What are precursor concepts in mathematics?

Even before very young children begin to develop their conceptual understanding about mathematics in more formal areas like Number, Measurement and Space, they are practising and developing the pre-cursor concepts of Attribute, Comparison, Pattern, and Change (Erikson, nd). Precursor concepts can be thought of as the initial skills that children explore from the moment they are born. They develop over time with exposure to different experiences, materials, and contexts. Children need to be very confident in these precursor skills and concepts as they move towards understanding more complex ones.

First concepts and skills

As well-meaning parents and educators, we can hurry childrens' progression, thinking that a child has mastered mathematical skills in one context so we move them onto ‘real maths’ like counting and naming shapes. It is important, however, to spend time exposing children to a variety of experiences and to keep revisiting these developing skills.

Rich and varied exposure to the same skill should be supported in the moment, but also explicitly planned for, extended, and practised on an ongoing basis.

Attributes

The most important of all the pre-cursor concepts is that of Attribute. It is the skill of being able to describe the world around us according to various properties or qualities that can be attributed to an object, place, or people. If we look at this picture of us making biscuits - the flour feels soft because it is like powder, the dough is sticky because we have added milk, the cutter is sharp because we need to press through the dough.

We can use this skill to sort and classify. For example, finding other things that are soft like the flour, or sticky like the dough. We use attributes to communicate our reasoning about why we have sorted and classified objects in a particular way.

Attribute is a concept that we often model to very young children, but do not consciously plan for. We ask children to describe objects all the time and we often will label an object using two or three attributes. If we stay with our biscuits, for example, they could be brown and squishy, or hot and puffy.

We also need consider how children themselves describe attributes with increasing precision and give them room to do so. To scaffold their progression, we model the use of adjectives to describe objects and purposefully increase the number of descriptive words we both use and seek from the children.

Providing many and varied experiences for children to use all of their senses and describe each of these is crucial. These experiences can and should be incidental, but they also should be consciously planned for, observed, and extended throughout a young child’s life.

Comparison

From the time children are born, their spatial awareness is developing as they use their senses to sort objects and people. A child needs to make a comparison to sort - this involves noticing sameness and difference. As discussed above, identifying attributes is the key to understanding what is the same and different about an object. If a child has a limited exposure to experiences and ways to communicate the attributes of that object or experience, then their ability to compare will also be limited, and in turn their sorting and classifying skills.

Matching is another important skill in this process. When identifying attributes that are the same, children can match items and group them together, which is the key idea behind classification. Much exposure to matching puzzles and games is a really important step to assist children to classify and later to create sets. The skill of matching is also an important pre-cursor step to early counting and one-to-one correspondence and subitising.

Planning for noticing and extending children's experiences and thinking related to sorting and classifying is vital so take your time and be creative!

You can read more about the important role of sorting, classifying, and matching as a distinct step in the process of making sets, pattern, and sorting out ideas in Shape, Space, Number and Measurement here.

Pattern

Young children identifying, exploring and making patterns is the beginning of more complex identification of patterns throughout the child’s mathematical journey. This precursor concept is based on a child's experiences of Attributes, and Sorting and Classifying.

Young children can begin to identify patterns. Spending time prompting them to notice patterns in nature, in songs, in books they are read, in the clothes they are wearing and the routines they follow each day is a great way to start. A child who is read Hop on Pop by Dr Seuss, will start to follow the lyrical rhyming patterns and predict what comes next. Including all the senses by making patterns with body parts, voice, through dance and movement will all build foundational skills in this area. Encourage children to record the patterns they see around them and copy these.

When starting to notice and record patterns, try starting with 2 attributes as children need time to form a solid basis for the principles of what a pattern is. Begin by asking a child to copy a pattern you have made using these two attributes, then extend that pattern. For example, if you were doing a sound pattern, ask them to join you in a "clap, click" pattern (clap, click, clap, click, clap...). The clap is one attribute of sound, a click is another. You would invite children to copy this pattern with you, then you might ask them to try it themselves. To read more about these ideas, go to our Patterns and Relationships page.

Spending time noticing, wondering about, continuing and making patterns connects with important mathematical processes, i.e finding the pattern (problem-solving); communicating the pattern (understanding and reasoning); and making and using patterns (fluency).

Change

The importance of many, varied and repeated experiences in the previous precursor concepts is evident when exploring the concept of Change. Children need to be able to describe an attribute, match, sort, classify and identify patterns to be able to identify change when it occurs.

In their play, as children transform objects by joining together objects or pulling them apart, they develop an understanding of concepts such as part-part-whole, counting, size, properties of shapes and measurement. As children identify change, either qualitative or quantitative, they will develop their understanding of patterns and systems.

The role of the adult

The support of a more knowledgeable other through modelling and exposure to multi-modal language (not just verbal but also gestural, graphic and symbolic text ) is vitally important for children to gain confidence with these skills.

Here are some tips:

Be knowledgeable before you observe. Take the time to read further about the pre-cursor concepts and their progressions.
Take the time to notice and label the skill the child is exploring or engaging with.
Lend the child the mathematical language appropriate for the concept (again not just verbally but where appropriate symbolically and through gesture).
Notice and document the skill/ concept the child or children are engaging with and plan for more experiences with that skill/ concept in other contexts.
When the time is right, extend the child's play in this area.
Make connections with other pre-cursor concepts and skills and consider this in your planning.

References

Cumbria County Council,(nd), Early Years Mathematics Toolkit, https://www.cumbria.gov.uk/elibrary/Content/Internet/537/1459/7037/17952/44048142650.pdf?timestamp=4439544938

Erikson,(nd) Early Math Collaborative, https://earlymath.erikson.edu/why-early-math-everyday-math/precursor-concepts/

Hurst and Hurrell (2014) Developing the Big Ideas of Number, https://researchonline.nd.edu.au/cgi/viewcontent.cgi?article=1156&context=edu_article

Macmillan, A. (2009). Numeracy in early childhood : shared contexts for teaching & learning. Oxford University Press

Reys, RE, Rogers, A, Bennett, S, Cooke, A, Robson, K, Ewing, B & West, J 2020, Chapter 7, Counting and number sense in early childhood and primary years, in Helping children learn mathematics Third [Australian] edition., John Wiley & Sons Australia, Milton, Qld, pp181-219