The Stages of Early Arithmetical Learning (SEAL) model is based on a comprehensive body of research into young children's number learning undertaken in the '80s by Les Steffe and Paul Cobb as well as the related research in the '90s by Bob Wright. This research involved longitudinal studies with children in their first and second years of school.
The Stages of Early Arithmetical Learning (SEAL) model is based on a comprehensive body of research into young children's number learning undertaken in the '80s by Les Steffe and Paul Cobb as well as the related research in the '90s by Bob Wright. This research involved longitudinal studies with children in their first and second years of school.
The Stages of Early Arithmetical Learning (SEAL) is a model that is used to understand the development of children’s numerical knowledge. It sets out a trajectory of the strategies children use in early additive thinking. Progression across the stages involves the child using counting in increasingly sophisticated ways to solve addition and subtraction tasks. These tasks were based on collection of counters and involved simple arithmetic, Typically in the range 1 to 20. The researchers identified in children's solutions, several major cognitive shifts called reorganisations. For this reason the learning progressions are referred to as stages.
The Stages of Early Arithmetical Learning (SEAL) is a model that is used to understand the development of children’s numerical knowledge. It sets out a trajectory of the strategies children use in early additive thinking. Progression across the stages involves the child using counting in increasingly sophisticated ways to solve addition and subtraction tasks. These tasks were based on collection of counters and involved simple arithmetic, Typically in the range 1 to 20. The researchers identified in children's solutions, several major cognitive shifts called reorganisations. For this reason the learning progressions are referred to as stages.
This research informed model is underpinned with the understanding that children acquire strategies and numerical knowledge through a series of different stages – the Stages of Early Arithmetical Learning. It looks at the relative sophistication of children’s strategies for dealing with number and allows teachers to build on those skills.
This research informed model is underpinned with the understanding that children acquire strategies and numerical knowledge through a series of different stages – the Stages of Early Arithmetical Learning. It looks at the relative sophistication of children’s strategies for dealing with number and allows teachers to build on those skills.
Fundamental to the research on which SEAL is based is the notion that, in order to understand children's mathematical learning, it is necessary to closely observe their behaviour in problem solving situations. in studying children's early number learning in particular, this observation focuses on children's verbal and non verbal responses in scenarios in which they solve problems involving counting, addition or subtraction.
Fundamental to the research on which SEAL is based is the notion that, in order to understand children's mathematical learning, it is necessary to closely observe their behaviour in problem solving situations. in studying children's early number learning in particular, this observation focuses on children's verbal and non verbal responses in scenarios in which they solve problems involving counting, addition or subtraction.
These problems typically involve presenting children with a range of tasks involving counters which may be displayed or screened.
These problems typically involve presenting children with a range of tasks involving counters which may be displayed or screened.
MODEL
MODEL
The Stages of Early Arithmetical Learning is based on increasingly sophisticated progressions of early arithmetical strategies: emergent counting, perceptual counting, figurative counting and counting-on-and-back.
The Stages of Early Arithmetical Learning is based on increasingly sophisticated progressions of early arithmetical strategies: emergent counting, perceptual counting, figurative counting and counting-on-and-back.
Stage 0: Emergent counting. Children at the Emergent Stage 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.
Stage 0: Emergent counting. Children at the Emergent Stage 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.
Stage 1: 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.
Stage 1: 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.
Stage 2: 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.
Stage 2: 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.
Stage 3: 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.
Stage 3: 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.
The progression through these stages demonstrates an increasing sophistication and understanding of counting and mathematics.
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.
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)
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)
This progression describes how a student becomes increasingly able to choose and use additive computational strategies for different purposes. The transition from counting by one to more flexible methods of dealing with quantity, where numbers are treated as the sums of their parts, is a critical hurdle to be addressed in students becoming fluent users of number. Rather than only focusing on the speed of producing correct answers, an emphasis on attending to the relation of given numbers to sums and differences is needed for flexibility. This supports the development of additive strategies such as adding the same to both numbers to reach an easier calculation (47 – 38 = 49 – 40).
This progression describes how a student becomes increasingly able to choose and use additive computational strategies for different purposes. The transition from counting by one to more flexible methods of dealing with quantity, where numbers are treated as the sums of their parts, is a critical hurdle to be addressed in students becoming fluent users of number. Rather than only focusing on the speed of producing correct answers, an emphasis on attending to the relation of given numbers to sums and differences is needed for flexibility. This supports the development of additive strategies such as adding the same to both numbers to reach an easier calculation (47 – 38 = 49 – 40).
