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Sophia Institute online Art of Teaching Waldorf Program

Art of Teaching Waldorf Grade 1

Lesson 6

HELP

Waldorf Curriculum

Introduction

A curriculum could be compared to the list of ingredients for a recipe. However good the recipe, the quality of the ingredients is crucial but to make a start the components also need to be available. When they are to hand, the next question is whether the cook is skilled enough to combine and adjust flavors so that each item plays its part without overwhelming the others. An experienced cook may be able to substitute one ingredient for another, even to improvise in such a way that something new is created. But we should not forget that emotion, even love, goes into the preparation of food and this will influence how it is received. And, of course, the expectations, health and culinary experience of the diners also makes a difference.

A curriculum guides an entire learning process. It should not, like a dish into which a chef has thrown every possible taste, explode in an overwhelming, sensation-bursting blowout; it should bring to the table ingredients that are well- balanced, digestible and nutritious, that promote health and stimulate, not stupefy, the senses. Over time, as with diet, a curriculum can introduce items that may not be immediately appealing, stronger tastes or more subtle and complex ones: intellectual chillis, subjects initially sour or astringent, as well as flavors, textures and scents that help to educate the palate. A primary school curriculum, in particular, sets out ingredients for the hors d'oeuvres of lifelong learning.

Of course, many school curriculums share common ingredients, but the distinctive qualities of the Steiner-Waldorf curriculum framework are, we believe, unique:
  • The curriculum unfolds over time, is wide and richly experiential: not merely designed towards narrowly-defined 'achievement', but intended to promote capability for the art of living
  • The curriculum is really only a series of 'indications', as Steiner described them, pointers inviting interpretation and free rendering, i.e. it calls on and encourages the creativity ( or artistry) of teachers
  • The importance of content is fully recognized (young people need certain skills and useful knowledge), but as a creative framework, the Steiner- Waldorf curriculum is embedded within a developing practice and method. The curriculum outline takes its cue from the development of the child: subject, or content, provides a medium for a meeting and collaboration of teacher and learner. Thus, since meaning and knowledge are built over  time, this is co-constructive learning in which understanding unfolds as a process of learning to learn encompassing both students and teacher
  • Subject content and necessary competence are always relative to the child: the curriculum is midwife to the emerging individuality, rather than suit of clothes into which the child must be made to fit
  • The shaping principles of the curriculum are extraordinarily robust and resilient. Many independent educators recognize this fundamental coherence, which has stood the test of time and many generations of children
  • The creative freedom within the Waldorf curriculum framework enables it to be successfully adapted for a variety of settings, languages and cultures. Schools founded on the principles and example of the first Waldorf School (Stuttgart 1919), can be found around the world, including every inhabited continent. What started as a central European curriculum has been modified by applying its essential principles to the education of children in -the Americas, many parts of Africa, the Middle East, India and the Far East, as well as most of the rest of Europe.

Course Outline

Sophia Institute Waldorf Courses: The Art of Teaching Waldorf Grade 1
Lesson 1 / Waldorf Curriculum / Introduction
Lesson 2 / Waldorf Curriculum / Grades 1 - 3 (Part 1)
Lesson 3 / Waldorf Curriculum / Grades 1 - 3 (Part 2)
Lesson 4 / Waldorf Methods / Reading and Math / Introduction
Lesson 5 / Waldorf Methods / Reading and Math / Reading / Grade 1
Lesson 6 / Waldorf Methods / Reading and Math / Math / Grade 1
Lesson 7 / Waldorf Methods / Sciences / Chemistry / Introduction
Lesson 8 / Waldorf Methods / Sciences / Physics / Introduction
Lesson 9 / Waldorf Methods / Sciences / Life Sciences / Introduction
Lesson 10 / Waldorf Methods / Sciences / Geography / Introduction
Lesson 11 / Waldorf Methods / Sciences / Geography / Grades 1 - 8
Lesson 12 / Waldorf Methods / Sciences / Gardening and Sustainable Living
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Tasks and Assignments for Art of Teaching Waldorf Grade 1 /AoT16

Please study and work with the study material provided for this lesson. Then please turn to the following tasks and assignments listed below.

1. Study the material provided and look up other resources as needed and appropriate.
2. Create examples of curriculum that addresses the learning method and content appropriate for grade 1 as follows, Curriculum examples should include outlines and goals, activities, circle/games, stories, and illustrations/drawings: Create 2 examples for grade 1.
3. Additionally submit comments and questions, if any.

Please send your completed assignment via the online form or via email.

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Study Material for this Lesson

​Arithmetic and Mathematics/Class 1

General Observations and Guidelines

Mathematics in the Waldorf School is divided  into three stages. In the first stage, which  covers the first five classes, mathematics is  developed as an activity intimately connected  to the life process of the child, and progresses  from the internal towards the external. In  the second stage, covering Classes 6 to 8,  the main emphasis is on the practical ... The  ninth year onwards is characterised by a  transfer towards a rational point of view.

Thus writes H. von Baravalle, the first mathematics teacher at the Waldorf School in Stuttgart. 

Classes 1 to 5 

Here two questions must be answered: 
1.      How should the first mathematical concepts be  tackled? 
2.      What is the psychological basis on which to  build them? 

In answer to question one, careful scrutiny shows  that the teaching of arithmetical and geometric  concepts is connected to the consciousness  and activity of the child's movement organism. Counting is inner movement by which outer  movement can be observed. E. Schuberth calls this  'the sensory content of mathematics teaching" The  results of Piaget's research on the development of  intelligence in children also point in this direction:  in the 'concrete operations stage' (twelve or thirteen  years old), children still carry out movements  when they want to connect one thing to another.  Anyway, these movements are connected to the  physical objects from which the children can as yet  barely free themselves, if at all. 

This leads on to question two: if the development  of mathematical concepts occurs in the static,  concrete phase, our purpose must not be to  'generalise and abstract', but to 'make concrete  and look at individual cases: 3 This defines the  means whereby it is possible to avoid confronting  children with abstract logical structures, but rather  to immerse their whole capacity for experience in  mathematics. We can now refer to form drawing  where the consciousness necessary for using  mathematics is nurtured and practised. This  physical experience is a basis and assumption for  a healthy immersion in the 'formal operations  stage' (Piaget). The rule 'from hand, through heart  to head' (which is meant by the child's above-  mentioned 'whole capacity for experience') makes it possible for the children to bring their own  capacities into play. 

It is evident that the best, most fruitful  questions about concepts and explanations  come from pupils who do not pose questions  using a quick intellectuality, but a capacity  for involved feeling, which allows clarity to  come into thinking:' 

To this concrete approach in mathematics at  primary school level we should add something  further which does not depend on the element of  movement. This is the quality, one might say the  identity, of the individual numbers. 

As the accent above is on a quantitative approach  to numbers, as the result of a brief pause in  movement or even based on the movement itself,  we need to place our introduction to qualitative  number concepts beside those of quantity. We  approach these qualities when we examine many  examples where the number in question is really  active in the world, as for example the number  five in the flowers of a rose. Here we use the child's  desire to question what lies behind the world and  human creations, that is, to seek what lies behind  the phenomena. The nuclear scientist W Heider  referred to this when he said in a lecture: 

One directs one's attention to qualitative  phenomena, to characteristics which have  something to do with the totality of the  objects observed. 

Steiner recommended taking this as the starting  point for an introduction to number concepts: 

We have gradually come to the point in the  course of civilisation where we can work with numbers in a synthetic manner. We have a  unity, a second unity, a third unity and  we struggle while counting in an additive  manner to join the one to the other, so that  one lies beside the other when we count. One  can become convinced that children do not  bring an inner understanding towards this.  Primitive human beings did not develop  counting in this way. Counting began from  unity. Two was not an external repetition  of unity but it lay within unity. One gave us  two, and two is contained in the one. One,  divided, gave us three, and three is contained  within one. If we wrote the number 1,  translated into modern terms, one could not  get away from the 1,for instance to 2. It was  an inner organic picture where two came  out of unity and this two was contained in  the one, likewise three and so on. Unity  encompassed everything and the numbers  were organic divisions of unity. 5 

This 'real' way of looking at numbers leads on  to written numbers, to symbols. It is not a picture  like that which should be used for introducing  letters, but pictures of number qualities. The  picture belongs to the being of the number, not to  the outer symbolic form. At this point we indicate  a further point of this 'quality-oriented' teaching:  today, especially, when we face the results of a  quantitative world view in ecological catastrophe  and destruction, it is increasingly important  to make a beginning of this kind in teaching  mathematics. 

By beginning with the concrete qualities of  number and by working with the properties of  movement in counting and calculating, children  develop a kind of intelligence which seeks and  finds the way to reality.

This brings us to the second stage: the approach  to mathematics teaching mentioned earlier. Here  we must deal with the practical use of calculation. 

If calculating has been practised thoroughly  enough during the first stage in the manner  indicated, then applied calculation also gets a  qualitative colouring. The forces of intelligence  which are served by business mathematics as well  as percentages and interest, are not 'value-free',  but can retain a colouring for balanced testing  and judging. The human significance of what is  thought out can and should be made clear. In this  connection one should point to the suggestion by  Steiner that elements of bookkeeping should also  be taken up in mathematics lessons. To see what  the general idea behind such an indication is, one  should ask what skills may be developed through  bookkeeping. There you will see how above all  a moral method of trading can be decisively  supported by these means. 

All these themes can lead us on to other  educational aims: inner mobility leads to  imaginative ability in solving mathematical  problems.  Through the experience of number qualities the  children experience trust and security: Number,  world and human being belong together.  The children can experience further security  through the correctness of solutions to problems  By this means they win some independence. For this reason mathematics is an activity  suited to freeing children from the fetters of  authority even if, at first, they depend on the  help of the teacher.  A final educational aim which should not be  undervalued and which is connected with the latter  is calculation. Calculation is not possible without regular practice, which also makes it an excellent  medium for schooling the will.  An explicit presentation of the third stage will  be given under the heading Classes 9 to 12 and is  therefore omitted here.  Geometry as part of mathematics teaching  begins in Classes 5 and 6 and is taught in separate  main -lessons. One of the principal intentions in  this subject is to develop and nurture the ability to  visualise space.  The controlled security of directed movement  and the estimation of proportions and relationships,  practised in freehand geometry, is well prepared  for by form drawing in Classes 1 to 4. 

The establishment of skills, knowledge and  techniques partly in connection with subjects is  taught with increasing complexity related to age.  
* Pupils should gradually learn to discover, to grasp mentally and to apply geometrical  properties, and the practical, drawn, solutions  representing them. 
* Work with geometric drawing instruments  should lead to clear and exact construction. 
* Patience, care and precision should be  developed, as well as independent creative  work through enjoyment of drawing.

​Classes 1 - 3

The dynamics of will activity should be internalised  by the experience of countability. Motivation  should be awakened through pictorial description  of number qualities. This dual aspect is important:  on the one hand it educates the bodily senses  through experience of movement, unfolding of  movement possibilities (both coarse and fine),  and co-ordination exercises. On the other hand  internalising of the expressed activities in soul activity (Le. calculation). Here the main medium  for achieving this is the use of pictures. Through  pictures, children can grasp internally what is  intended. Pure symbolic, logical presentation  can never achieve this. (Nevertheless one should  always be conscious that calculation is aiming at a  picture-less world, in contrast to the introduction  of letters of the alphabet.) In order to be able  to handle quantitative numbers freely, an inner  numerical space needs to be created, in which one  learns to move, rhythmically at first, with varied  number patterns. This is achieved, amongst other  means, by a memory developed by learning the  times-tables through rhythmic movement e.g.  through clapping, passing bean bags or skipping.  It appears important initially to approach actual  calculation as concretely and visually as possible  and to keep in mind the principle 'from the whole  to the parts: This means that the right connection  between analytical and synthetic thinking is  produced. Work with the temperaments should be  formed in the sense given in the ath discussion in  Discussions with Teachers? At the end of Class 3 the  pupils should have a confident grasp and clear view  of numbers up to at least 1,020. This does not mean  just the quantity or extent but equally the quality of  the numbers. ​

Class 1

In mathematics lessons the approach is analytical  in the sense of the reference by Steiner given above.  Starting with the number 1 as unity, numbers  (symbols) from 1 to 10 should be produced in a  qualitative manner (see above), which are contained  as manifold in unity. With written numbers one  can begin with Roman numerals which are less  abstract than the Arabic.  Alternatively, the Arabic numbers can be introduced in pictures as with the  letters of the alphabet. 

* Counting up to 110 
* Learning up to the 7 times table by heart and  through rhythmical practice 
* Introducing the four rules using numbers up to  20 and also in written form (in notation, the  sum is written first: 7 is 3 + 4) 
* Number riddles 
* First exercises in mental arithmetic ​

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