This study investigated 11 pre-service middle school teachers' solution strategies for exploring their knowledge of fraction division interpretations. Each participant solved six fraction division problems. The problems were organized into two sets: symbolic problems (involving numbers only) and contextual problems (involving measurement…

Aim of the study: This study examines numerical methods for solving the problems in gas dynamics, which are based on an exact or approximate solution to the problem of breakdown of an arbitrary discontinuity (the Riemann problem). Results: Comparative analysis of finite difference schemes for the Euler equations integration is conducted on the…

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

This study investigated whether a latent class of children with math difficulties (MD) or math learning disabilities (MLD) emerged within a heterogeneous sample of learners. A latent class analysis was computed on children (N = 447) in Grade 3 who were administered a battery of math, reading, and cognitive measures. The analysis yielded four…

This book is about inclusivity and open education in the digital age. It reports the latest data on this topic from the 2021 Cognition and Exploratory Learning in the Digital Age (CELDA) conference. This annual conference focuses on challenges pertaining to the evolution of the learning process, the role of pedagogical approaches and the progress…

This study reveals the transformation of prospective science teachers into knowledgeable individuals through classical, combination, and information theories. It distinguishes between knowledge and success, and between knowledge levels and success levels calculated each through three theories. The relation between the knowledge of prospective…

Conflicting explanations and unrelated information in science classrooms increase cognitive load and decrease efficiency in learning. This reduced efficiency ultimately limits one's ability to solve reasoning problems in the science. In reasoning, it is the ability of students to sift through and identify critical pieces of information that is of…

The move from additive to multiplicative thinking requires significant change in children's comprehension and manipulation of numerical relationships, involves various conceptual components, and can be a slow, multistage process for some. Unit arrays are a key visuospatial representation for supporting learning, but most research focuses on 2D…

This article presents a teaching intervention where programming was used to facilitate preschoolers' learning of mathematics, especially in their development of spatial thinking. In the intervention, the programming was made with a small programmable robot especially designed for young students. The results indicate that the children developed…

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…

Life tables are mathematical tables that document probabilities of dying and life expectancies at different ages in a society. Thus, the life table contains some essential features of the health of a population. Probability is often regarded as a difficult branch of mathematics. Life tables provide an interesting approach to introducing concepts…

Learning curves have proven to be a useful tool for understanding how a student learns a given skill as they progress through a curriculum. A learning curve for a given Knowledge Component (KC) is a plot of some measure of competence as a function of the number of opportunities the student has had to apply that KC. Consider the case where each…

This study proposes a computer-assisted system with a design based on Polya's problem-solving model. The system is designed to help average and low-achieving second graders in mathematics with word-based addition and subtraction questions. The emphasis of using the specific model was on dividing the problem-solving procedure into stages and the…

The paper examines how computational thinking can be taught to young children with the use of educational robotics using the kit LEGO WeDo. Computational thinking was measured in terms of four sub-skills, namely, sequencing, correspondence between actions and instructions, debugging, and flow of control. Students were assigned to an experimental…