I have this written on the board: “One of the most important practices we teach in math deals with the tools of mathematics. What are some of the tools we use in math class? How would you define or categorize different types of math tools? Are there problems which require certain types of math tools? Can you give examples?”
As students enter the room, I always give them a moment to settle and get ready. Once the class is ready, I introduce the questions of the day. Once we clarify the topic, I give students about two minutes to write their thoughts. I circulate as they write and write down interesting ideas from students. I make sure to quote students directly to help spark the conversation and sort responses into a table that identifies tools that require power and tools that don’t. When I finish circulating I ask the class to take another minute to compare their tool choices. I ask them to talk about why those chose their tools and see if they can work together to think of more tools in the classroom. I usually leave a bunch of tools out and ready for discussion. If students mention an angle ruler I show one. If they mention something common like a pencil, I show my favorite type. We discuss the merits of each tools and the rational behind each choice. Our students make deliberate choices about every tool they use. Whether it is a pencil or a computer, the tools in your classroom must be applicable and desirable for the given task.
I ask students to think about how this relates to technology. “Does this conversation sound a bit like our other conversations around technology? Why is that?” Students like to discuss the idea that tools represent different technological developments. They enjoy discussing the concept of paper as more than something we just happen to have. Students need to realize that this too is a technology.
I end this introduction by steering towards tools that do need power. I often do this by asking them, “are there problems that we can at least solve a lot faster with the help of technology. They are familiar with basic scientific calculators and basic four function calculators, but they have not used calculator’s meant for graphing and comparing functions. I ask them, “can we use graphing calculators to graph and compare functions?” This concept is new and it is important to show images of explain the fundamental connection between graphing and calculation. I explain to students that their goal is recognize that a computer is also a valuable tool in math. I usually preinstall or set up the machines to log in and open up webpages for my favorite graphing calculator applications: Desmos and Geogebra. The prompt is extremely simple: make a graph on Desmos and and Geogera.
When I use computers in the classroom, I always think carefully about the way in which I will manage their use of the devices and the level at which I limit access online. I make sure students understand the reason for using the laptops and the importance of helping each other graph a function when they are in need of help. On group or partner work days, I block many music sites as that would isolate students from one another. As this section of class begins, I stand around the computer cart as students take their supplies and begin. I keep the instruction very open. I want them to work with the application and try to make progress without my help. I want them to have fun, explore and then find other applications that help. This play time is essentially perfect to get them excited about using the machines in for mathematics. As I get more familiar with an operating system or device, I plan more specific activities with options for innovation as they work. However, when I first deploy a device or application, I let students lead. They always find great applications and ideas. I finish class by sharing their finds and strategies.