Math Class Helpers
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Posted on 6 August 1998
The following text was written by Brad
Sliger: Like most students with TI calculators, I have whiled away many
boring lectures playing games on my calculator. My TI-85 and then my TI-86 has kept me awake
and out of detention during high school. Now, as I approach my senior year, calculus,
physics, and college trig, I wonder what improvements could be made on these machines.
Taking a TI-86 to a math class is like taking a gun to a fist fight--it's hard to lose!
You do have to know how to use the calculator and how to do the math, but most people can
learn faster than the teacher teaches. Mind numbing, repetitive work can be made tolerable,
however the real edge comes from custom programs. There are many programs that make
up for the few shortcomings of your calculator. There are even collections of these
helpers. Each one of them asks for input then displays the output. This works great if the
problem that you are working has only one step, but when many steps are involved it fails.
Helper programs should optionally take input from the Ans variable and output to
Ans. If a program requires more than input or output, a list or matrix of the arguments or
outputs should be saved in Ans. This would speed the use of these helpers in multi-step
situations. I'm not saying the programs we've seen so far are not useful--they are.
I'm saying there should be a form of the program that works similar to a regular TI
function to save time and irritation. A collection of these functions would be very useful
in advanced classes and in, gasp, real life.
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Re: Article: "Math Class Helpers"
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Stephen Lindholm
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The designers at Texas Instruments did a simply astounding job of covering all of the univariate numerics that an undergraduate could need. That's not to say that it does everything -- it doesn't do proofs (duh!), the solver doesn't do complex numbers, and you can only use it to check your symbolic work by substituting numbers. But other than that, I love it. Now. Quite frankly, high-schoolers who spend all their time programming tables of integrals into their TI-85 or writing a program to do everything are only screwing themselves. In a few years, when you need you apply what you learned to more abstract cases, you won't be able to. I mean, if you aren't learning in high school, what *are* you doing?
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7 August 1998, 06:22 GMT
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Re: Article: "Math Class Helpers"
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Programmer
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I agree with many of the arguments given in these comments. It is very true that you must understand how to do it by hand before you program it.
I believe that personally-made programs are the best to have on your calculator because you learn and get the answers the way you need them. For me, these programs do NOT make me lazy and let the calculator do all the work. I must write down all the steps and I have no problem doing that without my calcs. If you don't believe me... well, I got a 5 for my AP Calculus BC exam w/ a 5 for AB subscore...
I mainly use programs that I wrote to check my answers... to CHECK answers. They are extremely useful, especially on AP exams (free-response). Anyone who uses programs to do their work for them is making a big mistake because they are not learning anything.
I believe that students should write their own programs. (All programs on my calcs are written by me and for me.) Learning TI-Basic is definitely worth it. It is a very simple language, but can be used to do many powerful things.
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7 August 1998, 07:30 GMT
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Re: Article: "Math Class Helpers"
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The Great aArdvark!
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Very true. It's very easy to do too. Several of the programs I've written work that way. It's user friendly since you just type argument:programname or argument:step1prog:step2prog and ans can be displayed at the end of each step (automatically if the last calculation is the last line of the program).
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7 August 1998, 08:05 GMT
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Re: Article: "Math Class Helpers"
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Aaron Hill
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I am proof that using BASIC to help with math works. I've been programming BASIC since when I can remember first turing on a computer (an old C64 and an Amiga! ha!). I've always excelled beyond the other students in math and science. Especially in my high school math courses, I would be programming some function to solve the problem while everyone else was learning from the teacher. Now our teacher also felt that programs are very useful. In fact, we programmed several in class! Another student who had the 85 led most of the programming, but of course he was totally unoptimized. I ended up fixing several of the slowdowns in his programming. It's the perfectionist in me.
But back to the point, all of my programs were functions. Everything I wrote accepted arguments through the command line. If there were too many to remember them, I'd write an ADDITIONAL helper app. Now I have a TI-92, so everything was done with one "Define MyFunc()=..." I'd rarely ever use the "Func:...:Return x:EndFunc". But since the class used mainly 82's, 83's and 85's, I'd have to write a program to work for them.
So I can speak from experience that FUNCTIONS work much better. Especially with the 92's symbolic solving, the nested functions I would create would enable the 92 to break down the seemingly "complex" answers (not always with i, but decimals that are hard to simplify). All of the simplifying makes the calculator run the stuff faster.
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7 August 1998, 08:24 GMT
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Re: Article: "Math Class Helpers"
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Programmer
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I have another thing to say...
Functions can be much better, but one problem I find sometimes is remembering what the arguments for the function are... are there one, two, or three... what are the arguments... the function, lower bound, upper bound, n divisions... what? That's probably the only bad thing about functions... other than that I agree with the statements made regarding functions.
One more thing... I like that response to my comment... Work Smarter not Harder... very good advice...
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8 August 1998, 02:39 GMT
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Re: Article: "Math Class Helpers"
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Matthew Read
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I agree that sometimes functions have too many arguments to remember easily...one solution to this would be in an upgraded flash rom. I seriously doubt TI has included the functionality of adding custom functions to the catalog. The catalog displays what the arguments of a function are, correct? A basic command could be added, perhaps catalog(custfunc,"arg1","arg2",
"arg3",...) This would be a great feature in my eyes. I'm sure if we express enough interest in this added functionality TI would consider adding it in a flash rom upgrade. I like it anyway!
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8 August 1998, 18:48 GMT
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Re: Article: "Math Class Helpers"
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Mike
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I think that when you go on programming on calculators, you are quote on quote "LEARNING" the formula. Let's say we have a simple geometry formula (I chose this so everyone knows what it is) : The distance formula. The formula is:
\SQRT\ (x1+x2)^2 + (y1+y1)^2 (\SQRT\ means the square root sign.
When you make a BASIC program, you must KNOW the formula, or it's merely IMPOSSIBLE. I have seen many people who tried out the BASIC programming on calculators, but they are never implememted. THEY TAKE MEMORY! I have made a program that is like 1024bytes, that is able to t figure out the slope, mid-point, pythagorean TH, Reducing Radicals, Quadratic Formula(FOR 83) and length. These thigs are what is important in the learning experience. (I AM NOT SAYING THAT MY PROGRAM IS COMPLETELY IMPLEMENTED, BUT I THINK IT IS SMALL, COMPARED TO MY FRIEND THAT CALLS HIMSELF "GENIUS" THAT TOOK ABOUT 3K TO MAKE A PROGRAM LIKE MINE) I got mad. He braggs and everything so I did that. Now, let's get back to topic. Like I have said, building the program it self is a learning process for the formulas. I think TI have taken in many aspects of the TI calc's Z80 chip, and I am happy that they are still present. Not that they will disappear, though.
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6 March 1999, 07:11 GMT
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