One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…

In this "Delving Deeper" article, the author introduces the slip-slide method for solving Algebra 1 mathematics problems. This article compares the traditional method approach of trial and error to the slip-slide method of factoring. Tools that used to be taken for granted now make it possible to investigate relationships visually,…

When examining transformations of the plane in geometry, teachers typically have students experiment with transformations of polygons. Students are usually quick to notice patterns with ordered pairs. The Common Core State Standard, Geometry, Congruence 2 (G-CO.2), requires students to describe transformations as functions that take points in the…

In this article, the authors discuss "function," a well-defined rule that relates inputs to outputs. They have found that by using the input-output definition of "function," they can examine transformations of functions simply by looking at changes to input or output and the respective changes to the graph. Applying transformations to the input…

Many American students begin their high school mathematics study with the algebra 1-geometry-algebra 2 sequence. After algebra 2, then, students with average or below-average mathematical ability face a dilemma in choosing their next mathematics course. For students to succeed in higher mathematics, understanding the concept of functions is…

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 provides for a fast extremely accurate approach to graphing functions that is based on learning function reference graphs and then applying algebraic transformations to these reference graphs.

The patterns of handmade quilts made in southern United States are utilized for studying the symmetries of the plane and transformational geometry. Quilts are made without sewing and then from the same block, students can make quilts with different wallpaper patterns by using various combinations of transformations and through this geometrical…

A study is conducted regarding the change in teaching process in the geometry of transformations, teaching by small steps rather than by a complicated method. In the process of making mathematics teaching better, many challenges are faced, and several risks are taken to solve the questions asked by the students.

Students learn more when they attempt to make sense of a mathematical situation they face. For example, a question like why square root of 25 is not + or - 5. Providing the intermediate steps and the reasoning of a technique with graphs can help make better sense of mathematics.