Introduction to the ESF Mathematics Scope and Sequence

7/30/2019 Introduction to the ESF Mathematics Scope and Sequence

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Introduction to the ESF mathematicsscope and sequence

The information in this scope and sequence document was developedfrom the IB Mathematics Scope and sequence (February 2009) ESFMathematics scope and sequence (2010) UK National Curriculum and

ACARA (Australian Curriculum Assessment and Reporting Authority) andshould be read in conjunction with the mathematics subject annex inMaking the PYP happen: A curriculum framework for international primaryeducation (2007).

What the PYP believes about learningmathematics

The power of mathematics for describing and analysing the world aroundus is such that it has become a highly effective tool for solving problems. Itis also recognized that students can appreciate the intrinsic fascination ofmathematics and explore the world through its unique perceptions. In the

same way that students describe themselves as authors or artists, aschools programme should also provide students with the opportunity tosee themselves as mathematicians, where they enjoy and areenthusiastic when exploring and learning about mathematics.

In the IB Primary Years Programme (PYP), mathematics is also viewed asa vehicle to support inquiry, providing a global language through which wemake sense of the world around us. It is intended that students becomecompetent users of the language of mathematics, and can begin to use itas a way of thinking, as opposed to seeing it as a series of facts and

equations to be memorized.


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How children learn mathematics

It is important that learners acquire mathematical understanding byconstructing their own meaning through ever-increasing levels ofabstraction, starting with exploring their own personal experiences,understandings and knowledge. Additionally, it is fundamental to thephilosophy of the PYP that, since it is to be used in real-life situations,mathematics needs to be taught in relevant, realistic contexts, rather thanby attempting to impart a fixed body of knowledge directly to students. Howchildren learn mathematics can be described using the following stages

Constructing meaning about mathematics

Learners construct meaning based on their previous experiences andunderstanding, and by reflecting upon their interactions with objects andideas. Therefore, involving learners in an active learning process, wherethey are provided with possibilities to interact with manipulatives and toengage in conversations with others, is paramount to this stage of learningmathematics.

When making sense of new ideas all learners either interpret these ideasto conform to their present understanding or they generate a newunderstanding that accounts for what they perceive to be occurring. Thisconstruct will continue to evolve as learners experience new situations andideas, have an opportunity to reflect on their understandings and makeconnections about their learning.


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Transferring meaning into symbols

Only when learners have constructed their ideas about a mathematicalconcept 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 theopportunity to describe their understanding using their own method ofsymbolic notation, then learning to transfer them into conventionalmathematical notation.

Applying with understanding

Applying with understanding can be viewed as the learners demonstratingand acting on their understanding. Through authentic activities, learnersshould independently select and use appropriate symbolic notation to

process and record their thinking. These authentic activities should includea range of practical hands-on problem-solving activities and realisticsituations that provide the opportunity to demonstrate mathematicalthinking through presented or recorded formats. In this way, learners areable to apply their understanding of mathematical concepts as well asutilize mathematical skills and knowledge.

As they work through these stages of learning, students and teachers usecertain 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 others 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 constructfrom 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.


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Mathematics in a transdisciplinaryprogramme

Wherever possible, mathematics should be taught through the relevant,realistic context of the units of inquiry. The direct teaching of mathematicsin a unit of inquiry may not always be feasible but, where appropriate, priorlearning or follow-up activities may be useful to help students makeconnections between the different aspects of the curriculum. Students alsoneed opportunities to identify and reflect on big ideas within and betweenthe different strands of mathematics, the programme of inquiry and othersubject areas. Links to the transdisciplinary themes should be explicitlymade, whether or not the mathematics is being taught within the

programme of inquiry. A developing understanding of these links willcontribute to the students understanding of mathematics in the world andto their understanding of the transdisciplinary theme. The role of inquiry inmathematics is important, regardless of whether it is being taught inside oroutside the programme of inquiry. However, it should also be recognizedthat there are occasions when it is preferable for students to be given aseries of strategies for learning mathematical skills in order to progress intheir mathematical understanding rather than struggling to proceed.

The structure of the ESF mathematicsscope and sequence

The scope and sequence has been designed in recognition that learningmathematics is a developmental process and that the phases a learnerpasses through are not always linear or age related. For this reason thecontent is presented in continuums for each of the five strands of

mathematicsdata handling, measurement, shape and space, pattern andfunction, and number. For each of the strands there is a strand descriptionand a set ofoverall expectations. The overall expectations provide asummary of the understandings and subsequent learning being developedfor each phase within a strand.

The content of each continuum has been organized into phasesof


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development, with each phase building upon and complementing theprevious phase. The continuums make explicit the conceptualunderstandings that need to be developed at each phase. Evidence ofthese understandings is described in the learning outcomes associatedwith each phase and these learning outcomes relate specifically to

mathematical concepts, knowledge and skills.

How to use the ESF mathematics scopeand sequence

This mathematics scope and sequence should be used in the context of atransdisciplinary, inquiry-based programme. The mathematics scope andsequence is structured around broad, transferable ideasconceptualunderstandingsthat all learners need to understand to become confidentmathematicians.

The following points should also be considered when using the document.

It is acknowledged that there are earlier and later phases that have notbeen described in these continuums.

Each learner is a unique individual with different life experiences and notwo learning pathways are the same.

Learners within the same age group will have different proficiency levelsand needs; therefore, teachers should consider a range of year levelphases when planning mathematics learning experiences for a class.

Learners are likely to display understanding and skills from more than oneof the year level phases at a time. Consequently, it is recognized thatteachers will interpret this scope and sequence according to the needs oftheir students and their particular teaching situations.

The continuums are not prescriptive tools that assume a learner mustattain all the outcomes of a particular phase before moving on to the nextyear level phase, nor that the learner should be in the same phase foreach strand. Prior knowledge should therefore never be assumed before embarking onthe presentation or introduction of a mathematical concept.

Documents

Introduction to the ESF Mathematics Scope and Sequence