Mathematics evidenced un/manifested in/active, un/changeable, im/pure and primordial nature; therefore, it is illimitable to define as finite. It exists in the engineering of this universe. Philosophy of Mathematics studies abstract entities such as assumption and implication. Mathematics educators regard it as deductive tool and relate to solving…

This paper reports our preliminary observations of a pilot project carried out from February to April 2019 with a group of students learning Spanish at the University of Central Missouri and students learning English at the University of León. The project combines challenging escape room activities with intercultural and interlinguistic…

The purpose of this study was to measure the mathematics-vocabulary performance of 3rd graders to determine if performance differences existed among English learners (ELs) and non-ELs with and without mathematics difficulty (MD). Using screening data from a large-scale intervention study, we categorized students into four groups based on equation…

Even before the COVID-19 pandemic, it was apparent that American jobs are undergoing massive technological transformation. In-demand careers increasingly require digital literacy skills, and for many industries digital skills are entry-level competencies for new hires and incumbent workers. Since the pandemic, digital demands in the U.S. workplace…

This book gathers work from over a decade of study, and seeks to better understand and support how learners become tradespeople. The research programme applies recent concepts from neuroscience, educational psychology and technology-enhanced learning to explain and help overcome the challenges of learning in trades-learning contexts. Due to the…

Today the school-wide behavior management program, Positive Behavioral Interventions and Supports, or PBIS, follows the Multi-Tiered Systems of Support (MTSS) framework when addressing students with behavior challenges in general education classrooms. PBIS provides a collaborative framework of problem solving and evidence-based strategies, thus…

[superscript 31]P{[superscript 1]H} nuclear magnetic resonance spectroscopy is a particularly useful tool for studying the reactions of P-donor ligands such as phosphines and phosphites with transition metals and other Lewis bases because the reactions take place on the nonbonding pair of electrons on the phosphorus. In addition, [superscript 31]P…

Background: The overarching goal of this study was to explore the underlying mechanism of solving statics or structural analysis problems by utilizing cognitive load theory to examine task characteristics (i.e., the characteristics of instructional materials) with a focus on working memory load (WML) and automaticity. Purpose/Hypothesis: According…

This article describes a study of how Chinese preservice teachers unpacked a learning goal pertaining to adding fractions and understanding the concepts underlying the operation. Based on work in the USA by Morris, Hiebert, and Spizter ("Journal for Research in Mathematics Education," 40(5), 491-529, 2009), 50 Chinese preservice teachers…

Problem solving is recognized as a critical component to becoming a self-determined individual. The development of this skill should be fostered in the early years through the use of age-appropriate direct and embedded activities. However, many early childhood teachers may not be providing adequate instruction in this area. This column provides a…

In this paper, we highlight examples from school mathematics in which invariance did not receive the attention it deserves. We describe how problems related to invariance stimulated the interest of both teachers and students. In school mathematics, invariance is of particular relevance in teaching and learning geometry. When permitted change…

One of the major aims of STEM education is the development of mathematical thinking. The common misconception is that "doing mathematics" is the same as getting involved in "mathematical thinking". Rallying to such argument, many would agree that mathematics should be taught as a thinking activity. Thus, this study endeavours…

This articles discusses the characteristics of students' mathematical understanding in solving multiple representation tasks. Qualitative explorative methods were used to clarify the characteristics of mathematical understanding. Data were obtained by assigning multiple representation tasks to and interviewing 25 students. It is concluded that…

Various studies have been conducted regarding the use of examples in a mathematical proof. This study aims to describe how the students use the example in the proof analyzed by argumentation and proving activity. Qualitative methods are used to explain the phenomena that arise in the use of examples on mathematical proof. The data collected is the…

Estimation is such an important yet sometimes overlooked skill. Enhancing estimation skills through exposing students to enumeration ('how many') problems where they are required to estimate before calculating is a critical aspect of developing number sense (Reys et al., 2012). This article describes a 'how many' problem undertaken with a small…