E. Ch. Wittmann advocated the concept of “Substantial Learning Environment”. In order to crystallize this concept, “Das Zahlenbuch” was edited by Wittmann and others. There are seven ground conceptions as editing principle in “Das Zahlenbuch”. “Aktive-entdeckendes und soziales lernen” (Active-finding and social learning) is one of them and is indispensable to compose the mathematical lesson.
The purpose of this paper is to reveal the concept of “Aktive-entdeckendes und soziales lernen”. Then I developed the mathematical material of negative numbers for 7th grade students which is based on “Aktive-entdeckendes und soziales lernen”. The mathematical material is “21 Number Cards” which are whole number from -10 to 10.
Finally I analyzed the students activities of the lesson and reported the results and identified meaningful of the lesson.
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