“Begin at the Beginning…”
The primary child lives in the world of the here and now. This is a world bound by untrained senses and lacking symbolic, quantified, theoretical explanations. It is a stream of continuous events, of frequently surprising changes. Some of which are purely physical but most of which, and the most important of which, are driven by living, conscious entities. This primary world contains a multitude of objects who’s functions and parts are unknown, often sensed but not perceived, and for which the child has no names, no language. It is a world in which discreet Entities, i.e., objects and creatures, dominate the child’s experience, while the Energies flowing from, through and around these entities, like the component parts of a complex object, have yet to be recognized in and of themselves. The primary world is macro in scale, that is, existing above the molecular level and within the local horizon, be that horizon a classroom’s walls or a view of the ocean.
The adult operates in a world of mathematical imagination, a place built of theories based upon prior theories and tested experimentally in decades long, billion dollar projects. To explain and teach these theories the adult conjures conditions, forces and entities that simply cannot manifest in the child’s concrete, sensory, macro-world. The adult develops postulates, gedanken (thought) experiments and, importantly, symbols both spoken and written, that cannot have meaning in the primary experience: ideal gasses, frictionless surfaces, perfectly isolated perfectly conserving systems, fields that extend to infinity, space that expands in and of itself, invisible particles and forces that can only be explained by more and as yet undiscovered invisible particles and forces. Regardless of how questionable or demonstrable these aspects of reality may turn out to be, the child does not live in that world, cannot understand its language, mathematics and models, and lacks the physical experiences prerequisite for such feats of imagination.
Theoretically, in the physical sciences, the adult attempts to isolate material reality from what is arguably the child’s dominant real experience. Most adult theories eliminate all consideration of Consciousness as an identifiable, measurable, causal agent, requiring integrated explanation every bit as much as does Gravity. The adult physicist can postulate a prosthesis that is directly connected and responsive to a human nervous system, but does not admit the conscious intention that drives the prosthesis. Yet, in the end, the adult is trapped by theory into admitting that the conscious observer inevitably plays a deterministic role in that which is observed through the very act of observation. Or, at least, so implies the collapse of the wave function.
As an extension the adult also employs a type of reductionism which disregards the child’s evident conscious experience. This takes the form of asserting, for instance, that Sound and Heat can in theory be reduced to molecular motion. This has no meaning in the child’s primary macro world where there are no molecules. Sound can only be heard, felt and seen as vibration on a macro level.
Adults have a comfortably assumed awareness of the existence of the real physical world beyond the senses: the micro, extrasensory and cosmological realms. Adults have myriad tools with which to perceive and manipulate that greater world: ultrasound, thermal imagery, magnetic levitation, optical data transmission, electron microscopes, orbiting multi spectral telescopes, to name a few. The primary child can and should become aware of this wider world as part of primary sensory education, but can only do so if the properly scaled means are provided. See A Child’s Extrasensory Experience.
In traditional education, adults tend to teach children about the physical world from their own adult point of view and hence do not begin presenting physical science in any organized fashion until a certain amount of mathematical understanding is in place. However, in the history of science, quantified theoretical explanation always followed upon physical discovery and exploration, which in turn refines theory and leads to prediction of further physical discovery. Traditional science education waits until after various sensitive periods in the child’s early development have been missed, sensitivities to language, small objects, moving parts, geometric and causal relationships, and then presents demonstrations of fundamental physical realities in ways that cast the student in the role of passive observer of demonstrations and imaginary images, rather than as an independent actor in a realm of well designed primary physical tools.
The Montessori Method is an exception to this ingrained math before physical experience method of education. The Montessori approach is clearly expressed in the Sensory and Mathematics materials which are exemplified by the Binomial Cube. The object and qualitative language are given first and when the child is most interested. The math, the binomial theorem, is derived when the child is ready.
Methodologically, evident arch-typical examples of sensory, geometric and arithmetic realities are expressed in physical equipment that enables both independent, self-correcting process and impressionistic exploration. Experience precedes Language. Language precedes Concept. This approach can be readily extended to fundamental, energetic physical phenomena such as light and electricity.
How do we present the abstract world of adult physics in a primary world bound by micro and cosmological limits, the limits of the senses, and a lack of language and measurement?
- What basic ideas does the child need in order to organize physical phenomena in a non-mathematical, non-ideal, macro environment?
- What phenomena do we present?
- Which aspects of generally accepted theories can be concretely presented?
Choosing Ideas
There are many theories to be studied in the realm of physics. They are often opposed to one another, counter-intuitive and, in some cases, substantially unproven. While we have a great deal of engineering prowess, we have limited fundamental certainty. At the primary macro level all theories are nonexistent . A prepared primary environment should present physical experiences expressing the component ideas the child will need to later construct abstract quantifying concepts along with the basic physical realities theory is intended to explain.
Organizationally, from the teacher’s point of view, these ideas can be thought of as being based in a series of dualities. In fact, duality itself, along with merging of apparent duality into continuum, are two of the eventual theoretical concepts. Newtonian space and time, for example, become relativistic space-time.
The most basic of these are:
- Time — Space
- Event — Entity
- Quantity — Measurement
- Energy — Matter
Time and space and Quantity and Measurement can be realized in the classroom through presentation of the basic and derived units that are counted and compared throughout the educational process. These include the base units seconds, meters, mass and charge and derived units such as speed, acceleration and force. They are capable of concrete macro presentation. They can be combination into qualitative three part equations which, like the Binomial Cube, use macro physical experience as the basis of abstract ideas. Primary equations describing relationships between Matter and Energy can be given physical manifestation on a macro level in the same way geometric solids manifest relationships between the parts of single solids and between combinations of solids. See The SI Units, Finalized 2019 and
A Child’s Equations.
Base and derived units are, for the adult, formally defined and experimentally realized on the micro level. They also can be given physical, qualitative content at the primary macro level, which can then be used to present the act of quantifying. It is important, in teaching at the primary level, to differentiate between quantifying and measuring.
To quantify is tosee a device react to an event or a substance and to recognize a relationship between numbers and physical aspects. This can be accomplished not only by simple counting but also by the use of devices that do the counting, that associate numbers with particular types of entities and energies. The child does not need to understand the specific units involved. For example, the child does not need to understand the gravitational constant to derive meaning from standing on a scale. For the child, there is a word, “pounds”. It means how much weight, how much mass she has and a scale associates that with a number. What such devices quantify can also frequently be expressed in direct physical exercises that identify, match and order. For instance, in the Montessori equipment set what a scale does is also expressed in a concrete, sensory experience called the Thermic bottles in which the child discriminates differences in temperature by feel.
The abstract idea and definition of units of matter and energy derives from the prior use of objects, devices and language. This is true of many things countable on the macro level: the intensity of light, the volume of sound, the voltage of a battery, an amount of heat. The primary child is as capable of the physical act of using a decibel meter, a volt meter or a thermometer as she is of standing on a scale.
To measure is to count some aspect of an entity or event and compare that number to a to a second selected entity which has been divided and numbered, or when counting events points to or displays numbers in steady succession and finally, which is defined and agreed upon as the standard. In other words, we use meter sticks, clocks, scales and sensors to associate numbers with specific samples physical aspects and events. This can be for time and space, and matter and energy. In simplest form the child uses a measuring device, say a light meter, to recognize different numerical results for different physical conditions. The light at a window is different from the light in a cabinet. The child does not need to know the definition of the unit named “Lux” to understand that actual intensities or amounts of Light are being identified, counted and compared, any more than one needs a formal definition of meter to grasp that the ten rod is ten one rods long.
The Montessori primary curriculum is particularly strong in the presentation of matter and entities, presenting solid geometries and, notably, discovered geometries in the life and earth sciences with equipment like the botany cabinet and land and water forms. But while shelf work exercises are always dynamic in the sense of involving the child’s independent action, the materials themselves are largely static, generating few changes or dynamic instances of different types of Energy during or at the end of a process. One exception is the Practical Life pouring exercises which, because they deal with the liquid state of matter, involve Motion inherent in the material beyond the child’s own action, which is the reason water exercises and water play are so interesting, so much fun. You do something and then something else happens.
Greater use of events counting, spatial geometry, and states of matter and energy are what is being suggested here. Most importantly, and the key idea of A Child’s Physics is the child’s recognition and awareness of the idea that Energy exists and can be manipulated and described. A key component of this understanding is the concrete transformation of energy from one type to another, which is described below. It is further possible on the primary macro level to approach the idea of converting matter and energy into one another, recognizing the limitation that this can only be presented in an open, non-conserving system. Energy is converted to matter, for instance, through photosynthesis. Matter can be perceptibly converted to energy through combustion, which can be presented through the heat of collision without the use of an open flame.
The central idea is that,
Energy exists and can be transformed.
The child experiences Energy in eight forms on the macro level. Each of these forms the basis for a section of a curriculum offering derivative ideas expressed in concrete equipment, exercises and language. The importance of a central unifying idea is that without it, primary science devolves into a series of disjointed, unrelated “experiments”, often chosen and designed more for entertainment value than for educational value.
A topic map organizes a primary energy curriculum from the child’s point of view. This is not intended to be a model of the physical world. It is a model of the child’s experience of the physical world. Consciousness is inclusive and light, sound and motion impinge most directly on the child’s consciousness. Electricity and Magnetism are the least obvious, being beyond direct sensory perception and also concealed by design. The wires that literally surround us with electromagnetic cages are inside the walls. At the same time, electricity and magnetism are technologically, and therefore culturally, central.
To move beyond presentation of static Matter and into the presentation of Energy, of dynamic effects and changes, requires event counting. To teach event counting means to formally present the literal action of clocks, which is that a clock counts some regular repeating event internal to its own mechanism, while something else happens and is also counted. This idea is emphasized by using different clock designs: dripping water and sand clocks, pendulums, counting mechanisms with visible movements, rhythmic events such as practiced clapping and metronomes, both mechanical and digital. The skill and idea of counting events is critically different from and in addition to the pragmatic skill of “telling time”, which means reading clocks in order to organize the events of the day. Counting events will be the concrete referent when the student eventually learns the international unit of clock time which now is, quite literally, oscillations of the hyper-fine ground state frequency of the element Cesium133.
A clock counts a regular, repeating event internal to its own mechanism, and that is all a clock does.
Dynamic phenomena will also eventually require 1)spatial geometry, which here refers to presenting empty wire frame shapes, 2)counting enclosed spaces on three axes and, 3) adding three additional solid shapes which curve through open space. Counting all three axes is well within the primary child’s abilities. There is a developmental period in which counting events and multiple dimensions is as natural a process as is counting bead chains. Counting three dimensions is easily accomplished with in the Montessori method by adding a numbered grid to the Number Rods, placing a rod vertically on a point in the grid and then counting to the base of the rod twice and the top of the rod once, thereby designating and naming that point in space, say, the point 3,3,3. Presenting a wire-frame construction sets, which can be made from plastic straws and pipe cleaners as joints, delineating and operating within them, provides a physical reference for the subsequent abstraction of an ideally isolated system, which will be integral to the thermodynamic principle of conservation of matter and energy.
In addition to empty, enclosed spaces certain solid but dimensionally complex curved shapes should be added to the primary geometric shape set because of the connection between these shapes and because of the actual physical behavior and manipulation of different energies. These shapes are the sine wave, the parabolic bowl and the coil.
Longitudinal wave shape, simplified as a sine wave, is clearly pertinent in the experience of the liquid state of matter and also provides a basic description of AC electrical and sound energies, though special care must be taken with sound as it is a compression wave in gas and a sine represents only a cross-sectional description. The sine wave already appears in one of the drawing exercises bound by the circular metal inset. That would be free hand drawing an unbroken curve from side to side within the circular frame. A set of solid sine waves with varying amplitudes and frequencies can be used to show the difference between amplitude and wavelength.
The parabola is important for its ability to reflect, focus and aim light, heat, sound and motion.
In the macro world it is the shape of lenses, mirrors, collectors and antennae.
The coil is important for its ability to transmit, reflect and store mechanical energy, motion. A fine coiled spring, like a Slinky, is used to present compression waves. Coils move liquids, fasten machine parts, redirect and absorb forces. Coils are further critical to the introduction of Electricity to the macro level because of their role in the demonstration of the critical phenomenon, Induction. See also A Child’s Magnetism.
Choosing Phenomena
Matter
Primary consideration of matter should be extended to include the forth state, plasma, and a formal presentation of the Elements. Presentation of states of matter should in general receive greater attention with regard to liquids and gases, particularly as they respond to heat and electricity and the fact that water in conduits provides a useful macro analogue of electricity in wires, which in itself is a micro phenomenon. The forth state, plasma, should be presented because it is common in the real world. But even more so because its ability to conduct electrical current makes it easy to present in its own right in a plasma ball. A plasma ball provides the means of presenting interactive, flowing electricity at the macro level. See A Child’s Electricity.
The Elements should be formalized in the primary classroom as they are the lower macro limit of the experience of matter. The molecular level cannot be presented in a concrete, sensory manner. Chemical reaction can be a macro experience but single atoms and individual molecules are not. Although, simple electrolysis does present a vivid case of comparative bubble size between Hydrogen and Oxygen, which can later be explained by the relative size of the molecules, still molecules themselves are not perceptible.
In general, we can direct the child toward the existence of the micro scale through the use of magnification to reveal details too small to see with the naked eye, but even that is still a macro experience of which the Elements present the boundary. One very effective example is to present melting snow under digital magnification.
A sufficient number of elements can be easily and economically provided, enough to present mechanical, electromagnetic and chemical properties and to provide a concrete, sensory basis for their vocabulary and the fundamental organizing image, the Period Table. They also serve to present and inform natural world phenomena in the form of ores, which deserve a place next to classroom collections of stones, bones and shells. Examples of readily available elements include iron, copper, zinc, aluminum, tin, nickle, hydrogen, helium, oxygen, neon, carbon and silicon, to name a few. Presentation can be then extended to the idea of combinations, i.e., alloys and compounds such as steel and water. See A Child’s Elements.
Energy
A Child’s Physics enhances the Montessori primary curriculum by addressing Energy in a meaningful and complimentary way, applying the methodology and design principles of the primary equipment set.
This addition to the equipment and curriculum is historically appropriate given the technological period in which the method was originally formulated and the technological culture in which the child now lives.
The primary child routinely experiences and interacts with energy in eight forms on the macro level: electricity, magnetism, light, sound, motion, heat, chemical reaction and consciousness. These are energy in its macro forms which, in accepted micro and cosmological theory, are reduced to idealized states, Classical and Standard Model particles and forces, and other theoretical combinations of quantum, gravitational and electromagnetic models which the child will eventually be challenged to learn.
The primary child routinely experiences and interacts with energy in eight forms on the macro level: electricity, magnetism, light, sound, motion, heat, chemical reaction and consciousness.
Energy in these eight macro forms, along with materials science and life science, are experiences at the root of the individual’s subsequent educational and career paths in a world where real engineering, environmental and socioeconomic problems are solved. While these eight types of energy are irreducible to their molecular level in a primary classroom, they can be easily and economically presented and manipulated in macro forms.
It is possible to present work which shows that electricity can be transformed into each of the other energies and each of the others can be transformed into electricity. This is a fundamental organizing principle which can be used to understand simple situations and complex processes.
Devices that perform energy transformation are called transducers. At this point in technological development, transducers exist which can be scaled to bring all of the basic transformations into the primary classroom.
Electricity can be transformed into each of the other energies and each of the others can be transformed into electricity.
Schematically these relationships can be visualized in this way,
It is also the case that through combinations or sequences of transducers any one of the energies could be placed at the center of the scheme and be transformed into each of the others, for example, chemical reaction becomes motion through a jet engine. Consciousness becomes language which becomes electrical signals which become patterns of light on a remote screen which become thoughts in a second consciousness.
It is further true that transformations can take the form of either a direct power transformation as when a turbine generates electricity, or of a control transformation as when a motion sensor generates an electrical signal which switches on a light.
Transformations can occur within a single type of energy, as when a cell phone charger converts 120v AC to 12v DC.
Here is a list of the basic direct energy transformations and some readily available, classroom appropriate, macro scale transducers:
- Electricity >< Magnetism
eddy current tubes, induction coils, electromagnets, motor/generators - Electricity >< Motion
piezoelectric cell/led, triboluminescent quartz, motor/generators - Electricity >< Light,
solar cell/ led, flash light/photoresistor - Electricity >< Heat
Peltier module - Electricity >< Sound
microphone/piezo buzzer - Electricity >< Chemical Reaction
electrolyzer, fuel cell, - Electricity >< Consciousness
binary code, bio feedback, remote control, prosthetic implant
The practical medium for the presentation of these electrical transformations is a simple circuit building set. The most accessible set of which I am aware is a set built on the action of snapping clearly constructed components into place on a plastic circuit board, which is literally an application of a Montessori Practical Life skill. The basic transformation circuits are appropriate for a primary classroom. The kit is a tool that can grow with the child and expand through years of increasing complexity. It is also important that a commercial set be echoed in an informal set consisting of the sort of real world materials that might be found in a maker space.
A word about Consciousness
In A Child’s Physics, Consciousness is recognized as a physically extant, directly perceptible, causal agent. While Electricity is pragmatically central to technology, Consciousness is qualitatively inclusive, the alpha and omega, to borrow a phrase.
Consciousness plays a direct and ubiquitous role in the child’s experience.
Consciousness has direct and sequential transformations with Electricity.
Consciousness can imbue all the other forms of energy with intention and be directly causal through deliberate energy transformation, for instance, the use of a hand tool, biofeedback or any form of remote control.
Consciousness can imbue other energies with meaning through any type of coding or language, expressed materially or digitally.
Above, in Choosing Ideas, it was mentioned that for the teacher’s use an organization of curriculum can be conceptualized through a number of dualities. In the presentation of energy, derivative dualities appear and can inform and be expressed in primary equipment design and discussion.
- particle/wave, concerning matter
- potential/kinetic, concerning energy
- collision/field effect, in physical interactions
- amplitude/frequency, in radiation and sound, wave forms in general
- positive/negative, in electrical charge and current,
- north/south, in magnetic field orientation
- hot/cold, in heat flow
- acid/base, in chemical reaction
Reducing theories to the macro level
There is no absolute list of correct choices concerning what to distill from the complexities of adult science. We are bound, on the one hand, by our own resources and on the other by the macro, non-ideal, pre-theoretical world of the child. The goal is to prepare the child to address the phenomena, language and mathematics basic to the theories he or she will inevitably encounter during the rest of the educational track and which will eventually be needed to understand and thrive in a technologically complex culture. What we can do here is summarize generally accepted theories qualitatively, and select the primary phenomena from which they were developed.
Newtonian Mechanics
The First Law is the law of inertia. Objects in uniform motion stay in that motion and direction unless a force is applied. This is an idealized condition. There is no way to present or observe a moving object perfectly free of forces. In the macro world just the opposite is true. For the child, all objects come to rest. And so the approach is to illustrate what transformations occur that either drive or reduce an object’s motion. These are collision, which includes friction, field effects, heat and chemical reactions. Experience of these builds to the observation that opposed forces tend to directly absorb and/or scatter an object’s motion and energy. This general spreading of energy will always tend to bring a real world system of objects to rest. Another basic observation is that real energy transformations always include unintended transformations. A specific goal might be to to produce motion and the actual result will also produce noise and heat. A fundamental real design challenge is always energy efficiency, how to reduce losses due to unwanted energy transformations. The primary step is to become aware that this is happening.
The Second Law, is the classic notion that force equals mass times acceleration, F = m x a. This actually is an elementary level equation because, as an equation, acceleration contains a squaring of time which has no physical referent, unlike squaring length. However, the qualitative meaning of acceleration can be experience either by pushing or being pushed especially when already moving, for instance, on a swing or a merry-go-round. Combining distance, time and additional energy like a direct push gives qualitative, physical meaning to both Speed and Acceleration. Varying the amount of mass as an actual physical experience gives meaning to Force. Collisions and field effects, along with variation of mass, create palpable differences in speed and direction. Marbles and billiards provide excellent experiences.
The Third Law is that every action has an equal and opposite reaction. This is not obvious in ordinary macro experience. It can, however, be demonstrated through controlled collisions between rigid balls and between balls and fixed plane barriers. Newton’s cradle is an excellent demonstration and particularly useful as a silence exercise on circle. For that matter, observing any change returning to equilibrium is a good silence exercise; Euler’s Disk spinning or a ball orbiting in a large shallow bowl are examples.
Equal and opposite is a consideration of the combination of mass and motion. Head on collisions make equal and opposite most clear and oblique collisions make acceleration and scattering most apparent. Reflection off a wall is especially useful when discussing angles and also the motion of light. Vertical bouncing is useful concerning the idea that in the real world energy always dissipates due to opposed forces. Collision in general is an important concept in programming, and also a basic experimental technique of particle physics.
A major consideration in mechanics not often approached at the primary level is that of Fluidics, the motion of liquids in conduits and of currents in fluids. Liquids are capable of physical and logical circuit constructions just as is electricity. These are especially useful in demonstrating Thermodynamics.
Thermodynamics
The First Law is that in an ideal isolated system energy, and thus matter, can neither be created or destroyed.
The Second Law is that the entropy, or disorder, of any ideal isolated system always increases. In other words, energy seeks its own level, like water.
The macro level presents no ideal isolated systems. However, both laws can be approached by observing the concrete intermediate state. That state is the inevitable return of energy to macro equilibrium. In any real system any energy invested, be it mechanical, thermal or electrical, does not disappear but scatters and transforms into smaller and smaller amounts until the objects in the local area are at apparent rest or, in terms of easily measured heat, all at approximately the same environmental temperature. A correlation is that heat always flows from hot toward the cold. And a system will remain at equilibrium until additional energy is invested. Anything not at equilibrium , like a refrigerator or a wound spring, must be using or storing energy. This can also be demonstrated with a Peltier module. As long as it is connected to a battery, one side will be warm and the other cold. Disconnect and both sides will return to their equilibrium temperature. The idea o equilibrium can be realized in the primary classroom by using an infrared thermometer to examine everything. The primary sensory enhancement of a thermometer enables quantification before actual measurement by the assigning comparative numbers to thermal energy states even before a unit definition is understood and the realization that everything in a certain area tends to show the same temperature number. It fascinating to the child that her own body temperature will never be at local environmental equilibrium because it is constantly processing energy.
This idea of equilibrium sets up the further idea of contained or potential energy. Some tools, like leyden jars or springs, can save energy that can be released later. In other words, such devices delay the return equilibrium. Saving energy by winding a spring or lifting water to an elevated reservoir is a concrete experience. The child feels the transfer of energy through her own action. Whereas simply asserting that an object not moving on a surface has “potential” energy has no real meaning at all. Literally nothing has or is happening. The potential side of the potential/kinetic duality only has meaning if the energy is physically invested by the child and stored in place by a perceptible mechanism.
The Third Law is that the entropy of a closed system approaches a constant value as the temperature in Kelvins approaches absolute zero.
This law depends on an ideal consideration and SI base units, physical referents that only exist on the micro level: the kelvin, plank’s constant, the speed of light and ΔvCs. See The Finalized SI Units, 2019 . There is no meaningful macro approach to the third law.
Thermodynamics is approached in general by working with the energy of Heat in its movement through conduction, convection and radiation, through quantification/measurement, through the saving of generated energy and through transduction into and from other forms of energy.
Chemistry
Principles of Chemistry depend heavily upon Thermodynamics and those macro limitations. Key to abstract chemistry are idealized gas laws and ideas concerning substance, more specifically the physical amount of substance involved in any reaction. These in turn depend the SI micro referents of a mole, which is a fixed number of elementary particles, and the Boltzmann constant, which relates the base unit for temperature in Kelvins, to the contained energy of an isolated system in in the derived unit, Joules.
Clearly this is all beyond the primary level. However, chemical reactions can be presented in simple examples such as vinegar and baking soda. Fluids can be shown to be electrolytes. Substances can be examined and classified according to Ph with simple test strips. Substances can also be classified as electrolytes or dielectrics using a simple electrolysis circuit. Changes in substances can be differentiated in terms of a reactions vs physical mixtures by filter, centrifugal and magnetic separation. Simple acts of combing and separating are well within the primary child’s abilities. Gas laws can be qualitatively introduced by varying the temperature of a balloon and observing changes in volume and pressure, giving physical meaning to these terms.
Electromagnetism, Maxwell’s Equations
James C. Maxwell’s equations are 20 mathematically dense equations that formalized electromagnetism, establishing the existence and meaning of electric Charge, recognizing Light as a form of electromagnetic radiation and showing that is has a finite, fixed maximum speed. The mathematics was later simplified into four basic laws by one Oliver Heaviside and these laws became associated with subsequent theorists and now carry their names as well.
These equations form the basis of modern electrical and electronic engineering. They can be realized at the primary macro level by presenting the basic electrical phenomena they quantify. These are qualitative interpretations.
1. Gauss’s Law is a micro scale consideration quantifying the sum effect elementary charges in an object or volume; which charges are mono-poles and necessarily either positive or negative. The macro approach is that a net charge on an object creates an electric field effect which can be either positive or negative. Like charges repel, opposite charges attract. This is realized in a primary classroom by presenting a tool, such as a PVC tube, that can be charged negatively at will, and used to demonstrate electromotive force of a field and its polarity.
2. Gauss’s Law for Magnetism. This is a micro concept stating that there are no magnetic charges analogous to a mono-polar electric charge. A magnet and its field is always a dipole having both a positive and a negative pole. This realized in the classroom by any number of exercises involving both permanent and electromagnets.
3. Maxwell-Faraday Law of Induction. This law relates motion, magnetic fields, conducting materials and electric current. It states that a moving magnetic field will induce an electric current(s) in a conductive material. Induction is a discovery on the level of the Lever and Fire in terms of human significance. It belongs on the primary level.
4. Ampere-Maxwell Law. This states that magnetic field can be induced in a conductor either by an electric current or by a changing electrical field.
Both 3 and 4 are realized by simple combinations of conductive coils, spinning permanent magnets, and electromagnets both stationary and moving. Simple motors provide physical examples of various configurations of magnetic fields, conducting materials, current and motion. The basic transformation is to show the reversibility of a motor-generator pair.
The introduction of charge, current and fields both electric and magnetic represents a profound change in the primary environment. Electromagnetism is an ubiquitous factor in the child’s real experience and key to any future scientific education. It is predominantly, structurally concealed due to standard commercial power levels, but can easily be scaled to perfectly acceptable primary physical experiences.
Quantum Mechanics, The Standard Model
Despite its predictive prowess, the Standard Model of particle physics with its 12 particles, Four Forces, plus the Higgs Field and Boson, plus a like number of anti-particles, not to mention speculations like Dark Matter and Energy, and the lack of an explanation of Gravity, the model is an intimidating presence lurking in the student’s future. While certain epistemological components can be approached, namely, the ideas of particle, wave and field, mass, charge and spin, all of model’s particles are exclusively micro in scale and not all of them have been shown to exist. Of its four forces, the strong and weak nuclear forces, gravity and electromagnetism, only the last can serve as a bridge to the primary macro world and as physical preparation for these complex theoretical abstractions. Electromagnetism can, in fact, be realized through macro scale presentation of the energies of light, electricity and magnetism.
Relativity
There is little direct preparation that can be done for the counter intuitive nature of relativity. However, the natures of Light, here referring to the entire spectrum, and Time are central to the theory. So familiarity with light as a dynamic reality having certain characteristics related to motion, particles and waves that can be experienced directly and be manipulated will later be of great use. The idea that there is something special about Light in terms of the energy of Motion can be indicated early on by establishing that, even though the motion of light cannot be perceived, light does move or propagate through space and also through various materials at slower speeds. In general, a natural, comfortable awareness of electromagnetic radiation will be a great advantage later in any scientific educational track. See A Child’s Light.
Likewise, a solid recognition of time as a method of counting and comparing, rather than some fixed substance or dimension, will make the more esoteric results of relativistic theory easier to accept. A classic one dimensional, homogeneous, directional idea of time is not the child’s real psychological experience and is a model that is unnecessary at the primary level and will only have to be unlearned.
An equal familiarity concerning the energy of Motion, both linear and angular, and how two examples of objects in motion can interact and have their motions combined will, along with wire frame experience, eventually be very helpful when lessons turn to the consideration of different frames of reference.
Gravity
Gravity is perhaps the foremost example of extensive engineering capacity paired with a lack of fundamental explanation. We can use gravity to sling probes accurately through the Solar System, but we don’t know what it is. It appears but is unexplained in the Standard Model. Since Newton’s Law of Universal Gravitation, we have had extensive knowledge of gravity’s effects, but Newton expressly left it to the reader to explain its origin and nature. Gravity is regarded as universally possessed by all matter, including hypothesized dark matter, and as being an infinitely extensive field force. It is regarded as causally formative with regard to the shape of space-time and the motion of all matter and radiation. Gravity is cosmological in scale and yet by comparison to the other forces, extremely weak. A small magnet on the surface of the earth can completely counter the force of the entire planet’s gravity. Gravity is indivisible. That is, while matter can be divided and the concomitant gravitational forces diminished, gravity itself cannot be isolated and manipulated.
At the same time, on the surface of the planet gravity is ubiquitous. It is invisible by dint of being pervasive in such a way that the gravity of the planet overwhelms the gravity of macro scale objects. We cannot present the gravitational effect of objects on each other within the overall gravitational field. Two balls dropped cannot detectably attract each other before they hit the ground.
It is also the case that we have no direct sense perception of gravity. We do have proprioception, which the sense of our own bodies, our own weight, our own motion, forces that we intentionally apply, and our orientation within forces such as gravity, high winds, centripetal forces. But this perception is of our own bodies, not the forces themselves. We have no ability to directly discriminate any particular type of force. The child does not feel gravity. The child feels motion. The child feels falling down.
The result of these factors is that gravity cannot be directly presented at the macro level. It can be named and given as the reason all things do fall down, but beyond that the words have little meaning. We cannot present it or do anything with it. There is no spoonful of gravity. In the same sense, we can say “the speed of light” but the words have no content. We have to show aspects of light’s motion, like reflection or wave interference. We can show aspects of gravity’s effect, like water seeking its own level, but all we actually perceive is the motion of the water.
So, Gravity cannot be isolated and presented as a type of energy in and of itself. It can be approached through the energy of Motion, through the simple observable universal limit of motion which is that what goes up will come down. We can also work with motion occurring within manageable fields, for example, bending a stream of water with a static electrical field or bending the path of a rolling steel ball with a magnetic field. We would then have some real physical meaning for the words force field. Gravity could then be described as a type of field. Care must be taken, however, as gravity has no charge. So it is unlike an electrical field. And gravity has no poles, so it is unlike a magnetic field. This makes the Earth somewhat complicated as it has both gravity and a magnetic field.
Gravity can also be approached through the idea of orbit. Keeping a ball orbiting in a bowl, either round or elliptical, is a good manual exercise, gives meaning to the words and gives a physical referent for later descriptions of gravity as a well, or a shape in and of space.
The Cosmological Level
The Montessori Curriculum presents the cosmological level through the Great Lessons, the birthday ceremony, and the land and water forms as models, along with extensive map work, i.e., models and images of what might be seen from very high up. Artistic representations of other planets and the Solar System are also acceptable. With preparation concerning motion, particularly on curved surfaces and within fields, Gravity can be described as a cosmological scale condition that keeps us on the Earth, the Moon moving around the Earth and all the planets moving around the Sun.
Presentation of the cosmological scale will be greatly enhanced when the community finally embraces the use of readily available, interactive, high definition imagery of the planet(s) and stars, imagery produced across the electromagnetic spectrum. The child’s understanding of such imagery will be greatly enhanced by experience with Motion and Light per se and with devices that indicate, measure and record the various forms of energy; devices such as an infrared enabled camera.
A Recommendation concerning the use of Imagery
Fortunately, we have easy access to high definition imagery from beyond both boundaries of the macro world; images derived from sound, magnetism, deflection of electrons, and from a wide swath of the electromagnetic spectrum, imagery Maria Montessori did not have.
Particularly with regard to the Earth we have highly detailed, interactive imagery so that the use of imagery can be more than passive observation. We now can not only present a clay model of an isthmus, we can navigate to real views of any isthmus on the planet using simple gestures well within the primary child’s skills.
We can lead the child to the brink of the micro world with simple lenses and basic technology, like digital magnification, demonstrating that there are things to be seen that cannot be seen with the eye alone. But in the end, we still can only imply the molecular and atomic worlds.
We can also use imagery, along with physical demonstrations, to begin revealing the real world that lies beyond the senses. Consider side-by-side images of any given flower in infrared, visible and ultraviolet light, accompanied by information about which animals and insects can actually see which image. Or thermal imagery revealing the patterns of radiant heat energy, for instance, the thermal contours of the child’s own face. See A Child’s Light and A Child’s Extrasensory Experience.
Finally, images can be used as fundamental tools to organize information. The two examples that should be in every primary classroom are The Periodic Table and the Electromagnetic Spectrum. Not for the purpose of detail examination of all the information contained, but in order to fix those organizational schemes in their appearance, language, and physical expression.
A final word about Language.
One of the most important effects of A Child’s Physics is the acquisition of language, vocabulary not necessarily encountered outside of a prepared environment. There three aspects to this.
First, is to give physical meaning to basic terms not ordinarily encountered in every day life but critical to further scientific education. For instance, giving actual content to words like pressure, volume, temperature and gas by exploring a balloon under different conditions, say, right out of a freezer into a warm water bath. Or, Electricity is what you see in a plasma ball and can guide with your finger. “Voltage” is how hard electricity is pushed, “resistance” is how hard it is to push and “current” is how much gets pushed through a circuit. Or, a magnet has a “field” and it can move solids and liquids and cause electric currents.
Second is the awareness that some words involve or name things or aspects of things that can be given numbers. For instance, how much you weigh is named pounds. How strongly a battery pushes is called voltage. How hot or cold is called temperature and changes of temperature are named degrees.
Third, and perhaps most important, is that as a common vocabulary becomes established, the entities, energies and ideas enter into daily conversation. Fundamental energies, such as electricity, become as comfortably ordinary as water and sand.
