About this resource

The format of Developing Efficient Numeracy Strategies One is based on four central progressions of early arithmetical strategies: emergent counting, perceptual counting, figurative counting and counting-on-and-back.

1. Emergent counting

   The word ‘emergent’ come from the Latin word ‘emergere’ which means to ‘bring to light’. Students at this level of learning are emerging into the world of numbers, and we as educators, are helping them to turn on their mathematical lights. They know some number words but are still learning about the principles of counting. A student at this stage of learning is unable to count visible items. He or she either does not know the correct sequence of number words or cannot coordinate the words with items yet.

2. Perceptual counting

   Perceptual means to ‘perceive, notice or see’ and so students at this stage are able to count visible items. Perceptual counting involves seeing, hearing or feeling items as students use some of the principles of counting to solve number problems. Students at this stage are not yet able to count items in concealed collections or solve problems with numbers they cannot see, hear or touch.

3. Figurative counting

   At the figurative stage, students are able to visualise amounts and mentally reconstruct representations of numbers. Students are able to count concealed items, however, they still start back at one to solve number problems.

4. Counting-on-and-back

   At the counting-on-and-back stage, students are able to use the names of numbers to represent a completed count. Students will count on or back from a completed count in order to solve number problems.

The progression through these stages demonstrates an increasing sophistication and understanding of counting and mathematics. A more detailed overview of the key features of each of these stages is provided at the start of each section. It is important to note, however, that students often move between stages as the range of numbers they are working with change and the problems they are trying to solve increase in complexity.

An understanding of the progression of strategies which students use in early arithmetic enables teaching decisions to be based on knowledge of children’s understanding of mathematics. The components of this progression are interrelated and interdependent. Each component, however, is presented separately to emphasise the fundamental skills and learning required at each stage to develop increasingly sophisticated mathematical skills and understanding.

Developing Efficient Numeracy Strategies One is organised into four main sections, mirroring the four stages students tend to progress through. It also includes the following information:

Where are they now?

This section describes the types of approaches which students may use in attempting to solve problems.

Where to next?

This section provides direction for teachers in determining what students need to learn and do next. It makes explicit the next level of sophistication required in students’ solutions to help them reach the goals of early mathematics learning.

How?

This section outlines learning activities designed to assist students’ arithmetical development. These learning activities are not sequenced within each section and teachers should modify activities and choose a learning pathway to suit the needs of their students.

Why?

This section provides the purpose of the learning activities.

Teachers should use a range of assessment strategies to ascertain their students’ current problem-solving strategies and counting skills before developing learning plans. Assessment information helps teachers make informed decisions about what students know and can do, enabling them to decide what students need to learn next. Assessment also informs teachers when students have progressed in their learning. Short, practical assessment tasks are included in each section.

Each section of this resource is introduced by The Nature of the Learner and Teaching Considerations.

• The Nature of the Learner provides a summary of strategies which students typically demonstrate at each stage of arithmetical development.
• Teaching Considerations provides a summary of the key factors that teachers need to consider in order to support student learning.