"Chapter 58—The Schools of the Prophets The Lord Himself directed the education of Israel. His care was not restricted to their religious interests; whatever affected their mental or physical well-being was also the subject of divine providence, and came within the sphere of divine law. PP 592"
"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."
The EGW passage directly reflects the principle of comprehensive education found in Deuteronomy 6:7, where parents are instructed to teach their children diligently in all aspects of life.
God had commanded the Hebrews to teach their children His requirements and to make them acquainted with all His dealings with their fathers. This was one of the special duties of every parent—one that was not to be delegated to another. In the place of stranger lips the loving hearts of the father and mother were to give instruction to their children. Thoughts of God were to be associated with all the events of daily life. The mighty works of God in the deliverance of His people and the promises of the Redeemer to come were to be often recounted in the homes of Israel; and the use of figures and symbols caused the lessons given to be more firmly fixed in the memory. The great truths of God's providence and of the future life were impressed on the young mind. It was trained to see God alike in the scenes of nature and the words of revelation. The stars of heaven, the trees and flowers of the field, the lofty mountains, the rippling brooks—all spoke of the Creator. The solemn service of …
"When I call to remembrance the unfeigned faith that is in thee, which dwelt first in thy grandmother Lois, and thy mother Eunice; and I am persuaded that in thee also."
Ellen White directly references 2 Timothy 1:5 in this passage.
"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."
The EGW passage directly references and expands upon the command in Deuteronomy 6:7 to teach children diligently.
"Only take heed to thyself, and keep thy soul diligently, lest thou forget the things which thine eyes have seen, and lest they depart from thy heart all the days of thy life: but teach them thy sons, and thy sons’ sons;"
The EGW passage is a clear allusion to Deuteronomy 4:9, focusing on the parental responsibility to teach their children about God's dealings.