Spatial thinking is ubiquitous in design. Design education across all age groups encompasses a range of spatially challenging activities, such as forming and modifying mental representations of ideas, and visualizing the scenarios of design prototypes being used. While extensive research has examined the cognitive processes of spatial thinking and…

This paper aims to shed light on an overlooked but essential aspect of informal reasoning and its radical implication to mathematics education research: Decentralising mathematics. We start to problematise that previous studies on informal reasoning implicitly overfocus on what students infer. Based on Walton's distinction between reasoning and…

The same and different routine offers an opportunity to build a strong foundation for future grades while also deepening the experiences of prekindergarten and transitional kindergarten students. Students have opportunities to make sense, share ideas, and engage in the ideas of others. We conjecture this type of experience supports students and…

Evaluating evidence and restructuring beliefs based on anomalous evidence are fundamental aspects of scientific reasoning. These skills can be challenging for both children and adults, especially in domains where they possess inaccurate prior beliefs that can interfere with the acquisition of correct scientific information (e.g., heavier objects…

Concepts and practices are widely used to assess students' development in computational thinking (CT). However, less is known about how the development of each construct relates to that of the other. With a sample of 997 grade 6 students (average age = 11.43 at the beginning of the school year) from 14 primary schools, we examined the…

Knowing functions and functional thinking have recently moved from just knowledge for older students to incorporating younger students, and functional thinking has been identified as one of the core competencies for algebra. Although it is significant for mathematical understanding, there is no unified view of functional thinking and how different…

How anthropomorphic reasoning functions in scientific thinking has been a controversial topic. There is evidence it is problematic as well as evidence it can play productive roles, for scientists and for students. In science education, however, the prevailing view remains that it is an impediment. For this study, we have chosen examples of what we…

In science, one of the most crucial representations for constructing meaning about physical events is graphs. The first graph students encounter in science class is the constant velocity motion graph. Therefore, examining students' understanding of structuring and interpreting these graphs for the relationship between distance, time, and velocity…

The study outlines the early-stage development of a free-response General Relativity Concept Inventory (GRCI), an educational instrument designed to test for conceptual understanding of General Relativity. Data were collected for the study by having 26 participants from General Relativity courses work through the questions on the GRCI. Interviews…

Argumentation-based classroom interventions are a growing alternative for stimulating conceptual learning, thinking, and communicative skills. However, not all classroom argumentation is desired, nor does every argumentation design lead students to develop their abilities and understanding. In the educational literature, productive argumentation…

The development of the mathematical concept of the infinite, through the reflections that arise from personal notions and perceptions and the analysis of some ideas of Galileo and Cantor, invites us to investigate the relationship between intuition and formalization for the understanding of the said concept. This paper aims to observe and describe…

How to influence and assess whether students engage in conceptual thinking are longstanding methodological problems in mathematics education. Recently, eye-tracking technology has fueled a discussion on whether eye movement analysis can support valid inferences about mathematical thinking. This study investigates whether eye movement analysis can…

Authors of calculus texts often include graphs in the text with the intent that the graph depicts relationships described in theorems and formulas. Similarly, graphs are often utilized in classroom lectures and discussions for the same purpose. The author or instructor includes function graphs to represent quantitative relationships and how a pair…

In a previous article, "The Shape of Reasoning: Using Geometry to Promote the Reasoning Proficiency Strand" (EJ1286217), the author put forward the argument that no medium is more powerful than geometry as a vehicle for developing the mathematical proficiency strand of Reasoning. Because geometry is so visual and tactile, the…

To promote the development of young children's probabilistic intuitions through experience, we focus on the dual nature of probability related to both belief (subjective notion) and frequency (objective notion). This paper reports on the responses of 7-8-year-olds on two tasks used to bridge subjective and objective notions of probability. We…