This study is the first to examine the associations between the occurrence, frequency, and adaptivity of children's subtraction by addition strategy use (SBA; e.g., 712 - 346 = ?; 346 + 54 = 400, 400 + 300 = 700, 700 + 12 = 712, and 54 + 300 + 12 = 366) and their underlying conceptual knowledge. Specifically, we focused on two rarely studied…

Ideation methods and outcomes have been evaluated in a variety of ways. Our study extends existing work through a qualitative analysis of idea characteristics based on the ideation method used. Beginning engineering students completed two short ideation sessions with a single design problem while following Individual Brainstorming and then Design…

There is extensive literature focusing on students' misconceptions in various subject domains. Several conceptual change approaches have been trying to understand how conceptual change occurs to help learners handle these misconceptions. This meta-analysis aims to integrate studies investigating the effectiveness of three types of conceptual…

In their recent article on teachers' proportional reasoning, Copur-Gencturk et al. (2022) draw attention to a type of strategy that they call "relative", lodged right between additive and multiplicative thinking. This strategy raised interest in our research team, as it aligned well and helped give stronger meaning to some strategies…

There is growing evidence that the ability to perceive structure is essential for students' mathematical development. Looking at students' structure sense in basic numerical and patterning tasks seems promising for understanding how these tasks set the foundation for the development of later mathematical skills. Previous studies have shown how…

Using Balacheff's (2013) model of conceptions, we inferred potential conceptions in three examples presented in the spanning sets section of an interactive linear algebra textbook. An analysis of student responses to two similar reading questions revealed additional strategies that students used to decide whether a vector was in the spanning set…

We offer a new angle to explain the comprehension of mathematical infinity. We use Action-Process-Object-Schema (APOS) theory to explore the construction of different aspects of the cognitive Object related to this notion. We focus our attention on different ways of interacting with infinity, and how to act on infinite entities. Our aim is to shed…

Idea evaluation has been identified as a critical step in the creative problem-solving process. Yet, it is unclear how exactly individuals evaluate and compensate for weaknesses in their creative ideas. In the present study, both qualitative and quantitative methods were used to identify the compensatory strategies that undergraduate participants…

This article explores the conceptual challenges that engineering students encounter with double integrals in a vector calculus course. Drawing on previous literature and utilising APOS (Activity- Process- Objects- Schema) as a theoretical framework, this study investigates the difficulties that students face in understanding and applying double…

This article discusses and elaborates on how concept mapping as a specific instructional strategy helps students to externalize and transform their understanding of qualitative research; and helps instructors to focus on their students' conceptual understanding of qualitative research. The discussion focuses on concept mapping as a learning…

The use of analogies is a well-known teaching strategy to bridge unfamiliar and familiar concepts. However, analogies may become ineffective if the familiar concept is not familiar anymore. For example, this may occur when we describe rotational sense as clockwise and counterclockwise, assuming students know how to read a clock with hour and…

The study advances the instrumental approach to mathematics education (Drijvers et al., 2013; Trouche, 2003), aiming to elucidate the interplay between students' reasoning competency, conceptual knowledge and tool utilisation in dynamic digital geometry and algebra environments. The dynamic properties of these environments pose a nuanced…

The present study explored the accuracy of participants' (N = 317) metacognitive awareness (self-reported difficulty and confidence) of psychology concepts and the moderating effects of their psychology background (academic major, number of psychology courses completed, and overall psychology course grades). Participants first rated the difficulty…

In today's dynamic and high-tech learning environment, offering flexible and innovative assignment options is crucial for engaging students across varied learning preferences and backgrounds. Alternative formats, such as gamification and storyboards, can boost engagement, spark creativity, and enhance learning outcomes in college classrooms. By…

The relation between learners' metacognitive skills and conceptual understanding is often portrayed as an input-output relation when dealing with science, technology, engineering, and mathematics (STEM) and non-STEM disciplines. However, studies indicate that not all pedagogies yield positive correlations between learners' metacognitive skills and…