Learning to reason spatially is increasingly recognized as an essential component of geometry education. Generally taken to be the "ability to represent, generate, transform, communicate, document, and reflect on visual information," "spatial reasoning" uses the spatial relationships between objects to form ideas. Spatial thinking takes a variety…

In the field of human cognition, language plays a special role that is connected directly to thinking and mental development (e.g., Vygotsky, "1938"). Thanks to "verbal thought", language allows humans to go beyond the limits of immediately perceived information, to form concepts and solve complex problems (Luria, "1975"). So, it appears language…

This study was an empirically substantive examination of mathematics achievement differences between urban and rural Taiwanese students at a cognitive attribute level. Participants were eighth-grade students who participated in the "Trends in International Mathematics and Science Study" of 1999. The rule-space method was applied to…

This paper describes changes in students' geometrical knowledge and their creativity associated with implementation of Multiple Solution Tasks (MSTs) in school geometry courses. Three hundred and three students from 14 geometry classes participated in the study, of whom 229 students from 11 classes learned in an experimental environment that…

We consider how the arc length integral of the graph of a function in the plane is connected with the hyperbola and its rational parameterization.

In this article, we give a brief history of the Feynman's Triangle problem and describe a simple method to solve a general version of this problem, which is called the Routh Theorem. This method could be found useful to school teachers, instructors or lecturers who are involved in teaching geometry.

The aim of this study is to evaluate the reasoning skills in geometry-related subjects of six 8th Grade students. The study data were obtained at the end of the 2011-2012 spring period in a public elementary school. The study uses a case study with qualitative research techniques to investigate how students use reasoning skills. In this study, six…

Diagnostic information is a centrepiece of educational decision making. Far-reaching decisions like placements within multi-tiered school systems may have a huge long-term impact on the achieved level of education. Therefore, such decisions should be substantiated or complemented by objective and prognostically valid information. To this end, we…

An experiment is reported comparing human performance on two kinds of visually presented traveling salesperson problems (TSPs), those reliant on Euclidean geometry and those reliant on city block geometry. Across multiple array sizes, human performance was near-optimal in both geometries, but was slightly better in the Euclidean format. Even so,…

As the end result of metaphysics, the Kantian and constructivist mind is not present in the world but withdrawn into the netherworld of its representations and constructions. First phenomenology then the embodied cognition research showed how there could be no cognition without the human body. There is something unsatisfying and lacking, however,…

In this article, the authors show how students can form familiar geometric figures on the calculator keypad and generate numbers that are all divisible by a common number. Students are intrigued by the results and want to know "why it works". The activities can be presented and students given an extended amount of time to think about…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

Providing standards-based instruction in core content areas for individuals with moderate and severe disabilities is a hot topic in the field of special education, and teachers struggle to find the best methods for providing high-quality standards-based instruction in core content areas that also has personal relevance for the students. This…

This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students' work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we…

This article reports the findings from a comparative analysis that examined several mathematical content strands, reasoning processes, and emphasis on technology in prior K-8 state mathematics standards and the Common Core State Standards for Mathematics (CCSSM). Various methodological tools were utilized to compare and contrast CCSSM with prior…