In a randomized controlled trial (RCT), some subjects assigned to the treatment condition may not fully comply. Often there is interest in the effect of the treatment within the "principal stratum" of subjects who would comply if assigned to treatment. However, it is unknown which control subjects would have complied if treated and which…

This paper presents an alternative approach of teaching systems of two linear equations to the students in Tanzanian ordinary secondary schools. I conducted a desk-based research on methods that have been used by in-service mathematics teachers for teaching systems of two linear equations in ordinary secondary schools. It was found that five…

In this article, we examine how 10th graders make use of different intertwined representations when solving algebraic word problems. It is structured in a quantitative phase, with 61 students and a subsequent follow-up case study with nine pairs of students. We found that drawings and tables, used as auxiliary representations within variants of…

The Higher-Order Thinking Skill Test Instrument on Quadratic Equations (HOTS-QE) was developed to measure the level of HOTS on the topic of quadratic equations among secondary school students. The HOTS-QE instrument consists of 17 structured subjective items divided into two smaller questions according to the three levels of HOTS, namely applying,…

The 3-equation model by Carlin and Soskice (2014) introduces the current consensus in modern monetary macroeconomics to undergraduates through a static framework in which adjustment occurs via the monetary policy rule of an inflation-targeting central bank. In this article, the authors present a dynamic extension of this model and an Excel-based…

Nonlinear equations are usually solved numerically. However, approximated analytical solutions of nonlinear equations are useful as an initial iteration point for numerical methods. Furthermore, these analytical approximations are sometimes quite close to the actual root. In order to teach at undergraduate level how to perform this kind of…

The static equilibrium properties of a spool, resting on an incline and subject to the tension exerted by a string wrapped around the core cylinder, are studied by means of Newtonian mechanics. The overall behaviour of this system is imagined to be similar to that of a doggie kept on a leash. Starting from the well-known mechanical properties of…

The purpose of this resource is to help math teachers unpack, understand, and implement the current math content and practice standards. It describes the progressions of learning within each course and provides content supports that include broad ideas about effective instruction as well as practical instructional strategies. Math teachers,…

Equations are often used in mathematics and other subjects, which means that a media can teach students how to solve equations, particularly linear equations of two variables, or "Sistem Persamaan Linear Dua Variabel" (SPLDV) as it is called in Indonesian, is needed. However, most teachers are still focused on developing the learning…

In this study, we investigated prospective secondary mathematics teachers' development of a meaning for the Cartesian form of complex numbers by examining the roots of quadratic equations through quantitative reasoning. Data included transcripts of the two sessions of classroom teaching experiments prospective teachers participated in, written…

We present the theoretical argument that the use of mathematics in physics can be productively conceptualized as using a language and that learning to make sense of physics equations and appropriating them into novel scientific inquiry can be understood as a process of learning to read fluently with a high level of reading comprehension and to…

In this article, we present research on eight kindergarten and eight first-grade students' understandings of the arithmetic properties of commutativity, additive identity, and additive inverse during a classroom teaching experiment, selected from a larger study that included 88 students. In this study, we explore the students' types of…

In an attempt to address the need for an alternative presentation of the quantum mechanical position and momentum spaces, we provide a presentation that is more constructive and less calculative than those found in literature. Our approach is based on a simple, intuitively understood relation that expresses the physical equivalence of the quantum…

Mathematics textbooks sometimes present worked examples as being generated by particular fictitious students (i.e., "person-presentation"). However, there are indicators that person-presentation of worked examples may harm generalization of the presented strategies to new problems. In the context of comparing and discussing worked…

The purpose of this study was to validate an alternative skinfold equation for women created from dual-energy x-ray absorptiometry (DXA). Anthropometrics and a whole-body DXA scan were completed on 77 women (mean age: 28.0 ± 10.2 years). Four Jackson-Pollack (JP) skinfold prediction equations and the DXA criterion (DC) equation were compared to…