We provide several constructions, both algebraic and geometric, for determining the ratio of the radii of two circles in an Apollonius-like packing problem. This problem was inspired by the art deco design in the transom window above the Shadek Fackenthal Library door on the Franklin & Marshall College campus.

The purpose of this study was to investigate the effect of technology on one student's solution methods when solving mathematical tasks that included algebra word problems. The student was presented with context tasks in both paper-pencil and computer environments. The results of this study revealed that the student's solution methods differed in…

GeoGebra is an emergent open-source Dynamic and Interactive Mathematics Learning Environment (DIMLE) (Martinovic & Karadag, 2012) that invites a modeling perspective in mathematics teaching and learning. In springs of 2010 and 2012, GeoGebra was integrated respectively into two online professional development courses on mathematical problem…

For students who have difficulty envisioning how the mathematics that they are learning is used outside the classroom, an adventure as field mathematicians can be enlightening. Measuring stream discharge is a field experience that allows students to engage in a hands-on (and boots-on) real-world, problem-solving activity and that integrates…

Students often view mathematics as a set of unrelated facts and procedures and fail to make the connections between and among related topics. One role of a teacher is to help students understand that mathematics is an interrelated discipline. Another role is to assist students in the scaffolding of their knowledge so that they can make connections…

Proving in school geometry is not just about validating the truth of a claim. In the school setting, the main function of the proof is to convince someone that a claim is true by providing an explanation. Students consider proving to be difficult; in fact, they find the very concept of proof demanding. Proving a claim in planar geometry involves…

We analyze the interaction of 3 students working on mathematics problems over several days in a virtual math team. Our analysis traces out how successful collaboration in a later session is contingent upon the work of prior sessions and shows how the development of representational practices is an important aspect of these participants' problem…

Generations have been inspired by Edwin A. Abbott's profound tour of the dimensions in his novella "Flatland: A Romance of Many Dimensions" (1884). This well-known satire is the story of a flat land inhabited by geometric shapes trying to navigate the subtleties of their geometric, social, and political positions. In this article, the authors…

This article describes an investigation of Buffon's coin problem and related problems with the aid of an applet. The problems are accessible at a variety of grade levels and facilitate making connections between geometry and probability.

The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six…

Determining how to provide good tutoring functions is an important research direction of intelligent tutoring systems. In this study, the authors develop an intelligent tutoring system with good tutoring functions, called "FUDAOWANG." The research domain that FUDAOWANG treats is junior middle school mathematics, which belongs to the objective…

Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among…

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations…

The activity of posing and solving problems can enrich learners' mathematical experiences because it fosters a spirit of inquisitiveness, cultivates their mathematical curiosity, and deepens their views of what it means to do mathematics. To achieve these goals, a mathematical problem needs to be at the appropriate level of difficulty,…

Students learning experiences were investigated in geometry lesson when using Dynamic Geometry Software (DGS) tool in geometry learning in 25 Ethiopian secondary students. The research data were drawn from the used worksheets, classroom observations, results of pre- and post-test, a questionnaire and interview responses. I used GeoGebra as a DGS…