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Mathematics

What the PYP believes about learning mathematics

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", a school's programme should also provide students with the opportunity to see themselves as "mathematicians", where they enjoy and are enthusiastic when exploring and learning about mathematics.

In the IB Primary Years Programme (PYP), mathematics is viewed 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 compatent 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.

How children learn mathematics

It is important that learners acquire mathematical understanding by constructing their own meaning through ever-increasing levels of abstraction, staring with exploring their own personal experiences, understanding 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:

Constructing meaning: Students construct meaning from direct experiences, including the use of manipulatives and conversation.

Transferring meaning: Students connect the mathematical notation system with concrete objects and associated mathematical processes. The teacher provides the symbols for students. Students begin to describe their understanding using symbolic notation.

Understanding and applying: Through authentic activities, students independently select and use appropriate symbolic notation to process and record their thinking. As they work through these stages, 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.

Play and exploration have a vital role in the learning and application of mathematical knowledge, particularly for younger students. In a PYP learning environment, mathematics skills and activities need to occur in authentic settings. As educators, we need to provide a variety of areas and resources to allow students to encounter situations that will introduce and develop these skills. In this environment, students will be actively involved in a range of activities that can be free or directed. In planning the learning environment and experiences, teachers need to consider that young students may need to revisit areas and skills many times before understanding can be reached. Applying mathematical skills to real-world tasks supports students’ learning.

The role of mathematics in the programme of inquiry

Wherever possible, mathematics should be 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, prior learning or follow-up activities may be useful to help students make connections between the different aspects of the curriculum. Students also need opportunities to identify and reflect on “big ideas” within and between the different strands of mathematics, the programme of inquiry and other subject areas.

Links to the transdisciplinary themes should be made explicitly, whether or not the mathematics is being taught within the programme of inquiry. A developing understanding of these links will contribute to the students’ understanding of mathematics in the world. The role of inquiry in mathematics is important, regardless of whether it is being taught inside or outside the programme of inquiry. However, it should also be recognized that there are occasions when it is preferable for students to be given a series of strategies for learning mathematical skills (including rote learning) in order to progress in their mathematical understanding rather than struggling to proceed.

Mathematics at QBS

Mathematics provides opportunities for students to engage in investigations into measurement, shape and number, and allows them to communicate in a language that is concise and unambiguous. Mathematical concepts and skills can also be applied to solve a variety of real-life problems. Students apply their mathematical reasoning to a number of situations in order to find an appropriate answer to the problems they wish to solve.
 
Students develop their knowledge and understanding of mathematics through inquiry in the form of practical activities, exploration and discussion.
 
Mathematics is arranged into five strands:
 
Data Handling
Data handling allows us to make a  summary of what we know about the world and to make inferences about what we do not know.
Data can be collected, organised represented and summarized in a variety of ways to highlight similarities, differences and trends; the chosen format should illustrate the information without bias or distortion. Probability can be expressed qualitatively by using terms such as “unlikely”, “certain” or “impossible”. It can be expressed quantitatively on a numerical scale.
Measurement
To measure is to attach a number to a quantity using a chosen unit. Since the attributes being measured are continuous, ways must be found to deal with quantities that fall between numbers. It is important to know how accurate a measurement needs to be or can ever be. 
Shape and Space
The regions, paths and boundaries of natural space can be described by shape. An understanding of the interrelationships of shape allows us to interpret, understand and appreciate our two-dimensional (2D) and three-dimensional (3D) world.
Pattern and Function
To identify pattern is to begin to understand how mathematics applies to the world in which we live. The repetitive features of patterns can be identified and described as generalized rules called “functions”. This builds a foundation for the later study of algebra.
Number
Our number system is a language for describing quantities and the relationships between quantities. For example, the value attributed to a digit depends on its place within a base system.
Numbers are used to interpret information, make decisions and solve problems. For example, the operations of addition, subtraction, multiplication and division are related to one another and are used to process information in order to solve problems. The degree of precision needed in calculating depends on how the result will be used.
 

Information on this page was taken in part from : "Making the PYP Happen" 2007
For further information, please visit: www.ibo.org