Well, they do teach as they have to define words in a concise way
If defining words were teaching. the school would hire dictionaries rather than native speakers, no?
It's an excellent way to fast-track the learning of beginners. The beauty of the method in the first few stages is subject/verb agreement and matching auxiliaries. Can you? Yes, I can or No, I can't. It also automates the response, instilling it sharply. It shows the rhythm of the language too.
OK I'll summarise what I know of the Callan method. It's seems to be a mixture of Audiolingualism and the Direct method in that while grammar is mentioned here and there, the main focus in on the students' spoken production, which is based on drills. The principle being that by repeating similar drills over and over really quickly, the student is conditioned into giving a certain response to a certain question.
The Callanoid stands at the front and takes the class through a series of drills in a definite order based roughly on increasing grammatical complexity, the principle here being that by improving your grammar, yuo improve your language skills. If the student says something correctly, they are rewarded with a smile from the teacher (positive reinforcement of good behaviour). Bad behaviour is discouraged with a frown and a disapproving tone in the Calbot's voice.
On the good side, the students are speaking from day one. But then again, in a well-managed communicative classroom, they would do so too. Also, untrained natives can be taken straight off the boat, given a book and be sent into the classroom. Aslo there;s nothing to prepare.
On the bad side, there's no interaction between students. There is no groupwork. There is no free practice. There is no exam practice. There is no ESP language. There is little development of the student's own idiolect. there is less development of the student's own ability as an active learner. There is no accommodation of student aims or learning styles. The student communicates with noone but the teacher, in fact there is no authentic communication at all. And that's just off the top of my head.
Not to mention that behaviourism was discredited as a guiding principle of language teaching 40 years ago and that language development can't be represented as a straght line from bad to good grammar.
Overall, the Callan method's only success is as a franchise. There's no teaching going on here. Move along.