Generalization is a critical component of mathematical reasoning, with researchers recommending that it be central to education at all grade levels. However, research on students' generalizing reveals pervasive difficulties in creating and expressing general statements, which underscores the need to better understand the processes that can support…

Science education motivates students to be problem solvers who utilize scientific knowledge for the social problems that they encounter in their lives. However, for better solutions for the problem, just knowledge of scientific concepts would not be enough because students need to approach problems aesthetically also. Understanding social,…

Algebraic thinking and strategy flexibility are essential to advanced mathematical thinking. Early algebra instruction uses 'missing-operand' problems (e.g., x - 7 = 2) solvable via two typical strategies: (1) direct retrieval of arithmetic facts (e.g., 9 - 7 = 2) and (2) performance of the inverse operation (e.g., 2 + 7 = 9). The current study…

The book that inspired millions of educators to refine their approach to teaching returns for an all-new third edition. Built on a more rigorous research base and updated to emphasize student diversity, equity, and inclusion, "The New Classroom Instruction That Works" offers a streamlined focus on the 14 instructional strategies proven…

Cognitive and psychomotor capabilities are two critical interrelated abilities to improve student learning outcomes. Both abilities play a role in understanding new information and developing fine motor skills. Hence, schools train students these two abilities to equip them with basic skills in solving mathematical problems such as basic…

Over the past two decades, the perennial low success rates of elementary students in mathematical problem solving and the difficulties experienced by teachers in meeting the various needs of their students with this type of task have become quite a hot topic. While there is a general consensus among education scholars about the crucial role played…

Wicked problems are large, complex problems involving multiple perspectives that present substantial future challenges. These challenges can be overwhelming for learners and pose difficulties in teaching for instructors. Herein a solutions-oriented teaching strategy that amalgamates proven active learning strategies is presented along with a…

The More A-More B intuitive rule has become a research hotspot in the field of mathematical education in recent years. The intuitive rule of More A-More B is often reflected in students' responses to comparison tasks. In such tasks, students are asked to compare 2 objects that differ in a certain salient quantity A (where A[subscript 1] >…

Student cognition in response to intuitive and counterintuitive stimuli in the school science curriculum is not well understood. To address this issue, this study examines high school students' cognitive responses to three counterintuitive physics problems. Our analysis reveals that student success in arriving at counter-intuitive physical…

Intelligent learning environments can be designed to support the development of learners' cognitive skills, strategies, and metacognitive processes as they work on complex decision-making and problem-solving tasks. However, the complexity of the tasks may impede the progress of novice learners. Providing adaptive feedback to learners who face…

Traditional high school physics instruction often comes across as a mere extension of the mathematics classroom to many of our students. Solving numerical physics problems using structures such as the GUESS method (given, unknown, equation, substitute, solve) doesn't help students with conceptual understanding. With the advent of physics education…

This article explores three processes involved in attending to evidence of students' thinking, one of the Mathematics Teaching Practices found in "Principles to Actions: Ensuring Mathematical Success for All." These processes, explored during a classroom activity on proportional relationships, are discussed in this article, another…

Critical thinking when engaged in science problem solving around even simple tasks such as the Piagetian volume conservation task is a complex endeavor. Tasks such as the conservation task often require the interaction of multiple cognitive systems. Parity judgment, retrieval, and lateral thinking are three examples of such systems interacting…

Information security practitioners and researchers who possess sufficient depth of conceptual understanding to reconstitute systems after attacks or adapt information security concepts to novel situations are in short supply. Education of new information security professionals with sufficient conceptual depth is one method by which this shortage…

Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually…