The power of the Mathematical Mind lay in its ability to quantify with precision, to reason through logic, and abstract pattern through observation and imagination. The Mathematical Mind also has the power, not only to hold measurements, patterns, sequences, and mathematical relationships in the mind as images, but also to translate them into invention through the work of the hands.
Every child can think like Pythagoras, especially as we have the help of Pythagoras in the classroom. We set up obstacles to comprehension by expecting the children to accept abstractions that have no foundation in their personal reality. We must allow them to know through experience what mathematical principles are all about. They themselves must come to the laws and definitions through the process of generalisation from a database. They must be given the time to learn from mistakes as well as successes, so that they will not be afraid and will know the rewards of perseverance.
The mathematical abstraction is the focus. The abstraction means “the quality of dealing with ideas rather than events”.