There are two logics in Mathematics. One is the logic of discovery and the other is the logic of justification. Heuristics is the method of the logic of discovery, and analysis(i.e. analytic ideas) is one of the representatives of heuristics in Mathematics. Until Now, although it has been focused on the logic of justification (i.e. demonstration) in school mathematics, the logic of discovery including heuristics was not valued in its educational role or methods. But recently, there is more concerns to the logic of discovery, as well as analogy, deduction, intuition in school mathematics, especially elementary school. This paper aims at investigating that what value is the analytic ideas in mathematics education and what areas can be role the analytic ideas in elementary mathematics, focusing to problem solving. In order to this goal, we search the prior studies on analysis, the types of analysis and problems in relation to analytic ideas. Together we suggest the method to teach the analytic ideas through quantitative thinking in elementary mathematics education.