Undergraduate mathematics curricula - A new approach
- Authors: Giri, Jason , Pierce, Robyn , Turville, Christopher
- Date: 2003
- Type: Text , Journal article
- Relation: New Zealand Journal of Mathematics Vol. 32 , no. Supplementary Issue (2003), p. 155-162
- Full Text: false
- Reviewed:
- Description: C1
- Description: 2003000363
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
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
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
Changes of names, contents and attitudes to mathematical units
- 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
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
- Full Text:
- Reviewed:
- Description: E1
- Description: 2003000921
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