The development and use of learning trajectories is a body of research that has made enormous contributions to the field of mathematics education, offering insight into the teaching and learning of topics at all levels. Simultaneously, the work of building learning trajectories can benefit from explicitly adopting an anti-deficit stance,…

This study examines how joint exploration is established and maintained among students and the teacher in secondary mathematics classrooms. We use the theoretical perspective of positioning to conceptualize joint exploration as involving the negotiation and coordination among participants to position students with epistemic agency and authority.…

This paper offers specific implications for teaching and learning and brings into conversation ideas from ethnomathematics (including Western mathematics), postcolonial theory, aesthetics, biology, and Indigenous knowledge in order to propose a new vision for practicing mathematics, what I call mathematx. I build upon the work of sustainability in…

Changes to students' understanding of mathematical notation may be brought about by using technology within mathematics. Taking equality as a case study, the paper provides brief epistemological, historical, didactical, and computational reviews of its symbolic representation in pen-and-paper and technology-assisted mathematics, most especially in…

This paper refers to the concept of semiotic and theoretic control describing resources to conduct decisions in epistemic processes. We consider an argumentation process from a complex problem-solving activity involving different conceptual frames related to parabolas. Using a micro-analytical interpretative lens, we will show that, in order to…

This paper challenges the way in which we are inclined to treat theory and suggests that our tendency to privilege it over method is counterproductive. Some consequences of privileging theory are pointed out and a remedy is proposed. The remedy entails a number of "reversals" in the way we treat theory and method in maths education research, the…

Protocols were obtained from 22 subjects as they discovered the conditions under which equilibrium is obtained on a balance beam by predicting and observing the outcomes of a series of problems. The interviews revealed that subjects used a variety of heuristics to make predictions once they had isolated the two relevant features of the problem,…

The relationship between cognitive psychologists and researchers in artificial intelligence carries substantial benefits for both. An ongoing investigation in causal reasoning in medical problem solving systems illustrates this interaction. This paper traces a dialectic of sorts in which three different types of causal resaoning for medical…

Describes the reconstruction of a conventional thermodynamics curriculum using the Galperin theory of stage-by-stage formation of mental actions and Landa's description of the "through" systematization of knowledge, and discusses the generalizability of the procedures followed in developing the plan for instruction. A 33-item…

Much has been said on matter of aesthetics and mathematics--perhaps most commonly articulated in relation to properties such as "beauty" and "elegance," which are used to distinguish good from not-so-good mathematical products. Despite its importance in the work of mathematicians, it has been argued that aesthetics cannot be incorporated into…

A technique to teach cognitive skills to directly facilitate abstract and rational thinking is described. Based on George Kelly's theory of personal constructs, his Role Construct Repertory Test has students construe similarities and differences among important course concepts rather than provide individual definitions or examples of those…

Models and modeling are frequently used as instructional tools in science education to convey important information concerning both the explanatory and structural features of topic areas in science. The efficacy of models as such rests almost entirely upon students' ability to conceptualize them as abstracted "representations" of…

This paper discusses two related areas in which recent advancements in cognitive science and educational technology may affect instructional design theory. These are: (1) the analysis of information-to-be-learned; and (2) the linkage of learning theory to instructional prescriptions. The first area proposes extensions to current methods of…

Difficulty in comprehending mathematical concepts is a consequence of the system of knowledge acquisition prevailing in schools, and more specifically, of the typical pattern of classroom interaction. In the common task-setting/task-solving pattern, the teacher divides the subject matter into segments. Students are involved interactively in…

This paper reviews the book "Problem-Based Methodology," by Viviane Robinson. Consisting of 12 chapters divided into 4 parts, the book's general argument is that educational research must be grounded in problem-based methodology (PBM) if it is to contribute to the improvement of teaching and administrative practice. The reviewer first…