Proportional reasoning is important to the field of mathematics education because it lies at the crossroads of additive reasoning in the elementary school and multiplicative reasoning needed for more advanced mathematics. This research reports on the representations used by pre-service teachers (PSTs) as they responded to tasks involving…

The purpose of this causal comparative study is to determine whether the assistant principal decision-making process and their years of experience influence the advanced diploma rates in high schools on Long Island, New York. The subjects for this study were 75 assistant principals in Long Island high schools during 2016. Assistant principals'…

This study focused on discovering what instructors' experiences help elementary school students develop not only academically but also socially. This qualitative multiple case study method was guided by Yin, and the purpose of the study was to investigate effective instruction strategies from the perspective of instructors who worked in an…

Math fluency, which refers to the ability to solve single digit arithmetic problems quickly and accurately, is a foundational mathematical skill. Recent research has examined the role of phonological processing, executive control, and number sense in explaining differences in math fluency performance in school-aged children. Identifying the links…

The aim of this research is to determine the predictive level of physics self-efficacy with regard to physics anxiety and the correlations between the physics anxiety and self-efficacy of pre-service teachers, also to examine whether physics anxiety and self-efficacy beliefs differ depending on pre-service teachers' achievement in physics and…

In this paper, I share a hybrid quantitative reasoning/algebra two-course sequence that challenges the common assumption that quantitative literacy and reasoning are less rigorous mathematics alternatives to algebra and illustrates that a quantitative reasoning framework can be used to teach traditional algebra. The presentation is made in two…

Many educators face the challenge of engaging students in science and mathematics, often struggling to bridge the gap between theoretical concepts taught in classrooms and their real-world applications. This disconnect can lead to disinterest and disengagement among students, hindering their learning outcomes. "Cases on Informal Learning for…

Many teachers are using the Five Practices model to guide them in orchestrating whole-class mathematics discussions that focus on understanding: (1) anticipate an array of possible student-generated solution strategies to a mathematical task before implementing the lesson; (2) monitor students' work as they grapple with the task; (3) select a…

Design research (DR) promises to simultaneously solve practical problems of education and develop theory to guide future interventions. However, educational DR remains paradigmatically underdeveloped, making it difficult to train new researchers, to agree upon what makes a theoretical contribution, and to promise clear outputs to funders--all of…

Today, experts agree that the level of cognitive development of modern young people affects the long-term life goals and outcomes that they set for themselves. During the course of numerous studies experts have identified such key competencies as problem solving, information literacy, and critical thinking. However, there are still many unanswered…

This article reports on a project that used a game-creation tool to introduce middle-school students ages 10 to 13 to problem-solving strategies similar to those in computer science through the lens of studio-based design arts. Drawing on historic paradigms in design pedagogy and contemporary educational approaches in the digital arts to teach…

Building on Dörner's (1996) theory of complex problem-solving, a learning scenario for teacher students was created and tested. Classroom management is interpreted as a complex problem, which requires the integration of competing interests and tackling multiple, simultaneous tasks under time pressure and with limited information. In addition,…

In response to a desire to strengthen the economy, educational settings are emphasizing science, technology, engineering, and mathematics (STEM) curriculum and programs. Yet, because of the narrow approach to STEM, educational leaders continue to call for a more balanced approach to teaching and learning, which includes the arts, design, and…

Today's engineers, designers, and technologists are often thrust into the role of problem solver, from the initial design phase of a product or process all the way to final development. Many engineers in manufacturing environments are tasked with solving problems and continuously improving processes to enhance company profitability, efficiency,…

When dividing one fraction by a second fraction, invert, that is, flip the second fraction, then multiply it by the first fraction. To multiply fractions, simply multiply across the denominators, and multiply across the numerators to get the resultant fraction. So by inverting the division of fractions it is turned into an easy multiplication of…