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Teachers' Lounge Discussion: Geometer's Sketchpad

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From: Loyd Epperly

To: Teacher2Teacher Public Discussion
Date: 2002080913:06:10
Subject: Re: Re: Re: Exponents and grouping symbols

Re the problem 2^3^3. Using Microsoft EXCEL, the formula =2^3^3 results in 512. Same for the Texas Instruments TI-83 graphing Calculator. Parenthesis are required if you want the 3 to be cubed first. Thus, 2^(3^3) yields 134217728. which equals 2^27 Students often do not use grouping symbols such as braces {}, brackets [] and parenthesis (). Failure to use them can result in errors. For example, If a student wanted to write in three line form: 3 1 4 ---- + --- = --- 4+1 2+3 5 But because he/she was using a typewriter, and therefore used the one line form such as: 3/4+1 + 1/2+3 , the result would be 5 1/4 because of the failure to use grouping symbols. The student should write, 3/(4+1) + 1/(2+3) and that equals 4/5. The grouping symbols make the difference. I was out of college with a BA in math when I first wrote programs in FORTRAN programming language. It was that programming experience that made me keenly aware of the importance of proper use of grouping symbols. We wrote programs for a mainframe that was remotely located. Cards had to be punched. Two or three days later the program would come back for debug because the dumb computer had to be told precisely what you wanted to do. Math is that way too. I now often tutor, and most of the kids I tutor, fail to use grouping symbols. Maybe the teachers don't enforce that or were like me, and didn't use them properly at first.

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