According to the design principle of progressive schematization, learning trajectories towards procedural rules can be organized as independent discoveries when the learning arrangement invites the students first to develop models for mathematical concepts and model-based informal strategies; then to explore the strategies and to discover pattern…

In this paper, the knowledge dimension for Revised Bloom's taxonomy (RBT) is unpacked for integral calculus. As part of this work, the 11 subtypes of the knowledge dimension are introduced, and through document analysis of chapter 4 of the RBT handbook, these subtypes are defined. Then, by consulting materials frequently used for teaching integral…

This article presents a teaching proposal that emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. More concretely, these concepts were introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was designed after observing architecture students…

It is not every day that a former student greets a teacher with, "Your course changed my life." The authors are the professor and student of the transformative course. Alicia Gonzales wanted to understand how to work with students to co-construct an environment where persistent problem solving in a technologically rich classroom was the…

Problem solving is highlighted in many mathematics curricula and has recently become one of the most investigated topics in the field of mathematics education. Extensive studies report that developing students' problem solving skills enhances their understanding of mathematics. Therefore, there is a focus on investigating problem solving processes…

In this article we study the conceptions of an American and a French group of undergraduate pre-service teachers regarding the concept of independent events. Specifically, we study the role that intuition plays in their answers, ascertain the presence of probabilistic biases, and compare the findings with previous results collected on a different…

The positive correlation between spatial ability and mathematical ability has been well-documented, but not well-understood. Examining student work in spatial situations that require numerical operations provides us with insight into this elusive connection. Drawing on student work with angle, length, volume, and area, we examine the ways in which…

Mathematics is an important nature exploration tool used by all natural sciences. So it is usual that mathematical calculations are part of school science education. But how are these calculations perceived by the learners themselves? What are their attitudes to this part of the teaching process? The answer to this question is important for any…

This practice paper provides a detailed scaffolded layout of how to embed computational thinking concepts into a project-based math methods course. Parallel to completing a project in which the in-service teachers design solutions for math struggles of their P-12 students, the graduate students reflect on their problem-solving activities using…

This article reports on the explicit introduction of metacognitive strategies by an early career science teacher to support the application of mathematics skills. The research investigated the effectiveness of these strategies with three Year 11 physics students using an action research approach. Quantitative and qualitative data were collected…

To address the upcoming reform curriculum initiative following competency-based learning in Vietnam, this study examines how variations of a contextualized task allow students to experience the mathematical modelling process. We explore how Grade 10 students respond to tasks with different levels of authenticity when they first attempt such tasks.…

Methods of education in schools should promote students' activeness, self-awareness, initiative and creativity; be suitable with the characteristics of each class and subject; foster self-study methods, ability to work in groups, practice skills to apply knowledge into practice, and impact emotions to bring joy as well as excitement to students.…

This research presents the investigation of physics students' and physics faculty members' professional development and a design methodology via which we could best support them in their professional development. In particular, the first part of this dissertation will focus on undergraduate upper-division physics students' conceptual learning and…

The "mathematics problem" is a well-known source of difficulty for students attempting numerical problem solving questions in the context of science education. This paper illuminates this problem from a biology education perspective by invoking Hogan's numeracy framework. In doing so, this study has revealed that the contextualisation of…

This paper introduces a revised model for the development of basic computation skills. The model draws on four key phases, which have proven to be important for the development of calculation strategies and stresses the use of gestures and the verbalisation of concrete and mental images. This seems to be of crucial importance for children with…