This study aimed to characterise preservice teachers' (PSTs') noticing in a mathematics classroom and its influence on their lesson modification. Written narratives on video-taped lesson observation were analysed qualitatively in two components, attending and reasoning. The findings indicate that PSTs' initial noticing focused on general…

Pedagogical content knowledge (PCK) traditionally has been used in research concerning prospective and practicing classroom teachers. This essay argues that PCK is also relevant to other professions including those advancing quantitative reasoning (QR). To illustrate, the case of PCK for teaching QR is considered. Those in fields such as public…

This full paper considers how collaborative discourse can reveal ways upper-class engineering students mechanically reason about engineering concepts. Argumentation and negotiation during collaborative, multimodal discourse using speech and gestures helps establish common ground between learners and fosters reflection on their conceptual…

Flipped classrooms invert the traditional (lecture-based) classroom such that students review materials before class, and then participate in active learning techniques during class. While flipped classrooms have generally been shown to be beneficial, recent research indicates that there are numerous moderators that make an impact on learning…

Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this…

Much recent research and theorizing in the field of reasoning has been concerned with intuitive sensitivity to logical validity, such as the logic-brightness effect, in which logically valid arguments are judged to have a "brighter" typeface than invalid arguments. We propose and test a novel signal competition account of this…

The authors outline some of the ways in which they teach student teachers to think about the challenges of abstract concepts in science. They ask the student teachers to think about abstract ideas in a non-science context first, and find they are enabled to discuss and engage (and then later apply) their thinking better. The authors think that…

The relevance of this article is due to the need to form and develop algorithmic thinking of higher education students as the main requirement of the information society following 21st century skills and competences for new millennium learners. The purpose of the article is to consider algorithmic thinking as a new dimension of learning in higher…

An ongoing debate in the literature on human reasoning concerns whether or not the logical status (valid vs. invalid) of an argument can be intuitively detected. The finding that conclusions of logically valid inferences are liked more compared to conclusions of logically invalid ones--called the logic-liking effect--is one of the most prominent…

Developing scientific literacy, which involves applying scientific knowledge to solve real-world problems, is a primary goal in science education. Socioscientific Issue (SSI) provides students opportunities to reason through authentic and complex scientific dilemmas that reflect real-world issues, thus fostering a deeper understanding of…

This paper extends work in the areas of quantitative reasoning and covariational reasoning at the undergraduate level. Task-based interviews were used to examine third-semester calculus students' reasoning about partial derivatives in five tasks, two of which are situated in a mathematics context. The other three tasks are situated in real-world…

Mass balance (MB) reasoning offers a rich topic for examination of students' scientific thinking and skills, as it requires students to account for multiple inputs and outputs within a system and apply covariational reasoning. Using previously validated constructed response prompts for MB, we examined 1,920 student-constructed responses (CRs)…

Statistical mechanics has received limited attention in physics education research and remains a relatively underrepresented topic even in research on upper-division physics courses. The purpose of this study was to explore potential challenges that physics students encounter when they solve statistical mechanics problems in groups. Adopting a…

The retention of foundational knowledge is crucial in learning and teaching mathematics. However, a significant part of university students do not achieve long-term knowledge and problem-solving skills. A possible tool to increase further retention is testing, the strategic use of retrieval to enhance memory. In this study, the effect of a special…

Collaborative skills are crucial in knowledge-rich domains, such as medical diagnosing. The Collaborative Diagnostic Reasoning (CDR) model emphasizes the importance of high-quality collaborative diagnostic activities (CDAs; e.g., evidence elicitation and sharing), influenced by content and collaboration knowledge as well as more general social…