Angularity is a persistent quantity throughout K-12+ school mathematics, and many studies have shown that individuals often conflate angularity with linear attributes (e.g., the length of an angle model's sides). However, few studies have examined the productive ways in which students might reason about angularity while attending to linear…

Proofs are attempts to conclusively demonstrate the validity of the claim for all cases indicated within its domain, which implies that proving should involve thoughtful consideration of the domain. This study analyzed the enactment of three general claim tasks, or tasks where the domain of the claim referred to an infinite number of cases, that…

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…

The purpose of this study is to describe, critically analyse and discuss the Swedish system of assessing ethics education in compulsory school through national tests. The publicly available tests from 2013 for grades six and nine have been studied as have the assessment instructions for teachers. Staff responsible for the test construction have…

The article reports the results of a study, the main aim of which was to find out correlations among the three components of the Culture of problem solving (reading comprehension, creativity and ability to use the existing knowledge) and six dimensions of Scientific reasoning (conservation of matter and volume, proportional reasoning, control of…

Analogies have many advantages for students such as concretizing abstract concepts and enabling motivation. Analogies are frequently used in textbooks. Research shows that the analogies in textbooks are not used based on certain directives and sometimes lead to misconceptions for students. Therefore, analysing the analogies in textbooks on several…

The relationships between reasoning and school achievement were studied taking into account the multilevel nature (school- and class-levels) of the data. We gathered data from 51 classes at seven schools in metropolitan and Eastern Finland (N = 769, 395 males, 15-year-old students). To study scientific reasoning, we used a modified version of…

Mobilizing scientific knowledge for understanding the natural world and for critically appraise socio-scientific situations and make decisions are key competencies for today's' society. Therefore, it is essential to understand how students at the end of compulsory schooling use scientific knowledge for understanding the surrounding world. The…

Results are reported from a study in which teachers' views of highly achieving ninth grade classes in Norway (KappAbel national competition winners) were compared with teachers' views of average achievement classes with regard to the use of information and communication technologies (ICT) and pedagogical practices. The main purpose of the study…

Recently there has been a keen interest in the area of mathematics and finding the best methods of instruction. For instance, the No Child Left Behind Act (NCLB) has placed new levels of accountability on educators for the success of students with their education, especially in mathematics. Certain areas of mathematics, such as Algebra, have been…

Reasoning and learning are closely related, both being the methods of solving problems, learning usually results from the process of reasoning. All inventions, discoveries, art, literature and advances in culture and civilization are based on thinking, reasoning and problem solving capacity of human being. A sound reasoning leads to better…

A two-dimensional weather map is actually a physical representation of three-dimensional atmospheric conditions at a specific point in time. Abstract thinking is required to visualize this two-dimensional image in three-dimensional form. But once that visualization is accomplished, many of the meteorological concepts and processes conveyed by the…