The Common Core State Standards in Mathematics outline both the content and practices students must engage in at each grade level to become mathematically proficient. Mathematical processes include problem solving, reasoning and proof, communication, and procedural fluency, which includes flexible thinking. The purpose of this study was to…

Two common interest-enhancement approaches in mathematics curriculum design are illustrations and personalization of problems to students' interests. The objective of these experiments is to test a variety of illustrations and personalization approaches. In the illustrations experiment, students (n = 265) were randomly assigned to lessons with…

To efficiently create books and other instructional content from videos and further improve accessibility of our course content we needed to solve the scene detection (SD) problem for engineering educational content. We present the pedagogical applications of extracting video images for the purposes of digital book generation and other shareable…

Background: The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic…

As digital educational media use becomes more widespread, an opportunity exists to develop new methods to present abstract ideas to provide a more meaningful learning experience. Drawing from psychology and dynamic visualization research, new interactive tools can be thoughtfully designed but it is also necessary to establish how these media are…

Student problem solving in the context of a dynamic mathematics environment (DME) has previously been investigated primarily through the lens of whether or not the student could complete a problem-solving task. Herein, we investigate what trajectories students employ in the realms of mathematics, technology, and problem solving as they attempt to…

Making connections among multiple visual representations is key to students' learning. This article considers two learning processes involved in connection making: explicit sense making of connections and implicit perceptual induction of connections. Instructional interventions support these processes via different problem types: sense-making…

Students with autism spectrum disorders (ASD) are included more frequently in general education, and are increasingly expected to access and master core curricular content, including mathematics. However, mathematics often presents challenges to students with ASD. Studies on instructional interventions in mathematics for students with ASD are also…

Physics and Mathematics are two deeply interlinked domains of Science. Mathematics is considered as the language in which the Physics theories are built by employing mathematical symbols and operations to make equations and representations in the world of Physics completely meaningful. In spite of being the backbone of Physics, the use of…

In the United States, students with mild intellectual disability (MID) are expected to access the general education curriculum and some of these students are required to pass the same high-stakes exams as students without disabilities. Research supports that students with MID can demonstrate success with mathematics after receiving interventions…

Prior research shows that self-explanation promotes understanding by helping learners connect new knowledge with prior knowledge. However, despite ample evidence supporting the effectiveness of self-explanation, an instructional design challenge emerges in how best to scaffold self-explanation. In particular, it is an open challenge to design…

The use of structural representations to convey spatial and chemical information is an integral part of organic chemistry. As a result, students must acquire skills to interpret and translate between the various diagrammatic forms. This article summarizes the skills sets, problem-solving strategies, and identified student difficulties in…

Drawing appropriate diagrams is a useful problem solving heuristic that can transform a problem into a representation that is easier to exploit for solving it. One major focus while helping introductory physics students learn effective problem solving is to help them understand that drawing diagrams can facilitate problem solution. We conducted an…

Background: Given the context of low attainment in primary mathematics in South Africa, improving learners' understanding of multiplicative reasoning is important as it underpins much of later mathematics. Aim: Within a broader research programme aiming to improve Foundation Phase (Grades 1-3, 7-9-year-olds) learners' mathematical performance, the…

A multiple probe across participants design was used to examine the effectiveness of a treatment package to teach students with moderate intellectual disability how to solve simple linear equations. The investigator read realistic scenarios of a problem, used actual items as manipulatives, presented a visual aid of the equation, and used a system…