My favorite lesson is based on a problem my geometry students encounter. When we study similar triangles, students use indirect measurement to determine the height of an object.
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
Yating Liu and Mary C. Enderson
Similar assumptions seem to give rise to conflicting answers when students approach probability questions differently.
Encourage investigation of the conic-section attributes of focus, eccentricity, directrix, and semi-latus rectum using polar coordinates and projective geometry.
Miriam Gates, Tracy Cordner, Bowen Kerins, Al Cuoco, Eden Badertscher, and Gail Burrill
With this professional development program, teachers work with colleagues and experience a manner of teaching that embeds habits of mind.
James Metz, Lance Hemlow, and Anita Schuloff
Explore the relationship between families of quadratic expressions factorable over the integers and Pythagorean triples.
Lesson planning leads to a deeper consideration of what it means to study and learn mathematics.
Ruth N. Urbina-Lilback
Two instructional principles–being open to students' input and building on misconceptions–can open the door for mathematics learning in community college.
S. Asli Özgün-Koca
Student interviews inform us about their use of technology in multiple representations of linear functions.
Problem solving may incorporate wild guessing, but tame guessing when the answer is already known helps develop mathematical intuition.