Designing and implementing purposefully developed tasks have been linked to students' understanding of mathematical topics. We report on design principles and intentions that guided the development of "inquiry-oriented tasks." Through a qualitative analysis of the tasks, we identified seven themes that encapsulated these design…

Conjecturing has been considered to inspire the need for proof, enhance the understanding of proofs, and construct a valid proof. This study describes students' processes of formulating a Euclidean geometry conjecture in the form of a conditional statement through constructing a geometric figure and using measuring and dragging modalities of a…

The systematic design and analysis of tasks which can be implemented in first-year university courses and point to advanced inner- and extra-mathematically rich issues and their rationales is an open problem in the didactics of mathematics in higher education. Potentials of such tasks can be seen with regard to learning processes in the first year…

Storytelling is a valuable form of human expression that allows audience members to connect their own experiences with the narrative. As a pedagogical tool, storytelling has been explored mainly in primary school education but rarely in higher education. However, its potential for assisting students in learning mathematics and the societal…

The aim of the study was to examine how students generate problems about the concept of series, and how they evaluate and solve these problems. The difficulties experienced by the students while posing problems and their perceptions of the posing-evaluating-solving approach were also explored. In the first stage, 46 second-year university students…

This study focuses on computer-based formative assessment for supporting problem solving and reasoning in mathematics. To be able to assist students who find themselves in difficulties, the software suggested descriptions - diagnoses - of the encountered difficulty the students could choose from. Thereafter, the software provided metacognitive and…

From an APOS (Action-Process-Object-Schema) theory perspective, learning mathematics involves construction of knowledge through mental mechanisms, which evolves between different mental structures or stages. The focus of this study is to explore how transition occurs from an Action to a Process conception, in the context of a task related to the…

The purpose of this work was to explore how elementary pre-service' teachers (PSTs) responded to a volume task that asked for a coordination of changes in one dimension with changes in volume. We carried out both written pre-assessments and follow-up interviews with seventeen PSTs, focused on exploring volume content knowledge. Our findings…

We report on a series of task-based interviews in which nine mathematicians were asked to evaluate a series of six mathematical arguments, purportedly produced either by fellow mathematicians or undergraduate students. In this paper, we attend to the role of context in mathematicians' responses, leading to four themes in expectations when…

In this note, we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task design that gives students the opportunity to conjecture, refute and prove. What is new is that the complexity in our problems is limited and thus the tasks can also be used in homework…

This study explored prospective middle school mathematics teachers' developing understanding of geometric transformations through designing and implementing an instructional unit in a technology supported classroom environment. The instructional unit including seven activities was developed by considering past research on learners' pre-existing…

The modelling approach to teaching and learning mathematics emphasizes the usefulness of mathematics in the real-world. The aim of the current study is to examine whether engagement in modelling activities provides learners an opportunity to expand their knowledge of a specific concept -- the "average" concept. Our data include…

The aim of this study was to characterize and discuss ways of reasoning that prospective high school mathematics teachers develop and exhibit in a problem-solving scenario that involves the coordinated use of digital technologies. A conceptual framework that includes Virtual Learning Spaces (VLS) and Resources, Activities, Support and Evaluation…

Covariational reasoning has been the focus of many studies but only a few looked into this reasoning in the polar coordinate system. In fact, research on student's familiarity with polar coordinates and graphing in the polar coordinate system is scarce. This paper examines the challenges that students face when plotting polar curves using the…

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…