Mathematics

Aim

karamaAt Karama School we aim to ensure high-quality mathematics education for all students. Learning mathematics creates opportunity to enrich lives and society. It provides the capacity and confidence to meet the demands of learning, home, community, work, and civic life. It ensures preparation of a future workforce ready to contribute effectively and competitively in a continuously-changing global world.

Our vision of high quality mathematics includes conceptual understanding, problem solving, making connections across representations and mathematical concepts, and engaging in reasoning and argumentation necessary for everyday life. Mathematics is a core subject and forms a regular part of the daily program.

Implementation

  • The Karama Scope and Sequence is the document that teachers will use as a timeframe for their programing.
  • Focusing on the progression of Meaningful Maths (NZ) global stages through Emergent (stage 1) to Advanced Proportional (stage 8).
  • Number is the major strand delivered in class programs and is incorporated across the curriculum where, and as possible to develop understandings of numeracy of everyday life.
  • All other strands will be delivered across each term and revisited regularly to consolidate student knowledge and skills and integrated where possible.
  • High expectations and interventions are essential.
  • All students can achieve given sufficient time and support.
  • All teachers can teach to high standards given the right conditions and assistance.
  • All teachers will engage in professional learning and be reflective in their practice.
  • Teachers will document their learning goals so that all students will articulate their learning.
  • Modelling books will be incorporated as part of teachers and students mathematical resource.
  • All teachers will collaboratively plan with their colleagues of a similar year level.
  • Teachers will implement programs and focused explicit teaching in response to deliberate and regular assessment and monitoring.
  • Students will be exposed to numeracy specific vocabulary derived from the Australian Curriculum and Meaningful Maths (NZ)
  • The minimum recommended indicative hours per week for teaching and learning of Mathematics as per the NT DET requirements are:
    1. Transition to Year 4: 4.5hours
    2. Year 5-6: 4 hours

However, at Karama School we have a minimum expectation of 5 hours per week across the school.

Therefore:

  • Teachers are expected to program and plan using documents as below:
    1. Northern Territory Alignment of Australian Curriculum with NZ Mathsmaths
    2. Meaningful Maths Portal Site
    3. Linking to sites such as:- Scootle, Moodle T-9 Net
    4. Progressive Achievement Test (PAT) – Years 1 – 6
    5. GloSS and IKAN assessment (Primary)

Junior Assessment of Mathematics (JAM) (Early Childhood)

Australian Curriculum Alignment – Minimum expected achievements for Number

By the end of year:

End of Year Tiers
TIER 1 TIER 2 TIER 3 TIER 4
> Stage 3 = Stage 3 = Stage 2 < Stage 2
> Stage 4 = Stage 4 = Stage 3 < Stage 3
> Stage E5 = Stage E5 = Stage 4 < Stage 4
> Stage 5 = Stage 5 = Stage E5 < Stage E5
> Stage E6 = Stage E6 = Stage 5 < Stage 5
> Stage 6 = Stage 6 = Stage E6 < Stage E6
> Stage E7 = Stage E7 = Stage 6 < Stage 6

Measurement, Geometry, Statistics and Probability refer to the Australian Curriculum.

 Planning, Programming and Assessment

Term one Term two Term three Term four
Purpose of assessment Grouping & teaching &
Midyear Reports
Grouping and teaching & Final Reports
Assessment JAM, IKAN, GloSS, PAT MATHS JAM, IKAN, GloSS, PAT MATHS
Ongoing assessment Student evaluation will occur within Learning Goals
Date due Week 5 Week 5 Week 5 Week 5
Data entry Data to be entered by Week 5 Data to be entered by Week 5 Data to be entered by Week 5 Data to be entered by Week 5
  • Class grouping will initially be determined by JAM or IKAN and GloSS.
  • New students are required to be tested by their class teacher upon enrolment.

Year Planning

  • Refer to Karama Scope and Sequence for the year levels that you are teaching (U:Teacher Public – Curriculum – Maths)

 Term Planning

  • Term planning is to follow the Karama Scope and Sequence and the Karama School Term Planner template used (teacherpublic/programs2017/mathstemplate)

Areas to be included in Term plan:

  • A learner context (NZ Maths stages)
  • Content Descriptors and Elaborations that reflect the Karama Scope and Sequence and Australian Curriculum
  • Integrated Content Descriptors (How other strands are covered throughout the term)
  • Assessment
  • Teacher reflections

Karama

Weekly Planning (Number and Algebra)

  • Content Descriptors
  • Vocabulary
  • Teaching Strategies
  • Resource References (specific resources)

Lesson structure sequence

  • Knowledge focus (15 minutes)
  • Rotations (2 x 15 minutes) (see Page 4)
  • Reflection (5 minutes)
Phase Knowledge Focus Strategy Focus
Knowledge focus

15 minutes

·         Involving all students by enhancing the opportunities for a diversity of responses, effective modeling of the students’ strategies for others and developing a collective learning focus.

·         Share the knowledge focus with students as learning outcomes.

·         Present the concept to be learned through demonstration and discussion with the whole class.

·         Introduce the problem to the whole class.

·         Discuss the conditions of the problem as well as potentially useful strategies and sources of information.

·         Form the class into co-operative groups/pairs.

Rotations

2 x 15 minute groups

·         Have practice activities organized as seat work or stations for students to visit.

·         Students work in groups.

·         Students work in teams to solve the problem.

·         You may bring the class back together to discuss progress.

·         You may want to make available scaffolding ideas, such as hints and suggested strategies.

Class Warm down

5 minutes

·         Summarise the learning outcomes from today’s lesson, making connections to previous lessons and existing knowledge. ·         Students share their solutions with the whole class.

·         Provide connections to other mathematics and contexts and have students reflect on the power of their strategies.

Students At Risk in Numeracy

At Risk Students

  • At Risk students are those 2 stages or more below expectations and their future mathematics learning is determined to be in jeopardy
  • They require special teaching, extra support to continue their development and maintain positive attitudes
  • This support is beyond what the classroom teacher can be expected to do alone
Cause for Concern Students

  • Cause for concern students are 1 stage below expectations
  • They are at a stage where it is reasonable to expect the classroom teacher to move them to their expected stage with extra effort
Targeted Learning Groups

Focus

  • Any students 2 stages or more below expectations

Aim

  • Move students to be secure in strategies necessary for their appropriate stage, and the corresponding knowledge
Program Overview

  • Number identification
  • Number sequence and order
  • Grouping and place value
  • Basic facts
Delivery

  • 30 minutes each day for 3 days per week
  • Teacher aide, parent or peer tutor
  • Strategy teaching from teacher at least 2 times per week
  • Format – structured lesson format
Lesson Structure

  • Counting (in 1’s, 2’s, 5’s & 10’s forwards and backwards)
  • Order (numbers)
  • Say (double and corresponding halves)
  • Dictation (2, 3, 4 digit numbers – say numbers, children write down)
  • Basic facts (flash 10’s frames, children write equation)
  • Revise (known strategy – only at teacher request)
  • Revise (known game)
  • Introduce (new game – not daily)
  • Check (progress chart)
  • Set (homework)

The first 5 aspects should always be included and take at least half of the session

Things to Consider

  • Check list
  • Size of group – 4 students maximum
  • Time to establish social skills
  • In/out class
  • Rewards
  • Parents
  • Home packs
Evidence

Initial data from school records

Term 1 and 4 Pat Maths results

Mid term

  • Diagnostic questions to determine both strategy and knowledge stages
How to implement a lesson

  • Teachers must plan with tutors and be explicit about what tutors are to do (Specialist Teacher will deliver PL to SESA)
  • Plan a lesson following the lesson structure
  • Equipment needs to be organised
  • Students involvement – SAY, DO and SHOW

Classroom Resource Box

Each classroom teacher will receive a resource box with a content list attached to the top of box. The content of the box will differ depending on the year level.

  • Please ensure that you look after the box and equipment as it will need to be returned to the math resource room (library) at the end of the year with all of its contents included. Teachers will use a checklist provided by the Curriculum Leader to check off resources. If equipment is missing, you may need to replace missing pieces from your class budget.

Classroom Curriculum Folder

In the school curriculum folder the following documents can be found:Karama

  • Effective pedagogy in mathematics (Educational Practice Series)
  • Book 1 – The Number Framework
  • Book 2 – The Diagnostic Interview (assessment package)
  • Book 3 – Getting Started
  • Book 4 – Teaching Number Knowledge
  • Book 5 – Teaching Addition, Subtraction and Place Value
  • Book 6 – Teaching Multiplication and Division
  • Book 7 – Teaching Fractions, Decimals and Percentages
  • Book 8 – Teaching Number Sense and Algebraic thinking
  • Book 9 – Teaching Number through Measurement, Geometry, Algebra and Statistics

Teachers also have folders for:

  • JAM Testing
  • IKAN and GloSS tests (Tests 2&4) Test one for Term Two, Test Three for Term Four.

 Professional Development

All teachers will be involved in ongoing professional learning throughout the year.

  • New teachers will be given the opportunity to attend induction sessions, extra PL, observe other classrooms and receive model/team taught lesson demonstrations. All teachers can access the professional development link on the NZ Maths website as well as, the Meaningful Maths website via the School Portal.

 Shifts in Development – The Journey

Stage One – changing the organisation of your mathematics class

  • Trialing a taskboard
  • Establishing routines to enable students to work in groups
  • Reorganizing the classroom to cater for teacher space
  • Ensuring equipment is readily accessible to teacher and students
  • Establishing effective routines for use of equipment
  • Creating classroom mathematics displays
  • Developing resources, systems and expectations for independent work

 

Stage Two – Focus on the subject

  • Spending time working through how to teach each of the lessons in the booklets
  • Realising that each lesson in the book may in fact take several teaching sessions
  • Understanding the significance of the strategy development
  • Discussing the learning intentions with the students
  • Using a modeling book
  • Clarifying for themselves the interrelationship of knowledge and strategies
  • Deliberately and actively using the teaching model – using materials>imagine>number properties
  • Teaching a range of ways using independent activities

 

Stage three – Focus on the student

  • Having students work collaboratively
  • Having students model their understanding with equipment
  • Providing multiple opportunities for students to articulate their thinking
  • Expecting students to listen to others respectfully
  • Setting purposeful, practical student tasks which link to the learning intentions
  • Establishing student accountability for their independent work
  • Making links/connections for students
  • Teachers and students using a range of recording strategies

 

Stage four – Focus on student learning

  • Create an inclusive classroom environment
  • Convey high but realistic expectations
  • Promote risk taking
  • Encourage discussion and active listening
  • Use a variety of assessment data in setting goals
  • Provide scaffolding and feedback to students
  • Provide sufficient aligned learning experiences
  • Actively listen to and respond to individuals
  • Develop rich connections between ideas
  • Use powerful representations
  • Ask higher order questions
  • Challenge students to continually reflect on their learning

 

References

ACARA accessed 21/11/2017 (www.acara.edu.au) Source: BES Ministry (2003), Askew, Brown et al (2002)

New Zealand Maths, https://nzmaths.co.nz/ (2012)

Meaningful Maths Portal (Updated, 2017) http://web.ntschools.net/w/ntnzmathsacalignment/Pages/default.aspx