This paper presents methodology aimed at developing a rich understanding of the interplay of mathematical progress in the different social settings in which learning in inquiry-oriented classrooms occurs: individually; in small groups; and as a whole class. For this purpose, we enhance a theoretical-methodological approach of coordinating…

The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…

The movie "Frozen" took the world by storm and this global popularity of the movie and its music can be harnessed by teachers of mathematics. This article builds on the "frozen fractal" lyric from "Let It Go" to incorporate fractal geometry into primary mathematics classrooms.

Fractals describe many natural phenomena; their strong visual-figurative nature found its mathematical conceptualization in the concept of self-similarity. In the current study, we investigate how students construct (fully or partially) the self-similarity concept while recursively constructing the Sierpinski triangle, working in small group and…

Data collected from online learning and tutoring systems for individual students showed strong autocorrelation or dependence because of content connection, knowledge-based dependency, or persistence of learning behavior. When the response data show little dependence or negative autocorrelations for individual students, it is suspected that…

In this work, recurrent and linear sequences are studied, exploring the teaching of these numbers with the aid of a computational resource, known as Google Colab. Initially, a brief historical exploration inherent to these sequences is carried out, as well as the construction of the characteristic equation of each one. Thus, their respective roots…

This article builds on APREN-DO research project, which explores how secondary school teachers learn, using an inclusive research approach and visual and narrative methods. To this end, twenty-eight secondary school teachers created and narrated their learning cartographies, showing what, how, where, with whom, and with what they learn. This paper…

This study aimed to support the development of the scientific observation skills of children at an early age using a pattern selected from nearby nature. For this purpose, a simple, innovative and authentic observation activity was designed using thorny burnet ("Sarcopoterium spinosum" L.), a plant unique to the Mediterranean region. The…

Although it originates from the ancient Greeks, optics still arouses a lot of scientific interest, mainly due to the technological innovation associated with it. One of its most interesting applications is related to optical metrology and the characterization of materials through optical techniques. While some of these processes can be explained…

Subdividing an equilateral triangle into four congruent triangles, then doing likewise to each of the three non-central triangles, and then again and again, leads to the Sierpinski gasket, from which the chaos game originated. An analogous procedure is hereforth applied to a circle, where a subdivision consists of two pairs of inscribed circles,…

Twenty years have elapsed since the publication of the Revised Bloom's Taxonomy (RBT) in 2001, which has established itself as a major tool for defining the objectives of educational programs worldwide. It is, however, high time to revisit the efficacy of RBT in defining educational objectives of the digital natives. The current article initiates…

The chaos theory of careers was applied to identify the connections between multiple jobholders' careers and societal change. Multiple job holding is a form of employment that consists of two or more overlapping jobs. Six interviews with men born in the 1960s in Finnish North Karelia, whose multiple job holding included agricultural and forestry…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

For the last two decades, different authors have mentioned the need to have new pedagogies that respond better to current times, which are surrounded by a complex set of issues such as mobility, interculturality, curricular flexibility, accreditation and academic coverage. Fractal is an educational model proposal for online learning that is formed…

This article uses a cultural-developmental framework to illuminate the interplay between collective and individual activity in the mathematical reasoning displayed in a university Masters level lesson on fractals. During whole class and small group discussions, eleven students, guided by an instructor, engage in inductive reasoning about the area…