Nothing is perfect, but if you are able to derive results from it, with fairly accuracy, it is worth every effort you put in. Action speaks louder than words, and in this Internet age your words will be put to the test, only those that has burned with fire will come out shining as gold. I am not a mathematician, neither a professor, so there is a limit to what I can produce, but given this input, I am sure there are many others out there, who higher or above me, who can use this knowledge for the better of mankind. I welcome anyone out there who can help me complete this thesis, knowing full well I am unable to do so. I have spent more than a decade of my time on this, and like the example of the person who gave us the internet, i will not copyright but provide for free. Use this knowledge freely at your own risk.
I would give you an example and the methods used to train the mind, to exploit logical reasoning to the fullest.
Take a primary six student, I will first design worksheets that show simple intergers, and show the relationship between the intergers. The level of difficulty increases and answers will be provided to the student to learn from mistakes.
Next, in mid level, the student will be taught the method to compare. Finally, in the highest level, the student will be taught how to use all he has learned to apply to try to find the answer. This systematic approach trains the brain to recognise similar objects and use variations to find the solution. Finally, it is the speed test which will train the brain to find solutions in the least possible time. A series of apptitude tests could be conducted before and after this trainning session to determine if the student has absorbed it and to determine his performance.
Using this example, it can be utilised to cover any topics or any levels, with results you could never imagine.