Incomplete or incorrect understanding of decimals: An important deficit for student nurses
- Pierce, Robyn, Steinle, Vicki
- 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
- Full Text:
- Reviewed:
- 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
- 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
- Full Text:
- Reviewed:
- 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
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
- Full Text:
- Reviewed:
- 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
- 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
- Full Text:
- Reviewed:
- 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
Potential of technology and a familiar context to enhance students’ concept of rate of change
- Herbert, Sandra, Pierce, Robyn
- 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
- Full Text:
- Reviewed:
- 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
- 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
- Full Text:
- Reviewed:
- 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
- Full Text:
- Reviewed:
- 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
- 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
- Full Text:
- Reviewed:
- 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
CAS : Student engagement requires unambiguous advantages
- Pierce, Robyn, Herbert, Sandra, Giri, Jason
- 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
- Full Text:
- Reviewed:
- Description: E1
- Description: 2003000921
- 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
- Full Text:
- Reviewed:
- 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
- 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
- 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
Changes of names, contents and attitudes to mathematical units
- Turville, Christopher, Pierce, Robyn, Barker, Ewan, Giri, Jason
- Authors: Turville, Christopher , Pierce, Robyn , Barker, Ewan , Giri, Jason
- Date: 2002
- Type: Text , Conference paper
- Relation: Paper presented at the 2nd International Conference on the Teaching of Mathematics, Crete, Greece : 1st June, 2003
- Full Text:
- Reviewed:
- Description: Will this material be on the exam? Why do I need to know this stuff? These are the sorts of questions that have been regularly asked by our mathematics students. Pre-service mathematics teachers often suggest that they do not need to learn anything that they do not have to teach. Generally, these students appear to have very little aesthetic appreciation for mathematics and its applications. Currently, we teach five traditional mathematical content units that are provided mainly for pre-service mathematics teachers. These units have been adapted and modified over the years from units that were designed primarily for science students. They contained a heavy focus on calculus with a limited breadth of mathematical experience. After consulting widely on the best mathematical practices throughout Australia and internationally, it was decided to reform all of the mathematics units to make them more attractive to a wider audience. The units that are currently being developed are: Profit, Loss and Gambling; Upon the Shoulders of Giants; Logic and Imagination; Modelling and Change; Algorithms, Bits and Bytes; Space, Shape, and Design; and Modelling Reality. The overall goal of this redevelopment is to improve student attitudes and motivation by exposing them to a wide range of topics in mathematics that are usable and relevant. All of these units will incorporate current technology, contain realistic problems, and include visiting speakers. Student assessment in these units will consist of portfolios, projects and examinations. The introduction of these new units will result in students having a greater choice of the units they wish to study. In order to overcome potential logistical problems of a small mathematics department, innovative changes to the structure of the units will also be examined. This paper will provide the details of the establishment and content of these units.
- Description: E1
- Description: 2003000085
- Authors: Turville, Christopher , Pierce, Robyn , Barker, Ewan , Giri, Jason
- Date: 2002
- Type: Text , Conference paper
- Relation: Paper presented at the 2nd International Conference on the Teaching of Mathematics, Crete, Greece : 1st June, 2003
- Full Text:
- Reviewed:
- Description: Will this material be on the exam? Why do I need to know this stuff? These are the sorts of questions that have been regularly asked by our mathematics students. Pre-service mathematics teachers often suggest that they do not need to learn anything that they do not have to teach. Generally, these students appear to have very little aesthetic appreciation for mathematics and its applications. Currently, we teach five traditional mathematical content units that are provided mainly for pre-service mathematics teachers. These units have been adapted and modified over the years from units that were designed primarily for science students. They contained a heavy focus on calculus with a limited breadth of mathematical experience. After consulting widely on the best mathematical practices throughout Australia and internationally, it was decided to reform all of the mathematics units to make them more attractive to a wider audience. The units that are currently being developed are: Profit, Loss and Gambling; Upon the Shoulders of Giants; Logic and Imagination; Modelling and Change; Algorithms, Bits and Bytes; Space, Shape, and Design; and Modelling Reality. The overall goal of this redevelopment is to improve student attitudes and motivation by exposing them to a wide range of topics in mathematics that are usable and relevant. All of these units will incorporate current technology, contain realistic problems, and include visiting speakers. Student assessment in these units will consist of portfolios, projects and examinations. The introduction of these new units will result in students having a greater choice of the units they wish to study. In order to overcome potential logistical problems of a small mathematics department, innovative changes to the structure of the units will also be examined. This paper will provide the details of the establishment and content of these units.
- Description: E1
- Description: 2003000085
Making statistics relevant for undergraduate nurses
- Martin, Peter, Pierce, Robyn, Giri, Jason
- Authors: Martin, Peter , Pierce, Robyn , Giri, Jason
- Date: 2002
- Type: Text , Conference paper
- Relation: Paper presented at the Sixth International Conference on Teaching Statistics, Cape Town, South Africa 7th - 12th July, 2002
- Full Text:
- Reviewed:
- Description: In this paper we will explore the challenge of making statistics more meaningful to future nurses. In the fast moving undergraduate student world the expectations we place upon nursing students are considerable. Typically they experience high class-contact hours in addition to their clinical placements. Compounding the problem, undergraduate nursing students have diverse mathematical backgrounds and seldom perceive statistics as being relevant for them. Given these constraints we have adopted the relatively modest aim of producing informed and discriminating consumers of statistics and research, rather than skilled statistical practitioners or researchers. With a focus on computer output rather than by-hand calculations, we have made use of strategic examples, appropriate journal articles and an historical hypothetical. This approach has both relieved the anxiety and distraction associated with calculations and increased students’ engagement in the learning process.
- Description: E1
- Description: 2003000142
- Authors: Martin, Peter , Pierce, Robyn , Giri, Jason
- Date: 2002
- Type: Text , Conference paper
- Relation: Paper presented at the Sixth International Conference on Teaching Statistics, Cape Town, South Africa 7th - 12th July, 2002
- Full Text:
- Reviewed:
- Description: In this paper we will explore the challenge of making statistics more meaningful to future nurses. In the fast moving undergraduate student world the expectations we place upon nursing students are considerable. Typically they experience high class-contact hours in addition to their clinical placements. Compounding the problem, undergraduate nursing students have diverse mathematical backgrounds and seldom perceive statistics as being relevant for them. Given these constraints we have adopted the relatively modest aim of producing informed and discriminating consumers of statistics and research, rather than skilled statistical practitioners or researchers. With a focus on computer output rather than by-hand calculations, we have made use of strategic examples, appropriate journal articles and an historical hypothetical. This approach has both relieved the anxiety and distraction associated with calculations and increased students’ engagement in the learning process.
- Description: E1
- Description: 2003000142
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
- 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
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