We studied aspects of undergraduate STEM majors' mathematical reasoning as they engaged in mathematically modeling a predator-prey scenario. The study used theoretical viewpoints on quantitative reasoning to inform scaffolding moves that would assist modelers in overcoming blockages to their mathematization of real-world problems. Our contribution…

Prior research on students' productive understandings of definite integrals has reasonably focused on students' meanings associated to components and relationships within the standard definition of a limit of Riemann sums. Our analysis was aimed at identifying (i) the broader range of productive quantitative meanings that students invoke and (ii)…

In the precalculus curriculum, logistic growth generally appears in either a discrete or continuous setting. These actually feature distinct versions of logistic growth, and textbooks rarely provide exposure to both. In this paper, we show how each approach can be improved by incorporating an aspect of the other, based on a little known synthesis…

It has been over thirty years since the nuclear reactor meltdown at the Chernobyl nuclear power plant, but why there is still an officially designated exclusion zone? The Chernobyl Disaster Task combines the learning of exponential functions with properties of radioactive substances to help students understand the ongoing effects of the meltdown.…

The theoretical reflection on the nature of school algebra and the development of algebraic thinking from the first educational levels is a relevant topic in mathematics education. In this paper, we first summarize and clarify the positions held on this topic by two theoretical frameworks: the Theory of Objectification and the Onto-semiotic…

In this paper, we explore the role that examples play as mathematicians formulate conjectures, and we describe and exemplify one particular example-related activity that we observed in interviews with thirteen mathematicians. During our interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating…

Models are at the core of scientific reasoning and science education. They are especially crucial in scientific and educational contexts where the primary objects of study are unobservables. While empirical science education researchers apply philosophical arguments in their discussions of models and modeling, we in turn look at exemplary…

This article describes the results of an investigation based on a Models and Modeling Perspective [MMP]. We present the evolution of the models built by university students when solving a model development sequence designed to promote their learning of the exponential function. As a result, we observed that students' thinking was modified,…

This theoretical article explores the affordances and challenges of Euler diagrams as tools for supporting undergraduate introduction-to-proof students to make sense of, and reason about, logical implications. To theoretically frame students' meaning making with Euler diagrams, we introduce the notion of logico-spatial linked structuring (or…

Mathematical connections are essential to emphasize in the learning process, to make students see mathematics as useful, relevant, integrated, and able to solve various mathematical problems. This study was conducted to analyze the comparison of achievement and improvement of students' abilities on mathematical connections based on learning model…

Recursive reasoning is a powerful tool used extensively in problem solving. For us, recursive reasoning includes iteration, sequences, difference equations, discrete dynamical systems, pattern identification, and mathematical induction; all of these can represent how things change, but in discrete jumps. Given the school mathematics curriculum's…

The Multimedia Research Laboratory, inserted in the Federal University of Ceará has the Multimedia Mathematics Education Group, in which they study the mathematics teaching with the methodological contribution of the Fedathi sequence (FS). In one of the study meetings, the members raised the issue of how a class in the light of the FS could be,…

Programming is becoming increasingly common in mathematics degrees as it is a desirable skill for new graduates. However, research shows that its use is mostly restricted to computational or modelling tasks. This paper reports a study on students' perceptions of and difficulties with Lean, an interactive theorem prover introduced as part of a…

Task enrichment is an important teacher competency that can be considered as a special case of problem posing. For that reason, the theoretical framework of this article includes an overview of this topic, complemented with the analysis of inverse problems. The field work of this research was carried out in master courses in the University of…

The need to develop consistent theoretical frameworks for the teaching and learning of discrete mathematics, specifically of graph theory, has attracted the attention of the researchers in mathematics education. Responding to this demand, the scope of the Van Hiele model has been extended to the field of graphs through a proposal of four levels of…