This study compared area lessons from Korean textbooks and US standards-based textbooks to understand differences and similarities among these textbooks, as well as how these textbooks address known learning challenges in area measurement. Several well-known challenges have been identified in previous studies, such as covering, array structure,…

In this exploratory study, our goal was to engage students in dynamic experiences of area as a continuous quantity that can be measured by multiplicatively composing two linear measures (lengths), an approach we refer to as 'dynamic measurement,' or DYME. In this paper, we present the learning trajectory constructed from two cycles of teaching…

The aim of this paper is to build up an argument about the importance of a mathematical analysis of young children's activity in relevant for the age educational tasks. Most of current approaches (psychological, social, and pedagogical) are limited to the study of the development of children's thinking, paying less attention to the involved…

This is a study about the didactical organization of a research based group of activities designed using APOS theory to help university students make constructions, needed to understand and graph two-variable functions, but found to be lacking in previous studies. The model of the "moments of study" of the Anthropological Theory of…

This paper refers to the concept of semiotic and theoretic control describing resources to conduct decisions in epistemic processes. We consider an argumentation process from a complex problem-solving activity involving different conceptual frames related to parabolas. Using a micro-analytical interpretative lens, we will show that, in order to…