Over the past few decades there has been increased interest in how students and teachers think and learn about negative numbers from a variety of perspectives. In particular, there has been debate about when integers should be taught and how to teach them to best support students' learning. This book brings together recent work from researchers to…

Using memorized rules and algorithms without coherence and understanding is a perennial problem for teachers and students especially in the teaching and learning of fraction operations. I present data in which prospective middle school teachers explain a commonly used rule for fraction division--keep-change-flip. I argue that using both strip…

To gain insight into complex sustainability problems and acknowledge complexity is essential and can be achieved by creating an overview of the entire system, including interaction between variables. Therefore, systems thinking is recognized as a vital cognitive skill required to grasp complex global problems. Nevertheless, the implementation of…

Representation use is a critical skill for learning, problem solving, and communicating in science, especially in physics where multiple representations often scaffold the understanding of a phenomenon. University Modeling Instruction, which is an active-learning, research-based introductory physics curriculum centered on students' use of…

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems,…

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…

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'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,…

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

Computational thinking (CT) parallels the core practices of science, technology, engineering, and mathematics (STEM) education and is believed to effectively support students' learning of science and math concepts. However, despite the synergies between CT and STEM education, integrating the two to support synergistic learning remains an important…

Web-based problem-solving, a compound ability of critical thinking, creative thinking, reasoning thinking and information-searching abilities, has been recognised as an important competence for elementary school students. Some researchers have reported the possible correlations between problem-solving competence and information searching ability;…

Purpose: Entrepreneurial intentions have been extensively studied in student populations, with results suggesting that higher education does not promote formation of entrepreneurial intentions (e.g. Varamäki et al., 2013). However, the gap between intending to start a business and actually doing something to start one remains. The purpose of this…

Mathematical habits of prospective teachers affect problem comprehension and success and expose their beliefs about mathematics. Prospective elementary teachers (PSTs) (n = 121) engaged in a problem solving activity each week in class. Data were collected from PSTs enrolled in an undergraduate elementary mathematics methods course at a…

Tape diagrams, also known as strip diagrams, bar models, fraction strips, or length models, are linear representations that can be used to effectively model quantitative relationships during problem solving. Tape diagrams are a powerful model recommended by the Common Core, but they are relatively new to teachers and students in the United States.…

Researchers examined data from a national sample of 776 school counselors to further determine the factor structure of the School Counselor Leadership Survey. Confirmatory factor analyses supported use of a modified 5-factor model. Survey scores demonstrated good internal consistency and convergent validity. Differences between supervisors and…