Reflections: February 1998

EDITORIAL

MANSW ANNUAL CONFERENCE, CANBERRA 1997

• Opening comments, Anne Hastings and Bobby Gaensler 1

REFLECTIONS ON KEYNOTE ADDRESSES

• Our students coming alive as active investigators, Michael Norman 2
• The future of computation, Alistair McIntosh 4
• Statistical literacy: What's the chance?, Jane M. Watson 6

REFLECTIONS ON CHANCE AND DATA

• Investigating chance using data, Jonathan B. Moritz 15
• Investigating data exploration, Joanne Mulligan and Janette Bobis 19

REFLECTIONS ON TECHNOLOGY

• Starting to use the Internet in the Primary maths classroom, Robert Blanchfield 23
• Problem solving with dynamic geometry software, Mary Barnes 25
• Personal technology and the calculus, Barry Kissane 28
• What's new in mathematics software in 1997, Stephen Arnold 32
• Graphic calculators in Junior secondary school mathematics, Roger Brown 35

REFLECTIONS ON NUMBER

• Count me in too &emdash; In the bush, Garry Stanger 39
• Perfect numbers &emdash; Yes, they really do exist, Bill Baugh 41

REFLECTIONS ON ALGEBRA

• Algebraic acrobatics, Bruce Llewellyn 45
• Introducing algebra in Year 7: A beginner's guide, Robert Yen 47
• The general term of the Fibonacci sequence, James Taylor 51

REFLECTIONS ON SPACE

• Give me space, Beth Southwell 52
• Domes, George Anderberg 56
• REFLECTIONS ON TEACHING RESOURCES
• Building numeracy skills through media material, Alan Brady 58
• Investigating with paper, Kay Owens 62

REFLECTIONS ON PROBLEM SOLVING

• Problem-solving tasks and teacher questions, Mary Barnes 67
• A connectionist view of problem solving, Beth Southwell 69

REFLECTIONS ON ASSESSMENT

• Assessment alternatives in mathematics, Margaret Rowlands 74
• Analysing, tracking, and reporting student achievement in mathematics, Di Stubbs 78
• The development of a model of assessment principles for mathematical competence, Beth Lee 81

REFLECTIONS ON RESEARCH

• Frameworks for statistical thinking in Primary schools, Bob Perry 85
• An investigation into how children learn area: A case study, Mary Murdoch 88
• Understanding algebra: One student's approach, Anne Prescott 92
• The development of shared meaning between student and teacher
• of the concept of a variable: A case study, John Nicholls 96

REFLECTIONS ON COOPERATIVE LEARNING

• Cooperative learning, Jim Milford 100

REFLECTIONS ON THE CONFERENCE

• Talk show, Robert Yen 101

MANSW ANNUAL CONFERENCE, CANBERRA, 1997

• Conference program 103
• Conference participants 106

EDITORIAL

This combined issue of Reflections and Square One includes many of the excellent papers presented at the 1997 MANSW Annual Conference held in collaboration with the Canberra Mathematical Association. The conference theme of ACTive Investigations was embraced by many of the sessions and this is clearly reflected in several of the papers. Other themes include a focus on content areas such as Algebra, Chance and Data, Number, and Space. Authors have also addressed many issues including using technology, incorporating alternative assessment approaches, implementing problem solving and using innovative teaching practices. Some papers report on research findings that can support teachers in their efforts to promote learning in their classrooms.

We are fortunate to be able to publish papers from all three keynote speakers. Norman discusses the important role of educating young people; McIntosh reflects on the future of computation; and Watson raises many issues about developing statistical literacy. Chance and Data is also the focus of papers by Moritz, Mulligan and Bobis, and Perry.

Number, Algebra and Space form the focus of several papers that include many excellent teaching ideas. Stanger discusses the Count Me In Too Project and Baugh considers perfect numbers. Llewellyn investigates some interesting algebraic results; Yen describes an approach to introducing algebra; and Taylor develops the general term of the Fibonacci sequence. Prescott and Nicholls discuss findings from research studies about algebraic understanding. Southwell and Anderberg provide teaching ideas related to the development of spatial concepts. Brady shares his ideas about developing numeracy skills through media materials and Owens describes teaching approaches with the use of paper as a resource.

Teachers continue to seek advice and support for implementing technology into their mathematics lessons. Several papers address this issue. Arnold explores the latest mathematics software and Brown describes how graphic calculators can be used in many topic areas in the secondary school curriculum. Blanchfield suggests ways to use the Internet; Barnes discusses problem solving using dynamic geometry software; and Kissane describes approaches to teaching calculus with the graphic calculator.

Problem solving and assessment are also focus issues. Barnes explores the importance of teacher questions and Southwell describes a connectionist view of problem solving. Rowlands describes several alternative assessment strategies and Stubbs discusses the very successful professional development courses offered by the Primary Program Committee during 1997.

We have decided to include Robert Yen's reflections on the conference which were originally published in his column Mr Yen's World in Education. This paper provides an entertaining and light-hearted look at Robert's experiences and includes his reactions to his first presentation at a MANSW conference. We hope this may encourage other young teachers to consider presenting papers at a future conference.

Because of the increased number of papers submitted for publication, we have had to hold some for the next issue of Reflections. All of these papers have a secondary focus and include:

• Brady, A. C. An Innovative Approach to an Investigation of Lowest Common Multiples and Highest Common Factors.
• Buecher, C. Applications of Graphic Calculators to Selected Topics from NSW Mathematics Syllabuses.
• Campisi, L. An Investigation in the use of Writing Prompts to Promote Learning.
• Coupland, M. All Stations to Confusion?
• Grant, K. Locus.
• Hunter, L. Study skills for MIS/MIP: A different approach.
• Southwell, B. Understanding Reluctant Learners in Mathematics.
• Taylor, J. Proofs for the Irrationality of e and ’.
• Van Ravenstein, T. Fibonacci, Flowers and Fractals.

We would like to thank all of these authors for agreeing to have their papers published in a subsequent issue.

The photographs on the cover of this issue are from the Annual Conference. They include displays from exhibitors, activities during workshops, interactions at the Conference Dinner and floral delights from Floriade.

Judy Anderson, Janette Bobis, and Beth Southwell