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
- At QBS we follow the ESF 'Scope and Sequence Program.' This program is based on the 'UK Strategy,' in combination with 'The International Baccalaureate Scope and Sequence Program for Mathematics.'
- Key Objectives, known as Learning Outcomes, are covered over the course of the year.
- Mathematics is taught in 5 strands:
Applying and Using - Number - Data Handling - Measuring - Understanding Shape - Where possible, concepts are taught within the Units of Inquiry.
- If this is not possible, concepts are taught as 'stand alone.'
- Mental mathematics is vital to children's understanding, and is often taught at the start of a lesson.
- Such sessions would often include a range of 'mental strategies' and 'rapid recall of facts.'
Information on this page was taken in part from : "Making the PYP Happen" 2007
For further information, please visit: www.ibo.org
