The author shares the lesson that he used to introduce the quadratic unit to students in an extended second-year algebra class, demonstrate why it was appropriate for his struggling learners, and discuss possible future modifications to this lesson.

When the author first started teaching twenty years ago, he thought that as long as he was using dynamic geometry software (DGS) for students to "discover" conjectures instead of them learning the conjectures from a lecture or the textbook, he was maximizing their learning potential because they were using technology. Over the years, he…

Mathematics has been taught throughout history without much more than a straightedge, a compass, and an abacus. So there is little question that all the major concepts of mathematics can be delivered without the aid of modern technology. But clearly, just the time-saving aspect of using technology can greatly enhance the art of teaching. In this…

The Common Core State Standards for Mathematics envisions data analysis as a key component of K-grade 12 mathematics instruction with statistics introduced in the early grades. Nonetheless, deficiencies in statistical learning persist throughout elementary school and beyond. Too often, mathematics teachers lack the statistical knowledge for…

GeoGebra is a free tool that has the potential to change both how and what is taught in mathematics. GeoGebra allows teachers and students to explore various mathematical ideas either through the full applet (https://www.geogebra.org/graphing) or by sharing applets via GeoGebra's Materials site (https://www.geogebra. org/materials/). It has many…

Calculus, perhaps more than other areas of mathematics, has a reputation for being steeped with procedures. In fact, through the years, it has been noticed of many students getting caught in the trap of trying to memorize algorithms and rules without developing associated concept knowledge. Specifically, students often struggle with the…

Context is what makes mathematical modeling tasks different from more traditional textbook word problems. Math problems are sometimes stripped of context as they are worked on. For modeling problems, however, context is important for making sense of the mathematics. The task should be brought back to its real-world context as often as possible. In…

In the authors' attempts to incorporate problem solving into their mathematics courses, they have found that student ambition and creativity are often hampered by feelings of risk, as many students are conditioned to value a produced solution over the actual process of building one. Eliminating risk is neither possible nor desired. The challenge,…

Activities for Students appears five times each year in Mathematics Teacher, promoting student-centered activities that teachers can adapt for use in their own classroom. In the course of the activities presented here, students will "look for and make use of structure" by observing algebraic patterns in the power rule and "use…

A part of high school geometry is devoted to the study of parallelograms in the context of proving some of their properties using congruent triangles (CCSSI 2010). The typical high school geometry book's chapter on quadrilaterals focuses on parallelograms (e.g., their properties, proving that a given quadrilateral is a parallelogram, and special…

The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in…

Software programs such as Tinkerplots ® or Geometer's Sketchpad ® can help students solve problems in mathematics classes, but may not be available to them after high school. In contrast, many students who become familiar with Internet tools and programs in office packages (word processing, spreadsheets, etc.) may use them daily to enhance their…

Students' ability to use appropriate tools strategically is an important skill of mathematically proficient students (SMP 5, CCSSI 2010, p. 7). A parallel practice for teachers is using appropriate tools strategically for mathematics instruction. An important element of this practice is that the use of technology depends on the goals of…

Children of the Earth High School in Winnipeg, Manitoba, is a school dedicated to incorporating Aboriginal perspectives into all areas of the Manitoba curriculum and is attended by an almost exclusive Aboriginal population. Many of these students come from a First Nations community and are related to others who come from such communities, the…

Right triangles play a significant role in mathematics. In this favorite lesson, the authors help students understand variant and invariant properties by considering relationships among angle measures and side lengths in right triangles. Students explore these relationships using interactive mathematics software, changing one angle and observing…