In a series of mathematics education workshops in which teachers from adult basic education and vocational education worked together to design teaching situations on particular contents in mathematics in order to make explicit and bring into reflection the teaching strategies used by each group. The workshops constituted a common space of interaction for jointly designing teaching situations and creating common discourses that narrowed the distance between normative curriculum and actual teaching or real curriculum. In order for adult educators to teach effectively they must fulfill the following conditions: (1) they must provide a context for the teaching; (2) the knowledge taught must constitute a solution adapted to the problem; (3) there must be didactic variables that lead to the development of logic in a fruitful way; and (4) they must take into account students' previous experience. (Two teaching situations from the reference situations of a hairdressing class and a cooking class are described and a discussion of proportionality, including how proportional situations are recognized and how they can be modeled effectively is included. The document includes an appendix containing problems from each of the teaching situations, 5 figures, and 12 references.) (MO)