Popularly used in marketing and business, gamification has been gaining interest in educational contexts for its potential to invigorate otherwise mundane or difficult processes. A gamified environment transfers motivational elements of games to learning activities thereby engaging learners in the learning task thus transforming dull classroom…

The geometric habits of mind are a process that enables the adoption of ways of thinking about the problems encountered and that works for filling the gap between the results and the thoughts behind these results. It is also important that which cerebral hemisphere activates the geometric habits of mind, so geometric habits of mind and hemispheric…

In the seventeenth century, Guarino Guarini, mathematician and architect, affirmed that architecture, a discipline that primarily deals with measures, relies on geometry: therefore, the architect needs to know at least its basic principles. On behalf of Guarini's words, we designed a set of interdisciplinary teaching experiences, between…

In this work, we show the results of a research with pre-service mathematics secondary teachers about their Van Hiele level regarding the proof in Geometry. We observe three different profiles whose characteristics are described. These descriptions allow us to foresee certain differences when carrying out proof teaching in secondary school. The…

This study aims to address the teaching of integrals in multivariable calculus concerning the role taken by geometry, specifically, geometrical content dealing with boundaries in integrals that appear as curves and surfaces in R[superscript 2] and R[superscript 3]. Adopting the framework of the Anthropological Theory of the Didactic, we approached…

One of the cultural outcomes of the Madurese community is the traditional "tanean lanjang" house with a long front yard, designed from several "batih" (nuclear) families, consisting of a married couple with unmarried children. This study explores geometric concepts of the traditional house to demonstrate how they can be useful…

Euclidean geometry has formed the foundation of architecture, science, and technology for millennia, yet the development of human's intuitive reasoning about Euclidean geometry is not well understood. The present study explores the cognitive processes and representations that support the development of humans' intuitive reasoning about Euclidean…

Problem solving and reasoning are two key components of becoming numerate. Reports obtained from international assessments show that Australian students' problem solving ability is in a long-term decline. There is little evidence that teachers are embracing problem solving as part of the classroom routine. In this study, we analyse 598 Year 7 to…

The purpose of the study was to investigate the experiences and perceptions of middle school students about the flipped classroom applications used in geometry lessons. The research was designed as a case study. Data were collected through field notes, focus group interviews, and semi-structured interviews. The sample consisted of 26 eighth-grade…

In this article special sequences involving the Butterfly theorem are defined. The Butterfly theorem states that if M is the midpoint of a chord PQ of a circle, then following some definite instructions, it is possible to get two other points X and Y on PQ, such that M is also the midpoint of the segment XY. The convergence investigation of those…

In this study, the conceptualizations used by prospective middle school mathematics teachers when defining, representing, and exemplifying the slope concept and relating it with other mathematical situations were examined. Participants' conceptualizations were identified by Nagle, C., Moore-Russo, D., Viglietti, J., & Martin, K. [(2013).…

Tangent lines are often first introduced to students in geometry during the study of circles. The topic may be repeatedly reintroduced to students in different contexts throughout their schooling, and often each reintroduction is accompanied by a new, nonequivalent definition of tangent lines. In calculus, tangent lines are again reintroduced to…

This article shares an approach specifically for fostering equitable small-group, student-to-student discourse (S[superscript 3]D). The S[superscript 3]D approach is a two-phase process focusing on implicit strategies. Phase 1 involves assessment of current small-group discourse through three lenses: group dynamics, discourse quality, and teacher…

Mulla Sadra's philosophy has an ontological approach. However, his explicit texts or philosophical foundations in social issues such as education and especially the curriculum and its relationship with learning methods can be extracted. Mulla Sadra's different approach to learning has distinguished his educational system from other educational…

In this exploratory work, the discourse of first-year computer engineering undergraduate students of graph theory was analyzed with the aim of improving the teaching of this branch of mathematics. The theoretical framework used is the theory of commognition, specifically, we focus on commognitive conflicts because they are learning opportunities…