Curriculum: Learning, Teaching and Assessment > Literacy and Numeracy > Year 2 Diagnostic Net > Year 2 Diagnostic Net Training > Session 4: Number Developmental Continuum (Part 1) >

Session 4 - Structure of the session

Introduction
Part A: Organising framework - Number Developmental Continuum
Part B: Explorations - Counting and Patterning (organiser)
Part C: Comparing and analysing numbers - Number Concepts and numeration (organiser)
Part D: Syllabus links
Part E: Professional reflection and action

Introduction

Share the overall purpose of the session (OHT 4.1 (new window) 10k ).

Identify outcomes of the session (OHT 4.1 (new window) 10k ).

Part A: Organising framework - Number Developmental Continuum

Purpose

The purpose of Part A is to familiarise participants with the terminology of the Number Developmental Continuum.

Procedure

Explain the structure of the Number Developmental Continuum using OHT 4.2 (new window) 10k

Ask participants to refer to the fold-out page headed 'Overview of Number Developmental Continuum' at the front of their copy of Number Developmental Continuum.

Ask participants to locate the name of each phase.

Ask participants to turn to the fold-out pages headed 'Indicators for Number Developmental Continuum' and identify organisers and indicators.

Discuss similarities and differences across the phases - for example, using OHT 4.3 (new window) 10k , show how Phase A is different from Phases B-F.

Show OHT 4.4 (new window) 10k and read observation statements to group.

Ask participants to locate the phase, organiser and indicator which match each statement.

Emphasise to participants that when assigning a phase in the focus area of number, the student must demonstrate all the indicators of that phase.

Key message

Teachers need to develop a common understanding of the Year 2 Diagnostic Net terminology to implement the Net process.

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Part B: Explorations - Counting and Patterning (organiser)

Purpose

The purpose of Part B is to analyse the developmental sequence of the organising framework Counting and Patterning.

Procedure

Introduce the sorting buckets activity. (This activity is adapted from the Year 1 Mathematics Sourcebook, page 29.)

Ask participants to form groups of three.

Give each group a sorting bucket/container filled with a wide selection of sorting materials.

Give participants five minutes to explore/use the materials in any way they like.

Encourage discussion among participants about their manipulation of the materials.

Ask participants to list the processes they used while exploring the materials. Write these on the board.

Relate participants' answers to beginning mathematical processes for counting and patterning as shown on OHT 4.5 (new window) 10k

Draw attention to the developmental nature of the sequence.

Ask participants to brainstorm how the sorting buckets activity could be made more simple or difficult to cater for different students' needs.

Ask participants to read Number Developmental Continuum, pages 14-16.

Key messages

The Year 1 Mathematics Sourcebook provides activities to help children develop the key indicators of Phases A and B.
Class teachers should provide daily opportunities for students to explore mathematical concepts using concrete materials.

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To further support students, teachers can refer to the section 'Major teaching emphases at all phases' in the overview of the Number Developmental Continuum, and to the sections 'Patterning' and 'Counting' in Intervention Strategies: Number.

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Part C: Comparing and analysing numbers - Number Concepts and Numeration (organiser)

Purpose

The purpose of Part C is to analyse the developmental sequence of the organising framework Number Concepts and Numeration and to provide practice in modifying learning experiences to cater for all learning needs.

Procedure

Introduce the activity for investigating the conservation of number. (This activity is adapted from the Year 2 Mathematics Sourcebook, page 25.)

Ask participants to work in groups of three.

Explain to participants that they will use the materials from the previous sorting activity.

Ask participants to:

nominate a number between 2 and 10 to model with the materials (throw the dice to select the number);
arrange their materials in as many different shapes and patterns as they can;
count the number of items after each rearrangement to reinforce the idea that the number has not been changed by the rearrangement;
record their responses in as many ways as possible. (In a classroom situation, students could record their arrangements with simple line drawings.)

Discuss the mathematical processes participants used during the activity.

Brainstorm how the activity could be made more simple or difficult to cater for different students' needs.

Read page 17 of Number Developmental Continuum and discuss the importance of the progressive introduction of each form of representation.

Emphasise the following points:

Students should be encouraged to represent their explorations in a variety of ways - concretely, pictorially, verbally and symbolically.
By modifying a task with materials or language, teachers can create a challenging but supportive environment that caters for diverse learning needs.

Key message

The topic Comparing and Analysing Numbers in the Year 2 Mathematics Sourcebook links directly to the Number Developmental Continuum organiser Number Concepts and Numeration.

To further support students, teachers can refer to 'Major teaching emphases at all phases' in the overview of the Number Developmental Continuum.

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Part D: Syllabus links

Purpose

The purpose of Part D is to demonstrate the connections between syllabus documents.

Procedure

Enlarge Handout 4.1 (new window) 19k to A3.

Distribute copies of the handout to participants and discuss its content.

Ask participants to draw lines to match the processes used across the three frameworks.

Pose the focus question 'What other key learning areas use these processes?'.

Facilitate discussion.

Key messages

The processes used in mathematics underpin other syllabus documents.
Purposeful activity-based learning promotes the affective domain of the Mathematics Syllabus.

For further information on applying these investigations to other areas of the school curriculum refer to:

Years 1 to 10 Mathematics Sourcebook: Activities for Teaching Mathematics in Year 1 1989, Department of Education, Queensland, p. 32.

Years 1 to 10 Mathematics Sourcebook: Activities for Teaching Mathematics in Year 2 1990, Department of Education, Queensland, p. 63.

Years 1 to 10 Mathematics Sourcebook: Activities for Teaching Mathematics in Year 3 1991, Department of Education, Queensland, p. 58.

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Part E: Professional reflection and action

Purpose

The purpose of Part E is to encourage a commitment to learning and professional reflection.

Procedure

Select one of the following options for participants.

Notes:

Options A and B are offered in the final part of most sessions of this training and professional development program. Participants should complete Option A at some stage of the program. If they have done this activity in a previous session, choose one of the other options. Option B can be repeated as often as desired.
OHTs and handouts for Options A and B are included in Sessions 1 and 2 materials.

Option A

Display the diagram of the teaching-learning cycle on OHT 2.5 (new window) 11k

Give participants copies of the diagram (Handout 2.3 (new window) 11k ).

Encourage discussion about the diagram and the statement below it.

Ask participants to form pairs and to indicate onHandout 2.3 (new window) 11k where they see the continua fitting into the teaching-learning cycle.

Ask participants to share their ideas with the group.

Option B

Ask participants to complete one of the Reflective Journal sheets in Handout 1.4 (new window) 21k . Participants may like to compile their notes and observations in journal form. A cover sheet is provided for this purpose.

Option C

Select questions from the list below (or add alternatives) and ask participants to answer in view of the new information presented during the session.

What would I like to know more about?
How will the new information presented in this session affect my classroom
practice?
Who can support me in my new learning?
What resources are available to help me learn more?

Option D

Ask participants to undertake a between-session activity that incorporates or reflects the purpose of this session - for example, they could select a learning episode from their year-level sourcebook and work with a focus group. Participants may decide to concentrate on questioning techniques or observing children working.

Key messages

Some of the most powerful professional learning takes place when teachers identify interests or concerns and strategically plan to investigate and improve their teaching practice.
Teacher learning may take many forms, including:
- action research;
- teacher research;
- professional journal;
- peer coaching;
- professional networks.

Facilitator's reflection

Which participants require further support?
What form could this take?

Comments:

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