PLC Week 9 – The Story so far…

Input: Teachers formed a PLC to develop deeper understanding of a mathematical concept.

Time and resources have been key input factors in the PLC process. Time has been built into the Non-Instruction Time-table to enable each of the Year 5,6 and 7 teachers to meet weekly, for one lesson. A member of the Leadership Team has supported each week by guiding the process and providing resources. Useful resources have been: the Gavin Grift PLC model to guide the steps in the process, the National Numeracy Learning Progressions, PAT data, and student class lists which have highlighted the identified students in the different Partnership High Band Strategy categories of gain, retain, and elevate.

Activities: Exploration of teacher practices and student learning needs identified multiplicative thinking as an area of growth.

The activities that the PLC has been involved in are: establishing protocols and group goals, identifying focus areas and exploring these in more depth.

Initially, the group designed a survey to identify the current status of learner attitudes to mathematics. After identifying that Multiplicative Thinking was an area that needed some attention with most learners, the group explored the National Numeracy Learning Progression related to this area titled ‘Multiplicative Strategies’.

Directed reading of the Department of Education Big Ideas in Number paper has helped the group to focus thinking on Multiplicative Thinking/ Strategies. Key aspects of the development of understanding in this area were identified.

Translating the Multiplicative Strategies Progression into student friendly language, and designing pre-assessment questions to identify current knowledge of each student were the next steps.


Output: Publications and prototypes teachers have developed are a survey, a poster and a pre-assessment as well as a sustainable model that can be applied to future processes.

The group has produced a survey, which has provided some interesting information about the current attitudes of  students towards mathematics. A poster has also been created, outlining the Learning Progressions in student friendly language. A poster has been created using the student designed Mosaic Leaves as a motif to identify each level in the learning progression . Pre-assessment questions linked to each step of the Progression are currently being created by each team member, so that this is ready to use in Week 1 of next term.

Uptake: A translation of the multiplicative strategies progressions into student friendly use, created a pathway for deeper mathematcial thinking.

Positive, open discussion has characterised the way the group operates and participation has been maximised, with everyone making valued contributions. Members of the group have said that they have appreciated the pace. At the end of each meeting, values that have been evident are highlighted and celebrated. This has been built into the protocols. The strengths of each person have been utilised and appreciated by the group – logical thinking, mathematical knowledge, critical thinking, creative thinking, reflective thinking, and knowledge of resources which help develop students’ understanding in the focus areas.

Usage: Teachers described valued aspects of learning after reflecting on student dispositions.

The survey has highlighted most students have a positive disposition to mathematics. Several student surveys of interest identify particular areas to focus on.
The National Learning Progression (Mathematical Strategies) has been used to develop group consensus of the valued steps to work through to develop a good understanding in this area.
The resulting Mosaic Leaves Poster will be used in classrooms with students and will identify a common language used to describe valued aspects of this learning area.
The pre-assessment will be created and used in Week 1 of Term 3.

Impact: Shared teacher understandings clarified the identified multiplicative thinking to be developed.

The PLC process has provided opportunity to clarify specific language and develop a shared understanding. E.g. composite units, commutative and distributive properties, decomposition, partial products, difference between partition and quotation way of viewing division.

Benefit: Teachers collectively acting as informed agents for conceptual change.

Benefits  have been group consensus about processes used to meet the group’s needs, and opportunity to clarify understanding. Useful products have also been developed: a survey, the Learning Progression poster, and pre-assessment questions/ tasks. The biggest benefit is developing a process which can be sustainably applied to future areas/teams.

E.g. Process:

  • Identify Big Idea to focus on (using data)
  • Identify the Learning Progression levels
  • Translate the Learning Progression into student friendly language – poster format to display in the classroom
  • Develop a pre-assessment test/ series of tasks/ questions to identify where each student is in relation to the learning progression
  • Design learning opportunities to meet identified needs of each group

Mosaic Leaf Learning Progression Multiplicative Thinking-25gv89b

Maths Attitudinal Survey Yr 5 6 7-1dldba7



Multiplicative Thinking – PLC Resources 16th May

The Learning Assessment Framework for Multiplicative Thinking

Scaffolding Numeracy in the Middle Years

Common Misunderstandings – Multiplicative Thinking

Newman’s Error Analysis – You will need to log in to PAT Teaching Resources (email as user name) Then go to Teacher Resources

Multiplication and Division – Maths Assessment Project

Multiplicative Thinking Tasks

Our learning progression brainstorm (using Multiplicative Thinking article):


  • counting and splitting
  • skip counting
  • large collections
  • repeated addition (2s, 5s, etc.)
  • repeated subtraction
  • hold both numbers in head – number of objects within each group and number of groups
  • hold both numbers and the total
  • visualise 3×4, 4×3 move from additive to multiplicative strategies
  • factors, product – arrays
  • multiplication and division – commutative, inverse relations
  • language develops – for each, times, as many
  • symbolic representation, diagrams

Implications for teaching/ learning


  • Developing opportunities for students to use effective strategies – arrays
  • Challenge to show different ways
  • Communicate – in different ways
  • Explicit role modelling
  • Language used by students – allow opportunities for talk, and for listening in to hear their language (gaining insight into their thinking)
  • Variety of representations – words, pictures, symbols
  • Moving from familiar to unfamiliar contexts
  • Questioning and enabling prompts
  • Allow opportunities for collaboration
  • Think boards
  • Visualisation – drawing how they see the problem



Maths Proficiencies – High Band Strategy

Thanks Libby for creating the following rubric:
Maths Assessment Criteria Rubric-115uqwg

Formative Assessment strategies to add to your tool kit:

In this example, students fill out an exit pass and place it into the relevant box to show their level of understanding. The next day the teacher pairs up the level 3 and 4 students with students at the level 2 stage, asking level 2 students to ask lots of clarifying questions to their peers to really bring them into ‘the learning pit’. This allows opportunity for teacher to work more intensively with the students at level 1.

To enable students to activate each other as agents of their own learning, students can be encouraged to daily take up opportunities to:

  • offer help
  • accept help
  • politely decline help so that you can try by yourself
  • ask for help

Maths Resources – Thanks for sharing Libby

Estimation 180 has maths inquiries aligned to Aust curric

Has videos that are useful provocations

Has videos that are useful provocations

Other useful sites:

National Library of virtual manipulatives
This is a great resource too. Lots of practical tools and examples.

Visible Learning for Mathematics: What Works Best to Optimise Student Learning – Hattie, Fisher, Frey

Some notes:

According to The National Council of Teachers of Mathematics (NCTM) publication ‘Principles to Action: Ensuring Mathematical Success for All’ (2014) the 8 high leverage teaching practices that support meaningful learning are:

  1. Establish mathematics goals to focus learning
  2. Implement taks that promote reasoning and problem solving
  3. Use and connect mathematical representations
  4. Facilitate meaningful mathematical discourse
  5. Pose purposeful questions
  6. Build procedural fluency from conceptual understanding
  7. Support productive struggle in learning mathematics
  8. Elicit and use evidence of student thinking

Similarly the 2012 National Research Council report Education for Life and Work identifies the following essential features of instruction:

  • Engaging learners in challenging tasks, with supportive guidance and feedback
  • Using multiple and varied representations of concepts and tasks
  • Encouraging elaboration, questioning, and self-explanation
  • Teaching with examples and cases
  • Priming student motivation
  • Using formative assessment

Focus on rigor defined as a balance among conceptual understanding, procedural skills and fluency, and application with equal intensity.

Mathematics instruction should be intentionally designed and carefully orchestrated in the classroom, and should always focus on impacting student learning. Start with appropriately challenging learning intentions and success criteria. Teachers need to be clear about where their students are, where they need to go, and what achievement of learning milestones looks like. Good mathematics learning is embedded in discourse and collaboration – both with teachers and among peers – and is orchestrated around appropriately challenging tasks. Students should be doing more of the thinking and talking than the teacher. Must be partners in understanding with metacognition (thinking about their own thinking).

Surface, deep and transfer learning

Surface – initial development of conceptual understanding, procedural skills, and vocabulary of a new topic

Deep – begin to make connections among conceptual ideas, and practice and apply procedural skills with greater fluency. Plan, investigate, elaborate on their conceptual understandings and begin to make generalisations. Can facilitate transfer.

Transfer – ability to more independently apply deeply understood concepts and skills to new and novel situations