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                <term xml:lang="en">didactical variable</term>
                <term xml:lang="en">Frobenius problem</term>
                <term xml:lang="en">Race to 20</term>
                <term xml:lang="en">proof</term>
                <term xml:lang="en">adidactical situations</term>
                <term xml:lang="en">Theory of Didactical Situations</term>
                <term xml:lang="fr">Théorie des Situations Didactiques</term>
                <term xml:lang="fr">situations adidactiques</term>
                <term xml:lang="fr">variable didactique</term>
                <term xml:lang="fr">Course à 20</term>
                <term xml:lang="fr">problème de Frobenius</term>
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              <p>The framework of the theory of didactical situations is based on "experimental epistemology". It allows us to question mathematics and learning situations. This text will present mathematical and experimental tools derived from this theory for thinking about a typology of situations for didactic use. In particular, it will focus on didactic variables and proof situations. Two examples will illustrate these aspects. From the fields of game theory on the one hand and number theory on the other, these examples will be discussed and revisited: the Race to 20 and the Frobenius problem.</p>
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              <p>Le cadre de la théorie des situations didactiques s’est construit dans des travaux « d’épistémologie expérimentale ». Il permet d’interroger les mathématiques et les situations d’apprentissage. Ce texte présentera les moyens mathématiques et expérimentaux issus de cette théorie pour penser une typologie de situations à usage didactique. Un focus sera fait en particulier sur les variables didactiques et les situations de preuve. Deux exemples permettront d’illustrer ces aspects. Issus des domaines de la théorie des jeux d'une part et de la théorie des nombres d'autre part, ils seront discutés et revisités : la Course à 20 et le problème de Frobenius.</p>
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