Math in the PYP See the text below for information about how the PYP believes children learn mathematics best. Also included on this page are the benchmarks for each unit. Parents and studnets can see how these benchmarks are separated into the various strands of number, measurement, data handling, pattern & function, and shape & space. These strands and student earning within the strands are further elaborated on the other drop down pages under mathematics.
How children learn mathematics
It is important that learners acquire mathematical understanding by constructing their own meaning
through ever-increasing levels of abstraction, starting with exploring their own personal experiences,
understandings and knowledge. Additionally, it is fundamental to the philosophy of the PYP that, since it is to be used in real-life situations, mathematics needs to be taught in relevant, realistic contexts, rather than by attempting to impart a fixed body of knowledge directly to students. How children learn mathematics can be described using the following stages (see figure to the left).
Constructing meaning about mathematics
Learners construct meaning based on their previous experiences and understanding, and by reflecting
upon their interactions with objects and ideas. Therefore, involving learners in an active learning process, where they are provided with possibilities to interact with manipulatives and to engage in conversations with others, is paramount to this stage of learning mathematics. When making sense of new ideas all learners either interpret these ideas to conform to their present understanding or they generate a new understanding that accounts for what they perceive to be occurring. This construct will continue to evolve as learners experience new situations and ideas, have an opportunity to reflect on their understandings and make connections about their learning.
Transferring meaning into symbols
Only when learners have constructed their ideas about a mathematical concept should they attempt
to transfer this understanding into symbols. Symbolic notation can take the form of pictures, diagrams,
modelling with concrete objects and mathematical notation. Learners should be given the opportunity to
describe their understanding using their own method of symbolic notation, then learning to transfer them
into conventional mathematical notation.
Applying with understanding
Applying with understanding can be viewed as the learners demonstrating and acting on their understanding. Through authentic activities, learners should independently select and use appropriate symbolic notation to process and record their thinking. These authentic activities should include a range of practical hands-on problem-solving activities and realistic situations that provide the opportunity to demonstrate mathematical thinking through presented or recorded formats. In this way, learners are able to apply their understanding of mathematical concepts as well as utilize mathematical skills and knowledge. As they work through these stages of learning, students and teachers use certain processes of mathematical reasoning.
• They use patterns and relationships to analyse the problem situations upon which they are working.
• They make and evaluate their own and each other’s ideas.
• They use models, facts, properties and relationships to explain their thinking.
• They justify their answers and the processes by which they arrive at solutions.
In this way, students validate the meaning they construct from their experiences with mathematical situations. By explaining their ideas, theories and results, both orally and in writing, they invite constructive feedback and also lay out alternative models of thinking for the class. Consequently, all benefit from this interactive process.
It is important that learners acquire mathematical understanding by constructing their own meaning
through ever-increasing levels of abstraction, starting with exploring their own personal experiences,
understandings and knowledge. Additionally, it is fundamental to the philosophy of the PYP that, since it is to be used in real-life situations, mathematics needs to be taught in relevant, realistic contexts, rather than by attempting to impart a fixed body of knowledge directly to students. How children learn mathematics can be described using the following stages (see figure to the left).
Constructing meaning about mathematics
Learners construct meaning based on their previous experiences and understanding, and by reflecting
upon their interactions with objects and ideas. Therefore, involving learners in an active learning process, where they are provided with possibilities to interact with manipulatives and to engage in conversations with others, is paramount to this stage of learning mathematics. When making sense of new ideas all learners either interpret these ideas to conform to their present understanding or they generate a new understanding that accounts for what they perceive to be occurring. This construct will continue to evolve as learners experience new situations and ideas, have an opportunity to reflect on their understandings and make connections about their learning.
Transferring meaning into symbols
Only when learners have constructed their ideas about a mathematical concept should they attempt
to transfer this understanding into symbols. Symbolic notation can take the form of pictures, diagrams,
modelling with concrete objects and mathematical notation. Learners should be given the opportunity to
describe their understanding using their own method of symbolic notation, then learning to transfer them
into conventional mathematical notation.
Applying with understanding
Applying with understanding can be viewed as the learners demonstrating and acting on their understanding. Through authentic activities, learners should independently select and use appropriate symbolic notation to process and record their thinking. These authentic activities should include a range of practical hands-on problem-solving activities and realistic situations that provide the opportunity to demonstrate mathematical thinking through presented or recorded formats. In this way, learners are able to apply their understanding of mathematical concepts as well as utilize mathematical skills and knowledge. As they work through these stages of learning, students and teachers use certain processes of mathematical reasoning.
• They use patterns and relationships to analyse the problem situations upon which they are working.
• They make and evaluate their own and each other’s ideas.
• They use models, facts, properties and relationships to explain their thinking.
• They justify their answers and the processes by which they arrive at solutions.
In this way, students validate the meaning they construct from their experiences with mathematical situations. By explaining their ideas, theories and results, both orally and in writing, they invite constructive feedback and also lay out alternative models of thinking for the class. Consequently, all benefit from this interactive process.