MATHEMATICS
Mathematics in the PYP is covered in five strands
- Number
- Pattern and Function
- Data Handling
- Measurement
- Shape and Space
In Number, Pattern and Function, students inquire into number systems, their operations, patterns and functions. This is where students become fluent users of the language of arithmetic, as they learn to encode and decode its meaning, symbols and conventions.
The remaining strands, data handling, measurement and shape and space are the areas of mathematics that other disciplines use to research, describe, represent and understand aspects of, their subject areas.
The language of mathematics is part of everyday life and communications. Every time we conduct business, do our shopping, or enjoy sports we need diverse knowledge of number, shape and measurement to be able to communicate effectively.
Problem solving is at the very core of mathematics. Virtually all mathematical endeavour is concerned with applying learning to real world situations and hence to solving problems.
“Beliefs and values in mathematics
All students deserve an opportunity to understand the power and beauty of mathematics.
Principles and standards for school mathematics
National Council of Teachers of Mathematics (NCTM 2000)
In the PYP, mathematics is viewed primarily as a vehicle to support inquiry, providing a global language through which we make sense of the world around us. It is intended that students become competent users of the language of mathematics, and can begin to use it as a way of thinking, as opposed to seeing it as a series of facts and equations to be memorized. The power of mathematics for describing and analysing the world around us is such that it has become a highly effective tool for solving problems.
It is also recognized that students can appreciate the intrinsic fascination of mathematics and explore the world through its unique perceptions. In the same way that students describe themselves as “authors” or “artists”. The programme also provides students with the opportunity to see themselves as “mathematicians”, where they enjoy and are enthusiastic when exploring and learning about mathematics.” (IBO, 2009, Pg.81)
Math in the PYP has 3 key components
“Constructing meaning about mathematics
Learners construct meaning based on their previous experiences and understanding, and by reflecting upon their interactions with objects and ideas.
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 are 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 independently select and use appropriate symbolic notation to process and record their thinking. These authentic activities include a range of practical hands-on problem solving activities and realistic situation that provide the opportunity to demonstrate mathematical thinking.
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 experience 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.
Play and exploration have a vital role in the learning and application of mathematical knowledge, particularly for younger students. In a class students will be actively involved in a range of activities that can be free or directed. In planning the learning environment and experiences, teachers consider that young students may need to revisit areas and skills many times before understanding can be reached.
The role of Mathematics in the Programme of Inquiry
Whenever possible, mathematics is taught through the relevant, realistic context of the units of inquiry. The direct teaching of mathematics in a unit of inquiry may not always be feasible but, where appropriate, introductory or follow-up activities are useful.
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 contexts, rather than by attempting to impart a fixed body of knowledge directly to students.” (IBO 2009, pgs. 81-83)
“Overall expectations in mathematics
MBIS uses the PYP Mathematics Scope and Sequence document that has been designed in recognition that learning mathematics is a developmental process and that the phases a learner passes through are not always linear or age related. The content is presented in continuums for each of the five strands of mathematics. The content of each continuum has been organized into four phases of development, with each phase building upon and complementing the previous phase.