I found this explanation and illustration regarding true saving faith from Tedd Tripp to be very helpful:
We want our children to have faith in God. But what does it mean to have saving faith? Starting with Martin Luther, and further explicated by Philip Melanchthon and others who followed them, Reformed theology has traditionally used a threefold definition of faith as notitia (knowledge), assensus (assent), and fiducia (trust). Our major confessions of faith show this understanding. The Westminster Confession of Faith 14.2 maintains that saving faith joins believing in God’s Word, accepting Christ’s claims, and “receiving and resting on Christ alone” for all that salvation provides.
As a parent who desires his children to exercise saving faith, I am concerned with all three aspects of saving faith. Therefore, my shepherding must intentionally promote notitia, assensus, and fiducia.
… We must always set before them the gospel truth. Every family should have some intentional and structured times in which the children are taught about what the Scriptures contain. We must faithfully urge them to believe the things we have taught. Some basic apologetics will inevitably be essential as we persuade them to believe the truth.
None of this will be enough unless they entrust themselves to Jesus Christ. If they are to be partakers of eternal life, they must trust in this Jesus Christ who saves. Our children must receive Him, turn to Him, hold fast to Him, and rest in Him alone for salvation. Ultimately, the work of the Holy Spirit must transform our children into people who rest in Christ alone for salvation. Our role is to bring them the gospel and urge them to embrace Christ the Savior.
I used to tell my children about the man who watched a tightrope walker crossing Niagara Falls pushing a wheel barrow. After seeing the feat performed repeatedly, he was asked by the performer, “Can I walk across the falls pushing this wheelbarrow.” “Yes,” was the answer (notitia). “Do you believe that I can do it again?” “Yes” (assensus). “Would you jump in the wheelbarrow and let me push you across?” (fiducia). This is the question of trust.
Our children must know that Jesus is the Savior who died for sinners. They must believe that He will save sinners who come to Him. But to cross from death to life they must believe that Jesus is their Savior. They must get into the wheelbarrow. What they will find is that He is willing and able to get them safely to the other shore.
You can read the entire article, “A Child’s Call to Conversion: Faith as a Christian Mark,”posted at Ligonier Ministries.