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.
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
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