Barry Kissane | Murdoch University (original) (raw)

Papers by Barry Kissane

Yearbook 2010, Association of Mathematics Educators, 2010

Yearbook 2010, Association of Mathematics Educators, 2010

Graphics calculators have the potential to influence the curriculum in several ways, including af... more Graphics calculators have the potential to influence the curriculum in several ways, including affecting what is taught, how it is taught and learned and how it is assessed. These relationships are exemplified for the particular case of sequences and series, which frequently appear in mathematics curricula near the end of secondary school and in the early undergraduate years. Attention will

Synopsis: Although there are a number of technologies related to school algebra, it is only the p... more Synopsis: Although there are a number of technologies related to school algebra, it is only the personal technology of the graphics calculator that seems likely to be available widely enough to influence curriculum design and implementation on a large scale. The algebra curriculum of the past is overburdened with symbolic manipulation at the expense of understanding for most students. But

The Internet offers new opportunities for school students to learn mathematics. This paper analys... more The Internet offers new opportunities for school students to learn mathematics. This paper analyses these opportunities, based on presently available web sites that do not involve subscriptions by users. A typology of six different sorts of opportunities is described, justified and exemplified: (i) Interactive opportunities allow students to interact directly with mathematical objects; (ii) Reading interesting materials allows supplementation of

The graphics calculator has found many uses in secondary school algebra and calculus, but possibi... more The graphics calculator has found many uses in secondary school algebra and calculus, but possibilities in relation to chance and data have been less well publicised. This paper provides an analysis of the potential for using graphics calculators in the chance and data components of school curricula. Differences between scientific and graphics calculators are highlighted, most notably concerned with an

As graphics calculators are mainly devices for student learning, it is important that curricula a... more As graphics calculators are mainly devices for student learning, it is important that curricula and examinations are constructed to incorporate them in a coherent way. Three recent developments in graphics calculators are described and analysed to determine their implications for examinations. Symbolic manipulation on algebraic calculators challenges existing emphases in many examinations and their associated curricula. Flash memory allows calculators

This paper outlines some of the complex relationships between the curriculum and technology, with... more This paper outlines some of the complex relationships between the curriculum and technology, with particular attention on graphics calculators. Graphics calculators are of key significance for practical reasons of availability and affordability Until technology is available, curricula are not likely to be adjusted to accommodate them. Particular features of graphics calculators, including their recent extensions to algebraic calculators, are highlighted,

This paper describes the recent development of hand-held algebraic calculators and evaluates thei... more This paper describes the recent development of hand-held algebraic calculators and evaluates their significance for secondary education. Sophisticated computer algebra systems (CAS) have been available to mathematicians for some years now but have been too powerful, too sophisticated and too expensive and have required too much access to powerful computers to have had much impact on teaching and learning elementary

As graphics calculators become more available, interest will focus on how to incorporate them app... more As graphics calculators become more available, interest will focus on how to incorporate them appropriately into curriculum structures, and particularly into examinations. We describe and exemplify a typology of use of graphics calculators in mathematics examinations, from the perspective of people designing examinations, together with some principles for the awarding of partial credit to student responses. This typology can be

this paper are to explain and justify this heightened level of interest in graphics calculators a... more this paper are to explain and justify this heightened level of interest in graphics calculators atthe secondary school level, and to identify some of the resulting implications for mathematics education, bothgenerally, and in the South-East Asian region.Descriptions and definitions

Yearbook 2012, Association of Mathematics Educators, 2012

ABSTRACT Outline • An Australian perspective on connections • What is 'numeracy'?... more ABSTRACT Outline • An Australian perspective on connections • What is 'numeracy'? • What does it have to do with mathematics? • Some Australian projects related to numeracy across the curriculum • Numeracy and the Australian Curriculum • Two other Australian connected activities Connections Connections refer to the ability to see and make linkages among mathematical ideas, between mathematics and other subjects, and between mathematics and everyday life. This helps students make sense of what they learn in mathematics  MOE (2006) Singapore Secondary Syllabuses, 2006, p. 4 Numeracy and maths Students develop numeracy, reasoning, thinking skills, and problem solving skills through the learning and application of mathematics. MOE (2006) Secondary Mathematics Syllabuses, p. 1 Aims for mathematics (1) Acquire the necessary mathematical concepts and skills for everyday life, and for continuous learning in mathematics and related disciplines. (4) Recognise and use connections among mathematical ideas, and between mathematics and other disciplines.

Australian Mathematics Teacher, Oct 1, 1982

Although modern technology and humanistic perspectives on mathematics education seem unrelated, i... more Although modern technology and humanistic perspectives on mathematics education seem unrelated, it is suggested that important and positive connections can be made between the two. Three roles for technology in mathematics education are described, exe mplified and defended, and some implications of these for a humanistic view of mathematics education are drawn. A computational role is concerned with humans using technology to complete otherwise tedious or difficult mathematical tasks. An influential role suggests that the availability of technology needs to be considered in deciding what mathematics is most important for the mathematics curriculum. An experiential role emphasizes the new possibilities for teaching and learning mathematics afforded by technology. It is suggested that these roles are only important when technologies are genuinely available to students, so that attention is focused on the graphics calculator, which is interpreted as a humanising device, the best available example of a personal technology for secondary school mathematics.

In recent years, the Internet has increasingly been used to provide significant resources for stu... more In recent years, the Internet has increasingly been used to provide significant resources for student to learn mathematics and to learn about mathematics, as well as significant resources for teachers to support these. Effective access to and use of these has been hampered in practice by limited facilities in schools and the limited experience of many mathematics teachers with the Internet for mathematical purposes. This paper offers models for understanding the effective use of Internet resources, based on typologies of resources for learning and teaching mathematics. Six categories of Internet resources for mathematics student use are identified: (i) Interactive resources; (ii) Reading interesting materials; (iii) Reference information; (iv) Communication; (v) Problem solving; and (vi) Webquests. Similarly, five categories of Internet resources for mathematics teacher use are identified: (i) Lesson preparation; (ii) Official advice and support; (iii) Professional engagement; (iv) ...

Yearbook 2010, Association of Mathematics Educators, 2010

Yearbook 2010, Association of Mathematics Educators, 2010

Graphics calculators have the potential to influence the curriculum in several ways, including af... more Graphics calculators have the potential to influence the curriculum in several ways, including affecting what is taught, how it is taught and learned and how it is assessed. These relationships are exemplified for the particular case of sequences and series, which frequently appear in mathematics curricula near the end of secondary school and in the early undergraduate years. Attention will

Synopsis: Although there are a number of technologies related to school algebra, it is only the p... more Synopsis: Although there are a number of technologies related to school algebra, it is only the personal technology of the graphics calculator that seems likely to be available widely enough to influence curriculum design and implementation on a large scale. The algebra curriculum of the past is overburdened with symbolic manipulation at the expense of understanding for most students. But

The Internet offers new opportunities for school students to learn mathematics. This paper analys... more The Internet offers new opportunities for school students to learn mathematics. This paper analyses these opportunities, based on presently available web sites that do not involve subscriptions by users. A typology of six different sorts of opportunities is described, justified and exemplified: (i) Interactive opportunities allow students to interact directly with mathematical objects; (ii) Reading interesting materials allows supplementation of

The graphics calculator has found many uses in secondary school algebra and calculus, but possibi... more The graphics calculator has found many uses in secondary school algebra and calculus, but possibilities in relation to chance and data have been less well publicised. This paper provides an analysis of the potential for using graphics calculators in the chance and data components of school curricula. Differences between scientific and graphics calculators are highlighted, most notably concerned with an

As graphics calculators are mainly devices for student learning, it is important that curricula a... more As graphics calculators are mainly devices for student learning, it is important that curricula and examinations are constructed to incorporate them in a coherent way. Three recent developments in graphics calculators are described and analysed to determine their implications for examinations. Symbolic manipulation on algebraic calculators challenges existing emphases in many examinations and their associated curricula. Flash memory allows calculators

This paper outlines some of the complex relationships between the curriculum and technology, with... more This paper outlines some of the complex relationships between the curriculum and technology, with particular attention on graphics calculators. Graphics calculators are of key significance for practical reasons of availability and affordability Until technology is available, curricula are not likely to be adjusted to accommodate them. Particular features of graphics calculators, including their recent extensions to algebraic calculators, are highlighted,

This paper describes the recent development of hand-held algebraic calculators and evaluates thei... more This paper describes the recent development of hand-held algebraic calculators and evaluates their significance for secondary education. Sophisticated computer algebra systems (CAS) have been available to mathematicians for some years now but have been too powerful, too sophisticated and too expensive and have required too much access to powerful computers to have had much impact on teaching and learning elementary

As graphics calculators become more available, interest will focus on how to incorporate them app... more As graphics calculators become more available, interest will focus on how to incorporate them appropriately into curriculum structures, and particularly into examinations. We describe and exemplify a typology of use of graphics calculators in mathematics examinations, from the perspective of people designing examinations, together with some principles for the awarding of partial credit to student responses. This typology can be

this paper are to explain and justify this heightened level of interest in graphics calculators a... more this paper are to explain and justify this heightened level of interest in graphics calculators atthe secondary school level, and to identify some of the resulting implications for mathematics education, bothgenerally, and in the South-East Asian region.Descriptions and definitions

Yearbook 2012, Association of Mathematics Educators, 2012

ABSTRACT Outline • An Australian perspective on connections • What is 'numeracy'?... more ABSTRACT Outline • An Australian perspective on connections • What is 'numeracy'? • What does it have to do with mathematics? • Some Australian projects related to numeracy across the curriculum • Numeracy and the Australian Curriculum • Two other Australian connected activities Connections Connections refer to the ability to see and make linkages among mathematical ideas, between mathematics and other subjects, and between mathematics and everyday life. This helps students make sense of what they learn in mathematics  MOE (2006) Singapore Secondary Syllabuses, 2006, p. 4 Numeracy and maths Students develop numeracy, reasoning, thinking skills, and problem solving skills through the learning and application of mathematics. MOE (2006) Secondary Mathematics Syllabuses, p. 1 Aims for mathematics (1) Acquire the necessary mathematical concepts and skills for everyday life, and for continuous learning in mathematics and related disciplines. (4) Recognise and use connections among mathematical ideas, and between mathematics and other disciplines.

Australian Mathematics Teacher, Oct 1, 1982

Although modern technology and humanistic perspectives on mathematics education seem unrelated, i... more Although modern technology and humanistic perspectives on mathematics education seem unrelated, it is suggested that important and positive connections can be made between the two. Three roles for technology in mathematics education are described, exe mplified and defended, and some implications of these for a humanistic view of mathematics education are drawn. A computational role is concerned with humans using technology to complete otherwise tedious or difficult mathematical tasks. An influential role suggests that the availability of technology needs to be considered in deciding what mathematics is most important for the mathematics curriculum. An experiential role emphasizes the new possibilities for teaching and learning mathematics afforded by technology. It is suggested that these roles are only important when technologies are genuinely available to students, so that attention is focused on the graphics calculator, which is interpreted as a humanising device, the best available example of a personal technology for secondary school mathematics.

In recent years, the Internet has increasingly been used to provide significant resources for stu... more In recent years, the Internet has increasingly been used to provide significant resources for student to learn mathematics and to learn about mathematics, as well as significant resources for teachers to support these. Effective access to and use of these has been hampered in practice by limited facilities in schools and the limited experience of many mathematics teachers with the Internet for mathematical purposes. This paper offers models for understanding the effective use of Internet resources, based on typologies of resources for learning and teaching mathematics. Six categories of Internet resources for mathematics student use are identified: (i) Interactive resources; (ii) Reading interesting materials; (iii) Reference information; (iv) Communication; (v) Problem solving; and (vi) Webquests. Similarly, five categories of Internet resources for mathematics teacher use are identified: (i) Lesson preparation; (ii) Official advice and support; (iii) Professional engagement; (iv) ...