The Calculator Issue

I was talking with an editor from one of the larger publishing companies earlier this week, and one of the issues the editor saw as critical was “the calculator issue”, which this editor saw as both basic and divisive in the profession.

I would like to start by asking “When do YOU reach for your calculator?”

For my own work, and perhaps yours, I use calculating devices for several categories of work. First, if the quantities are ‘complex’ and a precise answer is needed. Second, if a procedure will need to be repeated more than twice (like finding a table of values for a function). Third, if the calculation deals with a high-stakes question (like grades for my students). Fourth, if the situation involves the exploration of ideas which are still in the ‘learning process’ (like a new mathematical concept or a review of long-lost treasures). There might be a few other situations.

You might wonder why I start with our use of calculators. So often, the comments we make are about our students’ “over-use” or “dependency” on calculators; we see calculator use as creating a risk for learning mathematics. Many of us do allow calculators, and even embed their use in the learning process. Some of us forbid their use, and some of us have a blended approach. Most of us, however, believe that there is an issue with calculator dependency.

My conclusion is that the problem is not with calculators being used. The problems occur when student attitudes about mathematics and their own efficacy create motivation to use calculators when the human brain is a better device. If a student is doing a problem in the homework, or an example in class, and reaches for their calculator to add two one-digit numbers, this is part of the problem — the human brain is a better device, and the use of the calculator in this situation provides a clear ‘bad at math’ message about the student (and the student is the one sending the message).

Of course, we can not ignore the impact of culture on the use of tools, even calculators. Some students temporarily feel ‘smarter’ when they use a technological tool frequently; I suppose this is not so much ‘smarter’ as ‘good’. In the case of mathematics, the cultural bias towards technology combines with a norm that “it is okay to be bad at math” to encourage over-use of calculators. These comments about culture are not universal for our students, some of whom come from cultures where very little technology is available … some even come from cultures with a positive attitude towards mathematics.

If this analysis is correct, then the issue is not whether we allow calculators or not. The first basic issue is our outlook on learning — maximizing understanding, connections, and abilities to work with quantities … these are traits of the emerging models of developmental mathematics. Students should develop their strategies for good uses of calculating technology, and they can do this as long as we do not focus so obsessively on ‘correct answers’; if we assess representation and communication, the use of calculators will not create problems. As you probably know, technology does not really “solve” problems either; problems are solved by people and what we do.

I encourage you to ponder your approach to calculators in your classes. Are you creating a calculator policy to make a personal statement, or are you creating a calculator policy which reflects your understanding of how technology affects learning of important mathematics? Does your calculator policy encourage, or does it discourage, the development of mathematical proficiency in your students?

These issues are complex, and will not be solved by a simple yes/no policy on calculators.

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