Curriculum: Learning, Teaching and Assessment > Literacy and Numeracy > Year 2 Diagnostic Net > Year 2 Diagnostic Net Training > Session 5: Number Developmental Continuum (Part 2) >

Session 5 - Structure of the session

Introduction
Part A: Organising framework of the Number Developmental Continuum - Using a Whole Class Profile
Part B: Operations - Operations and Computations (organiser)
Part C: Problem solving - Working Mathematically with Numbers (organiser)
Part D: Locating and creating problem-solving situations - Working Mathematically with Numbers (organiser)
Part E: Professional reflection and action

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Introduction

Share the overall purpose of the session (OHT 5.1 (new window) 10k ).

Identify outcomes of the session (OHT 5.1 (new window) 10k ).

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Part A: Organising framework of the Number Developmental Continuum - Using a Whole Class Profile

Purpose

The purpose of Part A is to highlight the benefits of using a Whole Class Profile as a means of catering for students ' needs, and to give participants an opportunity to map on a Whole Class Profile.

Procedure

Revise the structure of the Number Developmental Continuum.

Ask participants to refer to the fold-out pages at the front of their copy of Number Developmental Continuum and to locate the names of each of the phases.

Ask participants to identify organisers and indicators in the continuum.

Ask participants to trace the developmental sequence of the counting and patterning organiser across all phases of the continuum, beginning with Phase B. (Note: Phase F is on pages 64-73.)

Discuss key indicators and other indicators in each phase and note the developmental sequence - for example:
Phase B: Demonstrates the ability to rote count
Phase C: Counts forwards and backwards (forwards to 20; backwards from 10)
Phase D: Counts forwards and backwards (forwards to 100; backwards from 20)

Display the observation statements on OHT 5.2 (new window) 34k .

Read the statements with participants and discuss ways of recording observations.

Distribute the sample of a Whole Class Profile on Handout 5.1 (new window) 33k and discuss strengths and weaknesses of the listed students in counting and patterning

Ask participants to map students according to the observations on OHT 5.2 (new window) 34k . They should block only the indicators that show students' achievements. This should form groups of students with similar needs. (Whole Class Profiles for all phases are provided on pages 111-140 of Number Developmental Continuum.)

Pose the focus question 'How could you use the Whole Class Profile?'.

Key messages

Implementing the Year 2 Diagnostic Net requires a common use and
understanding of terms such as 'organiser', 'key indicator' and 'Whole Class Profile'.
The phases of the continuum are developmental in nature.
When assigning a phase in the focus area of number, teachers must ensure that a student achieves all the indicators of that phase.
Mapping to develop a Whole Class Profile is one way to group students with similar needs.

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Part B: Operations - Operations and Computations (organiser)

Purpose

The purpose of Part B is to demonstrate the various representations of addition operations. These variations highlight the different ways these operations can be recorded.

Procedure

Explain to participants that this part of the session is based on the activity 'Throw the dice' (adapted from the Year 2 Maths Sourcebook, page 80).

Ask participants to form pairs and to prepare for the activity by reading through and discussing the key indicators and other indicators of Operations and Computations in Phase C of the continuum.

Explain that participants will need to jot down all the mathematical behaviours (indicators) that they observe during the activity.

Give participants materials for the activity and explain the rules:

Player 1 throws the two dice and mentally calculates the total of the numbers displayed.
Player 2 checks his/her partner's answer with the counting materials or calculator.
Players change roles and continue to take turns throwing the dice and calculating totals.
A correct answer scores one point. Players can keep score by tallying or using counting materials.
The player with the most points at the end of the game is the winner.

Ask participants to perform the activity and remind them to record observable mathematical behaviours.

Ask participants to share their observations with the group when the activity is completed.

Ask them to check these observations with the indicators in Phase C of the continuum.

Encourage participants to brainstorm ways of making the activity more simple or difficult to cater for the different needs of students.

Direct participants to the section 'Operations and computations' on page 19 of Number Developmental Continuum and ask them to discuss the dot points in column 1 and the information under the heading 'Representing operations ' in column 2.

Direct participants to pages 20-22 of Number Developmental Continuum for more information about the concept of addition and a suggested sequence for teaching this concept.

Explain that organisers in the Number Developmental Continuum are supported by activities and information in year-level Mathematics Sourcebooks.

Key messages

Addition computations can be represented in a variety of ways - for example, concrete, pictorial, verbal and symbolic.
These representations reflect the developmental sequence incorporated in the Number Developmental Continuum.

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Part C: Problem solving - Working Mathematically with Numbers (organiser)

Purpose

The purpose of Part C is to identify the processes that underpin the Mathematics Syllabus and strategies that support the development of students' problem-solving skills.

Procedure

Explain to participants that this part of the session is based on a problem-solving activity.

Display the problem on OHT 5.3 (new window) 10k

Ask participants to read the problem and jot down their ideas or strategies for solving it.

Ask them to share their ideas with the group.

Highlight the fact that there are a variety of ways to approach problem solving.

Emphasise the need to encourage an approach that involves investigation and decision making.

Ask participants to discuss, in pairs, how they structure problem-solving activities in their classrooms.

Ask participants to share their strategies with the group. (Record these on the blackboard or whiteboard.)

Direct participants to the organiser Working Mathematically with Numbers in Phase B of the continuum.

Ask them to read and discuss the key indicators and other indicators.

Continue discussing this organiser for all phases of the continuum, noting the development of problem-solving skills.

Ask participants to read the section headed 'Problem solving' on pages 28-29 of Number Developmental Continuum and to discuss the dot points.

Refer participants to the following sources if they require further information on the development of problem-solving skills:

year-level Mathematics Sourcebooks, page 3;
A National Statement on Mathematics for Australian Schools, chapter 6, 'Mathematical inquiry'.

Key messages

The global process 'Problem solving' in the Mathematics Syllabus (page 11) links directly to the organiser Working Mathematically with Numbers.
The key indicators and other indicators in the organiser Working Mathematically with Numbers support an approach to problem solving that is based on investigation and decision making.

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Part D: Locating and creating problem-solving situations - Working Mathematically with Numbers (organiser)

Purpose

The purpose of Part D is to encourage participants to identify everyday situations in the classroom to develop students' problem-solving skills.

Procedure

Remind participants of the problem-solving activity they did in Part C (placement of the shorts).

Ask the following questions:

What strategies did you use to solve this problem?
What other problem-solving strategies do you know?

List these strategies on the blackboard or whiteboard. The list should include strategies such as:

using objects;
drawing pictures;
acting out the problem;
logical reasoning.

Refer participants to Intervention Strategies: Number, pages 159-164, for further information and ideas about problem solving.

Emphasise that problem-solving activities in the classroom can be related to real-life or life-like situations - for example: 'It's raining heavily and we have to go to the library. How are we going to get there without getting wet?'.

Ask participants to list and discuss strategies that could be used to solve this real-life problem.

Ask participants, in pairs, to identify everyday problem-solving situations that could arise in the classroom setting. These could be shared with the group.

Discuss with participants how mathematical concepts and operations can be identified and consolidated through problem-solving activities in all curriculum areas.

For example, in a physical education lesson, students could be asked to solve the following: 'We have ten children but only six balls. How many more balls do we need so that each child has one?'.

Emphasise that problem-solving activities should be related to what the students are doing.

Ask participants to share any texts or materials they have found useful for developing students' problem-solving skills.

Key messages

There are many different strategies for solving problems.
Problem-solving activities should be based on real-life or life-like situations.
Problem-solving strategies can be used in all curriculum areas.

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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 on Handout 2.3 (new window) 11k where they see the continual 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?
What resources are available to support planning and implementation in the areas discussed during this session?
What are some opportunities for problem solving in my classroom?

Option D

Ask participants to undertake a between-session activity that incorporates or reflects the purpose of this session - for example, they could ask students in their class to perform the 'Throw the dice' activity discussed in Part B. Participants could observe and make notes about the mathematical behaviours displayed by students and use this information to identify the phases students are working in.

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 practices.
Teacher learning may take many forms, including:
- action research;
- teacher research;
- professional journals;
- peer coaching;
- professional networks.

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Facilitator's reflection

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

Comments:

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