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…

The aim of this paper is to describe and analyze how a group of prospective teachers create problems to develop proportional reasoning either freely or from a given situation across different contexts, and the difficulties they encounter. Additionally, it identifies their beliefs about what constitutes a good problem and assesses whether these…

The evolution of mathematics coincided with advancements in its teaching. The 19th and 20th centuries marked a pedagogical revolution in mathematics education. This paper argues that Bruner's (1966) model, Gagné's (1985) taxonomy, innovative teaching methods emphasizing research and problem-solving, and the inclusion of data analysis topics have…

Game-based learning has gained significant attention from educational researchers because of its ability to create an engaging and enjoyable learning environment for students. However, there was a research gap regarding the design of game mechanics that specifically helped students understand abstract scientific concepts. Also, the impact of…

Mathematical reasoning, a fundamental aspect of human cognition, poses significant challenges for artificial intelligence (AI) systems. Despite recent advancements in natural language processing (NLP) and large language models (LLMs), AI's ability to replicate human-like reasoning, generalization, and efficiency remains an ongoing research…

Previous research suggests that preschoolers struggle with understanding abstract relations and with "reasoning by analogy." Four experiments find, in contrast, that 3- and 4-year-olds (N = 168) are surprisingly adept at relational and analogical reasoning within a causal context. In earlier studies preschoolers routinely favored images…

In many discussions of the ways in which abstraction is applied in computer science (CS), researchers and advocates of CS education argue that CS students should be taught to consciously and explicitly move among levels of abstraction (Armoni "Journal of Computers in Mathematics and Science Teaching," 32(3), 265-284, 2013; Kramer…

The present study cross-sectionally investigated proportional reasoning abilities in 5- to 9-year-old children (n = 185) before they received instruction in proportional reasoning. This study addressed two important aspects of the development of proportional reasoning that remain unclear in the current literature: (1) the age range in which it…

The goal of our research program is to explicate the learning of mathematical concepts in ways that are useful for instructional design and to develop design principles based on those explications. I review one type of concept and our elaboration of reflective abstraction, coordination of actions (COA) that accounts for its construction. I then…

In order to teach Computational Thinking (CT) skills to young students, Block-Based Programming Environments (BBPEs) are integrated into secondary school computer science (CS) education curricula. As a CT skill, abstraction is one of the prominent skills, which is difficult to enhance and measure. Researchers developed some scales for measuring…

Recursive reasoning is a powerful tool used extensively in problem solving. For us, recursive reasoning includes iteration, sequences, difference equations, discrete dynamical systems, pattern identification, and mathematical induction; all of these can represent how things change, but in discrete jumps. Given the school mathematics curriculum's…

This paper presents data from the first of three iterations of teaching experiments conducted with secondary teachers. The purpose of the experiments was to investigate how teachers' combinatorial reasoning could support their development of algebraic structure, specifically structural relationships between the roots and coefficients of…

Reading fluency (RF) involves the automaticity of many distinct reading skills (e.g., pacing, word recognition, phonological awareness) and allows cognitive resources to be allocated to higher-order reading skills (e.g., comprehension, synthesis). Early identification of students at-risk for RF deficits is critical, but many screeners require a…

This study investigates first-year undergraduate students of Primary Education Mathematics Teacher Education's knowledge and understanding of rotational symmetry in geometric shapes. Three students participated in this study, which was designed within the framework of a one-to-one teaching experiment (a qualitative research method) in the fall…