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Allow calculators in math class? Four questions to ask.

Let’s say I’m writing the syllabus for my new math class, at the Algebra level or higher. What’s the best strategy for deciding if, how, or when students should use a calculator in class and for homework? I’ve seen class summaries that ask students to bring graphing calculators every day. I’ve also heard other teachers warn that calculators are not allowed in their Algebra 2 classes. Assuming that I want to be more flexible regarding the use of technology in class, how will I plan to use these tools lesson by lesson, or minute by minute?

Four questions: What to ask to set your strategy.

1) Are students developing fluency or concepts that would be hurt by relying on technology too extensively? Immediate access to calculators might have a harmful effect while my class explores operations with negative numbers or fractions as this is when students are building mental models and senses of scale. Overdependence on calculators can sometimes prevent full understanding.

2) Are students really benefiting from performing a task with pencil and paper? Is it truly important that I take my eighth graders through the Quadratic Formula and then have them use the formula on paper a dozen times? If I reveal it to them as a “magical formula” and allow them to program it into their calculators, will they learn less about quadratics? I’m still not sure about this one, but I’m willing to consider both sides of the argument.

3) Will students use these computing tools after school and in their careers? I would enjoy having a dialogue with individual students (and the whole class) about how using calculators can help in particular situations. How might you use a calculator (or cell phone) in a particular instance? How will that be more efficient/clever/illuminating? Can arguments for and against be presented to the class? Let’s look at how a professional would use technology in the same situation.

4) How can technology free up space and time to explore deeper math questions? I’ve seen students intuit the general properties of quadratic equations by rapidly graphing a series of parabolas on a calculator.

The answer: Using technology intelligently.

If all the homework questions I develop can be answered by Desmos or WolframAlpha in under a minute, that means I’m not asking the right questions, and I need to go back to the drawing board and rethink my approach. The key is setting the bar high enough and making sure that you’re encouraging mathematical thinking. If students use the answers they find on these sites to help support an argument, I’m teaching them to use technology intelligently.

Have any experiences or hints about using calculators/technology in the classroom? Please share them!