We describe a procedure that utilizes symmetric curves for building artistic tiles. One particular curve was found to mesh nicely with hundreds other curves, resulting in eye-catching tiling designs. The results of our work serve as a good example of using ideas from 2-D graphics and algorithms in a practical web-based application.

Acid-base equilibrium is one of the most important and most challenging topics in a typical general chemistry course. This article introduces an alternative to the algebraic approach generally used in textbooks, the graphical log "C" method. Log "C" diagrams provide conceptual insight into the behavior of aqueous acid-base systems and allow…

3D visualization assists in identifying diverse mechanisms of protein-DNA recognition that can be observed for transcription factors and other DNA binding proteins. We used Proteopedia to illustrate transcription factor-DNA readout modes with a focus on DNA shape, which can be a function of either nucleotide sequence (Hox proteins) or base pairing…

In mathematics education, there is a continuing debate about the nature of mathematics, which some claim to be an objective science, whereas others note its socially and individually constructed nature. From a strict cultural-historical perspective, the objective and subjective sides of mathematics are but manifestations of a higher-order…

Given a set of oriented hyperplanes P = {p1, . . . , pk} in R[superscript n], define v : R[superscript n] [right arrow] R by v(X) = the sum of the signed distances from X to p[subscript 1], . . . , p[subscript k], for any point X [is a member of] R[superscript n]. We give a simple geometric characterization of P for which v is constant, leading to…

The article begins with a well-known property regarding tangent lines to a cubic polynomial that has distinct, real zeros. We were then able to generalize this property to any polynomial with distinct, real zeros. We also considered a certain family of cubics with two fixed zeros and one variable zero, and explored the loci of centroids of…

There is a consensus among mathematicians and mathematics educators that creativity plays an essential role in doing mathematics. Creative students are self-regulated students who take control over processes and experience high self-efficacy beliefs. The aim of this case study was to promote mathematical creativity and self-efficacy of elementary…

Providing instruction on spatial geometry, specifically how to calculate the surface areas of composite solids, challenges many elementary school teachers. Determining the surface areas of composite solids involves complex calculations and advanced spatial concepts. The goals of this study were to build on students' learning processes for…

This paper illustrates how young children (ages 7-8, grade 2/3) can use the potential of dynamic geometry environments to develop an understanding of, and reasoning about, the properties and behaviours of different triangles (scalene, isosceles, equilateral). It provides a detailed description of a geometry unit, during which children worked both…

This study analyzes six seventh grade Israeli mathematics textbooks, examining (1) the extent to which students are required to justify and explain their mathematical work, and (2) whether students are asked to justify a mathematical claim that is stated by the textbook or a mathematical claim that they themselves generated when solving a problem.…

Teacher education has become an area of considerable interest among policymakers in many countries over recent years. Teacher's knowledge and skills in qualified teaching is of great importance. The main purpose was to study the level and depth of the school mathematics and related teaching knowledge attained by prospective Ukrainian secondary…

Modern classrooms are often comprised of a heterogeneous student population with varying abilities. To address this variance, third-grade teachers implemented researcher-designed, pre-differentiated, and enriched math curricula in algebra, geometry and measurement, and graphing and data analysis. The goal of the curricula was to provide academic…

Even though dynamic geometry software (DGS) is becoming an emergent instructional tool for mathematics teachers, many teachers are still in the process of consideration about whether to use it. In order to encourage teachers to use DGS, this study seeks to discover mathematics teachers' salient beliefs about the use of DGS in mathematics class.…

"Opportunity to learn" (OTL), a term first coined by Carroll (1963, 727) to capture the ''time allowed for learning'', is known to be a factor in successful learning during education programmes. In a major study of teacher preparation across 17 countries (the Teacher education and development study in mathematics, TEDS-M), Tatto et al.…

Two problems from high school mathematics on finding minimum or maximum are discussed. The focus is on students' approaches and difficulties in identifying a correct solution and how dynamic geometry systems can help.