Browse

You are looking at 1 - 10 of 56items for :

• Functions and Trigonometry
• Twelfth
• Refine by Access: All content
Clear All
Restricted access

Students' Understanding of Counterexamples

This article focuses on students use and understanding of counterexamples and is part of a research project on the role of examples in proving. We share student interviews and offer suggestions for how teachers can support student reasoning and thinking and promote productive struggle by incorporating counterexamples into the classroom.

Restricted access

In this 3-part activity, students use paper-folding and an interactive computer sketch to develop the equation of a parabola given the focus and directrix.

Restricted access

Solving and Graphing Quadratics with Symmetry and Transformations

One of the central components of high school algebra is the study of quadratic functions and equations. The Common Core State Standards (CCSSI 2010) for Mathematics states that students should learn to solve quadratic equations through a variety of methods (CCSSM A-REI.4b) and use the information learned from those methods to sketch the graphs of quadratic (and other polynomial) functions (CCSSM A-APR.3). More specifically, students learn to graph a quadratic function by doing some combination of the following:

• Locating its zeros (x-intercepts)

• Locating its y-intercept

• Locating its vertex and axis of symmetry

• Plotting additional points, as needed

Restricted access

Happy Families, Continued

Explore the relationship between families of quadratic expressions factorable over the integers and Pythagorean triples.

Restricted access

The Joy of Paper Folding

A paper-folding problem is easy to understand and model, yet its solution involves rich mathematical thinking in the areas of geometry and algebra.

Restricted access

Formative Assessment at Work in the Classroom

Assessment tools–a rubric, exit slips–inform instruction, clarify expectations, and support learning.

Restricted access

Delving Deeper: What's So Special about 3?

A few years ago, I encountered two different problems in which the number 3 played surprising roles. I found myself wondering, “Why 3? What's so special about 3?” Further investigation led to continuous extensions involving exponents, logarithms, a parametric equation, maxmin problems, and some history of mathematics. As you read, pause to try the problems and play with the applets (the article's title is a big hint!)

Restricted access

Calendar and Solutions – May 2014

A set of problems of many types.

Restricted access

Technology-Enhanced Discovery

Exploration, innovation, proof: For students, teachers, and others who are curious, keeping your mind open and ready to investigate unusual or unexpected properties will always lead to learning something new. Technology can further this process, allowing various behaviors to be analyzed that were previously memorized or poorly understood. This article shares the adventure of one such discovery of exploration, innovation, and proof that was uncovered when a teacher tried to find a smoother way to model conic sections using dynamic technology. When an unexpected pattern regarding the locus of an ellipse's or hyperbola's foci emerged, he pitched the problem to a ninth grader as a challenge, resulting in a marvelous adventure for both teacher and student. Beginning with the evolution of the ideas that led to the discovery of the focal locus and ending with the significant student-written proof and conclusion, we hope to inspire further classroom use of technology to enhance student learning and discovery.

Restricted access

Calendar and Solutions – April 2014

A set of problems of many types.