Geometry is a key course in this process. Be sure you use a geometry text which requires students to read and understand the proofs of theorems and to prove new theorems on their own. While doing proofs, students learn that they must have reasons for every statement and that reasons can be right or wrong just like statements. The same is true of algebra. Every step in the solution of an equation has a reason, such as the distributive law, the commutative law, or the addition property of equality.
Application is also necessary in math.
However, there must be a proper conceptual basis. Evaluate the applications in the textbook you teach from. When a text presents word problems that promote speeding, gambling, or other inappropriate activities, we immediately recognize an inappropriate application. Look through the word problems in your text. There is a place for imagination, but math is a real part of God's creation.