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I wanted to make this a little separate from the skills thread. I was grading math test yesterday and realized that now that they are in Algebra 1/2, the points being tested aren't really about how to do calculations as much as they are about how to set up a problem in order to extract the correct answer.

 

I am a huge calculator grinch. I think that they tend to be handed to kids in schools well before the kids have mastered the skills that the calculator replaces. But it would appear that I also need to realize that there is a time for transition and we are there.

 

Of the 40 questions I graded last night (2 tests' worth), there was only one question where just plugging the number sentence into the calculator would have gotten the answer. The rest of the questions required knowing what to do.

 

I think part of the reason I missed the transition is that, living in an area that didn't require testing, I missed the cue that being allowed to use a calculator on a test would have provided.

 

There are some tricks to knowing how to use a calculator. The one my kids have is a little different from what I grew up using. There are some techniques and skills to using them fluently. And that needs to be part of their math education too. So as of today, they get calculators on both lessons and tests.

 

The third grader, on the other hand, will still be doing his math the old fashioned way.

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I am so glad you asked this question. We just had a calculator discussion at our kitchen table this morning.

 

My oldest is using Lial's Introductory Algebra for math this year. I got the "clue" you refer to when the calculator icon began to appear next to selective questions in certain sections of the text. I too have always been a "calculator grinch".

 

So we agreed calculator use for the calculator questions in the book was appropriate. However, yesterday, we ran into some graphing questions marked for calculator use that I could not remember how to do on the calculator. I am quite sure at one time I could do these without much thought. In fact I tutored my niece on this topic a mere 2 summers ago. My 40+ yo brain has clearly not retained this information or it is in a recess not yet reached by my caffeine deprived brain. So I am brushing up on it this week and we have set aside some math time next week for some calculator lessons.

 

I think math does reach a place when calculator use is appropriate. They will have calculators and computers as future engineers, scientists etc. This should not replace the thinking required to solve math problems. I am a firm believer in mastering math concepts first and then giving them the calculator to make the solving of the problem easier. It sounds like you have reached that place.

 

I hope your kids are as happy as my DD was. I expected and heard "that's not fair :glare:" from my boys (3rd and 4th) who have not yet reached the point of mastery. I did let them use the calculator to check their facts practice today.

Edited by Beach Mom
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You'll need to teach graphing calculator usage before the SATs. They allow the caclulator and most kids use a calculator on the problems that need it. Your kids will be at a disadvantage if they can't use their TI-83 properly when the time comes, and part of knowing how to use it is knowing when it is quicker to just figure out the problem yourself. Having said that, there is no reason for caclulors until that time.

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My DD 13 learned to use a calculator for her physics class.

Otherwise, we use no calculator until needed for trigonometry and exponential functions and numerical calculations involving pi.

Algebra is done without a calculator.

 

:iagree:

 

I made it to algebra without a calculator. I finally got a scientific (non-graphing) calculator in high school. That calculator lasted me through the rest of my math classes, ending with college calculus. It was essential in high school science.

 

I plan to do the same for my kids. My math program has a few lessons on calculator usage, and we do those lessons just for the sake of doing the math program, but that's the only time my kids use a calculator.

Edited by Kuovonne
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I bought a scientific calculator for my kids to use this year in 7th. Before that we've never allowed one - I'm also a calculator grinch.

 

Both their books (Lial's Pre-Algebra & Singapore Discovering Mathematics) have mini-lessons on calculator use. At first I only let them use it for those. My dd in Lial's is still only using it for problems with the calculator icon next to them. I've just recently, in DM 1b, become more lenient on its use for my other dd. The problems, as the OP said, are more about setting up and doing the problems the right way. The number are no longer 'easy' to do manually, and with all the steps it was taking her forever to get through, so I decided as long as she was getting them set up and worked correctly, I'd relax on the calculator.

 

I'm going to try to re-dedicate to having them spend time daily on Quarter Mile math to keep the computational abilities up.

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I see you are using Saxon. I have used it with all my kids. We started using a calculator toward the end of Algebra 1. Before that they did every long calculation by hand. I get the mean mom award around here.

 

Linda

 

Well, I don't mind having a mean mom nomination. On the other hand I have shepherded them through a lot of calculations at this point. I don't mind now allowing a calculator to do the assisting, say in adding a string of numbers to find the mean. They still have to know the difference between mean and median or the answer will be wrong.

Edited by Sebastian (a lady)
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You'll need to teach graphing calculator usage before the SATs. They allow the caclulator and most kids use a calculator on the problems that need it. Your kids will be at a disadvantage if they can't use their TI-83 properly when the time comes, and part of knowing how to use it is knowing when it is quicker to just figure out the problem yourself. Having said that, there is no reason for caclulors until that time.

 

Karen, this is the point where we are now and I have never used one.:tongue_smilie: My oldest knows how to roughly use one. The middle child was required to have one for geometry this year, but up to this point has only used it for playing games and the youngest is in Algebra I. It is time to give up my "no calculator" stance. One of my dd's friends is coming over next weekend to give me a lesson on it. Maybe he can help me with my math too. Double :tongue_smilie::tongue_smilie:

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The problems, as the OP said, are more about setting up and doing the problems the right way. The number are no longer 'easy' to do manually, and with all the steps it was taking her forever to get through, so I decided as long as she was getting them set up and worked correctly, I'd relax on the calculator.

 

 

I don't mind now allowing a calculator to do the assisting, say in adding a string of numbers to find the mean. They still have to know the difference between mean and median or the answer will be wrong.

 

I allow calculator use on enrichment math like Edward Zaccaro's Challenge Math books but not in the main program (Singapore).

 

:iagree: with the above. With a hairy problem, a kid can spend just way too long on the arithmatic. She gets plenty of practice doing calculations with her regular math so I allow calculator use at other times (with my approval, of course).

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In my local Universites Calculators aren't used or allowed in College Algebra, or PreCalc classes OR tests.

 

At the Comm. College, we can use calculators in Intermediate, and they are req. for graphing in College Algebra and up.

 

I have friends who went from CC to Uni and had a hard time with higher maths because they were calc-dependent.

 

Just my .02.

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Karen, this is the point where we are now and I have never used one.:tongue_smilie: My oldest knows how to roughly use one. The middle child was required to have one for geometry this year, but up to this point has only used it for playing games and the youngest is in Algebra I. It is time to give up my "no calculator" stance. One of my dd's friends is coming over next weekend to give me a lesson on it. Maybe he can help me with my math too. Double :tongue_smilie::tongue_smilie:

 

One of the things that has swung me into the with calculator camp is that it will also be an option on a portion of the Stanford tests they are taking in May. Now that we are entering a stage where they want to apply to selective academic camps, I need some good normed test scores to stand in the place of grades and class rank.

 

I don't see a reason why my kids should go into the test with the disadvantage of not using or being less familiar with a calculator.

 

I have no problem taking it away again if they show that they are relying on it for thinking.

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In my local Universites Calculators aren't used or allowed in College Algebra, or PreCalc classes OR tests.

 

At the Comm. College, we can use calculators in Intermediate, and they are req. for graphing in College Algebra and up.

 

I have friends who went from CC to Uni and had a hard time with higher maths because they were calc-dependent.

 

Just my .02.

 

I took four semester of college level calculus, and many courses of engineering and science courses. My experience was that it was assumed that you not only had a scientific calculator, but were already proficient in how to use it.

 

I imagine that each prof is different in what they expect of their students.

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In my local Universites Calculators aren't used or allowed in College Algebra, or PreCalc classes OR tests.

At the Comm. College, we can use calculators in Intermediate, and they are req. for graphing in College Algebra and up.

I have friends who went from CC to Uni and had a hard time with higher maths because they were calc-dependent.

 

 

I completely agree.

We do not allow calculators on tests in the calculus based physics classes (homework is OK)- and boy, it's not pretty what we see in terms of simple arithmetic mistakes.

Often universities don't allow calculators in calculus classes either.

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I completely agree.

We do not allow calculators on tests in the calculus based physics classes (homework is OK)- and boy, it's not pretty what we see in terms of simple arithmetic mistakes.

Often universities don't allow calculators in calculus classes either.

 

I wonder why such the difference from what I experienced. I was not an engineering student, but was at a science and engineering school.

 

Is part of it the much higher capabilities that calculators have now? It's not like I could have stored formulas or other cheats in the old TI I was using. Graphing calculators were new my freshman year.

 

Guess I have to both make sure they are fluent calculator users AND don't get lazy.

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I wonder why such the difference from what I experienced. I was not an engineering student, but was at a science and engineering school.

 

Is part of it the much higher capabilities that calculators have now? It's not like I could have stored formulas or other cheats in the old TI I was using. Graphing calculators were new my freshman year.

 

Guess I have to both make sure they are fluent calculator users AND don't get lazy.

 

The main reasons we do not allow calculators on exams is that you can store absolutely anything on the programmable ones. Allowing calculators means that there is no way to check what the students are using - some may just have the allowed equation sheet, while others have stored half the textbook in theirs. With large classes this is impossible to police.

Of course, an exam designed for use without calculator will not involve complicated arithmetic - the problems are then purely in symbols, with minimal arithmetic needed. Tests the same concepts.

 

I do allow calculators in one of my classes for pre-meds. It is a much smaller class, and the students have trouble with the abstraction of

just working in symbols. For those, I settle if they can work out the numbers.

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The main reasons we do not allow calculators on exams is that you can store absolutely anything on the programmable ones. Allowing calculators means that there is no way to check what the students are using - some may just have the allowed equation sheet, while others have stored half the textbook in theirs. With large classes this is impossible to police.

Of course, an exam designed for use without calculator will not involve complicated arithmetic - the problems are then purely in symbols, with minimal arithmetic needed. Tests the same concepts.

 

I do allow calculators in one of my classes for pre-meds. It is a much smaller class, and the students have trouble with the abstraction of

just working in symbols. For those, I settle if they can work out the numbers.

 

Ah, that makes sense.

 

Does this prove a hard transition for incoming freshmen or is it similar to the standards in their high school tests. (Maybe I need to rethink my rethinking?)

 

Could you give an example of problems in symbols. Do you mean standard xyz variables or something more like wingdings?

 

(There is an infamous military foreign language aptitude test that is in symbols rather than any actual language. I've heard it called the Lucky Charms test.)

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I don't mind now allowing a calculator to do the assisting, say in adding a string of numbers to find the mean. They still have to know the difference between mean and median or the answer will be wrong.

 

And you're better off not using the calculator to find the median!

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Could you give an example of problems in symbols. Do you mean standard xyz variables or something more like wingdings?

 

 

Normal characters. But instead of saying stuff like "a 5 kg block slides down a 3 m long ramp that is 30 degrees above the horizontal and compresses a spring by 5 cm- how fast is it going?", it would read: "A block of mass M slides down a distance D on a ramp that is inclined by theta with respect to the horizontal and compresses a spring a distance s. Derive an expression for the speed in terms of system parameters..."

So instead of calculating a number in m/s, the students derive V= and a combination of the symbols on the right side of the equation, without producing an actual numerical answer. Don't need calculator - tests all concepts just fine.

 

And yes, it is hard for the freshmen who are used to just sticking numbers everywhere - even though a much better techniques would be to always just derive a symbolic answer and insert numbers at the very last moment (easier to find mistakes, takes less time, better for doing multiple similar calculations, answer contains much more information about behavior than just a single number... long list of advanatges.) They fight it tooth and nail for a few weeks until they give in... and eventually they'll find it easier. but the first few weeks are an uphill battle.

Edited by regentrude
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even though a much better techniques would be to always just derive a symbolic answer and insert numbers at the very last moment (easier to find mistakes, takes less time, better for doing multiple similar calculations, answer contains much more information about behavior than just a single number... long list of advanatges.)

 

Very good point. Maybe I can convince my ds to use this. Of course, that would also require his showing work.

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I have avoided calculator usage thus far.

 

I do agree that I don't want my kids at a disadvantage on tests because they aren't using a calculator. Nothing like the pressure of a room full of kids taking an SAT to make you forget simple math facts you actually know.

 

While I'd like to think they would succeed no matter what--I'm not silly enough to make them compete on a less than equal playing field. If the other kids have 2 pencils and an eraser I'm not sending mine in with 1/2 pencil with the eraser worn off.

 

I suspect that some where in Algebra and certainly in Geometry we will allow a calculator for solving basic math. I am guessing when they spend to much time doing basic math problems in order to complete the greater problem that is being studied-then it may be time for a calculator.

 

I don't know when a graphing calculator will show up but I'm sure the time will present itself in due course.

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I have to go back and read the thread... but I just bought calculators for my older two children last week - TI-30XS - for them to take practice ACt sessions with. I also let them play with them on their own to figure out all the functions. I still don't let them use them for their actual school work unless approximate answers are needed. I wasn't allowed to use when when I took Calculus I & II at an engineering school in 1990 or when I went back a couple years ago and took DiffEQ and Linear Algebra... so I am only allowing them for major standardized tests. I resent that we will have buy them expensive graphing calculators and teach them to use them for calculus because AP and our local cc's require them even though many engineering schools still do not allow their use. I think there is much to be said for learning to curve sketch by hand rather than relying on calculators to do it for you all the time.

 

ETA: Now that I have read the thread.... I will allow calculator use in their science classes, However, for the most part I don;t see any reason for them to use them for their pure math classes. We do, however, leave answers in terms of pi and radicals such as sqrt{2} or sqrt{3} in pure math which is how we were expected to do it in my college math classes, but find approximate answers using significant figures for science classes.

Edited by Elizabeth in WA
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