One of the great things about technology in mathematics is how it can make explorations about ‘what if’ quick and easy, allowing students to explore and ‘discover’ the rules and relationships around concepts. For example, rather than a teacher telling a student, “here’s the process for how to factor to find the roots of a quadratic”, technology allows a student to see a visual and the equation, try out different values and immediately see the result. Through this type of exploration, testing out their ideas, or their “what if I tried this - what would happen?”, they begin to discover relationships, make connections, and come up with the process on their own.
When students use technology to manipulate and explore, they can figure things out for themselves without ever having to rely on memorized rules or facts which are so easily forgotten once the test is over. Exploration helps them build their own rules and connections - which is the nature of conceptual understanding. They will always have these understandings that they built on their own, and be better able to transfer to new concepts or applications because the process is always with them - it can be ‘rebuilt’ or ‘remembered’ - unlike memorized, disconnected facts and rules.
That being said, I am going to spend the next few blog posts sharing some ways to explore quadratics with technology, bringing in some real-world applications in a later post related to the upcoming Olympics to tie everything together. In this first post I am going to focus on building an understanding of the role of coefficients of a quadratic function to develop an awareness of how changes in these values shift the function and how key points (vertex, roots, max/min, etc.) are impacted by these changes. There are already some videos on Casio’s YouTube channel using the fx-9750GIII and the fx-CG50 graphing calculators and the dynamic graphing mode to explore changing the coefficients and the shifts. I thought it would be a fun idea for this series of posts to focus on a scientific calculator, the fx-991CW. Most people don’t associate a scientific calculator with the ability to graph and visualize and explore, but with its QR code functionality that allows you to expand a scientific calculator to an amazing interactive dynamic graphing tool, this calculator is an incredible and versatile technology tool.
The easiest way to demonstrate this exploration is to show you, so the video below goes through how to set up the functions with the calculator, access the QR code, and then explore the graph, table, and equations in the dynamic ClassPad.net using a mobile device, such as your phone or a tablet. The images below show the process using the handheld calculator, with the final image being the dynamic graph on the phone that students can then manipulate and explore.
In the video, it looks a bit different because I am using the web-based emulator version of the handheld calculator, so it is already in ClassPad.net, which is where the QR code takes you. But the process for setting up the table and functions and accessing the graph is the same as on the handheld.
I have also included a PDF from our Casio Essentials Activities related to finding key points of a quadratic. This is a nice little summary and includes the calculator steps and some practice problems.
Stay tuned for the next post where I will explore horizontal shifts of quadratic functions.
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