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…

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…

The work presented in the following chapters was undertaken with the goal of understanding and improving education in organic chemistry. Initial work, described in Chapters 1 and 2, focuses on students' ability to explain and rationalize the outcomes of organic chemistry reactions. Chapter 1 explores the relationship between assessment emphasis…

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…

Digital history-based project-based learning (PjBL) in history learning is a learning medium that can provide a special attraction for students who can improve historical concept skills and historical awareness. However, there are still many teachers who have not used it, so it is very important to study it. This research aims to analyze the…

Educational tools like EdPuzzle, PlayPosit, and Kaltura have gained recent attention, as they purportedly empower educators to incorporate questions, quizzes, and discussions into instructional videos. However, there is no empirical evidence on how or under what circumstances these platforms may impact students' learning. A quasi-experimental…

Current educational systems are making shifts from teacher-centered to learner-centered environments. This shift creates space for more involvement from students in their own instructional and assessment processes that sets them up for success in a method that allows them control of their achievement. Teachers have to assess and reflect on their…

Literature suggests that "current characterizations of the terms procedural knowledge and conceptual knowledge are limiting and are, in fact, impediments to careful investigation of these constructs" (Star, 2005, p. 405). We examined secondary mathematics teachers' understanding of procedural and conceptual knowledge at superficial and…