When the new programming language Pascal was developed in the 1970's, Walter Gander did not like it because because many features which he appreciated in prior programming languages were missing in Pascal. For example the block structure was gone, there were no dynamical arrays, no functions or procedures were allowed as parameters of a procedure,…

Windmill images and shapes have a long history in geometry and can be found in problems in different mathematical contexts. In this paper, we share and discuss various problems involving windmill shapes and solutions from geometry, algebra, to elementary number theory. These problems can be used, separately or together, for students to explore…

In this paper we studied the personal mathematical work of 14 students in initial teacher training, in their first year of studies at a public university in Chile, based on two tasks on complex numbers. These tasks were set in a Computer Aided Assessment System (CAA) based on Moodle and Wiris and it was proposed to solve them using different…

The number line is a model that is used to measure, count, order and even operate, which requires a symbolic interpretation. Then, we investigate the conceptions of 72 in service secondary teachers, when they manage the model of the number line associated with order, spatial location and the relative position between numbers and marks. In a…

In three experiments, we used a masked prime in a verification task to investigate the processing stages occurring during multiplication fact retrieval. We aimed to investigate the retrieval process by overlapping its execution with the processing of a masked prime consisting of a number. Participants evaluated the correctness of multiplication…

The aim of this research is to propose indicators of epistemic and mediational suitability to assess tasks designed in a mobile learning context, using theoretical and methodological elements of the onto-semiotic approach (OSA) and the SAMR model (substitution, augmentation, modification, and redefinition). With these indicators, 110 tasks…

The main purpose of this study is to develop a conceptual understanding of the irrational number of the square root of 2 ([square root]2 ). Participants in the study were 20 ninth-grade male students. Activity Theory was used as a framework to show the development of the conceptual understanding. Since this study was conducted during the COVID-19…

This research synthesizes studies that used a Digitalized Interactive Component (DIC) to assess K-12 student mathematics performance during Computer-based-Assessments (CBAs) in mathematics. A systematic search identified ten studies that categorized existing DICs according to the tools that provided language assistance to students and tools that…