The first part of the above title is more than just an arbitrary phrase. It gets right to the core of defining my very approach (as stated in my profile) toward successful tutoring in these subjects. One would not set out on a long road trip from a familiar starting point to an unfamiliar locale without having first mapped out an accurate and sequentially-detailed route. Likewise, this tends to be the case when solving many problems in both math and the various chemistries. A few specific examples will illustrate this idea.

In algebra students are called upon to solve many different types of equations where a series of operations that are performed in the proper succession lead to an answer which must be checked for validity. In word problems lacking a figure students must correctly construct and accurately label a diagram before proceeding further.

In geometry, 2-column proofs require establishing the appropriate starting point (the given information) and then accurately constructing the correct supporting steps placed in their proper order.

In trigonometry, identities can only be solved by this accurate and sequential approach.

Lastly, in general chemistry, application of the unit factor method in the solution of a wide-variety of problems leads to the correct answer only after the information is arranged accurately (again, starting with the given) and also in correct order of the conversion factors. Even when one is asked to predict a certain physical property (such as boiling point or solubility) of a molecular substance, an accurate Lewis structure must first be assembled, followed by a series of precisely-ordered steps which end up defining either the polar or nonpolar nature of the substance. Furthermore, in organic chemistry students must predict the product(s) of reactions starting with a given substance (or substances). The reaction mechanism is the sequence of the accurately-constructed and correctly-ordered steps depicting the most likely routes to the products.

Thus, it can be said that much of the aforementioned is very important in the development of a student as a lifelong critical thinker.