"Setting the Stage with Geometry" is a new math program aligned with the National Council of Teachers of Mathematics (NCTM) standards that is designed to help students in grades 6-8 build and reinforce basic geometry skills for measuring 2D and 3D shapes. Developed by The Actuarial Foundation, this program seeks to provide skill-building math…

In this study, the aim was to examine the factors that predict the geometry knowledge of pre-service elementary teachers. Data was collected on 387 pre-service elementary teachers from four universities by using a geometry knowledge test, the van Hiele geometric thinking level test, a geometry self efficacy scale and a geometry attitude scale.…

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.

This study aimed to improve the van Hiele levels of geometric understanding, proof-construction performance and beliefs about proofs of the research respondents: future mathematics teachers exposed to the traditional (instructor-based) method and the enhanced-group Moore method. By using the quasi-experimental method of research, the study…

This study examined teachers' use of student tasks involving dynamic geometry software, in which a figure is constructed then altered while maintaining its constructed properties. Although researchers, professional organizations, and policy makers generally have been proponents of dynamic geometry for instruction, there is little research about…

This paper describes a retrospective analysis of data collected during a 4-year longitudinal study on children's thinking about measurement through a teaching experiment methodology. It focuses on results from individual interviews with two students on volume measurement. Data analysis was guided by Sarama and Clements' (2009) learning trajectory…

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…

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…

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…