Circle, ellipse, parabola, hyperbolic curves are defined as conic sections from the intersection of a coni with a plane at different angles. These curves can be found in different positions depending on the different angles. In this case, rotation transformation can be applied to the curves so that their major axes are brought to the horizontal…

Thermodynamics challenges teachers and learners. Its pervasiveness about nature, mathematical abstractness, nonnumerical relations, and complexity in applications can inhibit understanding and usage, especially by undergraduates. Perspectives are given about these obstacles, and some suggestions are made to enhance comprehension of the discipline.

This paper articulates a stance on the study of students' meaningful mathematics understanding with multiple representations. We integrate Thompson's theory of quantitative reasoning and Dreyfus' theory of multiple representations in our approach to frame and conduct empirical investigations of the study of meaningful understanding of function. We…

Simulation educational technologies provide a convenient way to augment classroom learning in higher education. The University of Colorado Boulder has created many Physics Education Technology (PhET) computer simulations relevant to concepts in Sciences and Mathematics. There is a notable gap in the literature of simulation-based technologies,…

Feedback in exploratory learning systems has been depicted as an important contributor to encourage exploration. However, few studies have explored learners' interaction patterns associated with feedback and the use of external representations in exploratory learning environments. This study used Fractions Lab, an exploratory learning environment…

Problem solving is at the heart of mathematics, and is known to support learning for a diverse range of children. However, challenges can be encountered when teaching mathematics through problem solving. This article provides insights from research literature into: (1) the nature of the challenges; and (2) some ways that problem solving can be…

In this paper, we introduce 'Concept Questions,' a weekly writing assignment that has been incorporated into multiple upper-level engineering courses at a single university with the intent of enhancing students' conceptual understanding of the course content. To explore the influence of this activity on students in these courses, we compared…

In this set of tips, parents and caregivers will learn how to: (1) support children's understanding of fractions at home with activities on dividing objects (recommended for grades K-5); (2) support children's understanding of fractions at home with measurement activities (recommended for grades K-4); (3) support children's understanding of…

Systems thinking is recognized as an essential skill for understanding complex problem solving and decision making associated with many of the contemporary issues faced by individuals and communities. In this article, our goal is to contribute to the knowledge of curriculum and pedagogy of formal systems thinking teaching in higher education. We…

Mathematics is a particularly notable domain in which to understand the role of body movement for improving reasoning, instruction, and learning. One reason is that mathematics ideas are often expressed and taught through disembodied formalisms--diagrams and symbols that are culturally designed to be abstract, amodal, and arbitrary (Glenberg et…

Active participation in project-based learning (PBL) could develop students` knowledge and crucial learning skills across various disciplines. However, the implementation of PBL in the K-12 classroom is usually impeded by the stepby-step PBL cycle. Micro project-based learning (MPBL), which advocates and adheres to the learning principles and…

To fulfill the Standards for Mathematical Practice (National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA Center & CCSSO], 2010), it is important for teachers to empower students to critique, revise, and expand their ideas as they solve problems. However, students often face challenges such…

Multiplicative thinking is widely accepted as a critically important 'big idea' of mathematics that underpins much mathematical understanding beyond the primary years. It is therefore important to ensure not only that children can think multiplicatively, but that they can do so at a conceptual rather than procedural level. This paper reports on a…

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with…

Teaching mathematics in general and instructing mathematics at junior schools in particular not only create favorable conditions for students to develop essential and core competencies but also help students enhance mathematical competencies as a foundation for a good study of the subject and promote essential skills for society, in which…