I came across something interesting today. I ventured (for the first time) onto Google Books to see what they had to offer. I made my way to K-12 Mathematics – no big surprise there. And I came across this:
The Equation for Excellence: How to Make Your Child Excel at Math by Arvin Vohra.
Perhaps I’m naive, but I’m not familiar with Arvin or this book. I’m not going to talk about the author – I’ll let you form your own opinions based on his website.
I looked at the table of contents, and Chapter 11: The Calculator Fallacy caught my eye. So I started reading. I will admit that some of the points are valid and made me stop to think, but there is a general theme of “calculators make students lazy” and “teachers are misinformed.”
Then we get to this: “A student solving a complicated problem spends very little time doing actual calculations. Most of the time is spent examining relationships and determining what concepts apply.”
Wait. Didn’t he just make the case for calculators? I used graphing calculators to help students examine relationships and link concepts. If they used the calculator to multiply six and four, so be it.
The author then supports his statement: “The student who does math by hand has these concepts ingrained in his mind, and is adept at using them.”
Again, wait. Did he just tell us how students gain conceptual knowledge? Wow. We’ve been trying to figure that out for a while, and here was the answer all along. Make them do the work by hand. (Nobody’s ever tried that one before.)
Doing math by hand does not build a solid conceptual foundation for learning. Models help students build this foundation. Rich activities that apply learning help build this foundation. Regurgitating facts and working everything out by hand do not build conceptual understanding.
Finally, this assumption: “Thus, he rapidly sees relationships between various formulas and concepts, and can quickly figure out how to do the problem.”
I can count on one hand the number of students who made connections between formulas and concepts by simply doing problems by hand. I agree with the idea that a calculator in the hands of a less effective teacher is a dangerous thing. But the author discounts the role that a calculator can play in discovering patterns and understanding relationships, and the role of an effective teacher in promoting this kind of calculator use.