Robyn
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper presented at the Tenth Asian Technology Conference in Mathematics, Cheong-Ju, South Korea : 12th - 16th December, 2005
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- Description: Computer Algebra Systems (CAS) are powerful tools for both doing and learning mathematics. They may be used to perform algorithmic routines both quickly and correctly but harnessing this power in a manner which is effective for promoting learning is not trivial. Research undertaken with both secondary school and undergraduate students clearly indicates that, while students quickly come to appreciate the availability of CAS to check their answers, several key factors influence the development of their use of the facility of CAS to extend both access to mathematics and support learning of mathematical concepts. First, the institutional value which the technology is afforded influences the degree to which students are willing to apply themselves to the task of learning technical skills necessary to work with CAS. Second, the use of multiple representations may both increase students’ conceptual understanding and provide them with alternative methods through which to progress solution of problems. Finally, students need to be guided in judicious use of CAS. This will involve teaching students to be discriminating in their use of technology for functional purposes, that is, to find solutions to difficult or time consuming problems, and strategic in their use of CAS to explore patterns and link representations in order to gain greater insight into mathematical processes and concepts.
- Description: E1
- Description: 2003001445
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
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- 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
CAS : Student engagement requires unambiguous advantages
- Authors: Pierce, Robyn , Herbert, Sandra , Giri, Jason
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at 27th annual conference of the Mathematics Education Group of Australasia, Townsville, Australia : p. 462-469
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- Description: E1
- Description: 2003000921
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
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- 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
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
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- 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
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
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- 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
Interactive animation provides a vehicle for exploring students' understanding of derivatives
- Authors: Pierce, Robyn , Atkinson, Lyn
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at MERGA 26 MERINO -Mathematics Education Research: Innovation, Networking, Opportunity, Geelong, Victoria : 6th July 2003
- Full Text: false
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- Description: E1
- Description: 2003000364
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