# National Numeracy Learning Progression

Numeracy is fundamental to a student’s ability to learn at school and to engage productively in society.

In the Australian Curriculum, students become numerate as they develop the knowledge and skills to use mathematics confidently across learning areas at school and in their lives more broadly. The Australian Curriculum states:

Numeracy encompasses the knowledge, skills, behaviours and dispositions that students need to use mathematics in a wide range of situations. It involves students recognising and understanding the role of mathematics in the world and having the dispositions and capacities to use mathematical knowledge and skills purposefully (ACARA 2017).

Numeracy development influences student success in many areas of learning at school. The progression can be used to support students to successfully engage with the numeracy demands of the Foundation to Year 10 Australian Curriculum.

The National Numeracy Learning Progression outlines a sequence of observable indicators of increasingly sophisticated understanding of and skills in key numeracy concepts. By providing a comprehensive view of numeracy learning and how it develops over time, the progression gives teachers a conceptual tool that can assist them to develop targeted teaching and learning programs for students who are working above or below year-level expectations.

The progression does not advise on how to teach, plan, program, assess or report in schools. It recognises the importance of, but does not describe, the sequence for specific learning area content related to numeracy development such as graphing and constructing timelines.

The Australian Core Skills Framework has been used to guide decisions on the scope of the progressions. The progression is designed to assist students in reaching a level of proficiency in numeracy to at least Level 3 of the Core Skills Framework.

### Elements and sub-elements

The National Numeracy Learning Progression has three elements that reflect aspects of numeracy development necessary for successful learners of the F–10 Australian Curriculum and in everyday life. The three elements are:

• Number sense and algebra
• Measurement and geometry
• Statistics and probability.

Each of the elements includes sub-elements that present developmental sequences for important aspects of numeracy capability. There are nine sub-elements in Number sense and algebra, four in Measurement and geometry and two in Statistics and probability.

The diagram (Figure 1) represents the elements and sub-elements in relation to the numeracy development of the student.

Figure 1. Elements and sub-elements of the National Numeracy Learning Progression

### Levels and indicators

Within each sub-element indicators are grouped together to form developmental levels. Each indicator describes what a student says, does or produces and begins with the implicit stem ‘A student …’ as the subject of the sentence.

There are as many levels within each sub-element as can be supported by evidence. The listing of indicators within a level is non-hierarchical as the levels are collections of indicators. Each level within a sub-element has one or more indicators and is more sophisticated or complex than the preceding level.

In many of the sub-elements, subheadings have been included to assist teachers by grouping indicators into particular categories of skills that develop over a number of levels.

The amount of time it takes students to progress through each level is not specified since students progress in numeracy development at different rates.

The levels do not describe equal intervals of time in students’ learning. They are designed to indicate the order in which students acquire the knowledge and skills necessary to be numerate. As learning is very rapid in the early years of school, the initial levels tend to be more detailed than the later levels.

Moreover, the amount of detail in any level or sub-element is not an indication of importance. A single indicator at a higher level in the progression may rely on a substantial number of indicators being evident in earlier levels. The diagram (Figure 2) shows the various components included in the progression

Figure 2. Annotated example of a numeracy sub-element

Numeracy skills are explicit teaching in the Australian Curriculum: Mathematics. Students need opportunities to recognise that mathematics is constantly used outside the mathematics classroom and that numerate people apply general mathematical skills in a wide range of familiar and unfamiliar situations.

Using mathematical skills across the curriculum enriches the study of other learning areas and helps to develop a broader and deeper understanding of numeracy. It is essential that the mathematical ideas with which students interact are relevant to their lives.

### Australian Curriculum: Mathematics

The Australian Curriculum: Mathematics provides students with essential mathematical skills and knowledge in number and algebra, measurement and geometry, and statistics and probability … Mathematics is composed of multiple but interrelated and interdependent concepts and systems which students apply beyond the mathematics classroom … (Australian Curriculum: Mathematics, Rationale 2017)

The Australian Curriculum: Mathematics sets teaching expectations for mathematics learning at each year level, providing carefully paced, in-depth study of critical mathematical skills and concepts. The curriculum focuses on developing the mathematical proficiencies of understanding, fluency, reasoning and problem solving. These proficiencies are reflected in the National Numeracy Learning Progression rather than specifically identified.

The National Numeracy Learning Progression helps teachers to develop fine-grain understandings of student numeracy development in the Australian Curriculum: Mathematics, especially in the early years. It is particularly useful in guiding teachers to support students whose numeracy development is above or below the age-equivalent curriculum expectations of the Australian Curriculum: Mathematics. The progression has not been designed as a checklist and does not replace the Australian Curriculum: Mathematics.

Each sub-element has been mapped to the year-level expectations set by the Australian Curriculum: Mathematics.

### Other Australian Curriculum learning areas

This National Numeracy Learning Progression is designed to assist schools and teachers in all learning areas to support their students to successfully engage with the numeracy demands of the F–10 Australian Curriculum.

Advice on using the Numeracy Learning Progression with other learning areas and subjects can be viewed. This advice will assist teachers to plan how to teach specific literacy knowledge and skills essential to students’ understanding of subject content.

The National Numeracy Learning Progression can be used at a whole school, team or individual teacher level. However, the progression provides maximum student learning benefits when used as part of a whole-school strategy that involves professional learning and collaboration between teachers. Further advice on how to maximise the benefits of the progression is available on the progressions home page.

The numeracy progression can be used to identify the numeracy performance of individual students within and across the 15 sub-elements. In any class there may be a wide range of student abilities. Individual students may not neatly fit within a particular level of the progressions and may straddle two or more levels within a progression. While the progression provides a logical sequence, not all students will progress through every level in a uniform manner.

When making decisions about a student’s numeracy development, teachers select relevant indicators. It is important to remember indicators at a level are not a prescriptive list and the progression is not designed to be used as a checklist. Teacher judgements about student numeracy capability should be based on a range of learning experiences. Number talks, written or oral explanations, or tasks from any learning area can provide suitable evidence of a student’s numeracy capability.

Teachers can use the progressions to support the development of targeted teaching and learning programs and to set clearer learning goals for individual students. For example, teaching decisions can be based on judgements about student capability that relate to a single indicator rather than all indicators at a level.