The student friendly method of “Mathematics with Lochdoch” consists of four repeated mental activities, that you learn to apply for achieving mathematical insight:
Look. That is more than looking with your eyes. You look with your inner
eye, judge and ask yourself questions. It is all about achieving insight by
exercising, so less by cramming a lesson. Get a clear view and image on the
essence of the problem. What is i.e. the core question? What is the problem
about? Wich part of mathematics is the case?
Achieving insight requires that you seek some rest outwardly and inwardly. In silence you can concentrate easier. Develop a sharp view like that of an eagle to look through the problem.
2. Choose. If you can see what problem or part of mathematics is the case, you automatically look for the tools, you can solve the problem with. You look for, compare and choose one or more of the rules you will find in the list of Trilogie-keys: basic principles in three steps. You will find about 50 of those in this course. Later on you will detect more.
3. Do. Now go with one or two of the trilogies to reach step by step the solution writing it down in a logical sequence. One must accept making many errors at the outset. Learn to choose and find the easiest way every time.
a. Reflect a new problem against a previous solved one. Something “new” often appears to be something “old”.
b. Make it easier for yourself i.e. by keeping numbers small, simplify equations and reduce fractions and drawing a picture, sign diagram or a graph. A picture is worth a thousand words.
c. Go step by step and work through to the solution. Use small think steps and don’t “ramble on”. Don’t write or “knit” it all together.
d. Use compact mathematical language with the correct symbols. Work in telegram style.
e. You learn more from your errors than from your successes. Look critically at your errors and learn your personal lessons from them.
4. Check. Always double-check.
a. Check your solution by putting it into the primary equation. Does it fit?
b. In addition, apply a second solution if possible. Sometimes there are three or more ways to find the solution.
c. Is the solution intuitively correct? Often you can “feel” by intuition whether an answer is correct or not.
Goals for Lochdoch are:
1. Stimulate your selfconfidence.
2. Enlarging your insight.
3. Teaching you to think and act logically.