Tying your teaching approach to the Common Core Standard for Geometry and Congruence will help students understand why functions behave as they do.
Becky Hall and Rich Giacin
Hearts are the theme of a collection of problems and solutions.
Chris Harrow and Lillian Chin
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.
Jason Silverman, Gail L. Rosen, and Steve Essinger
Use digital signal processing to capitalize on an exciting intersection of mathematics and popular culture.
Jon D. Davis
Technology is in a constant state of flux. As a result, if we seek to use the latest forms of technology in our teaching, our teaching with technology must be ever changing. Edwards and Özgün-Koca (2009) describe an investigation involving the TI-Nspire CAS to understand the effect of b on the graphical representation of a quadratic function of the form f (x) = ax2 + bx + c. Adapting this idea, I show how updates to technology can enhance this investigation to create an even more motivating and compelling experience for students. The investigation will make use of sliders and the spreadsheet capability of the TI-Nspire (the directions provided here apply to the TI-Nspire CX CAS).
Julie Barnes and Kathy Jaqua
A kinesthetic approach to developing ideas of function transformations can get students physically and intellectually involved.
Dae S. Hong and Kyong Mi Choi
The mathematical concepts, skills, and problem-solving methods that Korean students need to know in preparation for high-stakes testing.
Three graphing activities lead students to discover the shapes and properties of the graphs for linear, quadratic, and absolute value functions and inequalities.
Christopher V. Cappiello
A high school student reflects on ways to use function composition to explain some interesting 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