calculators

I’ve done it both ways - with and without calculators. I found my best math students do their best with calculators. The calculators allowed them to get the nitty gritty stuff done quickly and allowed them to concentrate and focus on the concepts the problem was addressing.

I didn’t find that calculators did much one way or the other for my weak students.

Agree.

The weaker students have a tendency to plug numbers in and do an operation and hope. Most of the stronger students would get the calculations but it would take longer.

Yeah I agree. And I am confused about something. Seems I remember quite clearly writing about this very thing and also seeing a post by Susan on the exact topic. This was also a question by the same poster asking the same question. And now I can’t find them. Am I imagining this????
Am I posting in my sleep.

Anyway I think that unless the kid understands what they are doing they are not able to tell what operation to use. Unless it is some rote operation like doing a worksheet, the kid is not really able to figure out when he needs to add, subtract, etc. IF the problem was poor math calculation with good math comprehension, it makes a bit more sense.

Kids should also learn to understand negative numbers for practical matters like check books!!! :-}

—des

We are referring to l.d. kids? Gosh, I love my little scientific calculator because it helps me at least do adding and subtracting of integers where I can see how it means what it means, but I am quite far gone with my ld…so I will move on.
However, I have recently learned that, at least in the city I live, a fair amount of high schoolers are not learning their elementary and intermediate algebra in long hand…teachers are putting them right on the texas instruments 83 plus calculator. Does this help the student go to Algebra 1 or what have you quicker? Where I go to uni, a lot of students are just right there with the ti83 from day one. Do these graphing calulators add to your learning or take away from them? If you are ld do they help? I personally, though I am grown, use a baby calulator right now and will be working a ti83 in the spring as I take elementary algebra over again.
Does any educator think that calulators enhance the learning of algebra? Or take away from it. Like if you have a severe math ld, is a calulator the way to go?

I don’t think any of us are suggesting getting rid of calculators! :-)
But I think the use with young kids (or kids who don’t know the whys and wherefores of what they are doing) isn’t too helpful. You gotta know why you are dividing and then you need to know whether your answer makes sense! I could see kids using it the wrong way, get some odd answer, and just accepting it as that’s what the calculator says, not knowing that “garbage in =garbage out”. I think it’s a good thing for ld students who are slow (but know what they are doing) on the calculation side in such things as algebra.

—des

Like everything else - it depends :)

Our Math 098 students use that little puppy, too. It would have helped me *immensely* in the time-saving department with my inability to get graphs right. On the other hand, having to do ‘em by hand and hating it taught me *early* to figure out what they were supposed to look like from the equations (not great mathematics, just memorizing things like x^2 meant it should curve up, and -2 brought it down that axis two lines).

Math teachers argue this one at great length — and most of them have valid points. It’s definitely a case where it’s a powerful tool that used carefully can help teaching. I have also seen students learn the calculator steps and still be totally clueless about the math — but these were also students whose lives were being limited by the Math 098 requirement… and no, they really *weren’t* going to do this in real life. So the purist in me cringes but the individualist says “work the system! work the system!”

For your severe LD folks, I think the calculators are a lifeline, period, especially because it’s exactly the mental juggling of several abstractions at once before anything makes sense,that is often such an insurmountable hurdle to getting to right answers that often might just make sense if the brain weren’t already completely lost in the dust it just created with all that silly juggling.

Oh Yes, I don’t see any point in forcing college students to do by hand calculations whether they are ld or no. Anymore than I would have them write all their papers long hand to make sure they could. We live in the age we live in and not some earlier age (thank goodness).

—des

I’ve taught algebra with and without calculators. I’ve taught traditional courses and calculator-based curricula.

First, the calculator-based curricula were trash; the old rule applies that you have to filter the ideas through the brain first *before* punching into the machine; punching random non-meaningul numbers through the machine will guarantee garbage in and garbage out. Programs designed around the machinery lost sight of the students actually learning.

In a traditional program, the calculators make little difference. Good professors and teachers teach the thinking skills behind the processes, and bad ones mystify the students with weird recipes, calculators or not. Good students work to understand and use the calculator as a tool; weak and poorly-prepared students try every excuse and cheat they can come up with, calculators being only one way to try to avoid actually working and thinking.

The TI machines are fun toys! The 83 is the one that is high-pressure sold to schools, I don’t know why; it’s rather clunky and limited, in comparison to the others, and for a very small amount more you can get the ones that will do anything but slice bread. We had the 85 and 86 a few years ago; don’t know what number they’re up to by now. The 83 has five fixed buttons that do only one thing each; the 85 and 86 and presumably newer models have screen menus for each of these buttons so you can do hundreds of times as much with no more difficulty. The 83 has some built-in programs; the higher numbers allow you to put in your own programs of all sorts. If your school absolutely requires the 83, it’s a good machine, but if you have a choice, get the 86 or equivalent and you can do much more.

Again, these things are tools — they don’t learn for you. You still have to know about where to look for your graph (wrong window and bizarre things show up), about what your graph will look like (one typo …), what the mechanical limitations are (try 1/(x +1)), and so on.

The TI graphing calculators are good machines even for beginners in algebra because the screen shows exactly what you type in, you type things in in the normal order, and you have parentheses. Cheapie calculators show only one number at a time and often require bizarre reversed order typing (3 square root instead of square root of 3, for example). The screen display is a boon to those of us who have coordination problems and have to go over and proofread and correct everything twice. It’s also much clearer to a beginner why and how you have to calculate things in order and when parentheses are needed.

However none of this takes away from the need to develop number sense in your head first — one typo and you can be off by thousands.

The calculator that I really like is a Sharp that has a feature I don’t know how I could get along without — it displays what you have entered as well as the answer. I can see when I’ve just punched the wrong floggin’ button.
Another feature is the fraction feature which I have mixed feelings about, since it’s one of the more common quick-cheat buttons for my students that don’t really know what numbers mean at all. Fortunately the teachers have two-part tests - before you get your calculator out you have to hand in Part One. Otherwise reducing fractions would go unlearned.

Sue — this is where the much-maligned “show your work!” rule is an absolute necessity. Zero points for just writing down an answer; the marks are given for writing out your *process* of simplifying fractions or of finding common denominator and changing denominators to add, etc.

Yup, this is true. Writing out the steps is overly maligned — if you’re hopelessly dysgraphic, then get MathType, but 95% of the “brilliantly intuitive” folks who “just don’t want to write out the steps” benefit immensely from doing it.

[quote]Zero points for just writing down an answer; the marks are given for writing out your *process* [/quote]

Would you then give partial credit for problems that are worked correctly, but the answer is wrong? My son (6th grade) can work a long division problem correctly, but almost never get the answer right. He knows what to do, but just gets lost in the details.

I’m going to try breaking it down, so that he uses a calculator for the multiplying part of the process, but works out the steps on paper. I can’t think of another way to make sure that he understands the steps, but also gets the right answer. Both are obviously important in math.

absolutely on the partial credit thing.

There is one guy I steer our folks away from but even he will always give you a point if you got the “let x = the side of the triangle” statement right. (He does, however, have a tendency to take certain kinds of mistakes personally and write big red NO!!! s on your paper, with the occasional NEVER!!!… and yes, they tend to be “mathematically offensive” mistakes, but it really doesn’t help the learning process…)

I’ve seen students that benefit from using calculators and those who rely on it too much. When working at the college level I worked with Finite Mathematics (linear algebra and probablity) most. There were students who knew the steps and ideas, but couldn’t handle the basic math. For these students being with a class that allowed calculators was ideal.

My son’s math teacher insists on them writing down all the steps but they get NO credit for doing the steps correctly if the answer is wrong. No calculator use, period.

At my son’s school the 7th graders take 3 semesters of math. During my son’s “special topics” class, the teacher allowed them to use the calculator while they were working probability problems. They were doing factorials. The teacher didn’t show the kids how to properly use the calculator so my son missed MANY questions even though he had the steps written out properly. I really think that if math teachers are going to let students use calculators they should teach the kids how to use them.

We’ve just had a terrible year with math. I really hope next year is better.

In college partial credit is liberally applied. It’s a little subjective, so you sort of have to figure out a teacher’s priorities, but you do get it.

Is this unethical?

I am currently looking for upgrades to my ti 83 plus calculator, for example things like the quadratic equation and whatnot, nothing Stephen Hawking worthy. While looking for upgrades, I came across a product description for a ti 92 plus calculator that has something called a “pretty print” feature. The “pretty print” feature is something that will allow a student to be able to see all the steps of his/her equation. This is something that is also available with the ti voyage 2000 as well as the ti 89. What I am wondering is if any of you folks would consider it unethical to use a calculator of that sort on homework that a student is assigned to do at home, for Algebra I and Algebra II. I am thinking of buying one of these as a last resort kinda thing for when it takes me like three or four tries to do a problem and I still get the answer wrong, for I feel as though it would be a time saver of sorts. Now, I personally would NEVER use this sort of thing on tests because it would defeat the purpose and they are also not allowed on tests. I was just curious what all you folks thought of a student using a calculator like that as a last resort type of thing on homework. Would it aid the student to at least see how the equation they are having trouble doing is actually supposed to be done or would it be counter productive?

Ethically speaking, it would be no different than getting help from somebody else or using one of the “study books” that does the same thing. So I wouldn’t even consider it a last resort — not a first resort, either, since you’ll want to try to figure the stuff out on your own.

My third grader has to do long division. He uses a multiplication sheet or a calculator. The point of this kind of work when he doesn’t even have basic addition facts memorized is to make sure he understands the concepts. Even using aides 5 problems can take an hour (He has to remember the steps - divide, multiply, subtract, bring down next number.) Without the help it would be impossible - like testing for reading comprehension when the child can’t sound out most of the words and by the time they finish a sentence they forgot the first part of it.

Agree, agree, agree :(

It is futile, frustrating and fundamentally … oh, some other f word… I would unabashedly provide all assistance to make it happen fast. Perhaps ,if there aren’t too many steps, he can learn the four steps in order (Divide, Multiply, Subtract, Bring down)… and be proud of knowing them, so that he can use them later. And in the meantime, work on the stuff that is actually at his level.