When I went back to college after being out of school for ten years, I knew I had my work cut out for me. I tested into College Algebra, which was essentially the same material as the most advanced maths class I took in high school.
One of the requirements for this course, in addition to the textbook, was a graphing calculator. A TI-86 or equivalent was specified. So, I went calculator shopping.
Being an impoverished college student planning on taking lots of maths classes, I didn't see any sense in purchasing a TI-86 when I could get a TI-89 for about 15% more, and it had many more functions. So, I purchased the TI-89.
That TI-89 has been the best learning aid I could have hoped for. It does pretty much everything I needed to learn to do through multi-variable Calculus and most differential equations that I was expected to learn to solve.
Many times late at night doing homework, when I didn't understand a concept, I could break down a problem to see how solutions changed when I changed a single aspect of the problem, such as changing a constant or an exponent. This allowed me to see many patterns in the problems, and ultimately led to a deeper understanding of the material.
I don't particularly like doing Mathematics, but I am fascinated by all the stuff I can do with Maths. Therefore, I often take the lazy route and use my calculator find my derivatives and anti-derivatives, as well as messy arithmetic. Don't get me wrong, I can do these by hand (most of the time), but I find it's usually a pain, and significantly increases the likelihood of me making a stupid or careless mistake.
Now, I'm the first to admit that if you present me with a complicated integrate by parts problem, I'm going to struggle without my magic box. I don't do such problems by hand often enough to stay current. However, I am also aware that I live in a world where it is becoming increasingly likely that I can find a computer or a calculator before I can find a pencil and a piece of paper.
The vast majority of the Maths instructors I have had have all had a negative view towards calculators. They tend to believe that using a calculator as a learning tool is about teaching keystrokes instead of teaching concepts. I, on the other hand, believe that learning the mathematical concept is wholly different than learning the syntax used to solve the problem, whether it be with a pencil and paper or a calculator.
The calculator does the calculations for me. It does not know how to set up the problem so that I get the correct information as a solution. No matter how many functions my calculator has, if I don't understand the concepts behind those functions, the calculator is useless.
I've had this discussion with every single Maths instructor I've had in college. Only one has come remotely close to agreeing with me, yet not a single one has offered any logical counter argument, usually relying on the outdated "what if you don't have a calculator" response. Yet on occasions where I sought Calculus help from, for example, a Pre-Calculus professor, she was unable to assist me as it had been so long since she had done any Calculus exercises.
I feel we are fast approaching a time when pencil and paper syntax is completely outdated. I also think that many students would understand concepts more easily if teachers embraced calculators in the classroom instead of relying on traditional methods.
How do you feel about calculators in the classroom? Are they common learning / teaching tools in other areas? (I'm in central Florida, USA)
You can shear a sheep many times but skin him only once.