Mathematics learning does not only happen in classrooms. Children learn mathematical ideas from each other, from parents and others as they engage in everyday play and activities.
The Aistear framework has always recommended playful approaches for young children. The new primary mathematics curriculum emphasizes the importance of playful, creative and engaging learning experiences for children of ALL class levels. ‘Encouraging playfulness’ is named as a key pedagogical practice.
Play
Research recognises the importance of Play for children’s learning. However not all playful activities lead to mathematical understanding. Interaction with an adult who plans or notices opportunities to make mathematical connections is important. Research also suggests that the most effective approaches strike a balance between teacher-initiated mathematical activity and mathematical activity that arises incidentally from child-led play experiences.
In both approaches, sustained shared thinking time or extended discussions, are key to supporting the development of children’s mathematical thinking. (For more on this, see the section on Talk).
The Early Childhood Curriculum Framework, Aistear, describes a range of different types of play: ‘creative’, ‘games with rules’, ‘language’, ‘physical’ and ‘pretend’. Each of these can contribute to children’s mathematical learning across all strands of the mathematics curriculum as indicated on the table below.
Type of Play
Brief Description (from Aistear, The Early Childhood Curriculum Framework (NCCA, 2009))
Some Possibilities for Mathematics Teaching and Learning
Creative
Brief Description (from Aistear, The Early Childhood Curriculum Framework (NCCA, 2009))
Creative play involves children exploring and using their bodies and materials to make and do things and to share their feelings, ideas and thoughts. They enjoy being creative by dancing, painting, playing with junk and recycled materials, working with play-dough and clay, and using their imaginations.
Preschool and Junior Classes
- Sort and display collections of toys or other objects in creative ways.
- Identify 3D shapes during junk art. Create and describe structures, e.g. compare size and shapes.
- Draw, paint or glue with shapes. Create shape pictures using shapes or tangram pieces. (See First Class activity plan on Shape).
- Explore and describe 3D shapes and position during block play.
- Create and describe patterns using different materials.
- Use playdough/clay to make shapes, structures or patterns. Make comparisons and explore measures language.
- Explore rhythm and pattern within music and dance.
- Develop spatial awareness through dance and movement.
Preschool and Junior Classes
- Use CSO or other datasets to explore data of interest to (e.g., how popular is my name or investigating roller coasters)
- Explore Maths and Art outdoors by creating pictures and assigning numerical values .
- Create and describe patterns using different materials.
- Design and build complex 3D structures to specific measurements.
- Use amplify polypad music feature to explore connections between mathematics and music.
- Use spatial knowledge to programme robots or devices to move through space.
Type of Play
Brief Description (from Aistear, The Early Childhood Curriculum Framework (NCCA, 2009))
Some Possibilities for Mathematics Teaching and Learning
Games with rules
Brief Description (from Aistear, The Early Childhood Curriculum Framework (NCCA, 2009))
In the beginning children often play by their own rather flexible rules! In time they also partake in more conventional games with ‘external’ rules. Language is an important part of games with rules as children explain, question and negotiate the rules. Rules are often an important part of pretend play where children negotiate rules about what can and cannot be done.
Preschool and Junior Classes
See the ‘What’s my rule?’ game on the Junior Infant Sorting activity plan. Here the teacher only lets certain shapes into her set (e.g., four-sided shapes) and children must guess what the rule is. The game sets up the need to use mathematical language and provide explanations and justifications.
Nrich list of games for Junior Classes
Nrich list of interactives for Junior Classes
Senior Classes
As for Junior Classes, games with rules can be very effective for supporting (i) the exploration of shape properties, (ii) the learning of number facts, and (iii) analysing and developing strategies.
Math4Love games include examples of all of the above.
Nrich list of games for Senior Classes
Nrich list of interactives for Senior Classes
Type of Play
Brief Description (from Aistear, The Early Childhood Curriculum Framework (NCCA, 2009))
Some Possibilities for Mathematics Teaching and Learning
Preschool and Junior Classes
Language
Brief Description (from Aistear, The Early Childhood Curriculum Framework (NCCA, 2009))
Language play involves children playing with sounds and words. It includes unrehearsed and spontaneous manipulation of these, often with rhythmic and repetitive elements. Children like playing with language – enjoying patterns, sounds and nonsense words. They also love jokes and funny stories.
- At first glance, language games may look more appropriate to developing children’s literacy. However, all mathematics teaching must attend to developing language to reason with as well as mathematical vocabulary.
- Songs, chants and rhymes are examples of language games that may have mathematical content such as counting, addition and subtraction, shape or positional language, e.g., The Grand Old Duke of York or Five Little Monkeys.
- Consider how language is developed in the Billy Goats Gruff Preschool activity plan.
Further Rhymes available here.
Senior Classes
- Language games at the senior end may involve exploration and identification of patterns: quad; quadrilateral; quadrant; …
- There is also scope for children to solve and create riddles and puzzles which require mathematical concepts or logic to solve.
- Children could explore and create their own mathematical poems. Shel Silverstein’s work has been used as a stimulus. Richard Long’s text and art could be used as a stimulus for measurement and shape explorations.
Type of Play
Brief Description (from Aistear, The Early Childhood Curriculum Framework (NCCA, 2009))
Some Possibilities for Mathematics Teaching and Learning
Physical
Brief Description (from Aistear, The Early Childhood Curriculum Framework (NCCA, 2009))
Physical play involves children developing, practising and refining bodily movements and control. Exploratory play involves children using physical skills and their senses to find out what things feel like and what can be done with them. Manipulative play involves practising and refining motor skills. This type of play enhances physical dexterity and hand-eye coordination. Constructive play involves building something using natural and manufactured materials. As children develop, this type of play can become more complex and intricate.
Preschool and Junior Classes
- Children’s movements and positions, indoors and outdoors, can be described in spatial terms.
- Playing with water and sand provides opportunities to explore capacity and to devise ways of figuring out which containers hold more or less.
- Manipulative or construction objects offer opportunities for counting, but also for using comparative language (e.g. wider, taller, smallest) and the terminology of shape and position. For example, see the Preschool activity plan on Block.
- Placing clothes on a mini washing line encourages discussion about size and pattern (and also refines motor skills).
Senior Classes
- A empty grid painted or drawn with chalk on the school yard can serve as the basis for lots of different mathematical games involving movement (Outdoor activities from MathsWeek Scotland; ‘Out and About’ activities for upper primary )
- Links with physical education can allow for meaningful mathematics integration (see this meaningful maths plan, formerly NzMaths)
Type of Play
Brief Description (from Aistear, The Early Childhood Curriculum Framework (NCCA, 2009))
Some Possibilities for Mathematics Teaching and Learning
Pretend
Brief Description (from Aistear, The Early Childhood Curriculum Framework (NCCA, 2009))
Pretend, dramatic, make-believe, role, and fantasy play involves children using their imaginations. Children use their developing language to move from thinking in the concrete to thinking in the abstract. Children may act out real events but may also try out roles, occupations and experiences in their pretend play. Early numeracy is clearly evident in this type of play, for example when children pretend to buy items in a shop.
Small world play involves children using small-scale representations of real things like animals, people, cars and train sets as play props. Socio-dramatic play involves children playing with other children and/or adults. It provides opportunities for children to make friends, to negotiate with others, and to develop their communication skills. This play helps extend language. The ability to write stories also has its roots in socio-dramatic play.
Preschool and Junior Classes
- Exploring the concept of length while measuring in the building site (e.g. using vocabulary of long/short, longer/shorter than, imaginative play using measuring tape).
- Identifying and using coins (e.g. in the shop).
- Classifying and sorting (e.g. sorting food in different ways in the restaurant – fruit and vegetables, healthy and unhealthy).
- Matching (e.g. in the home corner matching items that belong together, e.g. knife and fork, cup and saucer).
- Opportunities for informal recording/writing (e.g. writing prices on receipts in shop).
Senior Classes
- Children can adopt roles as they engage in mathematical exploration of real life problems, e.g., different characters debating how yard space and equipment should be shared, or how a school event should be organised (first class child, sixth class child, teacher, principal).
- Scope for integrated cross-curricular mathematics and drama lessons, which have the potential to address challenging content in meaningful, engaging ways.
Analyse and Reflect
- Review the types of play described by Aistear and the sample mathematical activities provided on the table. Which types of play do you use most frequently in your teaching? Which strands of mathematics do you include (Number, Shape, Measures, Algebra, Data)? Are there opportunities to develop activities targeting other types of play/other mathematical areas?
- In your school/setting, what is the balance between teacher-initiated mathematical activity and mathematical activity that arises incidentally from child-led play experiences? What do you think children feel about the current approach? Could there be potential benefits from trying something new?
- Review the Early Years section of the Nrich website for other play-based or playful approaches to the teaching and learning of mathematics
- Think about the last five books you read to your class. Did they have explicit or implicit mathematical content?
- Think of three books you already have that might be used for the teaching of mathematics. See MathsthroughStories if you are short of ideas.