Some of My Best Friends are Calculators

Some years ago, we had an extended discussion about college credit for developmental courses (math in particular). The proposal being discussed was eventually superseded by other policies; however, strong opinions were voiced. During one commentary, a colleague was decrying students getting credit for such courses (though he had nothing against faculty who teach them. Our Divisional Dean leaned over to me and said “some of my best friends are developmental math teachers”, which I thought was quite funny (though the situation prevented me from laughing at the time).

When I hear some colleagues talk about calculators, I am reminded of that comment rephrased … “some of my best friends are calculators”. Calculators have their place, such colleagues say; calculators are not bad … it’s how students use them, so we need to prevent students from using calculators in a math class (as they say). In fact, I once took the position that graphing calculators not be allowed in a first algebra course (back in 1993). Since 1995, I have taught in an environment where graphing calculators are required starting with our first algebra course; although there are days when I find this frustrating, I have become a supporter of using calculators.

Unfortunately, the problem is much more complex than a ‘no calculator’ policy could solve; nor does a ‘required calculator’ policy solve these problems. Here are some of the problems that we can avoid discussing by focusing on a calculator policy issue:

Students want a calculator for basic operations for a reason — they feel ‘dumb’ at math; that’s a major issue.
Students view correct answers as being a valuable commodity, instead of seeing correct answers as suggesting good understanding
Numeracy leads to feeling smarter; having a sense of how quantities ‘behave’ is possible for almost all humans (just like language literacy).
Reasoning about quantities is a natural human endeavor, though we communicate this with language systems that are artificial (a necessary condition)
A single math class tends to be very ineffective at changing long-held beliefs and habits; data suggesting an impact normally are measuring temporary conditions.
The big picture ideas are more important than how a student calculates a particular value; the big picture includes their self-image about mathematics.

I like requiring a calculator in math classes, to provide a better venue to discuss these issues with students. Sometimes, a student ‘gets it’ (what we are talking about) and they change their math trajectory; for most students, it’s not that much of an issue either way — it took them 12 or more years to get to this point, mathematically, and a short-term experience is not likely to hurt them any more. Using the calculator, it seems, at least opens the doors to possible positive changes over a longer period.

This conversation with myself started when somebody reminded me of an article I wrote for the 1993 AMATYC journal; reading that article was an awkward experience, as I could see errors in my own thinking. Perhaps this post will encourage readers to examine their own position on calculators in math classes from a different perspective, one reflecting my course correction on the use of technology in mathematics.

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