\input zb-basic \input zb-matheduc \iteman{ZMATH 2016b.00401} \itemau{Falk de Losada, Mar\'{\i}a} \itemti{Further remarks on a research agenda for WFNMC: research into the nature and characterization of geometric thinking based on students' solutions of competition problems.} \itemso{Math. Compet. 28, No. 1, 42-56 (2015).} \itemab From the text: Recently I found myself reading an article written by Guershon Harel in which he stresses the fact that mathematics education should focus on the development of the mathematical reasoning of the student, reasoning which in turn he breaks up into two components: ways of understanding and ways of thinking an analysis that has both piqued my interest and stimulated much thought. Both understanding and thinking contribute to the construction of meaning for mathematical concepts, leading to strategic knowledge, strategic in that it is in turn used to foster further understanding and to empower new ways of thinking. Furthermore, Harel maintains that the field of mathematics education has focused almost exclusively on the component of mathematical understanding. I have been working somewhat sporadically on a project aimed at characterizing geometric thinking, and have found that the literature contains some advances on the theoretical level and others on the pedagogical-didactic level, altogether falling short when it comes to describing the nature and characterization of geometric thinking. The first year of the project was aimed at gleaning clues to mathematical thinking in historical contexts, not only from writings but also from artifacts, remnants of architecture, tools and ornaments that reveal the geometric knowledge, ideas and fancy of their makers. \itemrv{~} \itemcc{D50 E20 D20 B60} \itemut{mathematical thinking; research; understanding; problem-solving strategies; mathematical competitions; student competitions; geometric thinking; geometry; concept of area; Greek mathematics; Euclid; proofs; Pythagorean theorem; curriculum links; measurement; abstraction from actions; abstraction from objects; constructing; decomposing; recomposing; comparing; actions of the subject; transformation of the figure; analysis of the results} \itemli{} \end