Using the ingredients from Part 1 I created three draft lessons for iSimplifiedChinese. In this post I analyse them in order to learn how to improve and expand the course.
All lesson material is shared under CC-SA. A Chinese speaking friend of mine was kind enough to check the material for errors, but as usual use it at your own risk 🙂
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Update 15-02-2011: You can find the most recent lesson material including pronunciations here.
Analysis
Chinese words can be split in an initial and a final. If you learn how to properly pronounce all 21 initials and 33 finals and if you use the correct tone, you’re all set.
The two figures below show all initials and finals and how often they occur in the course material. As can be expected some are more common than others.
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What distribution should I strive for? I assume that if I don’t pay attention to it, I will end up with more or less the distribution found in the real world. That means students will practice pronunciation based on how frequently they’ll likely need it. I could also strive for an equal distribution, so all sounds receive the same amount of practice.
A third alternative would be to emphasize the ones that are difficult, as it may not be very useful to practice something that is easy. The figure below on the left splits the initials by difficulty level. I don’t have enough user data yet to get a quantitative picture of how difficult each initial is, so I manually divided them based on the pronunciation tips here:
- easy: b p m f d t n l g k h ch sh s
- medium: j zh r z c
- hard: q x
Most of the current material consists of easy initials. Would the course be more efficient with a higher percentage of orange and red?
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You can dive deeper into initials (consonants) and look at their place and manner of articulation. The resulting distribution is shown below.
In addition I looked at the distribution of aspirated (p, t, k, q, ch, c) versus their non-aspirated counterparts (b, d, g, j, zh, z). They show a 50/50 distribution (figure above on the right).
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Finally the one thing Chinese is famous for: tones. There’s five of them if you include the neutral tone. You can hear the difference in this wikipedia article. Probably not a correct sentence, but it makes the point: “妈妈是马吗?” = “Māmā shì mǎ, ma?” = “Mama is a horse?”. The pie chart below shows that all tones are used in the course, although the neutral and second tone are used less often.
Functional Load
In an update to the previous part I mentioned a paper by Surendran and Levow from the University of Chicago’s Computer Science Department. The authors describe a quantitative method to determine how important certain aspects of language, such as tone and vowels, are. The term they use is Functional Load and it’s related to the entropy of a language as measured using a large corpus of text.
Being a physicist and despite my math being a bit rusty, it always feels great to be presented with a mathematical framework that looks like something I can actually apply in the real world. The only thing I haven’t figured out yet is how.
In order to get my head around this problem a bit, I compared one table from their paper with my own data in the two tables below. Do keep in mind that they represent two completely different things, but that’s alright for now.
The question Surendran and Levow answer in the table on the left is something like this: “How important is it to correctly distinguish between the first (high) and third (low) tone?”. That is how important it is to hear the difference between mother (māmā) and horse (mǎ). They ask this question for each combination of tones.
The way they answer that question is by imagining a language where this difference doesn’t exist; mā and mǎ would become the same word, obviously leading to some confusion. The question is how much confusion; for example if English no longer had the distinction between the words “a” and “an” it wouldn’t be as bad as when it no longer had the distinction between “I” and “you”. If I understand correctly, they look at the amount of information that can be expressed in the normal language and compare it to the amount of information that is lost in the imaginary language.
You can do this for individual syllables or complete words. The difference is that if you mispronounce a single syllable it’s hard to figure out which syllable you meant, but if you mispronounce a syllable inside a larger word you can use the rest of the word to compensate, e.g. “nuclear” versus “nucular“.
They find that the distinction between the first (high) and fourth (falling) tone is the most important, followed closely by the first-third combination described above.
In the table on the right I looked at words that would be homonyms if tone is ignored. Should I add more unigrams, in particular those with high functional load? Or is it enough to just make sure all tones are covered in the course?
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The authors also looked at the functional load of other features in Mandarin, as shown in table 1 of their paper (figure on the right). I’m not sure if it’s correct to assume that consonants are four times more important than vowels because their functional load is four times higher. But I do think it makes sense to focus on consonants, vowels and tones, because that’s where most of the information is.
It also makes sense to pay more attention to correct pronunciation of place rather than manner. I.e. it’s more important that students correctly distinguish between b and d than between n and l.
Aspiration, the distribution of which I showed above, seems to have almost no significance.
Learning
So now I have all this data about the course material so far; how do I use this to make it better? I guess that all depends on how learning works. I need to answer, or at least make an educated guess about, questions like these:
How steep should a learning curve be? Is it safe to start with two syllable phrases and then increase rapidly with each lesson? Should I start with the easier initials and introduce the harder ones later on? How do you measure such steepness beforehand? I do have some ideas on how to measure it once I have enough data from students. One criterion could be that if a student gets four stars on average for a lesson, he should get two stars on the first attempt of a new lesson and reach four stars after an average of 2 more attempts per phrase.
If I need to learn the difference between two tones, which pattern is better? 11112222 or 12121212? Or should I “hide” the tones like in 1122344034140234?
Based on Surendran and Levows findings, I should focus on consonants, vowels and tones. Their relative values suggest 2/3rd, 1/6th and 1/6th respectively, but how do I express that in the course? Does it mean I should use more variation in initials? E.g. 4 different initials for each unique final? What other approach could I use?
Finally I should not just take into account what is most important in a language, but what’s both difficult and important. That of course depends on the native language of the student, which for now I’m assuming is English. This is one thing I could learn from the feedback data once students are practicing the course. I can start with an educated guess like the difficulty chart above.
Another approach could be to take a corpus of English text and find those aspects of pronunciation that are both different and have high functional load. Tones are a good example of that; they are only used in Mandarin and they have a high function load in that language. Of course with Chinese one could simply assume that everything is different, so you only need to pay attention to functional load. 🙂