Miss Arguello's Classroom

What Makes a High School Teacher "Good"?  We have all had high school teachers that have made a significant impact on us. For one person I spoke with, her pre-calculus teacher was great because he encouraged students to ask questions and made every student feel as if they had a significant mathematical ability. Another woman’s favorite teacher was her high school English teacher, who had his students turn their desks into a circle and collaborate with one another, facilitating deep discussion and fostering a love of literature into his students. For another, her high school teacher stood out as being great because she helped her student to navigate some tough family issues in the midst of her depression, and allowed the student to seek solace from her, even though this went far beyond her role as a classroom educator. Besides personal testimony, various articles have also been written about the definition of a “good” teacher. One writer defined a good teacher by thei...

I have always struggled with any mathematics that is inherently visual, and so when I missed a class about Khwarizimi's visual representation of completing the square and had to look online to teach myself about it, I knew I was in for a challenge. However, as an education major interested in new ways to present difficult mathematical concepts, I was interested in this visual algebra and how such a tool could be utilized to teach completing the square to students. I was also interested in examining its similarities to the "box method" way of teaching factoring. So, the questions I wish to explore today are: How beneficial are these methods of factoring? How can we utilize visual tools such as these in teaching? What can mathematicians such as Khwarizimi teach future teachers about new ways of presenting concepts? Khwarizimi's Visual Representation of Completing the Square  I'm not sure about my other fellow educators, but, to me, both in the classroom and whe...