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Stephen Speicher

Montessori - Order of materials

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I have heard some parents express that children exposed to material beyond their current level is setting them up for failure, and therefore bad. Personally I think that we should support and encourage such interests. My concern here is in not treating a hierarchy as if it were an out-of-context absolute. I know that Montessori materials are usually presented to a child at a stage of development appropriate for the material. But what if a child takes an interest in material that is not generally considered to be at the level of the child?.

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This is The Montessorian's reply to the question posed by Stephen Speicher.

What a good question! But  it's not clear to me what's meant by a topic which is 'beyond a child's "level".' The Montessori philosophy espouses that a teacher follow the interests of a child. If a child expresses curiosity about some subject, then that subject IS at the child's level. The child wants to know more about it. The teacher's concern then should be simply how to make that subject comprehensible to that child at his or her level.

I do not believe that there is anything about ANY topic which puts it out of the reach of ANY child at ANY age. An excellent teacher should be able to answer a question in such a way that it is tied to the conceptual level of that child.

Let me see if I can give you an example. Many people might consider it inappropriate to teach a young child about sex. And yet, it is common for preschool children to ask, "Where do babies come from?" The way to answer this question depends on the level of the child. A three year old can be told, "Babies grow inside their mothers' bodies." This answer may completely satisfy the young child's curiosity, and the discussion is then over.

If the child is 4 or 5, she might ask follow-up questions. A good teacher or parent does not volunteer information until the child asks questions. The questions help the teacher to gauge which concepts the child already has, in order to find an appropriate level of explanation. For instance, a child might ask, "How does the baby get out?" The answer can then depend on what the child knows. A general answer might be, "When a baby is ready to be born, it comes out of a special hole in the mother's body." Now, a six year old knows much more about human anatomy, so a six year old might then ask, "Where is the hole? Is it the hole where pee comes out or the hole where poop comes out?" A parent could then answer, "No, it's not either of those places. There is another place that mothers have that connects to the place inside the body where the baby is growing." A child might then be satisfied, and the discussion would be over.

A teenager, however, would have much more developed concepts about anatomy, and perhaps some ideas about sex, too. The parent or teacher would explore the teenager's context of knowledge before providing more specific information. It would be wise to consider, not only knowledge of anatomy, but the concepts the young person has formed about love, about relationships, about marriage, and many other related issues.

My point is this: "SEX" is a topic which many people consider inappropriate for children to learn about. Yet even this highly charged subject can be explained perfectly clearly to very young children, if their context of knowledge is taken into account. The only thing that would be inappropriate is to give a three year old a lecture about male and female anatomy, puberty, sexual technique, and birth control. But a good Montessori teacher - or any parent or any teacher who really knows how to teach - would never do that. Excellent teaching is more of a Socratic process which involves exploring what the child already knows and just what the child is curious about.

Is there any other reason why we might consider a topic inappropriate for a child? Some people might feel that some subjects are very abstract and complex and are best learned at particular ages. In fact, traditional curricula are usually based on this idea. For instance, let's look at the subject annoyingly named "Social Studies," which I suppose we would call simply History. In most public and private schools, the approach to teaching this subject is something like this. In third grade, we learn about our "community helpers," for instance, firemen and policemen. We learn that some people live in cities and other people live in the country. We learn that some people ride buses and other people ride cars. In fourth grade, having studied the concrete concept of our local community, we become a little more abstract, and study the history of our state. In fifth and sixth grade, we may study the history of our country, which is still more abstract, and so on.

The Montessori approach is quite different. Years of experimentation had shown Maria Montessori that young children are actually much more interested in the big picture than in the details of their local community. She found that six and seven year olds are very curious to know how there came to be human beings in the world. Responding to the child's curiosity, she developed a curriculum of Timeline Studies that takes 6-9 year old children through the entire history of life on Earth, starting from the time the Earth itself formed from clouds of dust, continuing through the millenia of volcanic eruptions, the formation of the atmosphere, and rain, and on to a simple explanation of how life came to be from chemicals floating in the seas. The Timeline of Life curriculum continues through the ages of evolution, and at each stage the child looks at organisms which evolved. To study the Proterozoic Era, the child uses a microscope to look at one-celled life which still exists today, grows cultures in petri dishes, performs experiments with plastic bags and water and solutions of iodine to see how diffusion occurs across cell membranes, and so on. In succession children may examine living specimens (and even dissect preserved specimens) of invertebrates, of amphibians, of reptiles, and of mammals. And finally the children will learn about advanced mammals such as primates, compare and contrast the anatomy and the behavior and the intelligence of monkeys, apes, and humans, and even learn about the development of early hominids such as Australopithecus, Homo Erectus, Neanderthal Man, and so on.

This curriculum is very concrete, in that at every stage the child sees real-life examples of each form of life. The child explores biology using all his senses. He has living animals in his classroom. He goes to zoos and aquariums. He may dissect specimens. He sees and feels and explores the similarities and differences among different types of animals and plants, so that it becomes almost perceptually obvious that amphibians have evolved from fish and reptiles from amphibians (especially after seeing films of mud-skipping lungfish, which are almost half-way between fish and amphibians.)

And yet this curriculum is very abstract. A traditional syllabus would never introduce the topic of evolution before high school biology class.

But when properly taught, the Timeline of Life is tied very concretely to the child's existing concepts about animals, and helps him to systematize these concepts and to integrate them into a broad and wide understanding of how one form of life is related to and has developed from another.

In my own school I have taken this Timeline Curriculum to another level. We follow a three-year cycle, so that when we reach the point at which the children understand where humans have come from and how humans are related to other animals, we keep going to study what happened next in the story of humans. We proceed to study the Timeline of Great Civilizations. In order, we consider civilizations such as Ancient Mesopotamia, Ancient Egypt, Classical Greece, and Rome. In the third year, we take up the Dark Ages, the Middle Ages, the Renaissance, the Enlightenment, and the Industrial Revolution.

As we study each of these ages, we learn simultaneously about Science, Art, Music, History, and Technology. When we study the Renaissance, for instance, we read certain sections of Shakespeare plays;  we learn about the life of Galileo; we experiment with pendulums as Galileo did, using water-clocks or our own pulses to time them, we experiment with concave and convex lenses to see how a telescope was first invented, and what Galileo saw when he looked at sunrise on the mountains of the Moon or at the moons of Jupiter; we learn to look at Renaissance art and we discuss the themes shown in works by Michelangelo or Leonardo da Vinci; we learn to portray distance in our own drawings and paintings by using the position on the page and the relative size of objects, atmospheric perspective, and finally vanishing points and lines meeting at the horizon; we dress up as men and women did in the Renaissance; we build a model of a dome like the one Brunelleschi built, and so on. All of these activities are very concrete. And yet the subject being studied is so abstract that most schools would not attempt to teach it before High School or College.

I want to point out that in our school, when we are studying the Renaissance, everyone in the school is studying it, whether they are in Kindergarten or in Eighth Grade. A Kindergartner might read a picture book about the life of Shakespeare and act out the scene from Macbeth in which witches circle the cauldron and chant, "Double, double, toil and trouble." A fifth grader might study idioms in modern English which come from Shakespeare. An eighth grader might attempt to write a sonnet or might read and act out scenes from Julius Caesar. But we would all be studying Shakespeare.

The same with the Galileo experiment. Children as young as 5 and 6 love to hear the story about Galileo and the pendulum. They learn that Galileo was studying to be a doctor, and so he had learned to take a patient's pulse.  But he didn't have any pocket watch: that hadn't been invented yet! He had to take a patient's pulse by comparing it to his own pulse. And then we would all feel our own pulses. We would feel them when we have been sitting quietly, and again when we have been exercising. And we would use our own pulses to see how many heartbeats it takes a pendulum to swing back and forth. And this young child would especially enjoy hearing how Galileo was so bored in church that he started to stare at that pendulum in the first place. Children always love to see the pictures I took years ago of the actual oil lamp hanging from the ceiling in the Cathedral at Pisa at which Galileo stared, wondering why it did not seem to slow down even as its motion became damped. (At least, the guide told me that was the oil lamp!)

But older children will be able to get much more from this experiment. They will graph the results. They will be able to perform controlled experiments in which they will vary the weight on the end of the pendulum, the length of the string, the height from which the pendulum is released, and other factors. They will explore the inverse square law algebraically.

So, if you were to ask me, is physics too abstract for a first grader, I would have to say, no, of course not. But one must teach to the child's context of knowledge.

I told you this story at such length because I think it illustrates perfectly the Objectivist idea of the spiral theory of knowledge. A seventh grader in my school might have studied the Renaissance twice before: once in first grade, and once in fourth grade. Yet each time we return to this subject, her knowledge becomes deeper, more specific, and yet also broader and more tied to all the other subjects in the universe.

You ask about the "hierarchy of concepts." I'm not sure just what you mean by that. First of all, I think we should beware of assuming that the conceptual hierarchy of concepts from concrete to abstract has anything to do with the order in which concepts are formed. The Objectivist theory of concepts certainly does not imply this. The sensory concepts "hard," and "brown," for instance, are much more concrete than the concept "table," and yet almost all children would form the concept "table" earlier than the concepts which name the sensory qualities of that table. "Table" is a good entry-level concept, but one can go in so many different directions from that entry level. One can go "up the hierarchy" to form the concept of "furniture," but one can also go "down the hierarchy" to form concepts of specific tables, such as kitchen tables or dining room tables, or to form concepts of parts of the table, such as the legs or the surface, or to form concepts of the material of which the table is made, such as formica or wood.

I think we need to be aware that knowledge is acquired in a spiral. Our knowledge of a concept becomes deeper, more detailed, and at the same time broader and more tied to other concepts, the more we study it. But for any concept, and for any age child, there is a place where that child can enter the spiral and begin to learn something about the concept which is relevant to her context of knowledge.

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I enjoyed reading The Montessorian's response. In one brief post I learned a few new things about the way kids learn.

I have a followup question that touches on the rational/scientific approach used to teach about life. How do you (The Montessorian) deal with religious parents who would object to using the "theory" (in scare quotes because it's as well established as the "theory" of atoms in chemistry) of evolution to teach about the origins and development of life? My guess is that such parents wouldn't want to send their kids to a secular school in the first place, but I'm curious nonetheless.

A corollary question that just occurs to me is: What sort of people are the parents of children who attend your school? Do they have above-average rationality?

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This is The Montessorian's reply to the question posed by Phil Oliver.

Dear Phil,

Very few parents have ever objected to our teaching of evolution. (Do you think they are fooled by the way I use words such as "development"  while avoiding the actual term "evolution" as much as possible?) When I trained as a Montessori teacher, I was taught to preface the Timeline of Life study with a look at some different "creation stories" (Genesis, Navaho creation myths, Greek myths, and so on) following which we were to present the "scientists' story" !! Well, you can imagine what I thought about that idea!

Since we advertise our curriculum very thoroughly up front, I assume that anyone who objected to the scientific study of evolution would not enroll.  Last year, I thought we might actually have some trouble, because we had a 6 year old boy whose father is a Baptist minister. When I explained how the Sun had condensed from a cloud of particles becoming denser and denser until it "burst into flame," Glenelle jumped up and called out, "Amen!" So I waited to see what would develop. When we got to human evolution, the minister accosted me one day and asked whether we were teaching the Bible's version. And I simply said, "No, of course not! It's not our place to teach any particular religion here. We wouldn't want to interfere with what you are teaching Glenelle at home." I was so confident that he simply said, "Oh, of course. You're right."

That, I think, is the important point. It's up to the parents to teach religion. The school's place is to teach science. Another time I had a Muslim student who told me she didn't want to study for tests in Timeline class because, "It's not true." I spoke to her mother, who is quite a reasonable person, in spite of wearing a headscarf, American born of Pakistani parents. I said I was worried that Zanab was going to be turned off in this class. Her mother told me that she had already explained to Zanab that in school we study science and at home we study the Koran, and promised to speak to her about studying harder.

It helps that New Jersey is not the Bible Belt. Every class in the school has its share of Hindus, Jews, Muslims, Sikhs, Christians, and Buddhists, and our approach is just to teach whatever is relevant to our studies of geography and history. How was Martin Luther important? What do the Touregs of the African Sahel believe? and so on. I think it's a wonderful lesson for children that people can believe so many different things, and in the end, learning about the great variety of beliefs can only lead to skepticism about the truth of any particular religion. Sometimes, if we're seeing a film, for instance, about voodoo rites in the West Indies, the children will ask, "Is that true?" and I'll always say, "You know I can't tell you that about any religion. That's up to you to decide." I think  the more I respect all religions and refuse to criticize any, the more that implicitly sends the message that voodoo and Martin Luther are equally arbitrary.

Oddly enough, I once had a teacher who - unknown to me when I hired her! - was a member of a fundamentalist Korean Christian church, the Joy Life Church, which does not believe in evolution. She asked one day whether she could present her views, and I thought it would be interesting for Middle School students to hear. She told us that she believes in "micro evolution," but not "macro-evolution," and she gave an example of a change she would credit, for instance, moths in New York City becoming, over time, sooty-colored rather than white because that provides more camouflage from predators. She just didn't think we could explain how new species can develop by the principles of survival of the fittest.

Her objections actually led to greater understanding, because some students were motivated to try to answer them. They did some research and told us about species which are obvious transitions between other species. For instance, they found wonderful video footage of lungfish, fish  who survive droughts by hopping from mud puddle to mud puddle on their powerful fins, which are clearly halfway in development between the fins of fish and the legs of amphibians.

Now, it seems to me you asked whether my parents are more rational than most. I certainly do have some wonderful clients. But I've found that in any group of people of any appreciable size, about 10% will have serious psychological problems. And I mean serious. And that 10% takes more emotional energy to deal with than the other 90% put together. So every few days there is going to be some kind of insanity. Such is life.

I always remember that people choose my school for many different reasons. I don't expect them to have any particular politics or religion.  They are simply people who want something other than public school education.

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You ask about the "hierarchy of concepts." I'm not sure just what you mean by that. First of all, I think we should beware of assuming that the conceptual hierarchy of concepts from concrete to abstract has anything to do with the order in which concepts are formed. The Objectivist theory of concepts certainly does not imply this. The sensory concepts "hard," and "brown," for instance, are much more concrete than the concept "table," and yet almost all children would form the concept "table" earlier than the concepts which name the sensory qualities of that table.

In ITOE, p. 32, Ayn Rand notes "concepts have a hierarchical structure, i.e., since the higher, more complex abstractions are derived from the simpler, basic ones (starting with the concepts of perceptually given concretes)..." This is the sense in which I referred to "hierarchy." And, I would say that "hard" and "brown" are more abstract, not more concrete, than "table." Table is a perceptual entity, a first-level concept, whereas "hard" and "brown" are attributes abstracted from entities.

But, regardless, when I asked about "treating a hierarchy as if it were an out-of-context absolute," I had in mind the sort of rigidity that treats as bad a child's interest in an area outside of what is considered to be their ken. Which is why your physics examples particularly interested me, including Galileo. My question is, when you teach physics to the children in your Montessori school, do you mix modern ideas of physics along with the historical ideas that you present? Do you find that children need parts of today's world in order to properly grasp the physics world of long ago?

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This is The Montessorian's reply to the question posed by Stephen Speicher.

Dear Stephen,

You ask whether it's necessary to use modern concepts in order to teach the history of science. This is a very interesting question for me, because I am in the process of re-working the science curriculum at my school. For many years I have been teaching science historically, as an integral part of our "Timeline Studies." There are many good reasons to do this. We can understand the "Renaissance" better by understanding particular people - not just scientists like Bacon or Galileo, but artists and writers, too, such as Leonardo, Michelangelo, and Shakespeare. Great scientists are great heroes, and it is motivating to study heroes. And it is also wonderful for students to understand the reasoning process behind an insight by reproducing it.  This inspires children to think scientifically, and teaches them methods for observing, measuring, and controlling variables.

However, I have been finding that this is not enough. Next year we are going to be supplementing our Timeline classes with a separate Physical Science Lab. The topics we cover will still be related to the history topics we are covering, but the lab will go much further.

Let me give you an example, before I answer your general question about whether one needs modern concepts to understand science history.

Next year we will be studying the Enlightenment, and this means, among others, Benjamin Franklin, Thomas Jefferson, and, of course, Isaac Newton. We'll be learning about Newton's life, which is bound up in interesting ways with the history of the Puritans vs. the Cavaliers in the English Civil War, with the English Restoration and with the Great Fire and Plague of London. We'll focus on two major areas of Newton's scientific interests: light and color; and the laws of motion. We'll see how Newton and Hooke had a vicious disagreement about color, and we'll see how Newton and Leibniz independently invented the calculus. All of this makes for a gripping story.

In the past, I have not had the children experiment with color very much except to play with a prism. We would observe the rainbow, and notice the order of the colors. This would lead to many questions. WHY does the prism bend the colors? At this point, I would start to tear out my hair, because I wanted to tell the children about wavelengths of light and show them charts of wavelengths that would include, not just visible light, but microwaves and radio waves. I would usually end up mumbling that in order to really understand what was happening we had to know some things that Newton didn't know, and I would just sort of assert that the prism "bends" the different colors of light differently. No one's curiosity was really satisfied by this.

However, this coming year, we are going to do things differently. I will use the story of Newton as a springboard to introduce the subject of light, but in the Science Lab, we will investigate the subject more fully in a logical order using a more modern understanding. We will learn that light travels in straight lines by looking at laser beams travelling through a smoky plexiglass tube with bends in it, so that we can see the light rays reflecting off the inside edges of the tube. Newton could never have done this experiment, needless to say, lacking both plexiglass and lasers. We will experiment with mirrors to find that the angle of incidence is equal to the angle of reflection. We will use a piece of equipment called a "ray box," (something Newton did not have, needless to say) which has an electric light bulb in the middle, and slits with colored filters in it to produce straight, colored lines. We will then use lenses to focus the rays. We will investigate how light rays are bent by concave and convex lenses. We will find focal points of lenses. We will combine colors of light to make white light.

I'm still working out the details for this curriculum, but the aim will be to have a reasonable modern understanding of some basics of optics.

We will also use a ripple tank, in which we make waves and project their shadows to see the different sorts of waves made by a point source, a moving wall, and so on. Then we can see how waves go around obstacles. And I will introduce the idea of the electromagnetic spectrum, even though we are going to be studying that much more fully when we get to the 19th century and focus on the life and insights of  Michael Faraday.

So, I intend to introduce the idea of the electromagnetic spectrum even though the students won't yet understand how electricity can make magnetism and magnetism can make electricity, or be conversant with the idea of a field, or any other concepts which would help them really understand what this spectrum is. I will show them waves of different amplitudes and frequencies using a rope and a very long slinky, and will tell them, pretty much as an article of faith at this point, that blue is a short wavelength, and so on. 

I am going to do this so that we can draw pictures of different wavelengths passing through the sides of a prism, and see how different wavelengths are slowed down differently. I think this will help them understand why a prism makes a rainbow, and satisfy the deep curiosity they feel on this point. They won't fully understand it, no. But next year, when we study electromagnetism, they'll understand more.To deprive children of this explanation would be to frustrate them and to stifle their curiosity.

Our other major lab topic will be force. We'll investigate Newton's three laws of motion. We'll use all sorts of wonderful equipment which I am now ordering from science catalogs: straight tracks along which cars can run almost without friction, for instance, and toys which suspend steel balls from a framework so that we can see their collisions.  We'll perform an experiment in which one ball is projected horizontally from a tall tower at the same time as another ball drops straight down from another tower, so that we can see why the balls hit the table at the same time by analyzing the horizontal and vertical vectors of their motion.

Here again, I will rely on many modern concepts which the children have and which Newton could not have imagined. Every 21st century child experiences, every day, accelerations which Newton could only dream of. Riding in cars at 50 miles per hour or more, we all know what it feels like when the driver suddenly slams on the brakes, and we fly forward towards the windshield; we know about seatbelts and air bags. We can see videos of crash test dummies. This gives us a visceral appreciation for the meaning of inertia.

We have roller blades, so that we can experience near frictionless motion. In fact, one experiment I want to do will involve teams of children on roller blades pulling on ropes held by other teams, and crashing into other children, so that we can experience conservation of momentum and see that an action has an equal and opposite reaction.

We can see this, also, by experimenting with bottle rockets. Every child of the space age knows how a rocket engine works, and every science book written for children explains Newton to children by using rockets as an example. Even preschoolers are taught about action/reaction by using balloons: the air rushes out one side, and the balloon is pushed opposite to the flow of air. Yet Newton could never have seen a balloon.

I have found, in the past, that velocity and acceleration are very difficult concepts for middle schoolers to grasp, and yet, I have succeeded in teaching them about velocity, acceleration, mass, and momentum.  This has meant measuring speed and distance to calculate velocity - which meant using little electric cars and stopwatches, both modern pieces of equpment. We have measured mass using modern scales. In the end, I think they understood what is meant by F=ma. But to understand such an equation is quite a feat. These are children who have not yet had algebra. We have to vary things very concretely, comparing, for instance, a heavy bowling ball going very slowly with a light ball going very fast.

Now, I would never say that I have discovered the one and only way to teach science, and I know that many wonderful teachers experiment, all the time, with curricula of their own devising. If anyone has found a way to teach science purely historically, I would certainly like to see it. I have heard some attempts at this which, in my opinion, failed. For instance, I have heard someone struggling to teach children about Greek ideas of motion who ended up explaining the Greek ideas by their contrast with our modern understanding of speed and acceleration. I have heard the Greek idea of "atoms" explained by assuming that children know what is meant by atoms today, and contrasting this idea with the Greek idea.

But let's think about it for a minute. As I've said, there are many powerful reasons to teach the history of science to children. But, is there any reason to think that phylogeny will recapitulate ontogeny? That is to say, is there any reason to think that the best way to learn science concepts is always to follow the order of discovery?

After all, the order of discovery is replete with dead ends. Should we teach children about alchemy? Should we teach them to calculate epicycles in the orbits of the planets? Should we teach them about the "four bodily humours," and if we do, will it help them to understand any better what really causes disease?

Once I did try to teach a dead end, in order to contrast it with an insight, and I failed miserably. I was teaching about Lavoisier - a fascinating figure in history, who lost his head to a guillotine in the French Revolution. I wanted students to understand what an insight it was to discover oxygen. Lavoisier was trying to clear up the confusions of his predecessors about why metals rust. He posited that metals combine with oxygen in the air in a process of combustion, and that rust is an oxide. But before this was understood, there was a theory about how metals create rust. I struggled to get children to understand what Lavoisier was arguing against, and even now I find that I can't remember it or explain it without going back to my sources. It just was not worth it. Believe me, we were more confused. We had to understand the truth first in order to understand the historical confusion.

I have come to realize, over the years, that you understand the history of science better if you already have learned some science by other means. It is also true, though, that you understand science best if you reproduce some of the great experiments in science history performed by focal figures such as Archimedes, Galileo, Newton, and Faraday.  I have found that there is an interaction between teaching history and teaching concepts in a logical order. But I have not found that the logical order is necessarily the historical order of discovery.

Now, I mentioned Faraday. I won't be getting to Faraday again until the year after next, when we study the 19th and 20th centuries. Faraday's life is an inspirational story which every child should know, a true 19th century story of rags to riches. Faraday was a poor boy who spent his meager savings to attend public lectures on science and talked his way into a job as a bottle washer and lab assistant.

In the future, I want to go beyond the few electromagnetic experiments I used to do when studying Faraday to present an entire integrated lab unit on magnetism and electricity. This unit would begin with concepts which pre-date Faraday's time, and draw on concepts which post-date Faraday. I haven't fully worked it out, but I think we need to start with some sensorial experiments with magnetism and electricity: playing with lodestones and other magnets to feel the forces of attraction and repulsion; rubbing glass rods and balloons with fur and silk to make and feel static shocks; setting up pith balls and charging them with static electricity; making an electroscope with thin foil so we can measure the amount of repulsion as the leaves are forced apart, and so on.

I think we then need to build electric circuits - using modern light bulbs and lantern batteries and switches - and investigate the properties of serial and parallel circuits. We need to learn to draw diagrams of circuits using modern symbols.

I think we need to see where the electricity in a battery comes from, so we need to make Voltaic piles out of stacks of coins in vinegar. We need to put strips of tin and copper in an electrolytic solution and see what happens when electricity passes through the water from one metal strip to the other, and we need to learn the terms anode and cathode. But, in order to understand this, we are going to have to draw little diagrams of "electrons"  (WARNING: HERE'S A CONCEPT FARADAY NEVER HAD!) We're going to learn that electricity is the flow of electrons. We're going to see that what makes our circuits work is that electrons come loose from the atoms of the copper wire, and flow through the wire around the circuit. This will be analagous to introducing the idea that light comes in wavelengths. We won't fully understand this idea until we have learned something about atomic theory in the 20th century, about Bohr's model of the atom, about Rutherford's experiments shooting particles through gold foil. But that's OK.

It will even be OK if we tell the children that some metals are magnetic and others are not because the electrons "line up" to spin in one direction. It will be OK if we demonstrate this, as teachers often do, by having children magnetize needles by stroking them over and over again in the same direction with a powerful magnet. No minds will be destroyed by introducing these ideas "out of sequence," and I truly believe the children will understand better, in the end, if we do it this way.

The children will have the sensorial experience of making a magnet. They will understand, very vaguely, that this to do with "lining something up." Later, when they study atoms, they will see that electrons can spin, and they'll then be able to make a connection. Spinning electrical forces make a magnetic force.Oh, yes! So that's why you can magnetize a needle! Electrons in the outer valence shells can come loose! Oh, yes! So that's why electrons can flow through a circuit.

As always, there's a spiral, revisiting the same idea for greater understanding. How absurd it would be to "protect" children from the experience of magnetizing a needle because they can't yet fully understand it. How frustrating for them to give them that experience and offer no explanation of it at all.

In our Faraday unit, finally children will  explore magnetic fields as Faraday did with iron filings. They will construct their own electromagnets. They will attempt to build motors and generators.

Children in the 21st century already know much more than Faraday could possibly imagine about how electric motors would transform the world. They live in a world where from earliest childhood they have flipped a switch to turn on an electric light and pressed buttons on a microwave to heat their food. They know about radio and television. They drive past power stations, and see the condensers which run the air conditioning in their house. This is their starting point; these are the wonders they want to have explained. So if it is a bit hard for them to wind a copper wire evenly enough to get their motors and generators to work, we can always point to motors and generators all around us. And a company called "Genecon" offers wonderful little hand powered generators so we can experiment with them.

I realize I've only begun to answer your question. Don't forget motivation, too. Children's lives today are chock full of computers and televisions and internal combustion engines. They are motivated to understand what makes these things work. For Benjamin Franklin, the most amazing thing he had ever seen was a demonstration of an electric shock offered by a travelling "science magician." Is this the most amazing thing a child has ever seen? Everyday experiences have to provide the hook, the motivation, for children to learn about science.

To sum up: Yes, I find it is useful to introduce some ideas out of their historical sequence in order to help children understand science. The examples I've given are the idea of an electromagnetic spectrum to understand prisms, and the idea of electrons in order to understand electric circuits and batteries.  I think anyone who imagines science can be taught effectively without doing this probably doesn't realize the extent to which she or he is in fact relying on modern concepts which children have already acquired.

This raises a deeper issue. I believe that a teacher needs to offer some concrete hands-on experiences, and yet combine them with some explanations which are offered as an authority. It is not necessary - or possible - for a child to "discover" every concept on his own from sensorial experience. In fact, this insistence on raw discovery is a fallacy of Dewey- type progressive education. Carried into the field of mathematics, it is what is leading to disaster in New York City today. This would be a subject for another essay.

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Dear Stephen,

You ask whether it's necessary to use modern concepts in order to teach the history of science....

What a marvelous answer you provided. Thank you.

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