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The Process of Learning Mathematics

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            Teaching mathematics for children requires careful planning.  This entails consideration of principles in learning mathematics to help guide teachers formulate strategies to achieve key objectives for children in different stages of learning.  These objectives are to set to serve as templates on how children should appropriately progress from the foundation and reception stage onwards.  Aside from rearing pupils to become properly numerate, planning mathematics learning for children should also include steps in making the process a satisfying experience for them.  This involves an understanding of the rapid physical and mental development of children and the age-related adaptive changes that accompany them.  The main goal is to provide a holistic approach in planning mathematics learning for children through a process that is suited for them.

Principles for Mathematics Learning for the Early Years

            The Curriculum Guidance for the Foundation Stage have provided several principles for early years education which are drawn from good and effective planning and teaching in the early years setting (Curriculum Guidance 2000, p.11).  The guidance is intended to help practitioners in the planning and teaching of an appropriate curriculum for areas of learning during the foundation which includes mathematical development.  It also provides examples on how to put those principles into practice and sets out common features that will result from good practice based on those principles.  It aims to serve as a reference for teachers as they plan for teaching children progress towards achieving the appropriate early learning goals including those related to mathematics (Curriculum Guidance 2000, p.5).

The Foundation Stage

            The foundation stage begins in children with three years of age (Curriculum Guidance 2000, p.6).  At this stage, most children will have attended some form of pre-school or nursery either part-time or full-time while a few may have stayed at home before entering primary schools.  This presents a marked variation in skills which teachers should consider when teaching mathematics in children at the foundation stage.  It is expected that through the curriculum guidance, teachers will be able to adapt a good practice of teaching.

            Among the first few principles of effective education requires a relevant curriculum and practitioners who not only understand it but are also able to implement its requirements.  Effective education also requires practitioners to understand the rapid developmental growth of children during the early years – physically, intellectually, emotionally and socially.  This necessitates a clear understanding by the practitioner of the developmental milestones of children from birth to age six and an awareness of their capacity for knowledge and skills (Curriculum Guidance 2000, p.13).  This will enable them to identify which areas require specific attention and encouragement as well as recognize the most effective approach in attaining early learning goals by the end of the foundation stage.

For early year education to be effective, the curriculum should also be carefully structured wherein the starting points of learning are build on what the children already know and are able to do.  This is achieved by working together with the parents in planning purposeful and stimulating activities in an environment conducive for learning, either indoors or outdoors (Curriculum Guidance 2000, p.11).   Working in partnership with parents also establishes the feeling of trust with each which allows for the smooth transition between the home and the community setting.  This will also give the practitioner the chance to find out about the child’s ethnic, faith and cultural heritage so that he or she will be able to plan an “environment free from stereotypical images and discriminatory practice.” (Curriculum Guidance 2000, p.11).  This is in support of the principle that “no child should be excluded or disadvantaged because of ethnicity, culture or religion, home language, family background, special educational needs, disability, gender or ability.” (Curriculum Guidance 2000, p.11).

Mathematical Development

            During the foundation stage, mathematical development should be focused on the use of numbers as labels and for counting and much later for calculating.  Teaching children to recognize numbers as labels should employ things that are already familiar to them like the channels appearing on the television set or the digital figures blinking on the microwave (Curriculum Guidance 2000, p.68).  This will help children not only recognize symbols as numbers but also expose them to the function of numbers associated with their use.  Counting during the foundation stage should involve “saying the number names in order,” while matching the numbers to the objects counted, at the same time “knowing that when you count, the last number you say gives the number of objects in the group.” (Curriculum Guidance 2000, p.68).   The act of calculating at this stage involves the comparison and combination of numbers of objects which leads to subtraction and addition while sharing objects equally among groups of children leads division and “adding groups of the same number of objects” exemplifies multiplication (Curriculum Guidance 2000, p.69).

Framework for teaching mathematics from Reception to Year 6

The purpose of the framework is to help primary and middle schools “set appropriately high expectations for their pupils and understand how pupils should progress through the primary years.”  The framework will complement the National Numeracy Strategy which has been launched in response to the Government’s National Literacy Strategy that was set out to address the growing need to improve the standards of literacy and numeracy.   The Numeracy Strategy was formulated for schools to provide a structured daily mathematics lesson of 45 minutes to one hour for all pupils of primary age (Dept. of Education and Skills 1999).

The very element of the framework is the key objectives of each year group.  The framework provides for each year group from reception to year 6 key objectives which pupils should learn at the end of the school year.  It offers in detail different approaches in attaining these objectives from the management of time of teaching to the organization of the class and the breakdown of the content of each typical lesson.  The framework puts emphasis on direct teaching suggesting to spending more time with it for each lesson to the whole class, a group of pupils, or individuals.  It states that high-quality direct teaching should encourage interactivity from the pupils, allowing them to answer questions and explaining and demonstrating their methods to the class (Dept. of Education and Skills 1999).

The framework also gives guidelines on how to assess the progress of the pupils with relation to the key objectives in various stages throughout the course.  These include short-term, medium-term, and long-term assessments and how they are utilized to inform about the teaching plans for each level in order to assimilate it with the continuous cycle of planning, teaching, and assessment.  These assessments, especially the long-term assessment, are also useful in supporting the year-end reports to parents.  For the next teacher, individual assessments of pupils will allow for smoother transition to the next year group as it gives a good indication of progress of the pupil during the year and helps identify areas which will require more attention for the next year.  This way, the next teacher will be able to build on what the pupil has already learned while at the same time focus on lessons which the pupil is having difficulty (Dept. of Education and Skills 1999).


Department for Education and Employment 2000, Curriculum guidance for the

foundation stage, Qualifications and Curriculum Authority, Retrieved May 1,

2006, from <http://www.qca.org.uk/downloads/5585_cg_foundation_stage.pdf>.

Department of Education and Skills 1999, Framework for teaching mathematics,

Retrieved May 1, 2006, from



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