Calculators or no calculators?

B

Bea

Legacy Member
I've studied mathematics in two countries now and I'm surprised by how different the teaching methods are. In the United States, where I studied for my high school education, students almost always use calculators for operations such as multiplication, division, etc. High school students have graphing calculators too so they don't have to graph by hand! But here in my home country, everything is done manually.

Personally, I can see the pros and cons of both methods. Using a calculator saves you time with tedious operations and lets you focus your attention on more difficult tasks such as, say, getting derivatives and integrals and whatnot. But at the same time, you end up relying on your calculator too much and forget how to do things manually.

What do you guys think? Do you prefer mathematics with calculators or without calculators?
 
I grew up usually using the manual method when it comes to simple mathematics such as addition, subtraction, multiplication, and division. Our teachers encouraged us to make use of the manual way because it will help exercise our brains more rather than relying on calculators. We have also manually used graphing papers instead of the electronic ones. The only times we were allowed to use calculators were during complex math topics needing the help of scientific calculators. Despite the prevalence of technology and having everything solved in just one click of a button nowadays, I still support the "no calculator" method in solving simple math problems especially in students who are just in their initial stages of learning math.
 
gracer said:
I grew up usually using the manual method when it comes to simple mathematics such as addition, subtraction, multiplication, and division. Our teachers encouraged us to make use of the manual way because it will help exercise our brains more rather than relying on calculators. We have also manually used graphing papers instead of the electronic ones. The only times we were allowed to use calculators were during complex math topics needing the help of scientific calculators. Despite the prevalence of technology and having everything solved in just one click of a button nowadays, I still support the "no calculator" method in solving simple math problems especially in students who are just in their initial stages of learning math.
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Right, I understand that thoroughly. But what about when they pursue higher math topics? In my experience with my university, even in higher calculus, we aren't allowed to use calculators - which makes for very tedious work. We may understand the topics but we get tied up when it comes to the simpler mathematics operations. It's quite silly, haha. Here we are, students majoring in math - and we can easily solve for double integrals and whatnot, but simple division makes us stop in our tracks, haha!
 
I think this is one of those debates that will rumble on and on, simply because there is no right or wrong answer. In this day and age, technology is taking over more and more parts of our life, and no even simple mathematics we use in every day life will be worked out by the use of a calculator, tablet, PC or even smartphone so the question is do children need to be taught without using those devices?

I can see why certain education systems say it's important to learn how to do mathematics without using instruments, but at the same time aren't we just teaching children something they will never need to know? If we allow the use of calculators then it would speed up the process and then maybe teachers could then use that time saved in teaching the children something that is going to be worthwhile in the future. I got taught algebra at school, and the last time I ever did algebra was...well, at school in those lessons I got taught it in, so looking back I could say that was just a waste of mine and the teachers time and effort.
 
pwarbi said:
I think this is one of those debates that will rumble on and on, simply because there is no right or wrong answer. In this day and age, technology is taking over more and more parts of our life, and no even simple mathematics we use in every day life will be worked out by the use of a calculator, tablet, PC or even smartphone so the question is do children need to be taught without using those devices?

I can see why certain education systems say it's important to learn how to do mathematics without using instruments, but at the same time aren't we just teaching children something they will never need to know? If we allow the use of calculators then it would speed up the process and then maybe teachers could then use that time saved in teaching the children something that is going to be worthwhile in the future. I got taught algebra at school, and the last time I ever did algebra was...well, at school in those lessons I got taught it in, so looking back I could say that was just a waste of mine and the teachers time and effort.
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Those are good points, definitely! I can understand not wanting to use calculators for students who might pursue more mathematics-oriented studies and careers - but for general education such as elementary school and high school, I don't see anything wrong with letting students use calculators. Especially if, like you said, the last time these students will ever use algebra is for a final exam in school.
 
Bea said:
Right, I understand that thoroughly. But what about when they pursue higher math topics? In my experience with my university, even in higher calculus, we aren't allowed to use calculators - which makes for very tedious work. We may understand the topics but we get tied up when it comes to the simpler mathematics operations. It's quite silly, haha. Here we are, students majoring in math - and we can easily solve for double integrals and whatnot, but simple division makes us stop in our tracks, haha!
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That is really one tough school you are in. lol! :) I understand your point though. When it comes to higher level maths, there are really those types of formulas which require the need of a calculator (a scientific one for most). I do think it's alright for higher levels of education because they already know basic math skills. It's another thing though for the elementary level where students are still feeding their minds with the basics so it's better for them to enrich their math skills through the manual methods of solving problems.
 
I'd imagine that for most of us, basic mathematics is all we're going to need in life, so being able to do those with out a calculator then will benefit a child's development and then later in life they can get through the day without having access to a calculator but anything else seems pointless to me. Taking up valuable lesson time learning things like algebra and complex formulas seems pointless to me, and while I can see why it's important to learn them, learning them without any help from calculators or technology doesn't make much sense a if they are ever needed in the future then the first thing they'll do is reach for a calculator because it's quicker, even if they are able to do them without.
 
pwarbi said:
I'd imagine that for most of us, basic mathematics is all we're going to need in life, so being able to do those with out a calculator then will benefit a child's development and then later in life they can get through the day without having access to a calculator but anything else seems pointless to me. Taking up valuable lesson time learning things like algebra and complex formulas seems pointless to me, and while I can see why it's important to learn them, learning them without any help from calculators or technology doesn't make much sense a if they are ever needed in the future then the first thing they'll do is reach for a calculator because it's quicker, even if they are able to do them without.
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With the advent of smartphones, too, learning things manually just seems pointless for algebra and other stuff. I guess, in the past, if you ever encountered algebraic problems in real life and had to solve it, you had to do it in your head. Not everyone carried a calculator with them at all times.

But these days almost everyone has a smartphone, so even without a calculator with them, they could answer algebra problems without having to do it manually anyway. Seems like learning math without the help of technology has become old-fashioned...
 
It has become old fashioned, and that's why I do think that children should be taught but be able to use a calculator or a smartphone because in the future that's what they're going to be using anyway. Sometimes the children might not be able to even do the equation or formulae WITH a calculator as while doing the basic mathematics is easy enough, sometimes the more complicated sums can be hard to work out how to do no matter what you are using.
 
The answer is "via media". We can not be fanatical and force every calculation to be manual. Using the calculator should be taught at school, I agree, but I also fully support everything that has to do with teaching the process of manual calculation too.

A solid theoretical foundation should be provided to students while embracing the reality of what will happen to their application in everyday life. Students will use their calculator out of school, no doubt about that, but they should know both methods. You don't always have a calculator handy... for those times then the theory must be dusted and used for doing manual calculation.

I would say it would be like teaching students to be "all-terrain".
 
While your right when you say that people won't always have a calculator, but most people will always have smartphone or access to another device that they can use if they need it. I'm not saying that the theory behind the calculation shouldn't be taught, I just think that more time needs to be spent on showing the future generations how to do the maths on these devices as this is primarily what they're going to be using.
 
This is always one of the things that is tough for teachers to explain. Students will raise their hands and ask, well at work I will be able to use a calculator, so why can't I in school. If we are really training these kids for the real world, shouldn't we skip the written-out method and stick to teaching them how to on a calculator. I guess it depends on whether you think of school as more than that, and if you want to develop a more complete mind. It is an interesting question, though, and for that I say thank you for sharing and getting my mind working on a Saturday morning.
 
rz3300 said:
This is always one of the things that is tough for teachers to explain. Students will raise their hands and ask, well at work I will be able to use a calculator, so why can't I in school. If we are really training these kids for the real world, shouldn't we skip the written-out method and stick to teaching them how to on a calculator. I guess it depends on whether you think of school as more than that, and if you want to develop a more complete mind. It is an interesting question, though, and for that I say thank you for sharing and getting my mind working on a Saturday morning.
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Educating and preparing children for the real world for me is what it should be mainly about. While I am an advocate of using new technology I do still think that the older, tried and trusted methods of teaching are also important, but they just need adapting as time goes on. We can still teach the children the basics but do it in a way that they can use in the future. While that might be hard to achieve, it's not impossible and something that we should at least try and do.
 
I prefer that students should be given calculators. In today's world we are trying to get used to gadgets that can make our work easier. By using calculators, students are given a chance to prepare themselves for a digital world where almost everybody uses computers. I know that the use of calculators can affect their memories but that's how they are being integrated into this changing world.
 
In our country, calculators are only allowed for the higher level education like engineering. For everything else, we have to do manually and even in the higher level education, we haven't ever used the graphing calculators and do the plotting as well as the calculation by hand.

The use of calculators is actually discouraged unless and until it is absolutely necessary.
 
Claire1 said:
In our country, calculators are only allowed for the higher level education like engineering. For everything else, we have to do manually and even in the higher level education, we haven't ever used the graphing calculators and do the plotting as well as the calculation by hand.

The use of calculators is actually discouraged unless and until it is absolutely necessary.
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Here in the UK the use of calculators is also discouraged in education, but like we've been saying, I'm not sure if that's actually a good thing or not. I think if a person is taught how to do calculations and maths from an early age, they will have the knowledge to be able to work problems out in their head but with a calculator they can do it a lot faster, and with technology taking over a lot of our lives these days, I'm sure that in the future calculators may become just part and parcel of teaching, and they won't be seen to be almost outlawed as they are now.
 
I'd rather do it without the calculator because it makes you think critically much more. You have to understand how to effectively do math without a calculator. But when the calculations are much more complex, then yeah I can see use of a calculator.

I guess here in America we use these instruments because the teachers know that these problems that we have on our assignments are better done with a calculator. When you go into a business where you need to apply your mathematics skills, you will be using them anyway so it's not like cheating.
 
I think that just as long as the students understand the reason that the calculator gives the value that it does is enough. If students are allowed to use calculators at an early age they can save a lot of time that can be used to introduce the students to more concepts. After all it's difficult to predict who will need these concepts later in life and who won't.
 
For basic math all the way to algebra, I think the aim should be to have the child do the math on paper. This is so they know the basics of how math works and they gain an innate understanding of numbers, functions, rules, etc... Once you have reached a certain level, usually by high school, then it is very important to begin learning how to use both the calculator and math programs like Mathematica and MatLab. Any student that is interested in the fields of math, engineering, GIS, or computer science, needs to have a very solid foundation of how these calculating programs work. Once you have reached a certain point in math, its not as necessary to know HOW to obtain the integral of a function as to WHY you need to obtain that integral and then WHAT you do with it. In industry engineers are not using pen and paper to solve complex functions, they have MatLab and Mathematica for that, but they still need to know how the program works and how to interpret the results.
 
I grew up in an environment where we didn't use calculators and we were expected to memorise mathematical tables. Manual calculations enhance the faculties of the brain through the development of neurological pathways in the critical faculties involved in calculation and memorization. There is such a thing as mental laziness. Following Lamarck's theories of use and disuse, you can see how overreliance on digital computation can result in slower thinkers.
 
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