The Interweaving of Arithmetic and Algebra: Some Questions About Syntactic, Relational and Structural Aspects and their Teaching and Learning

After a brief introduction and a few general considerations on syntactic difficulties in the interweaving of arithmetic and algebra, we analyse the conflict between additive and multiplicative notation in arithmetic-algebraic realm and present the first results of some activities carried out according to our hypothesis of research with the aim of overcoming such conflict and promoting the semantic control of complex writings. We conclude with some reflections concerning the choice and difficulties of the didactic activities in middle school on these topics.