We are to grow in knowledge of God through His Word. With Scripture as our ultimate authority, this means that we are to transform our thinking according to Scripture. Whatever Scripture says is true, whatever that Scripture refutes is false even if we in our human thinking think it is reasonable. This transformation of our mind is the submission of our mind to the lordship of Christ. We are after all to love God with our mind (Mt. 22:37).
How does this look like in practice? Scripture for example teaches creation. Man was created not from animals but from the personal shaping from dust followed by God breathing life into Man (Gen. 2: 7). Since Scripture teaches this truth, it means that evolution and descent from animal ancestry must be rejected as false. It matters little that the scientific community believes in evolution and animal ancestry. A mind submitted to Christ's lordship must obey God rather than Man.
Such submission holds true for every area of thought. Where Scripture speaks, all contrary "facts" are to be rejected. It matters little that the "fact" opposing Scripture has the backing of scientists, PhDs, teachers, even theologians, or any other authority.
Where is the one who is wise? Where is the scribe? Where is the debater of this age? Has not God made foolish the wisdom of the world? (1 Cor. 1:20)
In its context, 1 Cor. 1:20 is speaking of salvation. Yet the broader principle seen here is that God only is wise. True knowledge resides with God, not the fallible opinions of men who do change their theories.
In submitting to God and Scripture therefore, we are not saying that we do that in spite of the real world truths. Rather, God is the only wise One and the only perfect interpreter of all facts. As postmodernism has alerted us, there are no such things as brute facts. All facts are interpreted.
The issue therefore is not some kind of blind faith which disregards real world facts altogether. Rather, the issue is who do we trust as the perfect interpreter of facts. Do we trust God, or do we trust scientists and other human authorities? If we believe in God who created this world, then all real world facts will when rightly interpreted match with what the Scriptures teach. If they do not seem to at the moment, can we admit our finitude and ignorance and continue to trust God, knowing that in the end every real world fact will match the Scriptures?
On things Scripture does not speak about, one is free to hold any position (that does not contradict Scripture) as long as one attempts to think it through using principles taught in Scripture.
Growth in knowing God and His Word therefore implies that we should transform our minds to embrace all that Scripture teaches, and rejecting all that contradicts Scripture. This is the manner in which we are to grow in the area of knowing.
To the teaching and to the testimony! If they will not speak according to this word, it is because they have no dawn. (Is. 8: 20)