My fear, and I am sure it is shared by many teachers, is that students will be able to do calculations after taking my class but not understand the why you use certain formulas and how the formulas work. For example, it is important that students be able to calculate slope correctly. Can they then look at a graph of stock and tell me what the high point means, low point means and what is happening when the slope is the steepest? Similarly, students need to be able to use the quadratic formula to calculate roots. Do they know what a root is? If they know that the root is the x-intercept do they have any idea why that is such a vital problem in mathematics?
I have been using GeoGebra, an interactive mathematics program, in my classroom for three of the last four years. However, I have primarily been using it in Geometry, not Algebra II. And in Geometry I am the person who uses the applets. I wrote an applet for the triangle inequality theorem. I use the Socratic Method and inquiry and ask students to make conjectures as I slide the sliders. An example question: “When the segment AC reaches what number will the triangle disappear?” In a relatively short period of time, some students in the class are able to know when the triangle will disappear and can put it into words. It is one of my favorite lessons and clearly uses technology to cover my content and uses reasonable pedagogy.
While this is one of my more powerful lessons; I see how to improve it. What I need to do is relinquish more control and make students do more of the work. I remember many of my prompts; they don’t always have to come from me while I control the sliders. What would make the lesson even stronger would be to put students on computers with the prompts and make everyone “discover” the triangle inequality theorem. Instead of having one or two students explain to me and the rest of their class their understanding, this would be an excellent blog prompt. I see this as the true sweet spot of TPACK and includes writing across the curriculum.
Logistically, I see myself as the primary instructor using this method in my school district for another year with the other math teachers picking up pieces of this method after an additional year. This summer, I see myself finding applets that have been shared by other teachers, creating additional GeoGebra applets, especially for Algebra II, and coming up with prompts for students while they use the applets and write their blog posts. This will not be an every day lesson; not every lesson lends itself to inquiry and I like variety in my classroom. However, I can see doing this type of lesson once or twice most units. In the next two weeks my goal is to find at least three additional applets to use in my class and to add prompts for the applets and for student blogs. The rest of the summer I plan to add additional pieces and am sure I will have to do additional work during the school year. I will know if I have been successful depending on how my students engage with the lessons, the quality of the writing and mathematical thinking and how they perform on summative assessments.
“Dynamic geometry 1 is active, exploratory geometry carried out with interactive computer software. The papers in this volume will convince you, we think, that dynamic geometry is full of action, energy, and, yes, even hype–the hype of excited individuals (students, teachers, researchers) who can’t help but communicate their enthusiasm as they discuss the many implications of the software.”
List of applets with prompts, similar to my goal but at a college level.
“Inquiry not only tests what students know, it presses students to put what they know to the test. It uses “hands on” approaches to learning, in which students participate in activities, exercises, and real-life situations to both learn and apply lesson content. It teaches students not only what to learn but how to learn”