"Christ did not deal in abstract theories, but in that which is essential to the development of character, that which will enlarge man's capacity for knowing God, and increase his efficiency to do good. He spoke to men of those truths that relate to the conduct of life, and that take hold upon eternity. COL 23.1"
"And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent."
Both passages connect knowing God with eternal life and character development. John 17:3 defines eternal life as knowing God, and the EGW passage speaks of Christ's teachings leading to character development and knowing God.
It was Christ who directed the education of Israel. Concerning the commandments and ordinances of the Lord He said, “Thou shalt teach them diligently unto thy children, and shalt talk of them when thou sittest in thine house, and when thou walkest by the way, and when thou liest down, and when thou risest up. And thou shalt bind them for a sign upon thine hand, and they shall be as frontlets between thine eyes. And thou shalt write them upon the posts of thy house, and on thy gates.” Deuteronomy 6:7-9 . In His own teaching, Jesus showed how this command is to be fulfilled—how the laws and principles of God's kingdom can be so presented as to reveal their beauty and preciousness. When the Lord was training Israel to be the special representatives of Himself, He gave them homes among the hills and valleys. In their home life and their religious service they were brought in constant contact with nature and with the word of God. So Christ taught His disciples by the lake, on the mountainsi…
"And thou shalt teach them diligently unto thy children, and shalt talk of them when thou sittest in thine house, and when thou walkest by the way, and when thou liest down, and when thou risest up. And thou shalt bind them for a sign upon thine hand, and they shall be as frontlets between thine eyes. And thou shalt write them upon the posts of thy house, and on thy gates."
Ellen White directly references Deuteronomy 6:7-9 in this passage.