Meaningfulness and personal maps of reality.

"Eternal truths will be neither true nor eternal unless they have fresh meaning for every new social situation." Franklin D. Roosevelt

Meaning and meaningfulness. 

There is meaning inherent in ideas, concepts and words, but when we learn them, they have to have meaning for us, which is not the same thing. If they do not, we will not comprehend or understand them. Despite the fact that they have meaning, they will have no meaning for us. All knowledge has inherent meaning, but it may not be meaningful to us. On this page, when this site uses the word 'meaningfulness' in regards to some knowledge it is talking about whether it has meaning for the learner.

Assimilation and accommodation. 

If something has meaning for the learner, it is either instantly meaningful when the learner is exposed to it, or it becomes meaningful as the learner restructures his personal map of reality to accommodate it. In one, the jigsaw piece fits exactly into a hole that is waiting to be filled, and in the other, some of the jigsaw pieces must be rearranged so that a hole in the puzzle can be formed to fit the new piece. Piaget calls these two ways of making sense of incoming information assimilation and accommodation.

Two methods of absorbing information, deep learning and cramming. 

In his book "Educational Psychology a Cognitive View" David P. Ausubel suggests that there are two types of learning done in schools, meaningful learning, and non meaningful learning as exemplified by rote and drill. Ausubel has collected considerable evidence that meaningful learning (by which he means that the item to be learned has meaning for the learner, or that the learner creates meaning for it) is better in every way. While this site endorses this view of Ausubel's, this site regards drill and rote to not be forms of learning at all. Ausubel shows that meaningful learning is superior in every way and that drill and rote are positively harmful. This is not a new idea in learning or education, but rather a scientific corroboration of views long held by a few. This view was perhaps most ably presented by the philosopher and economist John Stuart Mill as follows:

"Most boys and youths who have had much knowledge drilled into them, have their capacities not strengthened, but overlaid by it. They are crammed with mere facts, and with the opinions and phrases of other people, and these are accepted as a substitute for the power to form opinions of their own: and thus the sons of eminent fathers, who have spared no pains in their education, so often grow up as mere parroters of what they have learnt, incapable of using their minds except in the furrows traced for them. Mine, however, was not an education of cram. My father never permitted anything which I learnt to degenerate into a mere exercise of memory. He strove to make the understanding not only go along with every step of teaching, but, if possible, precede it. Anything which could be found out by thinking I never was told, until I had exhausted my efforts to find it out for myself."

Brain rules from the world of neuroscience. 

In his book *"Brain Rules" John Medina explains that in terms of memory in brain biology, meaning is all important. In this book Medina tells of an easy to perform experiment. Write down a group of 14-15 unconnected words and show them to two separate groups of people. He then has this to say:

"Tell Group #1 to determine the number of letters that have diagonal lines in them and the number that do not. Tell Group #2 to think about the meaning of each word and rate, on a scale of 1 to 10, how much they like or dislike the word. Take the list away, let a few minutes pass , and ask each group to write down as many words as possible. The dramatic results you get have been replicated in laboratories around the world. The group that processes the meaning of the words always remembers two to three times as many words as as the group that looked only at the architecture of the individual letters.

...At this point, you may be saying to yourself,  'Well duh!' Isn't it obvious that the more meaning something has, the more memorable it becomes? Most researchers would answer, 'Well yeah!' The very naturalness of the tendency proves the point.  

...The more a learner focuses on the meaning of the presented information, the more elaborately the encoding is processed. This principle is so obvious that it is easy to miss. What it means is this: When you are trying to drive a piece of information into your brain's memory systems, make sure you understand exactly what the that information means. If you are trying to to drive information into someone else's brain, make sure they know what it means.

The directive has a negative corollary. If you don't know what the learning means, don't try to memorize the information by rote and pray the meaning will somehow reveal itself. And don't expect your students will do this either, especially if you have done an inadequate job of explaining things. This is like looking at the number of diagonal lines in a word and attempting to use this strategy to remember the words."

Meaningful learning. 

Meaningful learning is understood, it is easily recalled, it is consistent with other information and it is interlinked with many other ideas, concepts or words. If we consider how personal models of reality work, the reason why rote and drill do not work as educators would hope, becomes evident. When some idea or concept has meaning for the learner it is like placing a piece in a jigsaw, when the other four pieces around it are already in place. It is clear it is in the right place because it matches, continues and links into the four other pieces around it, and often part of the picture you are putting together becomes clear, because of it.

Meaningful learning in the mind. 

What follows is speculation on the understanding of what a concept is and how it is formed and memorized. These ideas are compatible with current information from Neuroscience, explaining what is known about memory and concepts. All meaning is built the way concepts are built. This is how they become meaningful and become understood. However, it is just a way of thinking about how learning, meaning and understanding take place and remain conjectural for the moment.

Building a concept.

When an item of meaningful learning is placed in the mind it matches, extends and links to numerous ideas and concepts, not in four simple directions, but often in thousands of directions. How this might work may be made clearer by a simple example. Let us consider the word or concept dog. Both the word dog (a symbol for the concept) and the concept dog are linked to all the different types of dogs that we know about. We may not be able to visualize them all, but if we see a dachshund, an Irish setter or a collie we will instantly recognize them as dogs, though they are a plethora of different shapes, sizes, and colors. Then there are all the different names for dogs, most of which we will recognize as a name for a breed of dog. The links to different things go on and on, such as Shep down the road or Lassie and Rin Tin Tin from the movies. The concept dog, and the word dog, are also linked to all the different types of noises and names for noises that dogs make, such as growling, howling, barking, whimpering, yapping and whining, all of which themselves, have many variations. I could go on, but you get the idea, dog has thousands of links to it and it is these links that define what the concept dog means to us.

Properties as links. 

The abilities and textures of an animal are also important in knowing what the animal is. Hairiness liveliness, playfulness, running and jumping ability, its teeth, its tail wagging. 

Emotional links. 

Current thought about the evolution of language as proposed by Greenspan and Shanker in their book "The First Idea" is that concepts may be constructed fundamentally out of emotions. That is to say that the emotional connections for a concept may provide the largest part of its meaning. In the case of the concept dog such emotions as fear, love friendship, loyalty etc. may underlie our understanding of what a dog is.

Chunking the gist.

So there are thousands of links to the word and concept dog. But when we see a dog and the idea of it is recalled or we simply recall what a dog is we do not activate these thousands of links. This is time consuming, wasteful of energy and an inefficient way to think. John Medina talks about the gist as being what is actually recalled. There are several ideas about what this might entail but the most popular idea is a kind of averaging of component elements and this seem to make a lot of sense as we tend to imagine a ball or a dog mostly as a kind of average of attributes. But this can not be the whole story as there are often wild outliers in a large inclusive concept like dog. So we also probably recall to some extent some outliers at the extreme of what being a dog is as well as our average template. This all happens in the conscious part of memory called working memory and is produced by a process called chunking.

Chunking. 

Chunking is where the brain compresses a large segment of memory into a much smaller segment that can represent it so it can be manipulated without having to be fully recalled. This happens on many levels so that very large sections of memory can be thought about and manipulated. Thus we get chunks within chunks within chunks. At some point we start to get no memory elements at all in the chunks but instead we get symbols that stand for the chunk. Symbols as a rule take up much less brain space and thus work well within the tiny working memory space. A single symbol can stand for a whole concept or a whole segment of memory.  

Meaning, links and recollection. 

Meaning. The meaning of an idea and therefore the understanding of that idea comes about because of the links and associations with the concept. In fact meaning is these connections. Without these connections there is no meaning and therefore no understanding. Just as concepts become more understandable with each link to it so does all knowledge. The more connections to previous knowledge the more it makes sense. These links not only give meaning and determine a unique position in the personal map of reality but they also provide pathways through which knowledge, ideas, concepts, conjectures, and theories may be reached, and thus recalled. 

Recall. So not only are connections important for understanding and meaning but they are also important for recall. Firstly, the amount of connections determines the likelihood of recall in that the more connections the more likely it is that the memory will be recalled. Secondly, the more connections the easier it is to find the memory if we are looking for it. If there are many paths to a memory it does not matter which path you start on it is more likely you will find your way to the memory.

Long term storage. There may be another reason why the number of and the different types of connections are important for learning. This quality and proliferation of connections may not only make concepts, ideas and theories more understandable and more easily recalled but they may also make the memory more permanent. In other words whether a memory stops being degraded, deleted or lost may depend on the number of connections to it from other ideas, concepts and theories. It may determine whether that memory is chosen to become a long term memory. Even if this is not so, it is obvious that the more connections to other knowledge the less likely a memory is to be lost, degraded or deleted.  

Learning as play and record.

Learning is not what we tend to think it is. We have been conditioned to think of learning as a kind of play and record process. The teacher plays the information as a message which students then record in their brains so they can play it back to themselves by means of recall. There are many problems with this idea. Firstly, the moment we recorded a message in this way it begins to degrade. Secondly, the rate at which it degrades depends on its emotional content and how often it is recalled. Thirdly, repetition of the message strengthens some connections like the ones within the message and one or two to cues that activate recall but the connection to the other material in each student brain will be very tenuous indeed. Not only is such information not understood but it is also much more likely to be degraded, deleted or lost.

Personal maps of reality.

Each of has within our brain a model of external reality. Kelly called this a cognitive structure this site refers to it mostly as a personal map of reality and it has also been called an atlas of reality. This is a structure, an edifice encompassing our understanding of external reality and how it works. It enables us predict that certain things will happen and thus makes planning, anticipation and expectation possible. This model includes everything we know and enables all meaning and understanding. Each element of this model must link back to other parts the model to provide both the meaning and understanding. The number of these links or connections embody what understanding and meaning is possible, as do the variety and different types of these connections. Experiencing the world in different ways through different senses etc. enable greater understanding, and provide more meaning. Without these links or connections information has little meaning and is poorly understood. It is little more than some trivia we can regurgitate.      

Hooks and eyes.   

Learning is mostly not like this at all. For any new information to become understandable it must connect with past knowledge that is already in storage. You can think of this in terms of hooks and eyes. The new information has to have many many hooks and these have to be able to be able to hook into into eyes in the store of previously collected knowledge residing in each student brain. When looked at this way we can see that learning has many ways it can fail. The new information presented may have insufficient hooks to connect with each student mind. It may have plenty of hooks but not ones capable of connecting with student minds. The eyes may be clogged with garbage or even completely wrong information. Given any of these problems deep learning (understanding) does not take place.

The house of knowledge.

Rote and drill. 

Information not learned in this way of being elaborated, remains peripheral, with often no more than one or two connections. What rote or drill do, in effect, is attempt to retain these bits of information by widening the pathways, the links, or connections between them and some important key activator. They do it by going down these pathways many many times. What seems to happen is that much of the information the mind is exposed to in this way never seems to retain any permanence in what is called long term memory. It seems to be deleted quickly unless conscious effort is made to keep it alive in short term memory by continually revisiting it. 

For instance in science and maths at schools we tend to learn a lot of formulas for obtaining correct answers and usually we are either simply taught them by rote or left to our own devices to somehow learn them. These formulas, however, are actual scientific or mathematical principles. If we simply memorize them and plug them into problems we have hardly learned anything even though we we may be able to get right answers. We simply do not understand what we are doing. Sometimes students do get some understanding of why these formulas work but usually this happens after the formula has already been memorized. These formulas manipulate scientific and mathematical ideas. 

To truly understand scientific and mathematical principles we need to know how the various people who came up with them did so. What were they thinking? What problem were they trying to solve? What else did they try? Where does this fit in with things I already know? How can I use this to solve what problems? If we were were taught these things instead of the formulas we would be much more likely to understand what the formulas were doing and why they worked. Formulas should never need to be memorized. They should be obvious from our understanding of the scientific and mathematical principles involved.    

Memory experts. 

Memory Experts can perform amazing feats of memory by remembering long lists of disconnected words or even nonsense words. Some memory experts have found that they can trick the mind into accepting nonsense or disconnected information if they consciously associate each of these items with some ideas or words that are already saturated with meaning. They do this by finding ways of connecting the words or nonsense to other words or symbols that do make sense and then ordering those words or symbols by some ordering principle. This is like sort of tricking the mind by providing extra meaning. At school we learned the word BOMDAS. BOMDAS is a way of remembering the order in which operators have to be used in Maths. The letters stand for "Brackets, Of, Multiply, Divide, Add, Subtract", and this is the order in which those operators should be performed. Actually its back to front. You 'subtract' first and do 'brackets' last. But as the teacher pointed out the other way would produce SADMOB, which has too many other distracting associations. The mind in a normal person will begin to delete information that has little meaning or little in the way of associations with other information. These associations or pathways begin to shrink the moment we stop using them. This is of course made more likely by the fact that having so few links and the fact that the memory can only be accessed by using those few paths, the possibility of recall is greatly reduced.

More is less in memory. 

Memory is, at first sight, anti intuitive. It seems we can improve recall by adding more information rather than streamlining the information. More information is easier to remember that less information. In his book "Brain Rules" John Medina tells the following story.

"Watching J.C. take an order is like watching Ken Jennings play Jeopardy! J.C. never writes anything down, yet he never gets the order wrong. As the menu offers more than 500 possible combinations of food (entries, side dishes, salad dressing etc.) per customer, this is an extraordinary achievement. J.C. has been recorded taking the orders of 20 people consecutively with zero percent error rate. J.C. worked in a restaurant frequented by University of Colorado brain scientist K Anders Ericsson. Noticing how unusual J.C.'s skills were, he asked J.C. if he would submit to being studied. The secret of J.C.'s success lay in the deployment of a powerful organizing strategy. He always divided the customer's order into discrete categories, such as entree, temperature, side dish and so on. He then coded the details of a particular order using a lettering system. For salad dressing, Blue Cheese was always 'B,' Thousand Island always 'T' and so on. Using this code with the other parts of the menu, he assigned the letters to an individual face and remembered the assignment. By creating a hierarchy of gist, he could easily apprehend the details.

J.C's strategy employs a principle well-known in the brain-science community: Memory is enhanced by creating associations between concepts. This experiment has been done hundreds of times, always with the same result: Words presented in a logically ordered, hierarchical structure are much better remembered than words placed randomly - typically 40 percent better. This result baffles scientists to this day. Embedding associations between data points necessarily increases the number of items to be memorized. More pieces of intellectual baggage to inventory should make learning more difficult. But that is exactly not what was found. If we can derive the meaning of the words to one another, we can much more easily recall the details. Meaning before details."  

Meaning and associations as memory. 

This site holds that meaning is provided by associations and that meaning makes memory possible. This site holds that meaning makes memory possible in two ways. Firstly it enables discrete memories to be found during retrieval by providing an organizing principle that makes locating the information possible. Secondly meaning provides pathways through which thoughts can travel while trying to locate some discrete memory.

If this is true it could be further suggested that associations perform four different functions in the brain. These four functions, in turn, could account for how memory is best recorded and retrieved.

1. Meaning. There are associations that give a particular memory it's meaning. Understanding then comes from a complex linking of associations.
2. Concept. There are associations that link specific memories to a central concept which in turn provides the meaning for that central concept.
3. Whole mind. There are associations that that link the mind or brain together into a whole entity. This makes it possible for the mind or brain to understand the reality of the external world, by constructing or being a model or map of that reality.
4. Peripheral. There are associations that are peripheral or situational. These are associations or links that connect specific memories with the situation in which they occur. They can be part of the meaning, but are often not part of the meaning of specific memories. Thus they simply provide door handles or hooks for accessing specific memories and through them the concepts those memories create. 

Meaning and context. 

We are all aware that if we lift a sentence out of a speech, or an article, or even a scientific paper, its meaning will probably change. If we quote a sentence like this, it is said to be quoted out of context. Meaning of course is not limited to a single context. If we take the words in a sentence and rearrange them we may also get a new meaning, but in this case it is more likely to produce no meaning or meaninglessness. The order of sentences within a speech or paper or article provide yet another context, which is also responsible for the meaning of the item. The order of the phonetic sounds within a word provide yet another context which gives meaning. If you were to rearrange these phonetic elements you might get a new meaning, but again would probably produce nonsense. When we start talking about communication, suddenly we find even more layers of context. Suddenly we have to deal with inflection, tone of voice, facial expression and body language all of which provide context which produces the meaning. This is by no means the limit of the layers of context that may produce a single meaning. There is also the contexts of time, place, prejudice, and cultural factors. The same words spoken the same way may have very different meanings for people of different cultures or even different ethnic groups. Consider how Muslims, Jews or Americans might view the same spoken words. It turns out that meaning is just multiple layers of context many of which are set one within the other. 

Meaningfulness and context. 

If external meaning has all these levels of context it becomes apparent that internal meaning or meaningfulness must also have all these levels of context to produce meaning. It must have all these levels of context so we can interpret incoming messages. Some of this is provided by the links connections or pathways but some of it is provided by the order or the arrangement of the links or connections. This is the structure of the personal map of reality, or the cognitive structure, or the personal construction system.

A person can hear and read much more in his native language than he can in a secondary language because the density of links is so much greater for a native language. For instance it is quite easy for a native English speaker (writer) to understand the following passage despite the fact that most of the words are spelled incorrectly. We understand words by the context in which they occur. If the context is correct we can fill in about every seventh word. Also, if the context is correct, how a word is spelled matters very little. The spelling can be very wrong and we will still understand it. Also it is now known that when reading words we tend to pick up mostly the first and last letters, and the rest is guesswork based on context with some occasional reference to a few of the other letters in the word. If you don't believe this, check how easy it is to read the next passage.

"I cdnuolt blveiee taht I cluod aulacity uesdnatnrd waht I was radgnieg. The phaonmneal pweor of the hmuan mnid. Aoccdrnig to rscheearch at Cmabrigde Uinevtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmkoatnt tihng is the frist and lsat ltteer be in the rghit pclae. The rset can be a taotl mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Amzanig huh?"

What is a word? 

A word is a symbol or a sign and we use it to stand for or represent a concept. Not all concepts can be represented by a single word but many can and some words stand for several completely different concepts. Many words are names for objects (an object is a special kind of concept). The main thing to know about words is that though they represent objects or concepts they are not those objects or concepts. The word is not the thing it stands for it is merely a convenient way of conveying the meaning of that thing to others or to ourself.

Learning words and context. 

We learn words from the context in which they occur. In a sense the context is always learned first. In a different sense words are always learned first. What happens is that we learn words and are able to speak words without understanding their meaning or knowing their meaning. This happens at every level of learning. Part of the context of words is the sentences in which they are used. Consequently we are able to place words correctly in sentences long before we fully understand what those words mean. To put that another way we can place words correctly in sentences long before we have completed forming the concept that the word stands for or symbolizes.

Babies first learn words not meaning. 

Babies imitate speech. Initially they imitate the overall sound of speech rhythm. Listen to a baby in another room and it sounds like somebody talking. But as you get closer to the baby you realize there are no recognizable words. The baby imitates the cadence but does not even realize the there are recognizable or distinguishable sounds. By watching the faces of parents and other care givers up close and after many repetitions of particular sounds babies will begin to realize that there are individual unique sounds and will try to imitate them. The first words a baby learns are probably mama or papa but when he speaks them for the first time he has no idea what they mean. It will mean much paying attention to the context in which those words are used and trying to use them in such contexts before the baby gets a glimmer of an idea what they may mean. These are word context iterations.

The first bit of context and thus meaning comes when he/she first realizes that certain objects (parents and other care givers) become different, and pleasurably so, when he the baby speaks those words. It has now been determined by many independent research teams that this response by parents and other care givers to babies efforts to communicate are all important in their development of language skills. Even so there is always a long time between initial responses to babies efforts, and when the baby finally realizes what is meant by papa or mama. First the words must be placed in context over and over and this cannot be done with sentences because the baby does not understand sentences. The clues for the baby are not easy to follow. Is mother always present when others use the word? Is mother indicated in some way when the word is used? The first meaning the child learns is probably something practical like drink but even then it will not be an exact meaning such as adults understand. It may mean to the child anything liquid of may include food and eating. (The word "gin" in Thai for instance has this kind less specific meaning. It can mean either to drink or to eat).

  The evolution of infant meanings.

Heaps, complexes and concepts.

The Russian Scientist Lev S. Vygotsky did considerable studies with young children in and effort to discover how language, speech and thought develop. His Book "Thought and Language" like the work of Piaget is considered a classic in the field. Vygotsky held that the meaning of words undergo evolution in childhood and set out to discover the basic steps in that evolution. He suggests this evolution goes through the following stages: 

Heaps. At first the words are associated with any experience the the child may have in conjunction with his experience of the word. Vygotsky calls these groups of associations heaps. 

Complexes. These heaps gradually evolve into more ordered structures that Vygotsky calls complexes. Unlike heaps complexes always have something in common. Some common element is seen to be similar or the same by the child and the associations built are then based on that. At first there are chain complexes which are very variable because the common element chosen may change each time the child makes a choice.

Potential Concepts. Gradually all the objects included in a complex will start to have a single central attribute that all the objects in the group have in common. These Vygotsky calls potential concepts.

Pseudo-concepts. The final type of complex is what Vygotsky calls a pseudo-concept here the complex has many central attributes that all the objects in the group have in common.

Concepts. Ultimately pseudo-concepts resolve into concepts at which point most people agree about their meaning.

Vygotsky's Understanding.

Complexes, a duck is not a duck.

Vygotsky gives a nice clear illustration from the Russian language of what he means by a chain complex as follows.

"There is a well known, frequently cited example of these shifts: a child's use of quah to designate first a duck swimming in a pond, then any liquid including the milk in his bottle; when he happens to see a coin with an eagle on it, the coin also is called quah, and then any round coin like object. This is a typical chain complex: Each new object included has some attribute in common with another element, but the attributes undergo endless changes."

As the evolution of words proceeds sometimes the associations formed in complexes seem to be opposite in meaning in the adult world. A child my use the word before to mean both before and after but of course they mean neither to the child. To the child the meaning is something more like close in time. Evolution of words continues further and we begin to see objects grouped under a word on the basis of participation in some activity. Thus the word spoon may come to mean for the child any object that participates in the eating of food. This seems at first more fixed, but is still variable in that the child may give an object more than one name if it participates in more than one activity. A spoon might be used to stir paint for instance in which case the child would have a different name for it.

"Dare to err and to dream. Deep meaning often lies in childish plays." Johann Friedrich Von Schiller

Potential concepts. 

Potential concepts start out having a single central attribute that all the objects in the group have in common. Gradually they will over time, with many subtractions and additions, expand to having many attributes in common.

Pseudo-concepts. 

Pseudo-concepts have many central attributes that all the members in the group have in common. It may seem like a true concept to observers but it is still not, for only some of the necessary attributes may may be chosen by the child. He may be right 9 out of 10 times, but one time he will still be wrong.

Problem (Communication), Tentative Conjecture, Error Elimination.

Vygotsky saw clearly that concepts were not built/based on abstracting or synthesizing similarities but were rather forced into similar groups by a process guess and error elimination. A child does not create an understanding of the meaning of a word grouping together attributes that seem similar and certainly not from an Aristotelian definition. This abstracting of similarities, a seemingly logical process, is in fact drawn from the same roots as induction and is incorrect for the same reason. 

The child has a problem. He wishes to communicate. He grasps the idea that words have meanings. He takes a word and forms a tentative conjecture as to what it means. He guesses usually incorporating many more elements/attributes than are correct. He then indulges in error elimination where he tries to discover where he is wrong. He does this by trying to communicate with care givers. He tests his theory in terms of how the care givers respond to what he is doing. 

Mostly the child ends up with many elements/attributes being eliminated as he/she struggles toward the correct meaning and with some new elements or attributes being included. This is done by subtracting members and adding members and not elements or attributes. As Vygotsky points out, the child is wrong again and again and again, but he/she struggles on because each time he/she gets a little bit closer to being right.

Vygotsky did not have Popper's learning model to make this clear. He explains it like this.

"Our experiments leave no doubt that on this point, at any rate the description of concept formation given by traditional psychology, which simply reproduced the schema of formal logic is totally unrelated to reality."

Categories, concepts and meaning. 

One of the ways in which we come to understand information is differentiating the things we see, hear, feel, taste and smell into categories. In his book "Blunder" Zachary Shore tells us the following:

"Since the time of  Aristotle, the accepted view of categorization assumed that we group things into categories when a group's members share common properties. These categories then form logical sets. In the Greek philosophical worldview, particular experiences that come through the senses were considered unreliable. Because a straight stick looks bent when half is under water, for example, they believed that we cannot trust our senses to guide our categorization. Instead only stable, abstract, logical universal categories could function as objects of knowledge. To fulfill these functions categories had to exact, not vague. They had to possess clearly defined boundaries, and their members had to have attributes in common that were the necessary and sufficient conditions for membership in the category. All members of the category had to be equally good with regard to membership; either they had the necessary common features or they didn't. A thing was either inside the category or outside it; there was no in between."

Prototypes. 

Although many cognitive scientists had over time questioned the rigidity of these Aristotelian definitions as a means of learning categories, it was Eleanor Rosch who first provided an alternative way of understanding categories and their meanings. She noticed that some categories such as colors had rather fuzzy boundaries and yet were very distinct in their best examples. Red, yellow and blue are very distinct. What she discovered was, that the best examples of categories were best remembered, most easily distinguished and had in fact symbolic properties that enabled recognition of things as being members of a category. Some breeds of dogs, for instance, were better representatives of the category 'dog' than others. A German shepherd or a Labrador retriever are better examples of 'dog' than say a poodle or a dachshund. They are in Rosch's words prototypical. When we think 'dog' they are part of a composite image that comes to mind and symbolizes 'dog'. Some types of dog such as the German shepherd therefore are more easily recognizable as dogs because they look more like the prototype.

Not only does this mean that categories are always fuzzy at the edges but it also means it is often slightly different from person to person because of the different examples of category members know to be included. Also a category is never really finished being defined because we are often still in the process of adding members and deleting members. Where this is still happening not only is the meaning of the category still in flux, but the actual prototype that symbolizes it may also be still morphing slightly. In his book "Everything is Miscellaneous" David Weinberger commented on Rosch's research as follows:

"Rosch's findings stand in stark contrast with the prevalent definitional view that thinks we start with criteria and then find some good examples. The prototype view thinks we start by having prototypes pointed out to us - 'Oh, look a birdie!' - and then cluster other things around them."   

A third alternative. 

While this seems a more probable way of building categories, than by definition, this site holds that that this idea of how categories are built cannot be correct either. When a person points out a birdie to a child, the child has no idea of which attributes are important and which are unimportant. The bird we point out is not automatically accepted by the child as a prototype for birds. Indeed, the bird we point out, may not in fact, be a prototypical bird. Maybe it is as swan, an eagle, an emu, a chicken or an ostrich. Now you may say, that it is more likely that we will in fact point out a prototypical bird when we say birdie, and use the words eagle or ostrich etc. when pointing them out. There is some sense to this, but it is not sure.

Even if the bird we identify is a robin, and most people understand a robin is a prototypical bird, the child has no way of knowing this is any different to when we point out a kiwi. The only thing the child has to go on is what seems to have some elements in common, or perhaps more importantly, what seems dissimilar. To do this children tend to form overly inclusive visual categories just as Vygotsky suggested and is explained above. Children then test these prototype theories and eliminate members that are incorrectly placed.  

Perhaps the important thing to notice here is that categories in children tend to be widely inclusive and tend to be pruned or trimmed back as the child subjects them to trial and error correction. Later in life when language has become fluent, categories can more easily have new examples added. This process of subtracting and adding members is what Vygotsky means about alternating between two directions, from the particular to the general, (becoming more inclusive) and from the general to the particular (becoming less inclusive).

Trial and error. 

Although members of categories can be added because we are told that a particular example should be a member of a particular category this is not typical of how we learn about category membership. Usually members of categories are discovered by a trial and error method. When a child incorrectly identifies say, a dog as a cat, parents and teachers tend to identify the correct category. In this way the child eliminates the example from one category and simultaneously may add it to the correct category. Typically learning the membership of categories takes place by others misunderstanding children's misidentification of category members, or others correcting children's misidentification of category members. Not much takes place because of direct identification of category members by others.

The fact that we all tend to end up with the same prototypical examples has little to do with indication of category members by others and everything to do with the fact that prototypical examples have more features or attributes in common with the other members of their category than do non prototypical examples. For instance a robin has a small beak, and so do most birds, but some birds have big beaks. Robins can fly, and so can most birds, but some birds can't fly. Just as we arrive at, 'what is a bird' by process of trial and error elimination, so too do we arrive at our prototypes through trial and error elimination conducted mostly while we were children. Both the category and its prototype are built by paring away provisional members, of an overly wide ranging inclusive category, that are ultimately identified as being incorrectly placed in the category and the addition of a few members that were not initially included.

The actual attributes are not part of the process of building or creating the category, and can really only be identified once the category becomes fairly stable. Remember categories were constructed by humans for their convenience, and are not universally and instinctively recognizable. It is possible to construct radically different categories.                    

Developing concepts, the evolution of meaning. 

With concepts the symbols we call words gain meaning. With words comes inner speech and conscious thought as we know it. Thus we have reached a point where it is possible to lay out stages in the evolutionary development of concepts in an orderly progression as follows.

1. In the beginning the infant arrives at solutions by accident and then proceeds to try those solutions out on various other problems. (No thinking required).

2. The infant begins to notice the sounds of speech without perceiving that is it composed of unique repeatable sounds (words). At this point babies need to hear care givers speaking normally.

3. The infant begins to imitate speech sounds without reference to meaning and indeed without understanding that there is meaning there. At this point care givers should try to pick out word like sounds from the babies gabble and respond to them. 

4. At some point the infant begins to suspect that his actions can affect the world. In this the baby needs lots of response from care givers to his attempts to imitate sounds. In this way a conjecture concerning intention is formed.

5. The infant begins to want to organize his actions to initiate outcomes of his anticipations. (The desire to think and solve problems consciously). At this point a strong reciprocal involvement should be set up between baby and care giver. The parent should be making every effort to understand the baby and what it wants. At the same time the baby should have become highly sensitive to the care giver/parent's responses.

6. The infant begins to notice the sounds made by others are composed of unique and repeatable sounds (words). At this point babies need to see the faces of care givers up close so they can separate language into individual sounds, which will normally be words, that they then may be motivated to imitate.

7. The infant then begins to imitate these words without any reference to their meaning and indeed without understanding that they have meaning. At this point babies are again greatly helped by seeing faces up close when trying to imitate these separate sounds.

8. The infant begins to associate with any experience that infant may have in conjunction with his experience of a word. Thus words begin to become for him part of heaps of images, sounds and actions that can be separated from other images, sounds and actions and the focus of amorphous heaps of experience. At this point care givers should be trying to pick up on what it is babies are trying to communicate and make it known to the baby that they understand or do not.

9. The infant begins to notice that words used by others often have similar contextual elements. Thus words begin to retain elements which are distinguishable as being representative of something. Initially elements are subject to change from moment to moment forming variable chain complexes. When this happens care givers can by trying to concentrate on what babies mean by words help stabilize their meaning for the child. Prolific response by parents and other care givers at this stage will enable the beginnings of a vocabulary which while still unstable and still in the process of error correction is nevertheless a vocabulary.

10. Gradually the infant begins to realize that words as used by adults have permanent elements that the adults mean when using the word and they begin their hunt for these elements. Thus they begin to create complexes that have some (possibly one) permanent element of meaning. At this stage care givers should concentrate on trying to make clear when infants seem to get the meaning right and ignore it when it seems to be wrong.

11. The infant begins to realize that words can have more than one element in common and sometimes the associations they form in complexes seem to include both one element and its opposite in meaning in the adult world. At this point care givers should not worry about this apparent mix up, but continue to recognize when words are used correctly.

12. The infant begins to realize that most of the meaning elements he is giving to words are not understood by adults and thus incorrect and must be eliminated if they are to be the same as adults and thus useful in communication. Thus they eliminate those elements and look for other elements of common meaning to include. At this point children do not need much from parents as the infants are continually running experiments on word to see if they are understanding and using them correctly. Parents should at this stage only correct if children ask them to help.

13. Somewhere along this series of steps, maybe here or maybe later, the infant comes to realize that some words denote categories that have members. A word like dog, for instance, will seem to include a whole host of creatures that can also be denoted by a whole host of words that each represent an individual member of that group. These are of course the breeds of dogs and individual dog names. From then on new complexes are shaped by this idea of a hierarchy of categories and members though the infant would still not familiar with the words 'category' or 'member'. 

14. The infant begins to eliminate members from each complex that do not have all the elements included that seem to be necessary for inclusion as a member of that complex. This may start by determining a single central attribute or element that each member has in common and gradually adding more and more attributes or elements that the member has in common. Thus (complexes) words at last begin to develop meanings that have permanence. This new complex is still not a concept however, it is still a complex, but one that could be referred to as a potential concept. At this point the child has become very active in testing words in different contexts but this time to see which members need to be deleted from each complex to be more closely matching adult concepts. Again infants need little in the way of input from care givers other than understanding and responding to the child's communication.

15. The infant continues refining the meanings of these potential concept words by adding new members to these potential concepts as well as deleting members from these potential concepts. They do this by gradually determining which elements and attributes each member of a potential concept must have in common. Gradually a very rough approximation of meaning emerges for each potential concept that is fairly consistent and stable. As meanings start to become clear to the child and true easy communication is possible the child begins to notice that the words he/she has been using in groups of words have different meanings depending on their order and thus very complex communication is possible. 

16. The infant then begins to notice how words go together in sentences and how this gives further meaning to the word. The child begins to use more and more correct and complete ordering of words to construct clearer meaning. Thus infants begin constructing sentences of their own and the beginnings of true communication emerges. At this point the process begins to repeat itself all over again with children trying out sentences and testing them for communication value. Again care givers should do little other than respond appropriately to the sentences and not try to correct them. 

17. The infant gradually refines the elements of meaning associated with words and the membership of each category to the point that most of the elements and members are correct by adult standards. But they may still include elements and members that are incorrect. These are still complexes but now very accurate ones, allowing children to have a high percentage of accuracy. These may be called pseudo-concepts. At this point everybody can respond to the children and will. Incorrect uses will be ironed out as the child makes occasional gaffs and quickly recognizes that he has done so.

18. Finally with the completion of adding and deleting of members, and a final determining of attributes or elements that need to be in common for each member the child is able to form clear correct concepts that are understandable to others when presented as their word symbols, and thus clear un-muddled communication with adults can take place. 

The infant/child stages not fixed to age. 

It should be noted that the the above is not a practical guide to the child's development of language. As both Piaget and Vygotsky have pointed out the child is never doing just one of these things at a time. It is possible that a child may, in his efforts to understand the world, have heaps, complexes, potential concepts, pseudo-concepts and fully formed concepts, all at the one time. Also these steps do not appear at a specific time in children's lives. They are simply a learning gradient caused by the fact that some things, as Piaget might say, simply cannot be learned unless some other things have been learned already. 

The learning of new words as adults.

Adults are conversant with the idea that words that have no personal meaning may have their meaning derived from elements of human and environmental cues and the structure of sentences in which they are placed. They can use their fully functioning maps of reality to make fairly accurate guesses as to the meanings of words, from those contexts in which they are used. Thus they can usually begin the formation of meaning somewhere between potential concepts and pseudo-concepts.

Words created for meanings and concepts without words.

Of course not all concepts have a single word that is able to stand as a symbol for that concept. All fields of study have their own jargon and that jargon is simply words that stand for concepts in that field of study. Usually those words are not used in normal conversation and thus not part of our common language. They are used instead only when conversing with colleagues in that particular field of knowledge. This is because like all symbols these words are a kind of shorthand for quickly conveying information. Also as new ideas and thus concepts are formed in science and other fields of knowledge there is a need to create new words to stand for those concepts or the co-option of an old word that is no longer used. Old words like 'icon' or 'avatar' or 'iteration' can thus gain new life with a new meaning or even an old meaning that becomes suddenly relevant. Some concepts, especially new ones, have no word to stand for them. Such concepts are difficult to use in our language, and are cumbersome in conveying meaning. It is natural to want to attach a word to any concept to have a way of anchoring its meaning. 

In science we have words like wave and particle. But sometimes we call some things both waves and particles. We clearly need a new word here. A light wave does not change into a light particle it is the same thing. It is not a wave or a particle it is something that has the properties of both a wave and a particle.

The response of care givers in the formation of language skills.

It used to be thought that the way parents etc. could ensure the development of good language skills for those in their care was to expose those children to to vast amounts of language. However, more recent research has shown that the amount of language and even the amount of diverse vocabulary are nowhere near as important in efforts to improve children's language skills as is the way parents and other care givers respond to the efforts of children in attempting to implement those skills.

Learning, recall, understanding and meaningfulness are four sides of the same thing.

Recall and meaningfulness are two sides of the same coin. If we understand something, it is because it is linked to other bits of information and its meaning is derived from those links. The more links there are the more meaning there is. Likewise our ability to recall something is also dependent on the number of other bits of information that are linked to it. Those links are entry points of handles for remembering that something. The more links there are, the more ways there are of returning to the information and thus remembering it. 

In his book *"Brain Rules" John Medina provides us with many ways the brain can be facilitated in enabling recall. These methods also, in the estimation of this site, have the added benefit of amplifying understanding and thus embellishing meaning. They do all this because each of these methods increases the number and variety of links or connections to the item to be recalled. 

This brings us back to learning. If we use repetition to make certain cues activate particular memories we may indeed be able to recall those memories but it is highly questionable as to whether we have learned anything. We are simply able to regurgitate information on demand. On the other hand if we have truly come to understand something we can recall it far more easily because we have learned it. Something that is understood is useful because our understanding enables us to see its application in a wide variety of contexts.

More links or connections means better learning, understanding, meaningfulness and recall.

Ways of creating more links.

1. Understanding. If you are trying to to drive information into someone else's brain, make sure they know what it means. Don't expect your students to memorize anything they do not understand in the hope meaning will somehow magically become clear. It won't.

2. Media. The more mediums a learner learns in the more links there are created in the brain and connecting to greatly varying parts of the brain. Some mediums use many sensory modes. Movies and video use both visual and sound modes. Similarly animation uses the same modes with the visual mode more abstracted. Reading uses the visual mode but is a completely different kind of abstraction. If you can find mediums that use more of the senses so much the better. Also older mediums like drawing, painting and radio are still useful as they can provide new and different links. In fact if you draw or paint yourself you can use that ability build Tony Buzan's mind maps a way of making the links themselves visible.  
   

3. Environment. Create an environmental context for the information to be learned, similar to the context in which it will be required to be recalled. Even using the same room for a particular class would be helpful in cuing the recall of the information. This is because the environment provides more associations that link back to the the memory to be retrieved. Other cues such as the mental state you were in when first acquiring information can help the information's recall if that state is repeated.  

4. Multi sensory. Encourage students to use as many different sensory modes as possible in learning. You can do this by using many different media as is possible. Obviously information acquired in different senses provides further associations to further elaborate the meaning in specific memories.

   1. Auditory. Information presented in the form of sound as in a lecture is the most common method used in teaching. This however, uses only one of our sensory modes and does not do it even by taking advantage of the full range of auditory presentation. It is now known that an auditory presentation can be improved by use of a greater range of sound or the addition of pictures in the form of slides or as narration for some visual animation.

   2. Visual. Pictorial information will always be better remembered than verbal information as conveyed in a lecture but the combination of the two is even easier to remember. Animation with a narrator or a movie will be even more effective if it is about the subject and not just a movie of someone giving a lecture.

   3. Doing. Being physically involved in active learning through exploration even if it is guided by a teacher will also help because the sensory modes of touch and the feeling of muscles in action are added to the mix further elaborating the memory.

   4. Taste. Obviously taste should also be incorporated if it is appropriate. I am sure cooking classes are memorable if you get to eat what you cook.

   5. Smell. Chemistry class was always more memorable probably because the reactions we were testing often involved smells.

5. Stress. Create an environment that is free from stress. Stress actively prevents the absorption of the extra information necessary for elaborated meaning. Although stress offsets this by providing an emotional association such as fear, it is toxic if repeated often. Fear may provide a way of allowing one memory to stand out against other memories that do not have this association, but if all memories have this association, the effect is lost and stress is unbearable.

Life long learning and meaningfulness.

When things are meaningful they are both understandable and interesting. Things that are meaningful to us are are things that we like and enjoy. Meaningful learning is enjoyable learning, internally consistent and compatible with our understanding of reality. It is only when learning becomes fragmented that it loses some of its meaning for us and becomes joyless and unpleasant. If all our learning could remain meaningful to us, we could be empowered with the desire to continue learning throughout our entire lives.