It corresponds directly to the textbook with a soundtrack in standard Mandarin Chinese. The exciting animations make learning Chinese interesting and fun! The English to Chinese is based on alphabetical order of the English words. The Chine Email Address:. Nursery Rhymes. Baby Board Books. Chinese Classics. Western Classics. Bilingual Books. For second language learners, who are often learning characters at a time when they know little of the language, this information is more difficult to use and the learning process is correspondingly more difficult.
But just as learning characters can be more challenging for second language learners it can also be particularly useful. The Chinese language abounds in homophones, syllables that have identical pronunciations but different meanings it has many fewer distinct syllables compared to English, around 6 times fewer if one accounts for tones and around 20 times fewer if one neglects them.
This gives a potential for ambiguity in the spoken language and acts to obscure some of the logic behind word formation. However, neither of these issues translate into written Chinese because homophones are often represented by different characters. Knowing characters can thus help the learner distinguish between homophones and assign distinct mental identities to the different meanings. This, in turn, can help with understanding and remembering words. There is substantial debate in the literature on how characters should be taught and on the level of knowledge that is required at different educational stages [ 10 — 13 ].
This debate, as well as the importance of the problem, is reflected in the wide variety of learning methodologies found in different courses, books and apps. Here we are largely agnostic regarding the best overall approach. Rather, we consider a general question that is relevant to most of them and suggest an answer that is based on broad educational principles. The question we address is the optimum order in which Chinese characters should be learned.
There are two orders that make intuitive sense: in order of usage frequency, from high to low, and in order of network hierarchy, starting with primitives and building up compound characters using components that have already been learned. The first of these follows directly from the goal of the learner but the second merits further discussion. In general terms, the desirability of learning characters in hierarchal order follows from a broad principle of human cognition, that mastery of a complex system rests on mastery of the relevant features of its sub-components [ 14 , 15 ].
This applies to Chinese characters if one assumes that it is productive to treat them as a complex system rather than as a set of unrelated symbols to be learned by rote. A number of experimental studies indicate that this assumption is valid.
They show that orthographic awareness is of critical importance to skilled native readers and in learning to read by both Chinese children and second language learners [ 16 — 22 ]. These also show that orthographic awareness is present whether or not it is taught explicitly and, among learners, that the extent of the awareness is correlated with performance [ 23 ]. We consider learning characters in order of hierarchy to be desirable because we infer that a learning order that explicitly reflects orthographic principles is more likely to generate accurate and productive orthographic awareness in students.
There is, however, necessarily a tension between learning by usage frequency and learning by hierarchy, because frequency is only weakly correlated with character complexity. Learning characters in order of frequency would therefore often mean learning characters before their components had been learned, whereas learning them in order of hierarchy would often mean learning rarer characters in advance of more common ones. This plot shows the weak relationship between character usage frequency and complexity, the latter represented by the number of unique components used to construct the character.
Usage frequency is normalized to 1. The six characters illustrated are the most common in each column. When devising a learning order one can choose either of the extremes, of frequency or hierarchy, or attempt to find a balance between them in which some common characters are learned in advance of their components. One previous approach that searched for such a balance was a network theory-based approach by Yan et al. They demonstrated that an algorithmically-optimized, balanced order can be substantially more efficient than one that follows frequency.
Yan et al. It is unconvincing because they compared their optimized order to only one of many possible hierarchal orders, and there is no reason to believe that the one they choose is representative. Indeed, it will be one of the conclusions of this work that extremely efficient hierarchal orders do exist, ones that can outperform the orders produced by their algorithm. The tension between frequency and hierarchy is a dominant consideration in determining the learning order but it is not the only one.
Small-scale character-to-character patterns are also known to be important, especially for encouraging orthographic awareness [ 25 — 27 ]. Patterns can be chosen to emphasize the logic of character construction, by introducing components directly before their compounds, or to emphasize the functional role of components, by presenting their compounds in sets.
These patterns are often found in human-curated orders, and especially in books on learning Chinese characters for example, those of Heisig and Richardson [ 28 , 29 ]. Patterns such as these are not present in orders produced by the Yan et al. Their procedure generates a degree of character-to-character noise that means that components are rarely adjacent to the compounds that motivate their introduction and sometimes even follow them.
This contrasts with the algorithm presented here, which produces orders with a high degree of logical transparency and strong clustering of related characters. Our algorithm is built on the fundamental assumption that hierarchal orders are the pedagogically desirable way to accumulate usage frequency and we search among this subset of orders for the one that is most efficient. The algorithm is implemented using the conceptual framework of network theory, within which we conceive the network of Chinese characters as a directed analytic graph [ 34 ].
The nodes in the graph represent characters and the edges represent the structural relationships between them. We then sort this list into topological hierarchal order using an algorithm designed to minimally disturb the starting order. The algorithm can be applied to any scheduling task where nodes have intrinsic differences in importance and must be visited in topological order. Following this introduction, we describe the structure of our algorithm in detail, including how we define learning efficiency and how we calculate the cost of learning characters.
We discuss the robustness of the algorithm and study the characteristics of the orders it produces. In the final section we apply our algorithm to a network that is expanded to include Chinese words. Chinese words can be single characters but they are more frequently compounds of two or more. They are the primary units of communication in the Chinese language and so characters, rather like letters in alphabetic scripts, may be considered useful only in so far as they help to build words or act as words themselves.
Reflecting this, words can be moved to center stage and, instead of having character usage frequencies drive the acquisition of components, word usage frequencies can be used to drive the acquisition of characters and their components. We explore the results of this more holistic approach.
The network of Chinese characters can be represented as a directed analytic graph. Nodes represent characters, with their visual forms, pronunciations and meanings, and edges represent the structural relationships between characters and the nature of those relationships, whether semantic, phonetic or otherwise.
Learning Chinese characters means memorizing a productive subset of this network.
Our aim is to derive a character learning order which maximizes learning efficiency. Such an order maximizes cumulative usage frequency while minimizing the effort required to learn it. To this end, we assign a usage frequency to each character along with an estimate for the effort required to learn it, its learning cost. Learning costs are calculated using a model that assumes that characters are learned in hierarchal order. We incorporate usage frequency and learning cost into a measure of character centrality. This measure indicates the relative importance of the character to the learner, prioritizing usage frequency and penalizing learning cost.
Ordering characters by this centrality provides a first approximation to the final learning order. This order is approximate because ordering by centrality does not imply ordering by hierarchy, which must be imposed in a separate step. Hierarchal ordering is imposed using an algorithm designed to topologically sort our centrality-ordered list in a way that minimally disturbs it. Higher-centrality characters are learned first only when allowed topologically.
The algorithm can easily account for characters that are already known to the learner their learning costs can be set to zero or characters that are partially known their learning costs can be suppressed. This capability could be useful in software applications, which could dynamically update the learning order as the student progresses. The algorithm has potential applications beyond the learning of Chinese characters, and can be applied to any scheduling task where nodes have intrinsic differences in importance yet must be visited in topological order.
A typical learning scenario is characterized by a fixed available effort, with which the learner seeks to acquire the maximum cumulative usage frequency as rapidly as possible. The learning process can be visualized as a learning curve in a space defined by axes of cumulative usage frequency and cumulative learning cost. This is illustrated in Fig 3. Efficient learning curves rise quickly and reach high end-points. The curves A and B represent two different learning curves. Learning curves for different orders can be compared visually, as in the figure, but it is convenient to parameterize them.
We propose a two-parameter scheme. The first parameter is the cumulative usage frequency at the end of the learning process, once the maximum cumulative learning cost C 0 is reached. Note that when comparing curves, it is necessary to use the same usage frequencies for characters that appear in both curves, even though the curves may not cover identical sets of characters. To ensure this, we normalize the entire usage frequency data set to 1. The second parameter concerns how the maximum cumulative usage frequency is approached.
Consider the two curves shown in Fig 3. Curve A might be one that prioritizes longer-term cumulative frequency at the cost of shorter-term. The difference would be immaterial if the learning process had a short extent in time but this is not typically the case. Learning may take place over many months, during which the learner would likely be exposed to other parts of the language.
In this case it might make sense to have a learning curve that rises quickly, even at the cost of some longer-term cumulative usage frequency. This quantity is the ratio of the benefit and cost that each character represents to the learner. These learning curves will rise steeply and have high end points, or, in the language of the previous section, be characterized by high integral and final learning efficiencies.
Values for f i can be extracted from corpora of written Chinese. Values for c i are more difficult to assign objectively and we estimate them using a learning model. In our model we use different procedures to assign costs to primitives and compound characters. The cost of learning a primitive i is taken to be 3 where s i is the number of strokes that make up the character. The cost of learning a compound i is taken to be 4 where m i is number of combinations used to build the character.
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This means that the cost of learning the simplest primitive would be similar to the cost of learning the simplest compound. A typical primitive would be around twice as difficult. Our learning cost model assumes that characters are learned in hierarchal order. When we calculate the cost of learning a compound character we do not include the cost of learning the components themselves, which we assume have already been learned. Our model implies that the total cost of learning a fixed set of characters is identical for all hierarchal orders.
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All final learning efficiencies will be identical, with the only differences being in the integral learning efficiencies. Learning characters in order of centrality prioritizes characters that are useful and easy to learn but it does not ensure that characters are ordered according to the character hierarchy.
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