A strand of thread is made up of many individual fibres. In the same way, each strand of the learning progressions is made up of several progressions, which together describe the development of expertise within the strand. The learning progressions for numeracy are organised in the following three strands:
The strands are interconnected. For example, learners need an understanding of place value (covered in the strand Make Sense of Number to Solve Problems) in order to convert between units of measurement (in the strand Measure and Interpret Shape and Space).
The term progression is used to describe a set of steps along a continuum, each step representing a significant learning stage as learners build their expertise. Each progression highlights a particular area of learning within a strand. The progressions are intended to illustrate a typical learning pathway3. The titles of the progressions are listed below:
Make Sense of Number to Solve Problems
Additive Strategies progression
Multiplicative Strategies progression
Proportional Reasoning Strategies progression
Number Sequence progression
Place Value progression
Number Facts progression
Preparing Data for Analysis progression
Analysing Data for Interpretation progression
Interpreting Data to Predict and Conclude progression
Measure and Interpret Shape and Space
Shapes and Transformations progression
A progression implies a continuous, sequential movement towards expertise rather than a series of separate tasks to be mastered in order to “move up”. For this reason, individual steps within a progression are distinguished from one another in this book by referring to their place in the sequence (for example, “the second step in the Additive Strategies progression”) rather than by using numbers, stages or levels. The learning progressions reflect the way all learners continually build on and extend their existing knowledge and skills.
The progressions are also interconnected. For example, the learners need to be able to sort and record data (in the progression Preparing Data for Analysis) in order to describe and interpret that data (in the progression Analysing Data for Interpretation).
Development within any one progression is not evenly spaced, and some of the shifts in development involve more learning than others. The amount of learning needed will also depend on the learner. Adults do not all learn in the same way. Some need to spend more time learning certain skills, or consolidating the learning, than others.
For each progression, the steps towards expertise in that progression are represented by pikopiko that have increasing numbers of fronds. The initial learning step is represented by a single koru, the next step by a pikopiko with two fronds and so on. The final step is represented in most cases by a pikopiko with six fronds.
The koru (in its mature forms, the pikopiko) was chosen as the symbol for the steps in each progression because it is a familiar and valued image for New Zealanders and because its natural and gradually unfolding growth pattern could be seen to reflect the process of successful learning, or ako. As fronds mature, new fronds begin to grow, nourished and sheltered by the work of the existing fronds, the plant’s root system and a favourable environment. Pikopiko is an indigenous food picked directly from ngahere (the forest) that can give and sustain life. In the same way, ako can give and sustain intellectual and spiritual life.
The steps vary in size and quantity from one progression to another. This variation is because the writers have tried to show steps at parallel stages of a typical learner’s development across all the progressions. The steps do not, however, all involve the same amount of learning, and the development of skills, strategies and knowledge does not always occur in evenly sized or spaced steps.
In the Make Sense of Number to Solve Problems strand, for example, only two progressions (the Additive Strategies progression and the Multiplicative Strategies progression) have six separate steps. In this and other strands, there are some progressions that have double steps (the movement in the progression is shown over two steps) because the learning described by the bullet points takes time to develop, consolidate and practise. This is considered to be the equivalent of two steps in a single progression.
A different kind of variation occurs in places where learning in one progression depends on prior learning in another. For example, numeracy learners cannot begin learning about place value, which involves counting in tens, until they have learned to count in ones, and this learning occurs at the first step of the Additive Strategies progression. Because of this, there is a gap at the first step in the progression for Place Value.