Abstract
In this research, I set "The thing is left after all you've learned has been forgotten" as "Ability to consider and to express mathematically" in mathematics education, that is "mathematical idea", purpose in this research is improving lesson for learners can acquire it. For such occasions, I checked theory of substantial learning environment by Wittmann and organization by Freudenthal, and show points to remember for designing substantial learning environment in algebra area, then I set out and put in practice. Purpose of this paper is show suggestion that get through analysis and prospect of lesson, and assignment for refining theory. As the result, show that mathematical thinking under thinking gives difficulty for learners, when they experience thinking of local organization.
