There are a few strange views regarding a number of linguistic matters in Taiwan. Even stranger in my opinion is that nobody seems to question them, not even in the academic world, even though there are contradictions every three steps. One of those strange views is to equal the Chinese 字 to the English "word". That is not correct and the myth is easily debunked.
Strangely, almost everywhere throughout language education in Taiwan, educators teach their students that "字" would equal to the English term "word". Since both the Chinese and the English term describe very basic elements in linguistics, this causes seriously distorted views towards many aspects of language. Directly related to this are terms like 單字 for vocabulary or 字母 for letters.
It appears there is no concept of "character" or "glyph" in Taiwan. While it is true that hanzi and letters are different, they also share identical aspects: They are all characters - or glyphs, if you prefer that term. In linguistics, this describes an optical appearance, an icon, a small picture that is used in written communication. Be it an "A", "啊" or "あ", they are all characters. These three accidentally represent similar sounds, but sounds are a different matter - as is meaning.
The term "character" only deals with the optical appearance, with what we see. While letters have sounds assigned, they do not incorporate a semantic component. A meaning is formed by combining letters into words. This is a bit different with hanzi, as they do not only contain a phonetic, but also a semantic component. They do actually have a meaning. One hanzi can be a word, but you can also combine several hanzi into different words.
Meaning (or better a morpheme, the smalles unit of meaning) however is not necessarily equal to words. The word "thermometer" has a meaning, but the word can be split into two components, "thermo" and "meter". "Thermo" is related to temperature, while a "meter" is a gauge, a display for values. So a thermometer is something displaying the value of temperature. "Thermo" and "meter" are both morphemes, forming the lexeme "thermometer". By the way, this paragraph was all about meaning, not the least bit about optical appearance. Linguistics needs ways to differentiate these elements.
Chinese works in the same way, but although it is obvious, people refuse to accept these principles. The idea of "character" as simply an optical, graphical appearance, with functions and properties different from phonetic or semantic components, seems unknown in Taiwan. Interestingly, both the PRC (where the same language and characters are used) and Japan (same characters) do not share this view. In both countries, 字 simply stands for character. And shattering the "system" used in Taiwan is very easy:
Let us start with "大". Two questions: How many 字? How many words? The answer to both questions will be "one". (大 means "big" by the way.)
Next is "大學". Again: How many 字? How many words? Every Taiwanese will answer the first question with "two". And then it gets embarrassing, because there is only one word, which is "university". There are two morphologic components, yes, just like in "thermometer", but it is one word.
And the final one: "大學生". The question for the number of 字 will be answered with "three", while the one for the number of words can again only be answered with "one", which is "student".
What happened? As mentioned before, Taiwanese are not used to applying the concept of characters or glyphs to their own writing system. People took the term for their characters (字) and since it has not only a sound but also a meaning assigned and can be a word, they simply claimed it to be a word. They ignore that although there are thousands of those characters, they still need to be combined at many occasions to create other words.
Unfortunately, it is not just this one character's wrong perception that causes problems. There are for example the two double-character words 單字 and 字母 that I had already mentioned. They reflect this view of 字 being equal to word: 單字 is used for vocabulary. 單 means one and 字 - well, in the Taiwanese view, this would be "one word", while it is really only "one character".
When pupils here in Taiwan learn hanzi at school, they have to memorize lots of them. The phrase for this is 背單字 and it means memorizing single/individual characters. Pupils have to memorize what a character looks like, the stroke order to write it, the assigned sound(s), and what it means. This is copied 1:1 on other languages, even though it does not apply there. Learning vocabulary (for English, for example), is also called 背單字, although "vocabulary" are words, not characters.
字母 is another example: The "mother of the word" is supposed to be a letter (the one from an alphabet). In alphabet-based writing systems, words are made of letters, and since a word is considered to be equal to 字, those letters must be the mother of 字 - which really only stands for character in all other places using this writing system. Calling letters 文字 as opposed to 數字 for numerals seems to be out of question in Taiwan.
By the way, this is just one problem of strange linguistic terminology/views here in Taiwan, there is more...