In the Bible, it seems to me, God teaches us both by his deeds and his words. As described in the Torah or Pentateuch, he is a God of action and words. John the baptist taught the people down by the Jordan River about the coming of the Messiah. And when Jesus did come, he came as both a teacher and a wonderworker. Certainly he spent a significant portion of his time during his public life teaching his twelve disciples the basic principles of the Gospel-love of God and neighbor, the Beatitudes, the Eucharist, the nature of God as Father, Son and Holy Spirit, the reality of the Church, and so forth.
Actions speak louder than words.
Finally he sent his only-begotten Son to teach us the way to heaven and to die and rise from the dead for us. Our God is a God of deeds and words. The words explain the deeds and the deeds give credence to the words. A real teacher, in order to persuade his students, must be something like that. If he is going to have an impact on his students, he must embody in his own life, at least in some way, the truth that he is trying to hand on to his pupils.