Reflections: February 1999

Contents of Volume 24, No. 1

Editorial

MANSW Annual Conference, parramatta, 1998, Measuring up in Parramatta

• Opening comments, Lynette Hunter and Carol Neville

Reflections on keynote addresses

• Measuring up; measuring down; all this measuring round and round, Bob Perry
• Measuring up - Linking learning and assessment, Gilah Leder

Reflections on assessment

• Measuring up: Techniques for assessing classroom outcomes, Beth Southwell
• We teach as we were taught, we test as we were tested: Breaking the cycle through alternative assessment practices, Nicola Thong
• Making outcomes-based education effective in your school, Alan Mills
• What mark will I get? Using item response theory to scale HSC results, Juho Looveer

Reflections on teaching aboriginal students

• Teaching Aboriginal students: A personal experience, Jay Quince

Reflections on geometrical understanding

• Framework for elementary school space mathematics, Kay Owens, Pat Leberne, and Ian Harrison
• Lost in space? Allan White
• Investigating patterns with patchwork, Diana Whitton
• Amazing mazes and nifty knots: Constructing patterns in Celtic art, Ed Lewis

Reflections on the philosophy of mathematics education

• The lowdown on the philosophy of mathematics education, Beth Southwell

Reflections on investigations

• Working mathematically: Using Internet resources, Bob Dengate and Joanne Mulligan
• Making learning visible: Using open-ended tasks and extended investigations, Di Stubbs
• Open-ended questions and investigations, Anne Joshua
• Mathematics in the kitchen, Deb Gilbert
• Investigations in Years 7-10, Helen Scanlon

Reflections on constructing early mathematical understandings

• Chance and probability: Snapshots from the classroom, Janette Bobis
• Fraction action, Val Badham
• Investigating measurement, Kay Owens
• Making meaning in mathematics lessons, John Benton

Reflections on teaching strategies in secondary classrooms

• Maths week - A success story, Margaret Bigelow and Jackie Homsy
• Mathematics camp for Years 8 and 9 students, Rae Deeley
• Fresh ideas for Year 8, Cyril Quinlan and Glenn Abrahams
• Classroom delights, practicalities and novelties, George Rezcallah

Reflections on research

• Can manipulatives constrain children's construction of mathematics?
• Bob Perry, Peter Howard and Danielle Tracey
• Children's ability to visualize three-dimensional shapes, Jill Everett
• Measuring up on recommended teaching strategies, Cyril Quinlan

Reflections on technology

• Using technology to find models which fit the data and the situation, David Tynan
• Graphic calculators: Windows of opportunity, Michael Cavanagh
• Useful ideas on technology in the upper secondary classroom, Allan White and John Hastings
• Applications of mathematics with a graphic calculator using Aplets, Milton Fuller
• Problem solving and the graphic calculator, Jim McCartan

Reflections on senior mathematics

• Does student-centred learning work for seniors? Jim Milford
• The literacy demands of senior mathematics, Jenny Tayler
• The National Mathematics Summer School, Margaret Jordan
• The conic sections, James Taylor

MANSW Annual Conference, Parramatta 1998

• Conference program
• Conference participants

Editorial

The 1998 Annual Conference held at Parramatta in August was another very successful event for the Mathematical Association of New South Wales (MANSW). The conference theme of Measuring Up was embraced by some of the sessions and this is reflected in several of the papers contained in this combined issue of Reflections and Square One. Other themes include a focus on the content area of geometry, ideas for investigations, a wide variety of innovative practices from Kindergarten to Year 12, outcomes of research studies, and uses of technology to enhance learning.

These proceedings contain papers from two of the keynote speakers. Perry examines a variety of ways to consider how teachers and students might measure up . Leder explores the what, why, and when of assessment practices and encourages us to reconsider the purposes of our assessment procedures and to continue to critically examine popular methods.

A wide range of assessment practices are examined in papers by several authors. Both Thong and Southwell recommend a variety of alternative approaches. Thong, particularly, suggests that we examine why many teachers continue to use practices that were used when they were students. Mills describes a program used in his school that incorporates outcomes-based approaches and Looveer explains aspects of the scaling procedures used for high-stakes examinations.

Geometry is the focus of some of the papers. Owens, Leberne & Harrison propose a framework for early geometrical understanding. White examines tessellations and associated teaching approaches, while Whitton explains the geometrical patterns in traditional patchwork designs. Lewis provides a selection of activities related to the fascinating geometrical patterns contained in Celtic art.

Early mathematical understandings are examined in Bobis's paper as she describes the classroom outcomes of chance and data activities. Badham presents a collection of activities that can be used to enhance fraction concepts. Owens explains teaching ideas for measurement and Benton provides an overview of meaning making.

Investigations using the Internet are described by Dengate and Mulligan, and Gilbert presents classroom investigations related to practical, hands-on activities. Stubbs supports the use of open-ended questions and extended investigations that encourage students to think about the mathematics they know, and challenges their incomplete understandings. Joshua provides a smorgasbord of challenging activities and Scanlon describes the introduction of investigative projects by the mathematics faculty at her school.

Innovative practices in secondary classrooms are examined in several papers. Bigelow and Homsy describe a variety of Maths Week activities; Deeley outlines his desire to organize mathematics camps similar to those conducted in other Australian states; Quinlan and Abrahams present a short selection of practical ideas; and Rezcallah provides a variety of ideas for enthusing students about mathematics.

Other papers that have a secondary mathematics focus include those relating to technology and a variety of teaching considerations. Papers by Tynan, Cavanagh, White and Hastings, Fuller, and McCartan provide many useful teaching ideas for using graphic calculators. Milford describes his experiences using group activities in senior classes and Tayler discusses the language aspects of Mathematics in Society and Mathematics in Practice papers. Jordan recommends the National Mathematics Summer School to all talented senior students and Taylor outlines the key content elements related to the conic sections.

Research studies examining the implementation and impact of teaching strategies are the focus of three papers. Perry, Howard and Tracey describe the findings of a study that explored the usefulness of manipulatives in primary mathematics classrooms. Everett examines the visualization strategies used by young children as they imagine three-dimensional shapes.

Quinlan discusses the use of a variety of teaching strategies by secondary mathematics teachers.

The papers by Quince and Southwell explore another two themes that attracted much interest at the conference. Quince describes his experiences teaching Aboriginal students in outback NSW and Southwell examines the philosophy of mathematics education.

Not all the papers submitted for publication have been included in this issue. Some were longer than the required length and will be published in subsequent issues of Reflections or Square One.

Annual Conference always provides a colourful display of books and educational resources, participants in workshops, discussions and collaborative activities, as well as gastronomic delights. The photographs in this issue include displays from exhibitors, activities during workshops, and interactions at the Conference Dinner. Carol Neville and Amanda Atkinson must be thanked for their contribution to the collage on the cover.

Judy Anderson and Beth Southwell