Education Commons^™

A Case Study Of Effective Practice In Mathematics Teaching And Learning Informed By Valsiner's Zone Theory, Vince Geiger, Vince Geiger, Judy Anderson, Judy Anderson, Derek Hurrell

Derek Hurrell

The characteristics that typify an effective teacher of mathematics and the environments that support effective teaching practices have been a long-term focus of educational research. In this article we report on an aspect of a larger study that investigated ‘best practice’ in mathematics teaching and learning across all Australian states and territories. A case study from one Australian state was developed from data collected via classroom observations and semi-structured interviews with school leaders and teachers and analysed using Valsiner’s zone theory. A finding of the study is that ‘successful’ practice is strongly tied to school context and the cultural practices …

Thinking Maths: Learning Impact Fund Evaluation Report: Addendum To The Evaluation Report, Katherine Dix, Hilary Hollingsworth, Toby Carslake

Dr Hilary Hollingsworth

Thinking Maths is a three-term structured professional learning program for Years 6 - 9 mathematics teachers to engage middle school students’ mathematics learning. The Thinking Maths program has been developed by the South Australian Department for Education based on its Teaching for Effective Learning (TfEL) Framework. The program aims to address a significant drop in students’ mathematics performance in NAPLAN from Years 7 to Year 9. Thinking Maths supports teachers to improve students’ learning of mathematical content during the transition between Primary and Secondary school. Years 6 - 9 teachers participate in five professional learning days at 4 - 5 …

Thinking Maths: Learning Impact Fund Evaluation Report: Evaluation Report And Executive Summary, Katherine Dix, Hilary Hollingsworth, Toby Carslake

Dr Hilary Hollingsworth

Thinking Maths is a three-term structured professional learning program for Years 6 - 9 mathematics teachers to engage middle school students’ mathematics learning. The Thinking Maths program has been developed by the South Australian Department for Education based on its Teaching for Effective Learning (TfEL) Framework. The program aims to address a significant drop in students’ mathematics performance in NAPLAN from Years 7 to Year 9. Thinking Maths supports teachers to improve students’ learning of mathematical content during the transition between Primary and Secondary school. Years 6 - 9 teachers participate in five professional learning days at 4 - 5 …

Thinking Maths: Learning Impact Fund Evaluation Report: Addendum To The Evaluation Report, Katherine Dix, Hilary Hollingsworth, Toby Carslake

Dr Katherine Dix

Thinking Maths is a three-term structured professional learning program for Years 6 - 9 mathematics teachers to engage middle school students’ mathematics learning. The Thinking Maths program has been developed by the South Australian Department for Education based on its Teaching for Effective Learning (TfEL) Framework. The program aims to address a significant drop in students’ mathematics performance in NAPLAN from Years 7 to Year 9. Thinking Maths supports teachers to improve students’ learning of mathematical content during the transition between Primary and Secondary school. Years 6 - 9 teachers participate in five professional learning days at 4 - 5 …

Thinking Maths: Learning Impact Fund Evaluation Report: Evaluation Report And Executive Summary, Katherine Dix, Hilary Hollingsworth, Toby Carslake

Dr Katherine Dix

Thinking Maths is a three-term structured professional learning program for Years 6 - 9 mathematics teachers to engage middle school students’ mathematics learning. The Thinking Maths program has been developed by the South Australian Department for Education based on its Teaching for Effective Learning (TfEL) Framework. The program aims to address a significant drop in students’ mathematics performance in NAPLAN from Years 7 to Year 9. Thinking Maths supports teachers to improve students’ learning of mathematical content during the transition between Primary and Secondary school. Years 6 - 9 teachers participate in five professional learning days at 4 - 5 …

Numeracy Education Through Mobile Apps, Boris Handal, Iona Novak, Kevin Watson, Marguerite Maher, Jean Macnish, Katrina Eddles-Hirsch

Kevin Watson

Numeracy achievement of Australian school children is a national priority according to the Australian Curriculum. There is increasingly compelling evidence that numeracy needs to be a focus in all curriculum areas, not solely in mathematics (Human Capital Working Group, 2008). At the same time, there is an ever-increasing scope for the use of mobile technologies to enhance learning and teaching. This article examines how numeracy and mobile learning work together as teachers in the Middle Years are mentored to use iPad applications (apps) effectively within their own curriculum area to enhance the learning of numeracy for children in their classes.

Numeracy Education Through Mobile Apps, Boris Handal, Iona Novak, Kevin Watson, Marguerite Maher, Jean Macnish, Katrina Eddles-Hirsch

Boris Handal

Numeracy achievement of Australian school children is a national priority according to the Australian Curriculum. There is increasingly compelling evidence that numeracy needs to be a focus in all curriculum areas, not solely in mathematics (Human Capital Working Group, 2008). At the same time, there is an ever-increasing scope for the use of mobile technologies to enhance learning and teaching. This article examines how numeracy and mobile learning work together as teachers in the Middle Years are mentored to use iPad applications (apps) effectively within their own curriculum area to enhance the learning of numeracy for children in their classes.

Numeracy Education Through Mobile Apps, Boris Handal, Iona Novak, Kevin Watson, Marguerite Maher, Jean Macnish, Katrina Eddles-Hirsch

Katrina Eddles-Hirsch

Numeracy achievement of Australian school children is a national priority according to the Australian Curriculum. There is increasingly compelling evidence that numeracy needs to be a focus in all curriculum areas, not solely in mathematics (Human Capital Working Group, 2008). At the same time, there is an ever-increasing scope for the use of mobile technologies to enhance learning and teaching. This article examines how numeracy and mobile learning work together as teachers in the Middle Years are mentored to use iPad applications (apps) effectively within their own curriculum area to enhance the learning of numeracy for children in their classes.

Numeracy Education Through Mobile Apps, Boris Handal, Iona Novak, Kevin Watson, Marguerite Maher, Jean Macnish, Katrina Eddles-Hirsch

Marguerite Maher

Numeracy achievement of Australian school children is a national priority according to the Australian Curriculum. There is increasingly compelling evidence that numeracy needs to be a focus in all curriculum areas, not solely in mathematics (Human Capital Working Group, 2008). At the same time, there is an ever-increasing scope for the use of mobile technologies to enhance learning and teaching. This article examines how numeracy and mobile learning work together as teachers in the Middle Years are mentored to use iPad applications (apps) effectively within their own curriculum area to enhance the learning of numeracy for children in their classes.

Numeracy Education Through Mobile Apps, Boris Handal, Iona Novak, Kevin Watson, Marguerite Maher, Jean Macnish, Katrina Eddles-Hirsch

Jean MacNish

Numeracy achievement of Australian school children is a national priority according to the Australian Curriculum. There is increasingly compelling evidence that numeracy needs to be a focus in all curriculum areas, not solely in mathematics (Human Capital Working Group, 2008). At the same time, there is an ever-increasing scope for the use of mobile technologies to enhance learning and teaching. This article examines how numeracy and mobile learning work together as teachers in the Middle Years are mentored to use iPad applications (apps) effectively within their own curriculum area to enhance the learning of numeracy for children in their classes.

Conceptualising Changes To Pre-Service Teachers’ Knowledge Of How To Best Facilitate Learning In Mathematics: A Tpack Inspired Initiative, Frank G. Bate, Lorraine Day, Jean Macnish

Jean MacNish

In 2010, the Australian Commonwealth government initiated an $8m project called Teaching Teachers for the Future. The aim of the project was to engage teacher educators in a professional learning network which focused on optimising exemplary use of information and communications technologies in teacher education. By taking part in this network, participants were afforded opportunities to transform their practice through a range of localised initiatives that applied information and communications technologies to the art and science of teaching and learning. One of these initiatives involved re-engineering a university mathematics unit targeted at pre-service teachers. Information and communications technologies were purposefully …

Tasks And Resources For Developing Children's Multiplicative Thinking, Derek Hurrell, Chris Hurst

Derek Hurrell

The development of multiplicative thinking determines largely the extent of the mathematics that a person learns beyond middle primary school. Our current research project has so far revealed that many primary children have a procedural view of aspects of multiplicative thinking that we believe inhibits their progress. This workshop focuses on some of the teaching resources and tasks that have been developed from our research. The purpose of these tasks is to promote the development of conceptual understanding of 'the multiplicative situation' and the many connections within it and with other big ideas such as proportional reasoning and algebraic thinking.

Investigating Children's Multiplicative Thinking, Chris Hurst, Derek Hurrell

Derek Hurrell

Multiplicative thinking is a ‘big idea’ of mathematics that underpins much of the mathematics learned beyond the early primary school years. The conference presentation reports on a recent study that utilised an interview tool to gather data about children’s multiplicative thinking. Using a workshop format, we present some of the interview tool and some of the findings, as well as demonstrate how the tool can be used for planning, teaching and assessment. The session also emphasises the importance of developing deep conceptual understanding as opposed to the teaching of procedures. This paper considers how evidence from the interview can be …

Conceptualising Changes To Pre-Service Teachers’ Knowledge Of How To Best Facilitate Learning In Mathematics: A Tpack Inspired Initiative, Frank G. Bate, Lorraine Day, Jean Macnish

Lorraine Day

In 2010, the Australian Commonwealth government initiated an $8m project called Teaching Teachers for the Future. The aim of the project was to engage teacher educators in a professional learning network which focused on optimising exemplary use of information and communications technologies in teacher education. By taking part in this network, participants were afforded opportunities to transform their practice through a range of localised initiatives that applied information and communications technologies to the art and science of teaching and learning. One of these initiatives involved re-engineering a university mathematics unit targeted at pre-service teachers. Information and communications technologies were purposefully …

Deconstructing Maths Anxiety: Helping Students To Develop A Positive Attitude Towards Learning Maths, Sarah Buckley

Dr Sarah Buckley

Higher maths ability is often believed to go hand-in-hand with greater levels of general intelligence. At the same time, many students have a negative attitude towards maths. Maths anxiety is defined in the research literature as feelings of concern, tension or nervousness that are experienced in combination with maths. In 2005, researchers in the United States estimated that approximately 20 per cent of the US population were highly maths anxious. Given the cultural similarities between the US and Australia, we can assume that the percentage would be comparable here. Research in education, cognitive psychology and neuroscience shows that anxiety can …

The Mathematics Education Of Future Primary And Secondary Teachers : Methods And Findings From The Teacher Education And Development Study In Mathematics, Maria Tatto, Sharon Senk, Glenn Rowley, Ray Peck

Ray Peck

In 2005, the International Association for the Evaluation of Educational Achievement (IEA), Michigan State University, and the Australian Council for Educational Research took an important step in advancing the field of education by partnering to develop and implement the first international and comparative study of mathematics teacher education. The study was made possible by the substantial funding received from the National Science Foundation, the IEA, and the collaboration of 17 participating countries. The purpose of this article is to illustrate the methodology used in this major cross-national study of teacher education—the IEA Teacher Education and Development Study in Mathematics, known …

An Analysis Of Teacher Education Context, Structure, And Quality- Assurance Arrangements In Teds-M Countries : Findings From The Iea Teacher Education And Development Study In Mathematics (Teds-M), Lawrence Ingvarson, John Schwille, Sharon Senk, Glenn Rowley, Ray Peck, Maria Tatto

Ray Peck

The present report is a companion report to the TEDS-M publication Policy, Practice, and Readiness to Teach Primary and Secondary Mathematics in 17 Countries: Findings from the IEA Teacher Education and Development Study in Mathematics (TEDS-M) written by Tatto et al., (2012). That report presented findings about the nature and content of teacher education programs in the 17 participating countries, as well as the mathematical knowledge and pedagogical knowledge of graduates from those programs. The present report focuses on reporting data gathered at the national level and placing those findings in context. When interpreting the findings presented in the aforementioned …

Using Mathematical Competencies To Predict Item Difficulty In Pisa, Ross Turner, J Dossey, W Blum, M Niss

Ross Turner

Mathematical Thinking Of Preschool Children In Rural And Regional Australia : Research And Practice, Robert Hunting, Janette Bobis, Brian Doig, Judith Mousley, Lyn English, Joanne Mulligan, Marina Papic, Catherine Pearn, Bob Perry, Jill Robbins, Jenny Young-Loveridge

Catherine Pearn

Results of a research project that investigated: early childhood educators' thoughts on young children's mathematical thinking and development; reviewed recent research literature on the mathematical learning and thinking of young children; and made this information accessible to early childhood educators at all levels. Sixty-four early childhood educators from regional and rural New South Wales, Queensland and Victoria were interviewed for the project. Questions focused on: children's mathematics learning; support for mathematics teaching; use of technology; attitudes to mathematics; and assessment and record keeping. [p.1]

The Digest Edition 2010/2 : Language In The Mathematics Classroom, Marion Meiers, Jenny Trevitt

Marion Meiers (1941-2018)

A recent Australian review of numeracy teaching noted the significant role of language in mathematics learning. The National Numeracy Review Report (2008), commissioned by the Council of Australian Governments (COAG), synthesised evidence on effective numeracy teaching to support the goal of improving numeracy outcomes for Australian students. The report of the review acknowledged the significance of language in mathematics learning, and recommended: That the language and literacies of mathematics be explicitly taught by all teachers of mathematics in recognition that language can provide a formidable barrier to both the understanding of mathematics concepts and to providing students access to assessment …

Examining The Use Of Ict In Mathematics And Science Teaching, John Ainley

Dr John Ainley

Australian science and mathematics teachers are leaders in the useof ICT in school education according to an international comparativestudy, and ACER is set to lead further research in this area.John Ainley explains.

Identifying Cognitive Processes Important To Mathematics Learning But Often Overlooked, Ross Turner

Ross Turner

Learning About Students' Mathematical Literacy From Pisa 2003, S Mccrone, J Dossey, Ross Turner, M Lindquist

Ross Turner

Teacher Education And Development Study In Mathematics (Teds-M) : Policy, Practice, And Readiness To Teach Primary And Secondary Mathematics : Conceptual Framework., Maria Tatto, John Schwille, Sharon Senk, Lawrence Ingvarson, Ray Peck, Glenn Rowley

Ray Peck

TEDS-M is a collaborative effort of worldwide institutions to study the mathematics preparation of future primary and secondary teachers. This study investigates whether what future teachers learn in teacher education leads to more effective knowledge of mathematics and mathematics for teaching. The lead centre is the International Study Center at Michigan State University, which along with the International Association for the Evaluation of Educational Achievement (IEA), the Australian Council of Educational Research, and national research centres (NRCs) in 17 countries, is analysing the costs of becoming a teacher prepared to teach mathematics, the policies governing mathematics teacher education (including recruitment, …

Stand Up And Be Counted : Who'd Be A Maths Teacher?, Mark Butler

Mark Butler

Teaching is not easy, but everyone who has never done it seems to think they can do a better job - just as comedians are often offered so- called 'good' jokes by non-comedians. The author of this article, who taught secondary school mathematics for five years, provides an amusing account describing the similarities between a maths teacher and a stand- up comedian.

Pisa 2003—Mathematical Literacy And Learning In The Americas, John Dossey, Sharon Mccrone, Ross Turner, Mary Lindquist

Ross Turner

Whole Number Knowledge And Number Lines Help To Develop Fraction Concepts, Catherine Pearn

Catherine Pearn

Many researchers have noted that students' whole number knowledge can interfere with their efforts to learn fractions. In this paper the authors discuss a teaching experiment conducted with students in Years 5 and 6 from an eastern suburban school in Melbourne. The focus of the teaching experiment was to use number lines to highlight students' understanding of whole numbers then fractions. The study used a screening test and interview using number lines to probe students' understanding of fractions as numbers. By using whole numbers on number lines first, the interview questions clearly helped many students to connect whole number and …

Lesson Study : A Professional Learning Model That Actually Makes A Difference, Hilary Hollingsworth, Delwyn Oliver

Dr Hilary Hollingsworth

Over the past year, a group of mathematics teachers from one Victorian school engaged in a process of professional learning called Lesson Study. In bi-weekly meetings that focused on the development of a single exemplary lesson, they questioned, pondered, discussed, debated, explored, and examined mathematics, and the teaching and learning of mathematics. This paper describes the process and the outcomes of what these teachers consider to be the most powerful professional learning they have experienced.

Mathematics Recovery : Frameworks To Assist Students' Construction Of Arithmetical Knowledge, Catherine Pearn

Catherine Pearn

Mathematics Recovery was the outcome of a three-year research and development project at Southern Cross University, conducted in 1992-5. The project received major funding from the Australian Research Council and major contributions in the form of teacher time, from regional government and Catholic school systems. Over the 3-year period, the project involved working in 18 schools with 20 teachers and approximately 200 participating first-grade students. MR can be regarded as consisting of two distinct but interrelated components. One component concerns an elaborated body of theory and practice for working with students, that is, teaching early number knowledge. The second component …

The Development Of Mathematical Strategies In The Early Years, Catherine Pearn

Catherine Pearn

Current research has shown that children develop a repertoire of mathematical strategies by progressing though five 'counting stages'. These are: perceptual - students are limited to counting those items they can perceive; figurative - students count from one when solving addition problems with screened collections; initial number sequence - students can now count on to solve addition and missing add-end problems with screened collections; implicitly nested number sequence - students are able to focus on the collection of unit items as one thing, as well as the abstract unit items; explicitly nested number sequence - students are simultaneously aware of …