Good calculator for moving into Algebra?

[Spy Car]

:lurk5:

[Caroline]

Is it? Tell me more, please...

I was under the impression that there were problems which could ONLY be solved using a graphing calculator, and that a curriculum can only be approved as AP if the use of the graphing calculator is incorporated. Has that changed? (I had looked through the syllabus aproval this summer...)

 

I didn't say it was completely away from the calculator. I said it is trending that way at the moment. It is shifting slowly. Now only 2 of the 6 free response questions are calculator. If you look at the released exams, fewer of the multiple choice in the graphing calculator section need a graphing calculator. If you look at the second free response question, a calculator one, it really uses the calculator very little, mostly to find the intersection and evaluate the first integral. Even that, if you find the intersection, take the integral by hand and then just plug in without evaluating, you would still get full credit. If you have an approved syllabus, you can get a new released multiple choice exam.

[EKS]

Every time we talk about this I get confused and maybe this has been answered somewhere in the thread. Are we talking about using a four function calculator for tedious computations once a kid gets into algebra and has "proven" their ability to do tedious computations, or are we talking about allowing unrestricted use of a full function graphing/scientific calculator?

 

FWIW, I allowed the use of a four function calculator once the kids hit algebra. Actually, as a special treat, I allowed its use prior to algebra as well. For example, I allowed my younger son to use one when doing the CWP books. It allowed him to focus his attention on problem solving and it made him feel like he was getting away with something.

 

On occasion, my kids need to use a scientific calculator for something and that's ok. Not all problem sets are written with no calculator use in mind. For example, my older son is taking IB HL Math, and they routinely assign problems where calculator use is expected.

[AngieW in Texas]

I can't stand any of the TI calculators. The best calculator I have found is a Casio:

http://www.amazon.com/Casio-Scientific-Calculator-FX-115ES-PLUS/dp/B007W7SGLO/ref=sr_1_2?ie=UTF8&qid=1352648921&sr=8-2&keywords=casio+fx+115es

 

What is fabulous about this calculator is that it will give you your answers in fractional and radical form. So when you type in sin(60), it will give you your answer as sqrt(3)/2 rather than a decimal answer (you can convert your answer to decimal form by hitting the s<>d button).

 

And I prefer the Casio graphing calculator to TI graphing calculators as well. They are much more intuitive and cost a lot less.

http://www.amazon.com/Casio-FX-9750GII-WE-Graphing-Calculator/dp/B00154GSQA/ref=sr_1_1?ie=UTF8&qid=1352649357&sr=8-1&keywords=casio+graphing

Edited November 11, 2012 by AngieW in Texas

[Dmmetler]

Every time we talk about this I get confused and maybe this has been answered somewhere in the thread. Are we talking about using a four function calculator for tedious computations once a kid gets into algebra and has "proven" their ability to do tedious computations, or are we talking about allowing unrestricted use of a full function graphing/scientific calculator?

 

FWIW, I allowed the use of a four function calculator once the kids hit algebra. Actually, as a special treat, I allowed its use prior to algebra as well. For example, I allowed my younger son to use one when doing the CWP books. It allowed him to focus his attention on problem solving and it made him feel like he was getting away with something.

 

On occasion, my kids need to use a scientific calculator for something and that's ok. Not all problem sets are written with no calculator use in mind. For example, my older son is taking IB HL Math, and they routinely assign problems where calculator use is expected.

 

 

I think I asked the wrong question. What I really wanted to know is "What calculator is good for high school level standardized tests, INCLUDING Algebra Exit exams which expect a calculator?". In my state, that means a graphing calculator for Algebra II. My initial thought was that, since DD needs one for the EXPLORE, I'd rather only buy ONE. DH still has the TI graphing calculator he got as a high school graduation present in 1989, and except that one quadrant of the screen has burned out, it still works.

[Caroline]

I think I asked the wrong question. What I really wanted to know is "What calculator is good for high school level standardized tests, INCLUDING Algebra Exit exams which expect a calculator?". In my state, that means a graphing calculator for Algebra II. My initial thought was that, since DD needs one for the EXPLORE, I'd rather only buy ONE. DH still has the TI graphing calculator he got as a high school graduation present in 1989, and except that one quadrant of the screen has burned out, it still works.

 

I have heard that the Common Core Smarter Balance and PARCC algebra exit exams will use calculators with TI-84 capabilities. These will be online with a drop down calculator. However, that changes on a daily basis it seems.

[Dana]

I think I asked the wrong question. What I really wanted to know is "What calculator is good for high school level standardized tests, INCLUDING Algebra Exit exams which expect a calculator?". In my state, that means a graphing calculator for Algebra II. My initial thought was that, since DD needs one for the EXPLORE, I'd rather only buy ONE. DH still has the TI graphing calculator he got as a high school graduation present in 1989, and except that one quadrant of the screen has burned out, it still works.

 

I don't trust that things won't have changed significantly by the time my son's taking AP exams etc. I'm fine spending under $20 on a scientific calculator for him now, letting him use my TI-84 if/when he "needs" a graphing calculator (or to demonstrate things), and then getting him whatever is current when it is a need.

 

The 84 has been constant for a while, but the N-Spire seems to be taking its place some. Until that settles down, I don't want to spend over $100 for something he won't be using regularly.

 

That's why I chose the 30XIIS to get for my son and why I'll wait on a graphing calculator until he's in high school or has an absolute need for one. If he only needs a graphing calculator briefly, he can use mine.

[EKS]

I think I asked the wrong question. What I really wanted to know is "What calculator is good for high school level standardized tests, INCLUDING Algebra Exit exams which expect a calculator?". In my state, that means a graphing calculator for Algebra II. My initial thought was that, since DD needs one for the EXPLORE, I'd rather only buy ONE. DH still has the TI graphing calculator he got as a high school graduation present in 1989, and except that one quadrant of the screen has burned out, it still works.

 

My 16yo son has been using the TI 84 Plus and has been very happy with it.

[8filltheheart]

Every time we talk about this I get confused and maybe this has been answered somewhere in the thread. Are we talking about using a four function calculator for tedious computations once a kid gets into algebra and has "proven" their ability to do tedious computations, or are we talking about allowing unrestricted use of a full function graphing/scientific calculator?

.

 

I can't speak for others, but my kids do not regularly use any type of calculator for alg 1 or geo. (alg 2+ they may use it more, but it is still far from "most of the time.") They may get one out to check their work or to convert to a different form to match our answer keys' form, but it isn't "standard" for our daily math---when they gather their stuff to do math, a calculator is not something they normally include. If they need it for something specific, they have to go find one. ;) I think my dd who is taking geometry this yr has used a calculator on 2 problems the entire yr so far (and we are 1/2 way through the text.)

[EKS]

I can't speak for others, but my kids do not regularly use any type of calculator for alg 1 or geo. (alg 2+ they may use it more, but it is still far from "most of the time.") They may get one out to check their work or to convert to a different form to match our answer keys' form, but it isn't "standard" for our daily math---when they gather their stuff to do math, a calculator is not something they normally include. If they need it for something specific, they have to go find one. ;) I think my dd who is taking geometry this yr has used a calculator on 2 problems the entire yr so far (and we are 1/2 way through the text.)

 

This is how it went for us with Algebra I and geometry. Generally the (4 function) calculator wasn't needed/wanted. But when it was, I didn't forbid its use.

 

In Algebra II, I did forbid scientific calculator use in the chapter about exponential and logarithmic functions (except for the problems where he was instructed by the book to use one). There may have been other instances where I did this as well, but I don't remember specifically.

[go_go_gadget]

Expectations of calculator use likely vary from course to course, as well. Most math texts are written to avoid approximations, so answers are often left in the form of improper fractions. In a physics, chemistry, or engineering course, however, approximations are often necessary, and a calculator can be useful in tedious calculations.

[regentrude]

I can't speak for others, but my kids do not regularly use any type of calculator for alg 1 or geo. (alg 2+ they may use it more, but it is still far from "most of the time."

 

Similar here. Except for extremely rare problems (once or twice a year, where the book specifically told the student to use one for computation), we have had no need for a calculator through calculus 1. the curriculum we use has problems designed to be worked without calculator; in most instances, using one would completely defeat the purpose and miss the learning objective.

 

DD has been using one for the numerical answers in her chemistry and physics homework. The calc based physics class she takes at the university does not allow calculators on the exams.

[quark]

Expectations of calculator use likely vary from course to course, as well. Most math texts are written to avoid approximations, so answers are often left in the form of improper fractions. In a physics, chemistry, or engineering course, however, approximations are often necessary, and a calculator can be useful in tedious calculations.

 

The above has been our experience so far.

 

What we did:

1. Simple desktop calc (4-function) for Explore but kiddo actually did not use it in the test.

 

2. Around that time, I bought him a Casio scientific from Staples for $8-$10 I think? This was used as a "toy", not for daily math work. In a few weeks, he knew how to use it very well by just plugging in numbers to play with it for fun. It actually helped trigger curiosity to learn some trig (because of the sin, cos etc buttons). He uses the Casio for his physics now.

 

3. Last April, we had a little money left from our annual charter stipend and it was enough for an NSpire so I ordered it. The NSpire has replaced the Casio's "toy" role. He plays with it for fun, plugging in random things to generate random graphs. The previous year, he started drawing various graphs by hand for fun so I wasn't worried about dependency. We will continue to work manually for daily assigned math.

 

None of his daily assigned math work so far (he alternates between geometry, algebra 2 and precalc) has required calculators.

 

OP, if you want to buy just one calculator, my suggestion is to go with an affordable Casio or TI scientific for now. By the time your DD actually needs a graphing calc, models could have changed too.

[mathwonk]

I do use a calculator for a few computations, where I teach students how to see that some famous numbers do have the expected decimal expansions.

 

 

e.g. using calculus we learn that the value of pi is the area under the graph of the curve 4/(1+x^2) between x=0 and x=1. This can be approximated by using rectangles below and above that graph. Doing this for a small number of rectangles gives 3.14 < pi < 3.1416.

 

E.g. the rectangle that fits just under this graph, touching it only at the right end x=1, has height 4/(1+1^2) =2. The rectangle that fits just above the graph, touching it only at the left end at x=0, has height 4/(1+0^2) = 4. So 2 < pi < 4. To do better you have to divide up the interval [0,1] into smaller intervals and use more rectangles. Using two intervals, [0,1/2] and [1/2,1] the lower rectangles have areas (BH) equal to

(1/2)(4/(1+(1/2)^2) and (1/2)(4/(1+1^2), which add to 16/10 + 1 = 2.3. so pi > 2.3, great. the upper rectangles have areas (1/2)(4/(1+^0^2) and (1/2)(4/(1+1/2)^2) = 2 + 16/10 = 3.3. so 2.3 < pi < 3.3. anyway you see how a 4 function calculator will become handy sooner or later.

 

You can do even better with trapezoids and with averaging more than one approach. Using an average of trapezoids and midpoint rectangles, gives 3.1415926, with 8 subintervals, which is off by less than 1/10,000,000. I used an old $12 calculator for this, just for adding and dividing and multiplying.

 

Amazingly however, Euler, on p.101 of his book Introduction to Analysis of the Infinite, (well before mechanical calculators, since he died in 1783) gives

pi = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132[7]23066470938446+...,

 

where the digit [7] is apparently erroneous and should be 8. I do not know if Euler made this strange error or if it was copied in error in the process of publishing.

 

This is intended to illustrate how much ground we have lost since the days when humans could make hand computations much more accurate than we can do today even with calculators. Of course high powered computers can go well beyond Euler today. If you are interested in seeing what the great mathematician Euler thought a PRE-calculus course should contain, you might take a look at Euler's incredible book.

 

http://www.amazon.com/Introduction-Analysis-Infinite-Book-I/dp/0387968245/ref=sr_1_1?s=books&ie=UTF8&qid=1353871814&sr=1-1&keywords=euler%2C+analysis+of+infinite

 

[but do not pay > $100 for it on amazon. just check it out of a university library for a look.]

Edited November 25, 2012 by mathwonk