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  • Teaching Secondary Mathematics

    Module 1Overview of learning in the Mathematics Domain 1

  • Published by the Student Learning Programs Division

    Office for Government School Education

    Department of Education and Early Childhood Development


    State of Victoria 2008

    The copyright in this document is owned by the State of Victoria. No part may be reproduced by any process

    except in accordance with the provisions of the Copyright Act 1968, NEALS (see below) or with permission.

    An educational institution situated in Australia which is not conducted for profit, or a body

    responsible for administering such an institution, may copy and communicate the materials, other

    than third-party materials, for the educational purposes of the institution.

    Authorised by the Department of Education and Early Childhood Development, 2 Treasury Place, East Melbourne,

    Victoria 3002.

    Also published on http://www.education.vic.gov.au


  • Module 1 Overview of learning in the Mathematics Domain | iii

    ContentsProgram Overview: 1

    Teaching Secondary Mathematics 1Background 1

    Program aims 1

    Program content and organisation 2

    Introduction to Module 1: Overview of Learning in the Mathematics Domain 4

    Use of this module 4

    Web connections 5

    Content of the module 5

    Organisation of the module 5

    Required resources 6

    Icons 6

    Users Guide to Module 1: Overview of Learning in the Mathematics Domain 7

    Outline 7

    Teaching Secondary Mathematics modules 7

    Main themes of the Teaching Secondary Mathematics resource 8

    The Learner at the Centre 8

    Scaffolding Learning Vygotsky 10

    Split screen thinking 10

    Mathematics in the VELS 10

    The Principles of Learning and Teaching P12 11

    International student achievement data 12

    Student achievement 13

    Useful resources located on the Mathematics Domain page 13

    Overarching themes 15

    Conclusion 15

    Resource 1: Principles of Learning and Teaching P12 and their components 16

    References 18

  • Module 1 Overview of learning in the Mathematics Domain | 1

    Program Overview: Teaching Secondary Mathematics

    The Teaching Secondary Mathematics Resource provides support and guidelines for effective

    practice for classroom teachers and school leaders of mathematics, especially from Years 710.

    This resource is for:


    This will inform their planning for mathematics and highlight opportunities for assessment of

    mathematics in other domains of the Victorian Essential Learning Standards (VELS)


    mathematics, in professional learning teams and/or for individual teachers


    BackgroundThe Teaching Secondary Mathematics Resource responds to the findings of the Parliament of

    Victorias Education and Training Committees Inquiry into the Promotion of Mathematics and

    Science Education in 2006. The inquiry recommended that all Victorian schools give higher priority to Mathematics and Science learning and teaching. The report noted that whilst there are

    currently some excellent outcomes in Victorian schools, there is a broad range of performance

    among students in mathematics. A need to provide opportunities to increase student engagement

    in Years 7 to 10 was noted, along with imbalances in participation and achievement of some groups

    of students. The inquiry stated that there is considerable scope for raising the achievement of the

    best students and in providing support to improve the performance of under-achieving students.

    This resource provides teachers with current research and strategies to address some of these


    Program aimsThe underlying purpose of this resource is to support schools and teachers make a difference to:



    meeting challenges, being valued as a person, learning things that have meaning in your life

    and getting rewards for making significant efforts.


    of the whole person: in the long term as a citizen with sufficient numeracy to live a fulfilling life

    contributing to the community; and immediately as a classroom member who interacts well with

    others, and assists in making school life productive.


    students experiences that increase their capacity to learn through ability to work independently,

    and their enhanced thinking and meta-cognitive processes.

  • 2 | Module 1 Overview of learning in the Mathematics Domain

    Program content and organisationThis program provides many options and ideas that have proved beneficial to some teachers.

    However, as usefulness depends on the particular circumstances of each school, community and

    student population, not all ideas will be appropriate to all teachers. Each school can chart its own

    pathway through the program, exploring areas of particular interest and value for its own needs

    and purposes.

    The Teaching Secondary Mathematics Resource consists of nine separate modules. It is

    recommended that all teachers complete Module 1: Introduction module and the concluding

    Module 9, Planning for improvement in mathematics.

    Module 1: Overview of learning in the Mathematics DomainThe introductory module orients teachers to the Teaching Secondary Mathematics resource

    and provides an overview of effective mathematical pedagogies, the need for teachers to build

    their craft, and how effective teaching reflects many of the initiatives currently being promoted by

    Department of Education and Early Childhood Development(DEECD).

    In the work undertaken by teachers and researchers it is seen that a number of pedagogical

    and mathematical themes have been found to be significant in improving learning outcomes

    for secondary students. Seven modules of the program are therefore dedicated to helping

    schools explore each of these themes. The concluding module explores how schools can plan for

    improvement in mathematics teaching.

    Module 2: Overview of the Mathematics Developmental Continuum P10This module will inform teachers about the Mathematics Developmental Continuum P10. It

    provides at outline of the main features of this Resource. The starting point is :

    Mathematics Continuum main page (http://www.education.vic.gov.au/studentlearning/


    Module 3: Narrowing the achievement gap: Focus on FractionsThe topic of fractions is a notorious hurdle that many students do not get over, effectively

    preventing them from meaningful participation in further mathematics learning. This module

    showcases how using diagnostic tests as assessment for learning, together with targeted teaching,

    can help students learn fractions with understanding in a meaningful way. This opens the door to

    future success.


  • Module 1 Overview of learning in the Mathematics Domain | 3

    Module 4: Conducting practical and collaborative work: Focus on contoursThis module uses the topic of Contours from the Space dimension of VELS to illustrate aspects of

    using practical work in mathematics for engaging students in collaborative work. There are also

    many links to skills required outside school.

    Module 5: Understanding students mathematical thinking: Focus on algebra and the meaning of lettersThis module illustrates how teaching becomes more responsive to students needs when the

    teacher understands students mathematical thinking and their common misconceptions.

    Module 6: Using a range of strategies and resources: Focus on percentages This module examines several resources used for teaching about percentages, and demonstrates

    a range of strategies to support the different ways in which students think and learn. These


    Scaffolding Numeracy in the Middle Years and Assessment for Common Misunderstandings tools.

    Module 7: Learning through investigation: Focus on chance and variabilityThis module focuses on chance and variability to illustrate key points about teaching mathematics

    through investigations. The main mathematical content is the contrast between short-run variability

    and long-run variability.

    Module 8: Working mathematically: Focus on a range of challenging problemsHaving a good appreciation of working mathematically is an important part of achievement

    in mathematics. Moreover, the processes of investigation, inquiry and explanation involved

    in working mathematically build each students capacity as a learner. These are all important

    outcomes of schooling.

    This module explores these issues in the context of some intriguing mathematical problems.

    Module 9: Conclusion: Planning for improvement in mathematicsThis module reviews the themes in the Teaching Secondary Mathematics Resource and provides

    an opportunity to start planning change in the teaching


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