This article presents a reflection on a teaching experience involving the use of the Brügner tangram, an interesting but little-known manipulative material. It details an activity conducted as part of an undergraduate mathematics education course for prospective primary school teachers. The main objective of this paper is to present the…

Although student covariation reasoning has been explored in depth to improve understanding of the correspondence between variables, research has focused on studying existing reasoning about variables in Cartesian representations. The working method had a qualitative approach, with a descriptive exploratory scope, the spontaneous representations…

Critical thinking is a skill that people must develop to navigate skillfully the information they receive through media channels. The cultivation of this skill must begin in the early stages of education and continue uninterrupted through the completion of academic training. For this reason, the search for tools to promote critical thinking in the…

This article reports on a study in which third-grade students (8-9 years) were given a degree of agency in conducting chance experiments and representing the outcomes. Students chose their own samples of 12 coloured counters, ensuring all colours were represented. They predicted the outcomes of item selection, tested their predictions, explained…

Emergent graphical shape thinking (EGST) entails conceiving a graph as being dynamically generated via the trace of a moving point constrained by two changing quantities. As such, Paoletti et al. (2023) argue that meanings for quantities within a situation and meanings for graphical representations must be connected, or bridged, to engage in EGST.…

Graphical analysis of the relationships between pairs of integrals and their corresponding derivatives resulted in the development of a procedure one may describe as 'pictorial integration'. The arctangent of the derivative of various functions was analysed to confirm that this accurately reports the magnitude of angles made by integral functions…

Graphing is a complex and critical skill for behavior analysts. We evaluated the effects of conceptual training modules and feedback checklists on verbal behavior about graphing conventions and adherence to graphing conventions with graduate students in behavior analysis. In Experiment 1, conceptual training increased the accuracy of verbal…

The use of full online learning is projected to continue indefinitely. An instructional design for online learning that incorporates didactic, active learning activities, and health welfare is proposed. A single-subject multiple baseline design with two controls and two experiments was implemented with a class of 30 nursing students. Four weeks of…

Laboratory activities are a prevalent and essential part of chemistry learning because of their potential to help students develop problem solving abilities, visualize chemistry concepts learned in lecture, and gain practical skills. However, learning in the laboratory environment is not without its challenges. For example, cookbook-style…

In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…

Traditional lecturing is the dominant method of teaching mathematics in undergraduate mathematical courses in many countries, whereas active student-centered approaches such as inquiry-based learning have been shown in some instances to be more effective. Most teaching resources (inquiry-based tasks) available at the tertiary level are related to…

We address a problem of promoting instructional transformation in early undergraduate mathematics courses, via an intervention incorporating novel digital resources ("techtivities"), in conjunction with a faculty learning community (FLC). The techtivities can serve as boundary objects, in order to bridge different communities to which…

Motivational factors have long attracted the attention of researchers and educators with their potential to shed light on what drives effective language learning. Although current research now views language learning motivation as a Complex Dynamic System (CDS), there is a dearth of empirical studies utilizing network analysis to understand how…

Teaching Computer Science concepts, such as graph theory, is often challenging. This study proposes an approach for teaching graph theory using an unplugged game ("GraphGame") developed through a participatory design process that includes usage observation, clarifying meaning, prototyping, and implementation. This process was carried out…

It is said that a picture is worth a thousand words, but what about graphs? Although graphs have the potential to bring data to life, numerous studies show that learners struggle with graphical comprehension. Furthermore, many textbook examples on graphs are boring and appear meaningless to students. Students want to know more about something…