An essential understanding of the uses and practices of algebra remain out of reach for many students. In this book, award-winning researcher Dr. Nicole Fonger addresses the issue of how to support all learners to experience algebra as meaningful. In a highly visual approach, the book details four research-based lenses with examples from 9th-grade…

This qualitative case study aimed at describing the level of students' metacognition in problem-solving using problem stories in the materials of the linear equation system of two variables of VIII class at MTs N 1 Pesawaran Lampung. The participants of the study comprised three students in VIII class of MTs N 1 Pesawaran Lampung in 2019-2020…

This is an article about abstraction, generalization, and the beauty of mathematics. We claim that abstraction and generalization in of itself may very well be a beauty of the human mind. The fact that we humans continue to explore and expand mathematics is truly beautiful and remarkable. Many years ago, our ancestors understood that seven stones,…

This research aims to develop an ocean wave energy converter kit from low-cost materials as a teaching tool. The kit is developed using the working principle of a wave energy converter that uses a buoy as a system drive and a weight balancer that is connected to a chain. The dimensions of the kit are 6.7 × 0.3 × 0.4 m (length × width × height)…

On November 16, 2018, at the 26th meeting of the General Conference on Weights and Measures (CGPM), a resolution was adopted that introduced historical changes into the International System of Units (SI). This decision, effective from May 20, 2019, established that the SI units of measurement will be defined by means of a set of seven fixed…

We present an algorithm for solving the time-dependent Schrödinger equation that is based on the finite-difference expression of the kinetic energy operator. Students who have some knowledge of linear algebra can understand the theory used to derive the algorithm. This is because the finite-difference kinetic energy matrix and the Hückel matrix…

The concept of determinant plays a central role in many linear algebra concepts and is also applied to other branches of mathematics and science. In this study, we focus on the application of determinant and inverse matrix concepts, in solving systems of equations by a group of 116 in-service mathematics teachers who were studying the topic at a…

As an alternative to Cronbach's [alpha] for estimating scale reliability, McDonald's [omega] has attracted increased attention within the methodological community for its less stringent measurement assumptions. Notwithstanding, [omega] is still seldom used by practitioners, likely due to its unavailability in popular software packages (e.g., SPSS)…

Limiting case analysis (LCA) is important to practicing physicists. Yet, there is little concrete guidance for physics educators, and a lack of consensus in the research community about how to help students learn, and learn from, limiting case analysis. In this study, we first review existing literature to find commonalities and variations in how…

In this paper we analyze common solutions that students often produce to isomorphic tasks involving proportional situations. We highlight some key distinctions across the tasks and between the different equations students write within each task to help elaborate the different interpretations of equivalence at play: numerical, transformational, and…

This study investigated differences between students' multiplication fact automaticity scores and student competencies on five problems from Intermediate Algebra assessments with a sample of university students. The five types of problems were: (1) linear equations with fractions, (2) system of linear equations, (3) factor by grouping, (4)…

Background: One criterion of adaptive learning is appropriate generalization to new instances based on the original learning context and avoiding overgeneralization. Appropriate generalization requires understanding what features of a solution are applicable in a new context and whether the new context requires modifications or a new approach. In…

One of the fundamental topics taught in the microeconomics class is minimizing economic costs. It includes understanding the concept of derivatives and applying them. However, most of the first-year undergraduate students find calculus difficult to understand, which also results in poor knowledge of optimization. We use the method based on the…

An elementary-level physics approach is used to calculate a number of interesting and useful quantities related to nuclear explosions. The set of eight exercises deals with nuclear fission fragments, the variation of fissile nucleus density in a fissioning nuclear device core with time, and the fireball.

A significant approach that should be followed by physics teachers at the secondary education level in order to enhance students' understanding is to highlight the generality of the mathematical procedures that describe different physical phenomena. In this paper, the common procedure that is used to calculate the duration of various physical…