This paper aims at critically analyzing the theoretical background which supports the importance of problem solving in math teaching within the perspective of productive thinking and of meaningful learning. To this end, contributions from the Gestalt field theories were analyzed, particularly those of Max Wertheimer and Kurt Lewin, in relation to these two concepts which complement each other: productive thinking has to do more specifically with problem solving within the scope of a meaningful learning, in the true sense of the word (Wertheimer); learning situations take into consideration the living space of the subject, encompassing the person and the environment, and represents the totality of possible events (Lewin). From the perspective of math education, both heuristics and intuition were dealt with, since they are two important elements which link this field to Gestalt concepts related to problem solving. Within this field, the contribution by significant authors, such as George Polya, Imre Lakatos and others, was also assessed. Keeping in mind that in the last few years math teaching programs have recommended that teachers use problem solving as a methodological basis for teaching, an exploratory study was also conducted which used as research tools interviews with math teachers from the Nova Escola (New School) program in Rio de Janeiro. Likewise, theoretical and pedagogical guidelines found in documents from the main national Brazilian high school assessment programs, such as Aneb and Enem, support math evaluation based on problem solving and on meaningful learning. The data collected in this part of the paper illustrated the theoretical study carried out, confirming the relationship found between these guidelines and the contributions by the Gestalt school, which turned out to be critical to the idea of productive thinking as a given of true meaningful learning. The research results demonstrated a viewpoint on reasons to solve problems which, much more than an end or a means, is intrinsic to math teaching and learning.