This question has been nagging in the back of my mind for the last couple of months. Calculator technology is readily available to us… whether it be a simple computation calculator or a complex graphing calculator, we literally have the technology at our fingertips. “But what about when you are in the real world?” you say. “You won’t have your graphing calculator with you in the middle of the grocery store, will you?” But we do! We have our phones, our ipods, our ipads… we are almost always within reach of a digital device that has some type of calculating power! So is there really any good reason we should ask kids to not use their calculators?
This has been my struggle… but my thought right now is yes! Yes, there are times that telling kids not to use a calculator can help develop there number sense. After all, a calculator is only as intelligent as the person using it, right? If students have no sense of the operations that need to be done, or if they have no sense of the reasonableness of an answer, the calculator may be of no use at all.
I have two examples to support my position (although I am up for debate about this!):
1) Fractions: What if I told you a race course, 26 miles long, had water stations at every 1/8th of the course. How far did you run when you had come to the 5th water station? (Problem courtesy of Cathy Fosnot). If you had a calculator you would solve this problem very differently than without a calculator. Both are correct, both are valid, but as a teacher I need to make a decision based on the number sense I want to bring out. If it’s decimals, or fractions to decimals, I would say using a calculator is the way to go with this problem (or at least leaving it as an option). However, if I want kids to explore and play with fractions then telling them not to use a calculator for this problem will encourage fractional reasoning.
2) Factoring: I’m jumping up to grade 10 now. I’ve always enjoyed teaching factoring, but there is technology available now that will factor for you. All I have to do is type the function in, and voila! It’s factored! So maybe I should just skip factoring and use the calculators to help us explore the deeper concepts of roots, curve sketching, etc. Although I do feel that factoring with calculators can be extremely useful in some cases (so that the factoring doesn’t get in the way of those deeper concepts), I think that it is important that students understand the relationship of factoring to multiplication and division. Algebra tiles are a great way at getting at that understanding. I love how we can relate the array model of multiplication to expanding and factoring polynomials. If we don’t let kids play with these concepts then they won’t have the opportunity to see the connections in the mathematics.
Alright, that’s my argument for now. Feel free to debate me! My opinion is fairly fragile so I need some conversation to convince me (just like how kids reinforce math concepts, get it?!)!! 🙂