The Museum of HP Calculators

HP Forum Archive 16

 RPN could save college students!Message #1 Posted by Han on 26 Sept 2006, 10:54 p.m. I had just finished looking over the exams of almost 300 students. Nothing bothered me more than the silly mistakes of not knowing the order of operations. They would lose points for, say, not distributing a negative sign before combining terms, or (as unreal as this may sound), having parentheses in the wrong place or missing completely. Then it dawned on me... why I love RPN/RPL so much. Every time I used one of the HP RPN/RPL calculators, it was implicit that I needed to know the order of operations. I had just been so used to the order of operations that it never occurred to me that RPN/RPL would be hard to figure out. If college students were required to use RPN, I think they would most certainly have a good understanding of the order of operations. You really cannot use RPN/RPL machines well unless you have a good understanding of the order of operations. What's sad is that college kids are still lacking the necessary comprehension of basic mathematical principles, and these algebraic-entry calculators are certainly not helping.

 Re: RPN could save college students!Message #2 Posted by John Smitherman on 27 Sept 2006, 8:05 a.m.,in response to message #1 by Han Hi Han. You might find this document regarding common math errors useful: http://www.math.vanderbilt.edu/~schectex/commerrs/ Regards, John

 Re: RPN could save college students!Message #3 Posted by Han on 27 Sept 2006, 2:58 p.m.,in response to message #2 by John Smitherman Thanks! This is a great link... and I even learned a few things as far as teaching goes. It's easy to fall into a habit and take for granted the smallest of details (referring to the article about differentiating x^k and requiring k be any CONSTANT).

 Re: common math errorsMessage #4 Posted by Palmer O. Hanson, Jr on 27 Sept 2006, 8:46 p.m.,in response to message #2 by John Smitherman A quotation from the treatise on common errors: "... Here is an example from Ian Morrison: What is –3^2 ? Many students think that the expression means (–3)^2, and so they arrive at an answer of 9. But that is wrong. The convention among mathematicians is to perform the exponentiation before the minus sign, and so –3^2 is correctly interpreted as –(3^2), which yields –9. ..." Didn't we beat tat subject to death in the Forum a month or so ago? I haven't been able to find it. My recollection is that we didn't come up with the same answer.

 Re: common math errorsMessage #5 Posted by Palmer O. Hanson, Jr. on 27 Sept 2006, 9:19 p.m.,in response to message #4 by Palmer O. Hanson, Jr The thread discussiing the -3^2 problem is "TI-84 Plus really that clumsy?" near the top of Archive 16: Early in the thread the -2^2 problem was introduced: "Re: TI84 plus really that clumsy?? Message #3 Posted by John Smitherman on 4 Sept 2006, 3:11 p.m., in response to message #1 by Hal Hi Hal. Also, tell your son to be careful with the TI-8x series as it interprets -2^2 as -(2^2) instead of (-2)^2. Regards, John Re: TI84 plus really that clumsy?? Message #4 Posted by Valentin Albillo on 4 Sept 2006, 3:22 p.m., in response to message #3 by John Smitherman Hi, John: John posted: " Also, tell your son to be careful with the TI-8x series as it interprets -2^2 as -(2^2) [...] As it should. That's the correct way of interpreting -2^2, and the HP-71B does exactly the same, returning -4. If you want (-2)^2, you should write it that way, parentheses and all. If in doubt, check any math books or articles and look for terms such as -a2 , you'll easily find them aplenty. Do you really think the author actually intends you, the reader, to interpret that term as (-a)2 instead ? Unary minus has lower precedence than exponentiation in standard math writing. Best regard from V." And the thread goes on and on from there explaining how a user can get different answers depending on how the problem is entered into different machines. What I think that all really says is that RPN really isn't the solution to reducing math errors by students. Neither is AOS, EOS, RPL, BASIC, FORTRAN, or whatever. First, the student has to know and understand the mathematics conventions. Then, the student has to understand the conventions for the machine he is using. Then, he has to be careful.

 Ditto! (N.T.)Message #6 Posted by Vieira, Luiz C. (Brazil) on 28 Sept 2006, 12:42 a.m.,in response to message #5 by Palmer O. Hanson, Jr.