TITLE: How to present math as something interesting?
QUESTION [7 upvotes]: If you are helping someone with mathematics in high school, what do you need to do to win his attention so she/he can focus on curriculum?

REPLY [2 votes]: Mathematics is INHERENTLY interesting if it is UNDERSTOOD.
"Understand" does not mean ability to remember and recite and mechanically perform and willingness to conform and follow directions. 
"Understand" means that you see what we are after, what we are about, what we want, what there IS to want, where we are going, what we are doing.
Mathematics as rules and arguments does reveal that or even hint at it. Neither does mathematics as rigor or reasoning or application or cognition or history or success or mathematicians or philosophy. Mathematics is about constructing and exploring. Promoting successes gives no clue to what it's about. It doesn't matter how many findings one remembers. Mathematics is ABOUT creating and searching, not pride in what was created and found. The relevance of mathematics is not in its application.
Mathematics is the physical science of quantity and the phenomenal developments that proceed from naming and symbolizing quantities, operations with quantities, relationships between and among quantities, and so on, including interest in the things to which quantity applies - mainly sets and fields and rings and algebras and whatever - and the astounding implications and properties of all of these and their descendants. The claim that mathematics is abstract surgically removes all possible interest in it except for exceptional jugglers or those who see beyond the claim. It is no more abstract than any other science. The fact that many of its findings can be proven is due to the nature of quantity and not the esotericness (esotericality, esotericosity, esotericicity) of the subject.