There are several textbook series out there that do a good job in taking you through the Japanese language in a structured fashion, though they do so in different ways.
The two most popular series (Genki and Minna no Nihongo) are written in English, have a long history and are well respected course books.
It will be up to the student to see with what book you would like to work, and I will do my best to point you in the right direction.
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Genki means something along the lines of 'healthy' or 'energetic' and the series of books under the Genki banner sure are enthusiastic in dishing out lots of grammar at a high rate.
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Minna no Nihongo in Japanese comes down to 'Japanese for everyone' and this series is also the one that's being used at Leiden University.
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Marugoto has the association of 'entirely' or 'completely', meaning that these course books will take you through the Japanese language in a comprehensive manner. Many classes in group setting opt for marugoto.
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When it comes to learning the writing systems (of which Japanese has three that work together) I always advice using the books from the 'Let's Learn' series to get accustomed to hiragana and katakana first.
These books do a good job in teaching you the correct writing style of these basic syllables.
My aim is to develop a teaching method the student is most comfortable with and takes into account your wishes and Japanese proficiency.
The private lessons can consist of the following:
Homework consists of mainly studying the grammar, trying to keep your vocabulary up-to-date, and making exercises in a workbook. I will also ask you to translate English sentences into Japanese or vice versa so that we can discuss these in class.
Naturally I am very open to the student's input too, so let's make a great lesson together!