Mathematics, Science & I.C.T.

Mathematics

Mathematical literacy is as important to the growth of the human being as is literacy in the mother tongue. Through Mathematics one has an alternative language with which to relate to and understand the world in terms of science, nature, art and music. It is important, in the education of a child, to bring both the utility and the beauty of the language of Maths. Mathematics is a subject that directly fosters the will activity and encourages independence of learning.

Method and Content

Mathematics is broadly divided into three stages:

  • Classes 1-5 – the subject is developed as an activity that connects to the direct experiences of the child – from the internal to the external
  • Classes 6-8 – the approach in these years concentrates on the practical
  • Classes 9-12 - Maths moves towards a more abstract perspective

In Classes 1-3 simple arithmetic is initially experienced through counting, sharing and combining real objects and through movement exercises (dancing the sums, rhythmic counting). The four processes (+, -, ×, ÷) are used in solving practical questions. Number games and puzzles keep the mental activity lively, with lots of mental arithmetic involved in playing shops and actually giving change, not only written calculations. Main lessons on weights and measurements involve much practical activity linked with farming and building.

Through form drawing Geometry has a free-hand beginning with much copying and transforming simple forms.  The qualities of various forms experienced as movement leads to an understanding for mirroring, translating or transforming two-dimensional geometric forms.

In Class 4 the curriculum reflects the nine year old change and as the child starts to distinguish themselves more from the world around them, many lessons - such as grammar - focus on the fragmentation of the whole.

In Class 5 we introduce the more abstract decimal fractions. Geometry continues to progress from earlier form drawing but is still based on skilled drawing without instruments.  The vigorous experience of Maths is felt to be as important as quick abstract mental calculation, and both are practised.

In Classes 6-8 the earlier body movement-based experience of Maths processes evolves. The 12 year olds internalise what they have learned so far, through the vigorous experience of internal logic. Algebra is introduced and children learn that, just as they gradually stopped using objects in calculations in Class 1, they can gradually stop using numbers in mathematics by making intelligible the formal processes.  Conceptual thinking emerges from the earlier aim of keeping thinking based on movement and imagination. In Geometry, the experience of geometrical proof also helps to facilitate this change.

When suitably presented, Mathematics can offer an important support to the inner life of children at this age. They can gain rigorous objectivity to balance the changes during puberty and a real trust in the value of thinking.

In Class 9 students experience through the golden ratio that nature, art, science and music have an underlying unity. Students own research and ideas are developed through project work and inquiry providing constancy and structure within their inner turmoil.

In Class 10 students are brought trigonometry which emphasises concepts and analysis brought to us by the Greeks. Students can literally ‘look out’ and see a world beyond that supports their journey and understanding of who they are and where have they come from.

In Class 11 projective geometry is taught, emphasising ideas of infinity, duality and continuity and the synthesis between them. This supports the balance and reflection of this developmental stage.

Students take GCSE Maths in Class 9/10 as one of their compulsory subjects and it is open to them to pursue these studies at AS/A2 level should they wish.

Science

Science is about understanding and discovering the material world around us: nature, life, our bodies and health, the earth, the universe. It is about clear logical reasoning, as in maths, but tied to clear objective observation and measurement, and applied to the world around us.

In Science, authority and dogma must be subservient to the evidence in nature. Theories are just that – the best way we have of understanding things at the moment, but our thinking may have to change as new evidence emerges. Our ideas have to be left loose enough to grow and change.

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We need to appreciate the value - and limits - of scientific method: a perpetual cycle of observation, hypothesis, experimentation and refinement, with an emphasis on accurate measurement, ‘fair tests’, controlled variables, repeatability and peer-review. The study of Science is about developing an understanding of how things behave, which allows us to make predictions. This, in turn, is crucial in understanding technology, farming and health, and critical to invention and innovation in those fields.

The ability to understand and participate in current, and future, scientific debates, such as stem-cell research or climate change fosters scientific literacy. In a broader sense, understanding the growth and development of scientific ideas and methods is important to understanding human development through history. An understanding of how beliefs, social mores and scientific ideas have, and continue to mutually shape each other, is also important. For all its efforts at objectivity, science is not separate from society.

Method and content

The approach to Science begins with observing phenomena, savouring a sense of wonder before seeking an explanation. Science begins in Kindergarten, with walks in the ‘natural world’, observing and gathering the wonder and beauty of nature through the seasons. Baking, painting, playing with water and mud, among many other activities, provide experiences and unconscious observations which can later be drawn on.

In Classes 1 and 2 the ‘home surroundings’ strand continues, with nature walks and nature stories, through crafts, and the child’s increasing awareness of their body in movement.

In Class 3 the child experiences the ‘rubicon’, a major transition, developing an awareness of time and of material needs; this is met through main lessons on building/shelter and farming/food, with many opportunities for practical experience and basic understanding of simple mechanics and Biology.

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In Classes 4 to 6 the emphasis shifts to include more and more of the natural world; from man and animal, to the plant kingdom and geology, from the more familiar and similar (to humans) to things which are increasingly removed.

More formal Science begins with Physics main-lessons starting in Class 6 and chemistry starting in Class 7, whilst the life-science strand returns to health, reproduction, anatomy and the senses.

From Class 6 to Class 10 there are generally 3 science main-lesson blocks each year. In Class 8 weekly science subject lessons begin, with an emphasis on understanding the basics of scientific method, laboratory practice and safety, with some key aspects of Physics and Chemistry.

IDSCF2792n Class 9 and 10, Science as a GCSE subject is compulsory, providing a good understanding of a broad range of Science. In addition main lessons are taught in Biology, Ecology, Physics (power and transport) and Chemistry (carbon).  Themes are introduced, in an age appropriate manner, to support the inner turmoil and impatience of the 14-15-year-old.  At the same time, the constancy of scientific processes helps to support their balance.

Class 10 main lessons answer the key questions of ‘How did I get here?’ ‘Who am I’ and ‘Where am I from?’  Topics covered include heredity, genetics and evolution in Biology; gravity, orbits and relativity in physics; and the chemistry of nitrogen.

 

A-level science is optional in Classes 11 and 12. We currently have only one Science main lesson block in Class 11: Botany and one short block in Class 12: Embryology and Zoology.

I.C.T.

Steiner Waldorf education prepares young people for life in the modern world and to enable this to happen the education supports the development of the child in their healthy growth. To introduce a subject like ICT too early into the child’s development presents several difficulties, including:

  • a tendency to become fixed by the medium, with the result that their innate creativity is hampered, compromised or constricted
  • harmful effects on brain development
  • diversion of time from more direct and hands-on skills which foster essential hand-eye-brain coordination and development
  • use of a ‘tool’ that has an abstraction beyond the comprehension of the growing child that opens them to areas of social questions that are beyond their understanding
  • social isolation

We embrace ICT with all it offers as a valuable and necessary tool in a busy world with diminishing resources. ICT has become a part of everyday life and our curriculum is continually adapting to meet these needs both from a technical and moral/social perspective. We introduce ICT in Class 8 when the students have begun to develop the ability to reason logically, and when the software will resemble that which they will be using in their adult life. ICT draws and builds on skills of literacy, problem-solving, judgment and creativity developed through classes 1-7 and these skills continue to be more consciously developed through ICT. It is crucial that students are presented with a sound understanding of the computer as a tool, with its related advantages and disadvantages and are introduced to the social issues surrounding the use of technology in our changing world.

The basic skills are easily and quickly learned and, as the technology and software are rapidly changing, ICT is introduced at the stage that students are ready, developmentally, to use ICT as a tool that supports their learning and serves their education. To this end the ultimate aim is to equip the students to be able to make judgments for themselves how best to use the computer, as a tool in the service of real perceived needs.

Method and content

Students are formally introduced to ICT within the school in Class 8, with a weekly 'subject-lesson'. This is the modern equivalent of the 'touch-typing' lessons of the original Waldorf curriculum which remains a valuable tool in computer use.

In Class 9, a Main Lesson in ICT follows and explores the development in technology that leads us to the present day. It is vital that young people have at least a basic understanding of how any technology they use works which supports the methodology of the ‘whole to the part’.

Throughout their time in the Upper School students develop and are encouraged to use their ICT skills. This manifests itself in many different ways:

  • Exam board interactive programmes and the use of virtual learning environments.
  • Laptops in classrooms for note taking and controlled assignment work.
  • Extended project work and European portfolio work which utilise and extend student ICT skills through desk top publishing, taking and editing digital photographs.
  • GCSE ICT as part of the Class 9/10 programme.
  • Graphics and photography as part of Class 11 and 12 options.
  • Private work and study by students.