Usually characters are acquired as isolated individual items that happen to be
present in a given context, and the learner is subjected to absorbing many characters
of diverse complexity in form and meaning. Usually a story of some kind is present,
and the prime interest of the learner is in the story aspect of the lesson. As
such, the main focus of attention is in the story, while character learning is
secondary and incidental. Traditionally, the teacher always makes a big point
about the proper stroke order of writing. It in not uncommon that a character
is copied 50 or 60 times, or more. A better way of teaching is needed, since thousands
of characters must be learned and used. However, the standard answer has been,
"But, this has always been the way traditionally taught, and for thousands
of years!", as if to say, "Who are we to question it?! It is the only
way we know, therefor, it must be right."

At this juncture, it seems most appropriate to quote Lew (1923): "But,

of the millions of (Chinese) children who started on the way of learning, only a small percentage ever arrive at the stage of "wen-li t’ung", which practically means to be able to read and write literature and composition intelligently." (p.6).

He continued, "It goes without saying that the problem is a tremendous and complicated one. One will be most fortunate and happy to be able to touch the corner of one phase of it. Even to do that much successfully is by no means the work of a few years" (p.13).

Indeed, this educational problem is an urgent as well as a tough one. But, something must be done to make this language more accessible to the vast school populations of Western China, and to the ever-widening circle of Western adults who need to have contact with some of the one million Chinese-speaking persons around the globe.

Fortunately, much progress has been made in cognitive psychology during the last decade; the science of cognition attempts to understand the nature of human intelligence and how people think (Anderson, 1980). This science is dominated by the information processing approach, which analyzes the cognitive process into a sequence of ordered steps, from which are discovered various aspects of human intelligence (Rumelhart, 1977). We desire to infuse this body of knowledge with that of Chinese orthography for arriving at some practical applications (PART IV).

 

A. PERCEPTION
In terms of "form", a Chinese character is a meaningful unit of information which is 2-dimensional in nature, in contrast to the 1-dimensional alphabetical system of the West. But, when actively looking at a character, just how does one perceive it? Is it by tracing out the character stroke-by-stroke the way the native Chinese learn it, or by some other means? This has been a central question in the minds of the linguists.

In essence, we are asking how the visual information from a character is perceived, and how perceptual patterns of a character are formed. In order to answer these more general questions, we need to have the specifics regarding: (1) sensory memory: How does it work when actively looking at a character? (2) attention: What is its nature, and its role in information storage? (3) pattern recognition: What is "feature analysis", and what are the features of a character? (4) context: What are the processes operative in reading a character?

How does one look? According to Stark and Ellis (1981), initially the saccadic eye movements continually reposition the fovea. And, in the checking phase, repetitious sequences of saccades are generated. These are called "scanpaths." This visual process is used for understanding the process of cognition. It is hypothesized that eye movements are controlled by cognitive models already existing in the brain.

The scanpath theory of Noton and Stark (1971) postulated the feature-ring model, which is an assembly of alternating sensory- motor elements (Fig4.1). These sensory elements are semantic sub- features of scenes or pictures being observed, and the motor elements are the saccades representing the syntactical structural organization of the scene. Scanpaths were observed during the first viewing of a picture, and re-occurred early in a reviewing session with a cognition test (Stark and ellis, 1981).

"Active looking" may be defined as an attempt to discern meaningful patterns. One does not obtain the whole pattern right away, but seeks to identify the sub-patterns. Thus, the pattern recognition process is hierarchical in nature.

How does one look at a character? A Chines character is a pattern. It may be viewed as a long sequence of individual stroke patterns, or as nested meaningful sub-patterns for a relatively complex character. Is there any difference in the way one looks between a beginner and an expert? An eye movement experiment was set up to measure the scanpaths by two different types of subjects on two different kinds of characters: simple, and compound.

.EYE MOVEMENT EXPERIMENT
As a joint project with F.C. Sun and L. Stark at University of California, Berkeley, a series of eye movement studies was conducted to determine how the eye moves in active looking at Chinese characters. The eye movement measurement used the scleral reflection technique (Stark, et al., 1962), sampled at 20 Hz by the computer. Computer programs, developed by Freksa et al. (1980) and Stark et al. (1979), were embedded in an online laboratory operating system. Two kinds of characters were used, namely: simple and compound characters, and two types of subjects were employed, namely: beginners and experts. The beginners were non-Chinese college students of the University of California, Berkeley, with 2 to 3 years of study of the Chinese language, while the experts were native Chinese scholars.

From the data collected on the beginners, it was not possible to discern a definitive pattern of eye movement either on simple or compound characters. However, interesting remarks may be made of the eye movements by the experts on both the simple and the compound characters.

Fig.4.2a shows the scanpath for a simple character, while Fig.4.2b displays the actual size of the test character MOUTH. Pertaining to Fig.4.2a, the starting point is at 1, then the eye dashed to point A and stayed there for a while in order to capture the significant features in that general area. Then the eye moved successively to points B, C, D, E, ending at E. The movement of the eye was never smooth as it dashed about in between the points. At each point, it lingered long enough to gather the local features. It is clear that the eye does not move according to the stroke order at all, but rather moves in such a way as to conserve the overall energy required. If the eye were to move in accordance with the stroke order, it would mean redundant movements in some paths, and thus a waste of energy. Fig.4.2b shows the test character MOUTH in its actual size, so designed that at a normal viewing distance of about 28.5 cm. by 10 cm. square, which corresponds to a viewing angle of 0.5 degree. By superimposing Fig.4.2a onto Fig.4.2b, a good 1-to-1 correspondence is observed between the two.

Fig.4.3a shows the scanpath for the compound character SPIRIT; Fig.4.3b shows the test character in its actual size. Upon superimposing the two corresponding figures, we see that the eye tends to dwell at the center of a given sub-feature of the character.

The above data shows that the eye moves in such a way that it dwells, not according to the stroke order of a character, but somewhat corresponding to the center of the sub-features of the formal elements of the test character.

As background information on the topic of perception, the work of Rumelhart (1977) may be cited, which provides a good introduction to human information processing. Specifically, it describes the flow of information from the environment through the information- processing system to the general knowledge system. Fig.4.4a is a block diagram that depicts the inter-relationship among the sensory system, attention, and the general knowledge system. Fig.4.4b is an alternative representation, while Fig.4.4c shows the sensory-motor interactions pictorially.

1. SENSORY MEMORY
When a character is first seen by a person, it is registered in the sense organ of perception, and then recorded in the sensory memories, namely: (i) The ionic memory, for visual information, and (ii) The echoic memory, for audio information. But, what is the nature of such memories? They possess two important characteristics: (1) regarding capacity, they can hold a great deal of information, but (2) regarding duration, they can hold it only for a brief period of time, say less than one second.

Consider the character SPIRIT. If the individual strokes were used as the basic information units, then it would take about 10 seconds to trace out the 24 strokes. This is simply too long a time duration. But, if thue same character is represented by the two meaningful sub-parts, HEAVY RAIN and MAGIC INCANTATION, then 2 units of meaningful information can easily be held in less than one second.

2. ATTENTION
The sensory memory is also called Very-Short-Term-Memory (VSTM), in which the information is lost if not quickly attended to. Thus, "attention" plays an important role in selecting sensory information for further processing (Anderson, 1980). Fig.4.4b shows that it is through attention that information is transferred from the VSTM into the Short-Term-Memory (STM). Attention is a very limited resource, which is sometimes thought of as being single-minded because generally one does not have the capacity to perform two demanding tasks simultaneously. But, tasks that are practiced to the point of perfection require little or no attention, and thus can be performed simultaneously.

If one attends to cued information units immediately, they will be saved from fading. But, if a cue is delayed, the corresponding information unit will be lost. Therefor, the fewer the number of information units, the smaller the processing time, and therefor the delays of the information may be saved from fading.

It would be ideal to have a minimum set of basic information units as building blocks for all characters. Thus, it would then be feasible and worthwhile to commit this set to repeated attention until little or no attention were required. The "building block" concept makes possible automatic elaboration of these basic units since they will appear again and again in different derived characters. For, elaboration enhances recall.

3. PATTERN RECOGNITION
How are perceptual patterns of a character known? It appears that patterns are not recognized as un-analyzed templets, nor broken down into meaningless strokes, but rather into smaller features of the formal elements of a character that can be recognized more economically and efficiently. The patterns we perceive are combinations of such features, with the "relational operators" and hierarchal levels as the connections. That is, we identify patterns by processes that recognize feature configurations.

If the pattern is familiar, the stimuli will be recognized automatically without intercession of "attention". But, if the pattern is unfamiliar, attention must ne directed to the stimuli to synthesize the features into a pattern.

According to the "feature analysis" theory, composition of patterns are first recognized and then combined. Pattern recognition involves the integration of bottom-up and top-down processing. The former refers to the use of sensory information in pattern recognition, and the latter to the use of "context" of the pattern and general knowledge in recognition.

There is more to pattern recognition than mere feature combination alone. "Context" also plays an important role. This will be discussed next.

4. CONTEXT
So far, the type of processing discussed here has been bottom-up, because the information flows from the little perceptual pieces (features) to larger units built from them. However, if perception were totally bottom-up, it would be impossible to read or hear (Anderson, 1980). On the other hand, we all have the experience that in normal reading we do not bother to detect every feature, every letter, every word, even every phrase. Sometimes, we read without even processing every sentence.

Consider the example of Fig.4.5. We perceive this as THE CAT, even though the H and A are shown as identical. The general context provided by the words forces the appropriate interpretation. When context, or general knowledge, guides perception, we refer to the processing as top-down, because high- level general knowledge determines the interpretation of the low- level perceptual units (Anderson, 1980).

 

B. REPRESENTATION OF KNOWLEDGE
How are images of a character formed? What is the mental imagery of a character? How is the information represented in the memories? What are "schemata" and what role do they play?

.MENTAL IMAGES
Mental images are encoded small units of knowledge, and we are interested in the internal representation and processing of such information. An image is not a mental picture in the head; differing from a picture, it is (i) segmented into meaningful pieces, (ii) not tied to visual modality, and (iii) not precise, and can be distorted. Therefore, mental images are abstract-analog representations of objects (Anderson, 1980).

Chinese characters are rich in images; some characters are even pictorial. But, a character in modern script differ from a picture in that a compound character can be segmented into meaningful pieces, called the formal elements. For example, in fig.4.6, the character DAWN is segmented into two meaningful pieces: The SUN, and the HORIZON. Thus, some Chinese characters are abstract-analog representations of objects.

Fig.4.6 shows that Chinese characters are, in fact, a perfect external representation of internal knowledge. But, instead of leaving it to the novice to haphazardly process the information, let the linguists design it properly for consumption by the learner. This is an instance of the "Importance-matching" concept in action (this concept will be elaborated in Chapter VII). But, where is such information stored?

The encoded small unit of knowledge are represented in the Long- Term Memory (LTM) in abstract form. A Propositional Network Representation (PNR) is shown in Fig.4.7, which reveals the association between concepts. The closer together the concepts are in the PNR, the better the cues for each other’s recall. Fig.4.8 is a corresponding PNR for the character SPIRIT of Fig.4.9, such that only the closest concepts are shown and with a minimum of hierarchy presented for optimum effectiveness and efficiency in learning.

.REPRESENTATION OF INFORMATION
The encoded small units of knowledge in the LTM are not tied to a particular sensory modality, but rather are the segmented meaningful features. Initial memory for an event contained both the verbal and visual details; however, these details were rapidly forgotten within the first minute following the stimulus, leaving only memory for the meaning of the event (Anderson, 1980).

Similarly, Fig.4.10 shows the initial unfolding process; a substantial amount of information was presented to the learner, but this would have been rapidly forgotten within a short time had it not been organized in the form of a hierarchical tree of Fig.4.9. The unfolding process of teaching Chinese characters may be described as follows: First, the meaning of the character is given, then, the character is decomposed into meaningful parts in terms of its formal elements. Subsequently; each meaningful part is explained. This process is repeated until all the atomic elements are arrived at and explained.

.SCHEMAS
Schemas are used for internally encoding larger and more complex units of knowledge (i.e., categories of objects, classes of events, etc.). Members of a large natural category do not all share the same set of defining features, but are related by a "family-resemblance" structure.

As a counter-part, we have constructed external schemas. Specifically, a group of characters is put into one category such that they become members, and together they share some key features. For example, Fig.4.11 shows a schema pertaining to the primary signific one, in which are contained two sub-schemas headed by the two derived significes, TWO and RAIN. Both of them share the same features, ONE.

Now, take the case of TWO, which in tern has two sub-schemas, vertically, and horizontally. Vertically, we have a direct lineage of these characters: TWO,THREE, KING, and PRINCE. In this vertical series, the members of the group possess the following mathematical properties: If A is a subset of B, then A is included in B. That is, every element of A is also an element of B. Specifically, A is a proper set of B, if A is included, and A dose not equal B (i.e., at least one element of B is not an element of A). Therefor, the relationship is referred to as "inclusion" in set theory. Thus, when applied to this group of characters, we may write:

@@@@@kkEsfKK@@@

and, this is called a "proper set".

 

C. HUMAN MEMORY
How does the human memory work? What is STM, and chunking? How is information stored and retrieved? What is recall? These questions will now be considered with particular reference to the learning of Chinese characters.

1. SHORT-TERM MEMORY
STM refers to the capacity for keeping a limited amount of information in the active state. Information can be used only when it is in this state. STM holds the "nodes" of the LTM network. The "connections", in contrast to the nodes, will disappear when information leaves the active state.

Since the nodes and connections are so vital to keeping information about the character(s) in the active state, these should be carefully constructed by linguists, especially the nodes, since they have long-lasting effects in the LTM. The hierarchical tree is the result of such an endeavor, its structure being derived from the PNR.

The nodes and connections should be carefully designed so that they are not only appropriate for the context proper, but also can be used outside of the context. Therefor, these qualities of the nodes and connections should be very much a vital part of the instructional design.

STM serves as a repository for knowledge that is required by the cognitive processes being performed. It contains the information we are immediately aware of (i.e., we have direct access to the contents of the STM only). The information processing procedures can not be applied to information outside of the STM.

.CHUNKING
The capacity of the STM varies with the meaningfulness of the material. Miller (1956) introduced the term "chunking" to describe these units of memory. He stated that memory is limited not by the number of physical units (letters, syllables, or words) in the stimulus, but by the number of meaningful chunks, and that the subjects remembered approximately seven chunks. There appears to be a STM encoding the information temporarily, as contrasted with the LTM, which holds information for hours, days, and years. A fundamental question is whether the STM is in a different mental location than that of the LTM, or whether it is in the same location but in a special state. Evidence favors the later conclusion (Anderson, 1980).

This knowledge when applied to Chinese characters suggests that it is not desirable to have a character with more than seven strokes, if the individual strokes are used as the basic units of information. Since there are many characters that are composed of seven strokes or more, learning by a stroke-oriented scheme may be inefficient. But, on the other hand, if the formal elements of a character are used as the basic units, then the problem is dissolved

2. LONG-TERM MEMORY (LTM)
These chunks are stored in the LTM In fact, they correspond to the nodes of the PNR. When the subject remembers a previously displayed stimulus, the corresponding nodes are activated for immediate access. The process of bringing the nodes into an active state is called "activation".

The items of the STM are the same items in the LTM permanently stored, but the network links connecting the nodes are not permanent. Since these connections are not permanent, a particular configuration of the STM information will not be permanently retained. However, the information about the connections between the nodes can be transferred into a permanent LTM state while being held in the STM. A case in point is when one permanently commits to memory a phone number.

.INFORMATION STORAGE
A piece of information is retained when properly transferred from the STM to the LTM. This process is called "information storage". But, how does this process work?

When information is committed to memory, it is elaborated. More fully elaborated materials result in better memory (Craik and Lockhart, 1972). But, elaboration is not merely repeating things, elaboration increases the redundancy which information is encoded in at least two ways: (i) structurally: The elaborated structure provides parallel paths in the information network. (ii) inferentially: Elaboration aids memory by inferring what can no longer be remembered. Both processes help recall because they provide more paths for retrieval, and bases for inferring and reconstructing the to-be-remembered information.

Elaboration increases the depth of processing, which reflects how fully processed is the meaning of the material. Memory can be improved by manipulations that increase the amount of elaborations. Such manipulations affect the depth of processing (Anderson, 1980).

When learning characters, we can externally create parallel paths to increase the redundancy for encoding information in the memory. In fig.4.11 and Fig.4.12, two parallel paths are created via connections al and cl. Specifically, the character Three can be explained in terms of the characters ONE and TWO. It can also mean TRINITY, which may then be explained in terms of HEAVEN- EARTH and HUMANITY.

On the other hand, elaboration may be achieved by inference. Suppose one could not remember the meaning for the character PRINCE; but, upon seeing its form, of which the two meaningful sub-parts are:’ and { , one is reminded of the flame and the lamp base. Thus, by connecting the two ideas, one gets the idea: "Flame rises above the lamp". Thus, by inference, he remembers: "Prince rises above the multitude", therefor, the meaning, Prince (connector bl of Figs.4.11 and 4.12).

Another example is shown in Fig.4.13, in which a "family- resemblance" structure is superimposed on a group of related characters (Fig.4.11). Such related characters were found through synthesis. The paths so created help recall during information retrieval.

Fig.4.7b demonstrates the phenomenon of the spread of activation: When the word "dog" is presented to the subject, other related concepts also get activated. This notion of the spread of activation is also fundamental to the understanding of recall from the LTM back to the STM.

Due to spreading, the amount of active information can be much more than the "approximate seven" (Miller, 1956), which merely represent the core focus of one’s immediate attention. Meanwhile, the spreading activation and the external stimuli continuously create a wide fluctuation in activation around this core. But, the spreading process is not entirely under one’s control. This unconscious priming of knowledge is called "associative priming", which affects the rate information items are scanned.

In Fig.4.14 and through the connector d1, a good example is shown of the spreading effect. It starts with the concept of ONE. In addition to the previously described path of TWO, THREE, KING and PRINCE, it also spreads through HEAVEN and EARTH, to the signs of YIN, and YANG, to the sign of ONENESS, and finally to the mondala for TAO.

.RECALL
Recall is often an act of reconstructing a memory event, in which are combined: (1)) information from the to-be-recalled event, (2) elaboration of the events (3) the context of the events, and (4) general relevant knowledge. Information is better recalled if presented in an organized framework, which makes possible systematic search during retrieval.

Regarding (1), Bower (1969) investigated hierarchical organizations involving a loose associative structure. Even such a presentation resulted in considerable advantage over a random one (Anderson, 1980). But, a more organized structure is much better. In more organized conditions, a memory network is formed during the study phase. To do this, the already existing connections are elaborated. This organization makes possible a structured search of information later. That is, it makes information retrieval more efficient.

But, the act of actual recall is not mealy the reconstruction of past events. In typical life situations, a great deal of inference is involved. The inferential process takes place at two different times: (i) at study, the subject uses it to elaborate a memory, and (ii) at test, the subject reconstructs the memory.

Regarding (2), subjects elaborate the information they study. This is done by means of: (a) connections to prior knowledge, (b) imaging and inferences about the material, and© features from the current context. The process of elaboration leads to improved memory by: (i) increasing the redundancy of interactions among the to-be- remembered information. But by redundancy is not meant simply making multiple copies of the same thing. Rather it is the storing of additional propositions that weakly or strongly imply the target event. (ii) imposing an organization on the information to guide the retrieval process. (iii) increasing the number of contextual elements overlapping between study and test. Regarding (3), context influence memory. Reviving the context of study aids recall, as the subject would have additional ways to reactivate the target memory. Such context effects are often referred to as "encoding effects", because the context is affecting what is encoded into the memory trace of the event recorded.

The encoding_specificity principle states that the probability of recalling an item at test depends on the similarity of its encoding to its original encoding at study.

Another factor influencing the learning contexts is the "spacing over time" of the context (Madign, 1969). Memory improves with the increase in lag between episodes up to a certain point. At longer lags, it is likely that the two study contexts will be quite different from each other. The greater this difference, the greater the possibility that one of these contexts will overlap with the test context. Therefor, we should space our study of a particular material over time. If such time-spacing is not possible, one should change the physical location in which one studies. Furthermore, on a more abstract level, one can change one’s perspective of study on the to-be -learned material.

We do not have direct access to information in the LTM; it must first be activated from the LTM in order to be recalled. Activation spreads along paths of the network from the currently active portion of the memory to the to-be-retrieved portion. The speed at which activation spreads along a path depends directly upon the strength of the path and inversely upon the number of competing paths.

The negative effect of competing paths on the rate of spread along the desired path is called "associative interference". If the speed is too low, it may result in failure to recall. The slowness may be due either to low strength of the desired path, or strong associative interference.

Activation takes time, and so recall of information already in the STM should be faster than in the LTM. More rapid activation is possible if the material is better learned, and strongly encoded (i.e., with a good memory trace). A memory trace is the e coding of a memory event. For instance, the repetition of a remembered event would constitute a memory trace. The speed of retrieval varies with the strength of the memory trace.

At short test delays, repetition has very little effect on the speed of recall. On the other hand, following a long delay between repetitions (say, three or more intervening items), considerably faster recall was found with the more frequently studied items. The effect on retrieval time and the effect on retention are manifestations of the same underlying mechanism.

The source node is defined as the node from which the spread of activation starts, which has a certain fixed capacity for emitting activation. This capacity is divided among all the paths emanating from the node. The more paths there are, the less the activation assigned to any one path, and the slower the rate of activation. "Fan-effect" is the mane given to this increase in reaction time due to increase in the number of facts associated with a given concept. "Interference" is the more general term when additional information about a concept interferes with the recall for a particular piece of information.

Interference can reduce the speed of retrieval. When the interference is very strong, or when the to-be-recalled fact is very weak, failure to remember occurs. Failure is the extreme case of a long retrieval time. It is not that the forgotten information is not in the memory, but rather that the information is too weak to be activated in the face of strong interference from other association. Thus forgetting is not loss of information, but the inability to activate that piece of information from the LTM.

 

D. LEARNING
In this section, we shall first distinguish the two basic kinds of learning: Learning by rote, and meaningful learning; then, discuss the key points of Ausubel’s theory of concept learning, and examine finally Millward’s computational theory which integrates the various concept formation models.

We have found that Ausubel’s theory fits in well with the modern theory, in that it constitutes the "descriptive knowledge" aspect of the modern theory.

.AUSUBEL’S THEORY OF CONCEPT LEARNING
According to Ausubel (1978), the two basic types of learning are: learning by rote, and meaningful learning. Their differences are clear from the following definition:

.LEARNING BY ROTE: A learning process by which new information is added to the learner’s knowledge structure (cognitive structure) without establishing any relationship with the concepts already existing in the knowledge structure of the learner.

.MEANINGFUL LEARNING: That learning process by which new information is related to the relevant concepts already existing in the knowledge structure of the learner.

Ausubel stressed the importance of meaningful learning (Ausubel, et al; 1978), as opposed to learning by rote. Meaningful learning takes place through a process of "subsumption": An interaction between the new concept (the subsumed) and the more inclusive concepts (subsumer). It results in a modification of both the subsumer and the subsumed concepts (Novak, 1977). While the subsumer gets enriched by the addition of a new specific instance, the subsumed becomes part of a more general concept.

The formation and assimilation of concepts are the main concern in Ausubel’s theory.

.CONCEPT: A concept is that which describes some attributes or relationship within a group of facts, and can be designated by a symbol (Novak, 1977).

Meaningfully learned material becomes part of the subsuming structure of the learner, which is the most crucial factor in facilitating subsequent learning. Things learned meaningfully are less likely to be forgotten (Norman, 1973; Mayer, 1975). Even when forgotten, (i.e., what remains is a richer general concept) (Novak, 1977). Knowledge tends to be organized hierarchically as a result of the subsumimg process (i.e., less inclusive concepts get subsumed under the more general ones).

The importance of "structure" to learning is that structure affects the stability of knowledge in memory (Norman, 1973). Subjects with well organized knowledge structure demonstrated better performance on delayed post-tests. Well organized knowledge facilitates the retrieval of appropriate knowledge during problem solving (Mayer, 1975).

Pertaining to meaningful learning, there are two different processes, namely: (i) Progressive Differentiation, and (ii) Super-ordinate learning.

Progressive differentiation is a process of successive refinements of a general concept. This is the most common way to acquire new knowledge. For example, to many young children, all animals with four legs are "horsies". But later, by successive subsuming processes, this concept gets more refined, as horsies are differentiated from other four-legged animals.

Super-ordinate learning, on the other hand, is a process of "ordering", in that concepts already existing in the knowledge structure get subsumed by a newly introduced more general concept. For example, "brothers", an already existing concept, becomes part of the newly introduced concept, "men". A particular case of super-ordinate learning is called "integrative reconciliation", in which several concepts are tied together by the acquisition of a new rule. For example, "papayas" and "mangos" become part of the concept, "fruits".

.DISCUSSION
It is clear from Ausubel that the traditional "learning by rote" is inferior to "meaningful learning". But, how to apply "meaningful learning" to the study of Chinese characters?

A new character to be learned is to be treated as a concept, and as such it must be related to the relevant concepts of the formal elements within the character. And, these relevant concepts should be already existing in the learner’s knowledge structure.

For example, consider the character SUDDEN RAIN, as a new concept to be learned. It must be related to the relevant concepts within the character. In this case, the relevant concepts are RAIN and BIRDS corresponding to the formal elements of the character, namely: ^{8), and} (). These two concepts, in order to be relevant, must have already been introduced in the previous lessons of the instructional design, and therefor, already existed in the knowledge structure of the learner. It is also important to note in the instructional design, the character RAIN should be introduced first because it is a general concept, while the character SUDDEN RAIN is a concept for a special kind of raining phenomena. This ordering in the instructional design corresponds to the process of "progressive differentiation", where a top-down learning process is at work, and whereby the general concept of RAIN is, by successive refinement, narrowed down to a more specific one, SUDDEN RAIN (Fig.4.15).

In summery, the main points of Ausubel’s theory are:

(1) Knowledge is organized hierarchically in the knowledge structure of the learner.

(2) More effective learning occurs when the more inclusive concepts (i.e., the more general, and more pervasive concepts) are introduced first.

(3) The most crucial factor in facilitating subsequent learning is to make the meaningfully learned material become part of the subsuming structure of the learner.

.MILLWARD’S COMPUTATIONAL THEORY OF CONCEPT FORMATION
According to Millaward (1981), "concept formation" is the process of learning appropriate concepts for a given situation, and the learner is guided by a schema of some kind.

A native individual is primarily guided by simple basic-level schemata that are not particularly appropriate for the situation. Thus, his behavior is not integrated into purposefully organized sequences efficiently.

Even though without a higher-level schema, one nevertheless learns from his experience. That is, after repeated interactions with the environment, one almost inevitable becomes less naive as one learns to adapt. Unfortunately, the events of experience so encoded are often inconvenient or inappropriate for later retrieval and use.

Millward’s computational theory begins by assuming that episodes are stored in the memory by encoding. Data presented to the system cause schemata to be active (data-driven). Each activated schema has built into it an anticipatory function (goal-driven) that elicits other schemata. Higher -level schemata activate and order other schemata. The frequency of features is especially important for perceptual schemata. However, schemata sequencing is not influenced by the frequency features. Schemata should not be thought of as fixed entities, but rather as dynamic structures constantly undergoing change. We are continually debugging our schemata and modifying the sequence of actions to make them function more efficiently. The relevance of Millward’s work to the learning of Chinese characters will be discussed in the ‘DISCUSSION’ section.

Millward’s computational theory consists of three phases: (i) formulation of concepts, (ii) usage of the concepts, and (iii) flow of concepts.

Regarding (i), he describes four types of models for concept formation, namely: Prototype models, the Exemplar model, Frequency models, and the Rule model. He says the main problem with the current state of theorizing is the lack of integration among existing ideas.

Regarding (ii), he states that experiences are encoded by rather elaborate cognitive structures: (a) Frames (Minsky, 1975), (b) Scripts (Schank, 1975), and© Schemata (Bobrow, 1977).

Regarding (iii), the conceptualization process during learning may be defined as: (a) finding identifying attributes, and (b) generating functional cores, and© establishing scripts (Nelson, 1977).

Finding attributes has been the focus of the classical concept- learning theory. The definition for concept has been based on features, and is dependent upon repeated experiences with the concept, which leads to its modification and refinement. The identifying attributes, once defined, allow a concept to be used outside of its original context. This is the important mechanism by which knowledge is accumulated and organized hierarchically.

"Functional cores", basic to the meaning of events, represent how concepts are used, while "scripts" organize the flow of concepts, and thus provide an inter-relationship.

.DISCUSSION
In the following, we shall discuss the relevance of Millward’s theory to character learning. It is important to define a minimum set of identifying attributes for Chinese characters. Once these atomic elements are defined, they can be used outside of their contexts for understanding and learning other characters. In so doing, the frequency of usage of the atomic elements is greatly increased, and repeated use leads to efficiency in learning. We shall formally define the "minimum set" (i.e., the minimum set of atomic elements for Chinese characters as that set of formal elements composed of significes, phonetics, and primitives (Wieger, 1965; Chu, 1981).

The "functional cores" concept when applied to Chinese characters refers to how the concepts of the formal elements of a character are used in relation to each other at different levels of the hierarchical tree.

The "script" concepts when applied to Chinese characters refer to the flow of concepts and the inter-relationship between them from level to level in the successive unfoldment of the meanings of the character.

The traditional way of learning Chinese characters is by rote Learning by rote is a typical example of inappropriateness of encoding and inconvenience of retrieval. One simply stores into the memory isolated facts without any connections to other concepts already existing in the knowledge structure of the learner. Such learning generally is slow and gradual, such memorization partial, and such knowledge organization clumsy for later retrieval and use.

We desire to know what learning processes are responsible for efficient learning by the expert learners. Three possibilities exist, namely:

(i) Existing schemata are modified so that they become more suitable for the environment.

(ii) Schemata are sequenced and combined into a higher-level scheme appropriate for the new environment.

(iii) New schemata are created for the specific context.

Now, let us see how this knowledge can be applied to learning characters. For example, regarding (i), let us first assume the existing schema to be the set-theory model of Ch.VII. Therefor, for the character SPIRIT, we have the following components according to the model:

a = magic incantation, b = heavy rain, and R = to invoke.

But, suppose that the learner simply does not understand the meanings of the words, "incantation" and "invoke"; then one is stuck, and the existing schema is inadequate. It, therefor, must be modified in order to make the meanings more accessible to the learner. This is done by nesting the set-theoretic model such that the meaning "magic incantation" is replaced by "the work of the witches". The latter meaning is certainly easier to understand since its meaning is more general.

The more general the knowledge, the more accessible it is to the learner. Likewise, we can replace the meaning of "to invoke" by "to get" (Fig.4.8).

Next, we consider another example for (iii). Fig.4.16 shows that the meaning for the character RAIN is "from the sky, clouds become falling droplets." Therefor, RAIN. But, since four entities are there, namely: SKY, CLOUDS, FALLING, and DROPLETS, the existing schema is not adequate. Therefor, some modifications must be made in order to be appropriate for the new environment. Specifically, in this case, two set-theoretic models are combined. They are placed side by side, by the intersection of the common element, CLOUDS