Mathematics is full of mystery. We illuminate the myth to expose two conflicting senses of mystery at work in mathematics and its education practices. There is a sense of boundlessness with mathematics--the idea that we never fully know. There is also a practice of concealment, in which an answer or solution is known by special people who may…

Reduction is one of the key techniques used for problem-solving in computer science. In particular, in the theory of computation and complexity (TCC), mapping and polynomial reductions are used for analysis of decidability and computational complexity of problems, including the core concept of NP-completeness. Reduction is a highly abstract…

The identification of conflict and development of common ground, important steps in the interdisciplinary research process, become challenging when applied to solving complex real-world problems that involve opposing interest groups, especially those whose members do not possess academic or interdisciplinary training. This article examines…

The old myth about the ability and variability of potential in children is a comforting myth, for those who are uneasy with the degree of inequality they see and would rather seek to justify it than confront it. The myth of inherent potential helps some explain to themselves why they are privileged. Extend the myth to believe in inherited ability…

Gain a new perspective on the sharing of erroneous solutions in classroom discussions. Based on their research in grades four and six, the authors reveal how student-to-student correction of errors promotes mathematical reasoning and understanding. Tips for teachers include strategies for using students' errors to encourage reasoning during…

Logarithms continue to play an important role in mathematics (most significantly in calculus), science, and engineering. It is therefore important for students to understand logarithms as real numbers as well as the characteristics of logarithmic functions. Exploration of challenges in understanding logarithms as real numbers and logarithmic…

We have been developing a digital concept maps website (www.conceptmapsforlearning.com) based on the principles of effective assessment for learning. The purpose of this paper is to reveal its promising contributions to formative evaluation practices. The website reduces the workload of teachers as well as provides immediate and delayed feedback…

In recent years, learning progressions (LPs) have captured the interest of educators and policy makers. There have been numerous efforts to develop LPs aligned to college and career readiness standards, to unpack these standards, and to provide more clarity on the pathways students follow to reach them. There is great variation, however, in the…

This paper discusses one step from the scientific method--that of identifying independent and dependent variables--from both scientific and mathematical perspectives. It begins by analyzing an episode from a middle school mathematics classroom that illustrates the need for students and teachers alike to develop a robust understanding of…

Some of mathematics teaching is routine, like an exercise from a textbook for which you have received instruction and already know what to do. On other occasions, however, teaching mathematics is challenging, involving problems of teaching for which the solutions may not be readily apparent. These situations require the application of mathematical…

Background: Historically, significant advances in scientific understanding have followed advances in measurement and observation. As the resolving power of an instrument increased, so have gains in the understanding of the phenomena being observed. Modern interactive systems are potentially the new "microscopes" when they are…

This is a narrative article, highlighting effective teaching strategies for teacher candidates at a four-year university in the South. The author examined preconceived negative notions teacher candidates expressed about being enrolled in a Math Block class and having to teach children about mathematics. After involving the teacher candidates in a…

This study presents and interprets some conceptual difficulties junior-level physics students experience with Ampere's law. We present both quantitative data, based on students' written responses to conceptual questions, and qualitative data, based on interviews of students solving Ampere's law problems. We find that some students struggle to…

This booklet is a summary of an extensive review of research and other literature undertaken to guide the development of the Wellbeing@School website self-review process, survey tools and content. This website is being developed by the New Zealand Council for Educational Research (NZCER). The "Wellbeing@School" website is one component…

A steady stream of research has shown that many elementary school teachers have weak mathematical knowledge in some areas, including place value and fractions. Since a teacher's mathematical knowledge affects their students' performance, improving elementary school teachers' knowledge is critical. A better understanding of the mathematical…