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Waldorf Methods/Sciences 1

Introduction

" ... ancient wisdom contained no contradiction between body and soul or between nature and spirit; because one knew: Spirit is in man in its archetypal form; the soul is none other than the message transmitted by spirit; the body is the image of spirit. Likewise, no contract was felt between man and surrounding nature because one bore an image of spirit in one's own body, and the same was true of every body in external nature. Hence, an inner kinship was experienced between one's own body and those in outer nature, and nature was not felt to be different from oneself. Man felt himself at one with the whole world. He could feel this because he could behold the archetype of spirit and because the cosmic expanses spoke to him. In consequence of the universe speaking to man, science simply could not exist. Just as we today cannot build a science of external nature out of what lives in our memory, ancient man could not develop one because, whether he looked into himself or outward at nature, he beheld the same image of spirit. No contrast existed between man himself and nature, and there was none between soul and body. The correspondence of soul and body was such that, in a manner of speaking, the body was only the vessel, the artistic reproduction, of the spiritual archetype, while the soul was the mediating messenger between the two. Everything as in a state of intimate union. There could be no question of comprehending anything. We grasp and comprehend what is outside our own life. Anything that we carry within ourselves is directly experienced and need not be first comprehended. ... Precisely because man had lost the connection with nature, he now sought a science of nature from outside." - Rudolf Steiner in "The Origins of Natural Science."

In Waldorf education, the science subjects do not start with nor are built from theories and formulas. Rather they start with the phenomena and develop in an experiential way, by first presenting the phenomenon, having the students make detailed observations, then guiding the students to derive the concepts that arise from the phenomena, and finally deriving the scientific formulas and laws behind the phenomena.This methodology reflects the way basic science actually has been developed by scientists and trains the pupils stepwise in basic scientific thinking and reflection on the basis of personal experience and observation of the phenomena of nature and the history of science. In kindergarten and the lower grades, the experience of nature through the seasons is brought to the children through nature walks, nature tables and observation of nature around. In later grades, there are specific main lesson blocks dealing with Man and Animal, and other themes. In grade 5, scientific ideas may be taught historically through the study of the Greeks, for example, Aristotle, Archimedes and Pythagoras. In grades 6-8 the science curriculum becomes more focused with blocks on physics (optics, acoustics, mechanics, magnetism and electricity), botany, chemistry (inorganic and organic), and anatomy. In high school, science is taught by specialists who have received college level training in biology, chemistry and physics and these three subjects are taught in each of the 4 years of high school.

Course Outlines

Waldorf Methods/Sciences 1
Lesson 1: Chemistry/Kindergarten/Grades
Lesson 2: Chemistry/Classes 9 - 12
Lesson 3: Physics/Introduction
Lesson 4: Physics/Classes 6 - 8
Lesson 5: Physics/Classes 9 - 12


Waldorf Methods/Sciences 2
Lesson 1: Life Sciences/Introduction
Lesson 2:
Life Sciences/Classes 4 - 5
Lesson 3: Life Sciences/Classes 6 -8
Lesson 4: Life Sciences/Classes 9 -10
Lesson 5: Life Sciences/Classes 11 -12


Waldorf Methods/Sciences 3
Lesson 1: Geography/Introduction
Lesson 2: Geography/Classes 1 - 8
Lesson 3: Geography/Classes 9 - 12
Lesson 4: Gardening and Sustainable Living
Lesson 5:
Technology
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Tasks and Assignments for Waldorf Methods/Sciences 1.5.

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 the age group in question. Curriculum examples should include outlines and goals, activities, circle/games, stories, and illustrations/drawings:
Create 2 examples for this age group.
3. Additionally submit comments and questions, if any.

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

Study Material for Waldorf Methods/Sciences Lesson 1.5.

Physics/Classes 9 - 12

In Classes 6 to 8 science lessons were given by a  generally trained class teacher who taught many  subjects. In particular, the relationship of the  subject matter to the human being was presented in  its physiological, economic, and ecological aspects.  The starting point generally for teaching was  experiments. Investigations were kept simple, so  that the children could recall most of them at home.  Where possible the children were encouraged to  observe physical phenomena. Experiments and  demonstrations of phenomena were arranged, and  the pupils went on to deliver independent, written  descriptions.
In science lessons in the Upper School, the  impressions based on experience of the Middle  school are then ordered further by thinking and  finally grasped as laws. The pupils should thereby  be protected from valuing half understood theories above their own experience and judgement while  building up their picture of the world. From this  it should be clear that theoretical content, which  today as a rule is considered the basis of subjects -  and for this reason is often placed at the beginning  of a teaching programme - is only taught in the  Upper School in Waldorf schools. Therefore the  model of the atom is only dealt with in the Classes  11 and 12. Where theories enter into the teaching,  they should at least be elaborated as thought spheres  about phenomena, as for instance the atomic  theory which comes from the quantitative laws  of chemistry, the emission of light etc. Otherwise  the world appears, as it surrounds mankind, as  meaningless compared to an elaborate model of it  and the ability to judge retreats when confronted  with the given content.

The aims for physics teaching in the Upper  School are:

Knowledge and understanding

* Fundamental physical phenomena and the  attempts to describe their processes
* Physical dimensions and concepts defined -  with consideration of aspects relevant to man  - as well as the main laws of measurement and  defining equations; estimates of the order of  magnitudes of physical results
* Understanding of certain phenomena of daily  life by means of physical processes
* Understanding of the physical basis of technical  apparatus
* A knowledge of the main lines of historical  development in physics and the biographies of  significant scientists
* A knowledge of the idea of physical models  and their capacity to predict


Abilities and skills

* To observe precisely and formulate observations 
* To carry out simple experiments and interpret  their results
* To construct independent concepts from  observations
* To construct independent experiments so as to  make observations
* To recognise uncertainties and evaluate their  influence
* To present measurements graphically and  evaluate them
* To understand physical processes with the help  of known laws
* To recognise the possibilities and limitations of physics in describing reality
* To be able to judge the real component in models 
* To produce independent reports of what is taught 
* To look at things in their entirety, holistic observation, and present their connection to  human life


Insights, evaluations and attitudes

* Readiness to communicate and co-operate in  observation, investigation and experimenting 
* Recognition of the difference between quantitative and qualitative investigation and their results
* Insight into the meaning of dynamic and feed-  back processes (change-causing-relationships)  and their challenge to human thinking
* Arrival at an awareness of environmental and  energy issues on the basis of their own insight 
* Insight that the physical method of thinking  must be constantly modified
* Insight that science and within it physics  represents and important part of human  culture
* The ability to judge information and  presentations of the mass media thoroughly
* The ordering of different scientific investigative  methods and their Significance for the  interpretation of results
* The evaluation of the wisdom of nature - also  as an example for human endeavour


Class 9

The pupils are guided in experiencing so that they  can understand the processes of the surrounding  world, especially those of technology. For this  reason questioning thinking and judgement  is practised especially in practical things from  the realm of technology. The manufacture of  materials should feature particularly in experiment  description. A mathematical formulation of the  rule is usually only given for certain examples,  e.g. for exercises to do with the area in hand,  where a meaningful calculation is possible, and  where the pupil can gain a feeling for quantities.  Understanding for physics and its methods should  be deepened and a glimpse of the physical content  of everyday objects and technology be given.

* Transformer
* Introduction to Potential difference, current, resistance
* Morse transmitter (telegraph) 
* Bells, relays
* Washing machine


Heat and engines

This is mostly built up on the suggestions of Rudolf  Steiner, leading to the understanding of the steam  engine, but a more contemporary development is  advisable.

* The investigation of air pressure by Otto von  Guericke
* Historical development of the steam engine and  its importance in the historical development of  Europe
* The function of the boiler
* Comparison of the heating value of various  fuels (in ideal combustion situations)
* As regards basic laws thereby you can arrive at:  '* 1 st and 2nd law of thermodynamics
* The development in new areas of technology  could for example take the following themes:
'* Absolute zero; the Kelvin scale
* The steam turbine
* Fridges and the contrasting function of the heat pump
* Internal combustion engines - 4 stroke, 2 stroke, diesel, perhaps the Stirling motor
* Radiation
* Rocket propulsion


Electricity and acoustics

Here one begins with the suggestion of Rudolf  Steiner's, to present everything that will make a  telephone comprehensible.

* Introduction or recapitulation of the concepts  of potential difference, current, and resistance  (see Class 8)
* Ohm's law with examples involving calculation 
* Introduction of the concept of electrical work,  electrical output and their units
* Calculation of electricity costs
* Function of the telephone: acoustically and  electronically
* Dialling technology
* Business significance of various communications technologies
* Fax machine, photocopier

For the Acoustic Doppler effect one can use  Rudolf Steiner's suggestion:

* The treatment of relative motion of binary stars  with the help of the Doppler effect (can also be  done in the geography main-lesson)

Further possible themes:
* Principle of the electric motor
* Comparison of the efficiency of various  machines
* Biographies of important physicists or alternatively independent presentations by  pupils on Watt, Guericke, Papin, Morse, etc.  Optional energy requirement and inquiry into  the means of energy saving
* Comparison of the readily available energy  sources
* Solar energy and its possible significance in the  future (could otherwise be done in Class 10 or  11, see technology curriculum)
* Hydrogen as possible energy carrier


Class 10

The pupils experience their relationship to  their surroundings increasingly consciously  and thus stand in a tension between high ideals  and uncertainty of appropriateness. In many  subjects one can address the question of origins.  Through transparent and fundamental concepts  in mechanics one can attempt in various ways  to give conscious clarity and security. For this  the mathematicisation of physics is handled in  an experiential way. The pupils can experience  satisfaction in the dominance of statements  won through mathematics using observation  and measurement (for instance in the parabolic  trajectory of a thrown object).

Discovering the principles, proportions and  conditions with equations of quantities is practised.

The pupils receive a living, conscious vision of  the great spiritual scientific turning point of the late  Renaissance and the birth of physics by grappling  with decisive historical questions as found in the  biographies of significant personalities (Galileo,  Bruno, Kepler, Tycho Brahe). They thus grasp how  the human being as observer is caught in the facts  of the physical world, its laws, from the outside,  and in the lawfulness oflogic, in thinking, from the  inside. By their own development in consciousness  as well af the recognition of their own mistakes the  students learn the conditions of research and see  the 'great spirits' of earlier times in the correct light.  They also learn the value of learning from failure  for all research and development. So the pupil  experiences, how security of understanding comes  about, and learns, to connect himself to the earth  and its laws in a new way.


Classical mechanics

Kinematics (uniform movement)  

* Measurement of speed
* The concept of average speed
* How to represent speed using vectors 
* Parallelogram of velocity
* The concept of acceleration
* Development of the laws of motion for  constant acceleration using an inclined plane  v=at, s=1;2 att
* Free fall, acceleration due to gravity, units of force 
* Vertical and horizontal motion perhaps  diagonal motion
* Principle of independence (of perpendicular  motion)


Statics

* Hook's law; application to balances
* Measurement of forces, force equations 
* Representation of forces by vectors
* Elastic and plastic deformation, pressure, stress 
* Centre of gravity of a body
* Force and reaction of a body on a slope


Dynamics

* Concept of mass, force 
* Newton's laws of motion
* Go into the historical development of these concepts and the biography of Newton 
* Law of conservation of energy
* Recapitulation of the golden rule of mechanics 
* Mechanical work
* The concept of energy
* Friction and static friction and cohesion 
* Rotary motion
* The rotation of the earth
* Centrifugal and centripetal force


Optional
, Coriolis effect
 
(see geography in Class 10)
* Law of moments and balancing using moments
* Impulse and momentum, elasticity 
* Newton's law of gravitation
* Kepler's laws
* Optional: Kepler's Harmonices Mundi (or in  astronomy main-lesson) 
* Pendulums
* Rhythms in the solar system 
* Wave motion in mechanics
* Mechanical oscillation and waves
* Superposition of waves (constructive and  destructive interference, if not in Class 11)


Astronomy

An astronomy main-lesson could be considered  (although otherwise covered in physics; Rudolf  Steiner did not expressly require a main lesson)  with the themes:
* The protective covering of the earth 
* The solar system heliocentrically
* The nine planets, asteroids and comets 
* The sun and its rhythms
* Solar effects on the earth -life-history of a star 
* Kepler's 'Harmony of Worlds'
* Sun and moon and their rhythms in relationship  to the earth


Optional

* The golden section as rhythmical principle of  form in the solar system
* Telescopes, microscopes, cameras, (human  eye) (and Class 11)


Class 11

Following Rudolf Steiner's indications, which  were to handle the modern discoveries of physics  (at that time alpha, beta and gamma rays),  electrical theory, electromagnetic theory, and  the basic phenomena of radioactivity as well as  the conceptual development in physics in the  nineteenth and twentieth centuries should be  worked through. Electrical and magnetic fields  in particular are investigated. With this the  students' intelligence, which has been schooled in  observation and measurement, is turned to areas requmng mathematical thought. The principle  of taking experiments as the point of departure,  should, however, remain as in earlier classes.


Electricity

* The history of electricity
* Optional: electrostatics (revision) 
* Concept of the electrical field
* Capacitors
* Van de Graaf generators (as examples for electrostatics)
* Current induced magnetic fields 
* Faraday's motor principle
* Revision work on the concept of potential  difference, charge, current, resistance but on a  more general level
* Connection between potential difference, current, resistance, force
* Warming effect of a current
* Conduction rules in various materials
* Induction: Inductive resistance, Lenzes rule, Lorenz force,
* Eddy current breaking effect 
* Superconductivity
* Energy as calculation standard (extension of  the energy laws from Class 10)
* Induction due to reciprocally acting currents;  polarity of the electric and magnetic field
* Change in time of current and potential  difference of a charging and discharging  capacitor
* Capacitor rules, units, calculation of capacity, dielectrics
* Oscillatory discharge 
* Current (quantitative)
* Potential difference and current diagrams for  damped electrical oscillations
* Phase in electrical oscillations
* Undamped electrical oscillations, synthesiser 
* Length of vibration and frequency; Thomson's  wave formulae


Signal generator, boundaries of  audibility

* Transmitters and receivers; to which belong  resonance, triodes, electron tubes (cathode ray tube), emission spectra (continuous, hot  wire spectra); development of the concept of  the electron as well as Millikan's investigations,  transistors
* Transmission dipole, dipole laws, electromagnetic vibration fields, electromagnetic wave-lengths
* The history of transmission
* Radio broadcasting, applied radio building  possibly


Atomic physics

* High tension spark inductors; gas emission  (emission tubes)
* Cathode rays, x-rays (details of subatomic  particle of moving positive and negative  charge carriers - ions, electrons) and their  counterparts in alpha, beta and gamma rays,  oscilloscope
Radioactivity, natural    occurrences of radioactivity, radioactive fallout; fission,  nuclear reactors, man made radioactive  isotopes, means of detection; (Geiger-Muller-  tubes, cloud chambers)
* History of the technological development of  the atom bomb (dangers, protection from  radiation)
* Atomic fusion
* Optional: semiconductors, diodes, transistors  (see Chapter 27, Technology).


Class 12

By now the maturity is reached which permits the  young person awareness of how he or she acquires  concepts. Now theoretical scientific questions can  properly be addressed; for example the significance  of the physical model of inductive and deductive  thinking etc. Thereby one attempts to develop  not blind belief in science but rather a personal  capacity for judgement. This can be a decisive aid  to the development of the personality. This can be  done in optics - if not already done in Class 11 - or  in the development of the atomic model. Besides  conveying important basic knowledge a survey  of the phenomena and ideas which characterise  modern scientific knowledge should be given.

The various ways in which light meets matter  can determine the approach to teaching.

The domain of optics can be used to show:

* Phenomena starting from their surroundings 
* Analytical thinking in the domain of a complete  manner of observation
* A symptomatic approach
* A discussion of points of view - development  of judgement
* Building bridges between optics, man and art 
* Cross curricular teaching is especially worth-  while here


Optics

(see list in Class 8)
* Aspects of geometrical optics
* Concept of shadow, umbral, penumbral 
* Brightness
* The concept of contrast and its significance for  vision
* Comparison: eyes - photo cells; qualities,  quantities, objectivity also in the domain of  qualitative investigation
* After images and coloured shadows (successive  contrast, simultaneous contrast) and their  physiological basis
* The human eye and equivalent technical  apparatus (e.g. lenses, aperture in a camera);  short- and long-sightedness, spectacles
* The Weber-Fechner law (properties of optical  stimulation and perception, geometric and  arithmetical consequences)
* Sense perception and consciousness, sensory  deception
* Goethe's theory of colour (prismatic colours);  colour qualities
* The polarity between the green and red  spectrum, its counterpart in plant and the  human being
* Optional: Chlorophyll, haemoglobin: chemical  structure
* The basic phenomena of chromatography  according to Goethe; the Goethean method  in science. Polarity of light and darkness  according to Goethe and its significance for  the creation of colours through darkening  (Rayleigh scattering)
* Additive and subtractive colour mixing (use of  technology) - difference in brightness
* Spectral and physical colours
* Plane mirrors
* Convex and concave mirrors
* Mirror laws: mirror plane (technical application) 
* Microscope - electron microscope (resolution capacity)
* Refraction, total internal reflection (laws)  (critical angle), Newton's basic experiment  with prisms
* Diffraction (point light, laser; laser light -  sunlight)
* Wavelength of light, spectroscope, spectrometer
* Polarisation - double refraction (technical  application in tension/compression optics),  asymmetrical structure of space - concept of  isotropy
* Atmospheric colour occurrences in nature and  their causes through diffraction, interference,  refraction, polarisation
* The rainbow and its cause; perhaps indications about the golden section applied to the rainbow 
* Photo-electric effect (technical application)
* Electron volt, Plancke's quantum effect
* Wave-particle duality and its significance for  the consciousness of physics in the twentieth  century (the development of models in  science); regarding the methodology in dealing  with borders of physics; making hypotheses
* The three models of light: wave, particle, ray,  their significance and evidence for them
* Theory of relativity, quantum theory
* Biographies of significant researchers of the  twentieth century (e.g. Einstein, Planck, Hahn,  Schroedinger, Bohr, Heisenberg)

The pupils learn here by example to know about  modern consciousness questions and the problem  of science and ethics

* Mathematicisation of physics and fallibility law 
* Formula structures, energy equivalence of  mass; light and matter
Optional:
* Line spectra in emission and absorption,  spectral analysis, meaning of spectral lines 
* The measurement of potential difference  by means of a photoelectric cell and the  sequence of wavelengths
* Millikan's experiments (if not in Class 11 in  connection with the electron), Rutherford's  ray experiment, wave-particle dualism in  matter.

In optics the following are taken up: 
* Colour generation using prisms
* Lenses, focal points
* Virtual and real images
* The means of collection sunlight using a  magnifying lens or concave mirror
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