As Schools Adopt General-purpose Technology for Classrooms,
Handheld Graphing Calculators Still Make a Difference in Math Instruction
A career spent teaching high school math can bring about some revelations. You’ll start to notice patterns over the years: math content remains unchanged (although statistics did sneak in a bit); students’ fashion trends fade away and return; and the latest way to improve learning becomes a big focus in schools one year, but disappears completely the next.
Still, year after year, for over 30 years, I have considered graphing calculators as core to my instruction. The best teachers around the world use graphing calculators in their classrooms, so I typically don’t have to defend their purpose to math educators. Yes, you can crunch numbers and display graphs; those are certainly utilities that benefit students. Graphing calculators capitalize on the power of visualization, helping students to create mental images that research has proven is central to learning. These visualizations help students form stronger connections to concepts, leading to a deeper understanding – kind of like watching a little movie in your head that shows how ideas and representations of these ideas are connected.
Today, schools are beginning to adopt technology for a broader purpose, giving students tools they can use in any class. Unless you have recently been in the classroom, it can be difficult to understand the real issues around the use of general-purpose devices in a math class. Research has shown that multitasking – which results in losing focus on the task at hand – is not just a distraction, but can prevent learning. This is particularly true when students are distracted by the plethora of apps and websites that are at their fingertips. For a teacher, it can be tough to deliver effective instruction that engages students fully in learning math if those students are staring at a screen that offers a relief from doing more mindful work. In my own classes, I have noticed that even students who have the intention of following along are frequently (even if momentarily) distracted by what is on their screen.
Handheld graphing calculators offer students only one alternative to focusing on their math work – more math. Even if they want to be off-task by exploring other things on their calculators, what they can do is limited by what is available on the tool – calculations, graphing, spreadsheets, geometry tools and data analysis. Handheld graphing calculators are like a sandbox, in which every student can play with math anywhere and at any time – but within the constraints of the sandbox, which prevents them from going too far astray. Once students have invested time in learning math with their handheld graphing calculator, they can take that same tool with them to an exam. As a teacher, I don’t shy away from allowing students to use their handheld graphing calculators for exams in class – I just have to think more carefully about the questions I ask and the tasks I give, which actually makes them better questions for helping me know what students really understand.
Tools like the TI-Nspire™ CX handheld – which I have used for the past several years – have fundamentally changed what I can do to support learning and to help students develop their understanding of math and statistics. This tool doesn’t just do graphing and data analysis: my students create and use dynamic interactive files to investigate the meaning of mathematical concepts, or why certain conditions are necessary in order to apply theorems; use data collection tools to explore science concepts and conduct experiments; and make conjectures about the geometric properties of a figure by using dynamic geometric constructions. Students connect their handhelds to the TI-Nspire™ CX Navigator™ System, allowing me to monitor and respond to their work from my computer – talk about formative assessment.
Given this enormous benefit to teachers and students, I still hear questions about whether and how schools should use handheld graphing calculators. I cannot imagine depriving students of the opportunities that graphing calculators provide to explore and investigate mathematics. Students just learn so much more when they are in charge of manipulating mathematical objects every day in their math class, and can make and test conjectures about what is happening.
Gail Burrill
Gail – your observation around the distraction of multi-purpose tools is bang on. At our school, we made the switch from student-owned TI-Nspire CAS handhelds to iPads with the TI-Nspire App several years ago. Teachers and students now struggle with the distraction of the iPad. Distraction was never a problem with the TI-Nspire CAS handhelds. The TI-Navigator is sorely missed by our teachers as well, as there is no equivalent functionality with the iPads. It was an invaluable formative assessment tool, giving us a real-time window into student models and thinking.