Artifact 1: In this observation from my supervising teacher, Pat Tyunaitis, she comments on a lesson we did in Geometry class discussing the XYZ coordinate plane in 3D. We not only demonstrated it, we had the students work within the XYZ plane by stretching string from each wall to the opposite side and also from the ceiling to the floor. We moved an object within the plane and had students report the position. We also had students put objects in the plane by giving them coordinates. The next step was to draw rectangular prisms on paper in a 3D representation. After students voiced some difficulty, I grabbed a box and held it up along the strings to mirror what I had drawn on the whiteboard. Pat liked this and commented as such in the observation.
Artifact 2: This artifact is a copy of a worksheet about factoring quadratic equations for a 9th grade Algebra class. I created this in order to replace the section in the textbook which my cooperating teacher and I felt was lacking in guidance. With this worksheet, a student can factor the equation, but also see the math behind the scenes. It is often difficult for some students to make the switch from operations involving numbers to those involving variables. This lesson can also show them that the same rules can apply to both. I often will have students check their work by multiplying the binomials together to see if they get the original quadratic equation.
Artifact 3: The following is an abstract from a session I attended in July 2011 at the NSF Robert Noyce Teacher Scholarship Program Conference. The speakers were promoting math education in urban areas with the Math for America group. The larger message was asking the question if teachers knew the reason why what they are teaching is true. This is extremely important in the high school level. It is important to plan different kinds of lessons to promote a better understanding of mathematics and fulfill the common core standards.