Within the commognitive perspective, ritual and explorative routines are used in a very particular way to distinguish students' routines according to whether they are driven by social reward or by generating a substantiated narrative. Explorative routines in this theorisation may refer not to inquiry-based activity but to the result of a student's…

Mathematical modelling emphasizes the connection between mathematics and reality -- still, tasks are often exclusively introduced inside the classroom. The paper examines the potential of different task settings for mathematical modelling with real objects: outdoors at the real object itself, with photographs and with a 3D model representation. It…

Example-generation tasks have been suggested as an effective way to both promote students' learning of mathematics and assess students' understanding of concepts. E-assessment offers the potential to use example-generation tasks with large groups of students, but there has been little research on this approach so far. Across two studies, we…

The aim of this study is to develop a descriptive phase model for problem-posing activities based on structured situations. For this purpose, 36 task-based interviews with pre-service primary and secondary mathematics teachers working in pairs who were given two structured problem-posing situations were conducted. Through an inductive-deductive…

We are interested in understanding how university students learn to use programming as a tool for "authentic" mathematical investigations (i.e., similar to how some mathematicians use programming in their research work). The theoretical perspective of the instrumental approach offers a way of interpreting this learning in terms of…

In this paper, we discuss discernment of invariants in dynamic geometry environments (DGE) based on a combined perspective that puts together the lens of variation and the maintaining dragging strategy developed previously by the authors. We interpret and describe a model of discerning invariants in DGE through types of variation awareness and…

In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes mathematical understanding. Building on a previous model used to analyze discursive practices of students engaged in mathematical problem solving, we introduce three types of collaboration and…

This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies…

This paper is centered on creating equitable opportunities for learners in mathematics education. Through observations of teacher practice, the paper seeks to theorize how teachers enact their dispositions toward mathematics instruction. These observed propensities, in relation to teachers' aims for students to "take up their space" in and beyond…

In some circles of mathematics education, repetition and rote are somehow conflated in terms of their pedagogical uses and ramifications. In this paper, I argue for the separation of the two, relying upon a framework suggested by Martin Buber's "I-Thou" ontology. In the presentation of Buber's ideas, I highlight the notion of…

The purpose of this article is to consider what methods from ethnopoetics--a field at the intersection of linguistics and anthropology--may add to narrative inquiry in mathematics education. I build a theoretical framework to argue for the use of narrative inquiry and ethnopoetics in studies of teacher knowledge. I report ethnopoetic analyses of…

According to theoretical concepts like constructivism, each learner has to build up knowledge on his or her own. The learner creates hypotheses in order to explain "facts". Hypotheses do not guarantee certainty. They have to be verified. In this article, a theoretical framework will be presented which can help to understand and analyse the…

This conceptual research framework addresses the problem of rote learning by characterising key aspects of the dominating imitative reasoning and the lack of creative mathematical reasoning found in empirical data. By relating reasoning to thinking processes, student competencies, and the learning milieu it explains origins and consequences of…

We illustrate and exemplify how the idea of reflection is framed by the enactive concept of "deliberate analysis". In keeping with this frame, we do not attempt to define reflection but rather work on the question of "how do we do reflecting?" within such a frame. We set out our enactivist theoretical stance, in particular pointing to implications…

Presents a process model developed for interaction and mathematical level raising focusing on the individual learning process and relates this model to research. The model is meant to show how level raising can be realized by allowing students to work in small groups on a mathematical problem. Contains 24 references. (Author/ASK)