The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…

Sometimes a student's unexpected solution turns a routine classroom task into a real problem, one that the teacher cannot resolve right away. Although not knowing the answer can be uncomfortable for a teacher, these moments of uncertainty are also an opportunity to model authentic problem solving. This article describes such a moment in Zahner's…

This article describes a geometrical solution to a problem that is usually solved geometrically as an example of how alternative solutions may enrich the teaching and learning of mathematics. (Contains 11 figures.)

This article describes the use of digital images of real-life phenomena and interactive software to carry out mathematics investigations. (Contains 13 figures.)

As geometry involves lot of graphics, it acts as a link between mathematical model and real-world phenomena. An effective tool like geometry software can help students to explore the ellipse.

Geometric analysis of a cube can motivate formulae for factoring algebraic expressions involving sums and differences of cubes. (SD)

The author describes an introduction to, and development of, the complex number field. (SD)

Vector space concepts are developed by consideration of solutions for linear homogeneous equations. (SD)

Illustrates how mathematicians work and do mathematical research through the use of a puzzle. Demonstrates how general rules, then theorems develop from special cases. This approach may be used as a research project in high school classrooms or math club settings with the teacher helping to formulate questions, set goals, and avoid becoming…

Presents new proofs of the Pythagorean theorem while exploring examination questions. Briefly reviews the work of Elisha Scott Loomis, a mathematician who amassed 320 different proofs of the theorem. (DDR)

Geometric interpretations and derivations of the six trigonometric relationships are demonstrated. Selected for discussion are limiting values, geometric verification of trigonometric identities, a one-dimensional illustration of the Pythagorean relationships, and the geometric derivation of infinite-series relationships. (DE)