This note describes two conjectures pertaining to repeated partitioning of an arbitrary triangle. The first conjecture turns out to be true, and hence gives rise to a new, more general, conjecture that is also addressed in this article. Both conjectures can be explored in a dynamic geometry environment. The proofs to the conjectures addressed in…

Two original problems in geometry are presented with solutions utilizing to differential calculus: (a) rectangle inscribed in a sector; (b) point on the ray of the angle. The possibility of applying mathematics in general and differential calculus in particular for solution of practical problems is discussed. (Contains 8 figures.)

Parabolic shapes are easy to find. Many homes outside the cable area have parabolic antennas to receive television transmissions from a satellite far out in space. Parabolic extrusions are used as reflectors behind fluorescent tubes and solar heated water pipes. Parabolic reflectors are used to build solar ovens, searchlights and radio telescopes.…

The impact of written and printed texts on the geometry curriculum has a very long history. Static diagrams, static definitions, and static proofs have dominated the classrooms for centuries. Geometry is about shape and space, and about the relationships between shapes in space. Movement is a key aspect of those relationships, but movement cannot…

As part of its proposal to the U.S. Department of Education, the Partnership for Assessment of Readiness for College and Careers (PARCC) committed to developing model content frameworks for mathematics to serve as a bridge between the Common Core State Standards and the PARCC assessments. The PARCC Model Content Frameworks were developed through a…

This study examines the relationship between performance on Utah's English proficiency assessment and English language arts and mathematics content assessments by English language learner students and compares the performance of English language learner and non-English language learner students on the content assessments. Two research questions…

This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM…

Discussed are implications and derivations from vux" triangles (triangles having one angle the integral multiple of another). (JG)

Assigning difficulty level indicators to the knowledge units helps the learners plan their learning activities more efficiently. This paper focuses on how to use the topology of a knowledge map to compute and rank the difficulty levels of knowledge units. Firstly, the authors present the hierarchical structure and properties of the knowledge map.…

This study investigated the geometric cognitive growth of pre-service mathematics teachers in terms of the Van Hiele levels in a technology-enriched environment, as opposed to that of students in a learning environment without any technological enhancements. In order to investigate this, a quasi-experimental non-equivalent comparison group design…

The study examined the difference in performance of boys and girls in solving problems on the properties of a rectangle. The conceptual framework of the study was based on the idea that teaching the learners content in a familiar context tends to facilitate geometry learning. The data were collected using semi-structured interviews with the…

This book examines the five key elements (meaningful use of symbols, mindful manipulation, reasoned solving, connection algebra with geometry, and linking expressions and functions) identified in "Focus in High School Mathematics: Reasoning and Sense Making" in more detail and elaborates on the associated reasoning habits. This volume is one of a…

The aim of this study is to identify the effects of formalism in teaching on primary and secondary school mathematics teacher trainees' algebraic and geometric interpretations of the notions of linear dependency/independency. Quantitative research methods are drawn in order to determine differences in success levels between algebraic and geometric…

This study concerns 182 first year mathematics undergraduates' perspectives on the tangent line of function graph in the light of a previous study on Year 12 pupils' perspectives. The aim was the investigation of tangency images that settle after undergraduates' distancing from the notion for a few months and after their participation in…

Today's classrooms pose many challenges for new mathematics teachers joining the teaching force. As they enter the teaching field, they bring a wide range of mathematical experiences that are often focused on calculations and memorization of concepts rather than problem solving and representation of ideas. Such experiences generally minimize what…