Is there any research about doing math with pencil and paper vs. calculator?

[Laurie4b]

I'm not talking about using a calculator for complex decimals, etc. but I see kids wanting to use their calculators to do a problem like 275 divided by 25. IOW, they are skipping the process of writing down the steps and then (unsurprisingly) don't remember well how to do that kind of problem). 

 

I know there is research about handwriting notes resulting in retaining more than typing notes, but when I looked, I didn't find similar research about calculators. 

[Petrichor]

Not research, but if they are doing it by hand, they are being exposed to/practicing math facts more frequently. If they are practicing the facts, they will be able to do the math in their head sooner. 

 

In "real life", there are times when a calculator will not be available. There will be times when using a calculator will only slow you down.

[wapiti]

Handwriting vs typing (same mental output - letters, words, sentences) is not analogous to math by hand vs calculator (entirely different mental output - actual calculation vs pushing buttons).

 

FWIW, the example problem is too simple.  For 275 divided by 25, I would expect that to be done mentally.  The number sense that comes with such practice is invaluable IMO.

 

More generally, yes, it would seem obvious that the steps of long division might be forgotten if they're not practiced once in a while.  That said, my ds13s are using calculators much more extensively than I'd like at their school in algebra and geometry (using Glencoe-McGraw Hill Common Core texts) though I'm not at all concerned that they'll forget long division - they've been doing it by hand for so many years.  If a really long amount of time went by, I suppose if it came up they might take a few seconds to recall the steps.

 

 

[Arcadia]

All research I have seen so far are inconclusive in that there is no significant negative to calculator use and positives for math anxiety/phobic or children with math LD.

 

This is one of the papers I found and there are many similar ones

http://archives.math.utk.edu/ICTCM/VOL13/C025/paper.pdf

 

My opinion is that calculator is only useful for the computation aspect of math and science. If the person does not set up the problem equation correctly, the calculator is going to be just garbage in garbage out.

 

For example, a store is having a 40% off store wide. The customers would still need to know what numbers to punch in their calculator on their phones if they don't want to work the final price out mentally.

[scoutingmom]

The problem I can see with calculator use is that it us easy to make mistakes, and people often don't seem to have enough number sense to see that the answer doesn't make any sense.

 

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[regentrude]

No research, but observation of a calculator dependent cohort of students whose math programs introduce calculators very early in school.

They do not develop a strong number sense, are incapable of doing mental math because they are not used to it, have difficulties doing simple calculations with simple numbers quickly and correctly, and have frequently never understood math conceptually.

We deal with the fallout every day at college.

 

 

[Guest]

This is how we do it, with no LDs present:

 

Calculators can inhibit deeper understanding of the process going on. We don't allow them until higher level algebra and calculus, essentially, at the specific instruction of a trusted math instructor. For the rare computation before that which requires a calculator we may make an exception but that's about it. We do allow slide rules for certain things as well, but these are more a combination of computing with the logarithm and not just entering in numbers and spitting out an answer divorced from the process behind it.

 

Even in their math thus far the calculator chapters we have done as mental math and they handle it very well.

 

None of my kids have learning disorders, I'm talking neurotypical or gifted children.

 

Here are some articles discussing part of the subject:

http://ohsjagwire.org/2334/feburary/calculators/

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4129781/

 

Here is a nice little pro and con article:

http://education.cu-portland.edu/blog/classroom-resources/pros-and-cons-of-allowing-kids-to-use-calculators-in-math-class/

Edited April 17, 2016 by Arctic Mama

[kbutton]

An acquaintance teaches calculus at a local school district with lots of math and science families (parents are chemists, engineers, etc.). She is always pulling out her hair over students who can't divide 144 by 12 without a calculator or who can't extrapolate on a fact that is ten or one hundred times bigger than something in the 10 x 10 range. She pretty much blames it on calculator use.  

[Lanny]

No research to link to, but IMO, Math Instructors MUST require that their students write out the problems and submit that to the Instructor.  That is what DD is always required to do.  My hope is that if her Instructor saw DD doing something wrong, she would correct it and explain to DD what DD did wrong.  I remember Slide Rules and  when I was young, we didn't have Calculators...  Calculators have their place, but one should know how to solve the problem, without a calculator.  Especially someone studying Math...

[Ali in OR]

I don't count as official research, but my humble opinion is that many schools turn to calculators too early. Around here it is 3rd grade. I think calculators should not be used in elementary school except for problem-solving situations where the focus is more on how to solve multi-step word problems rather than brute calculation. In our homeschool, that meant calculators were fine for the Singapore Challenging Word Problem days, but not for everyday math lessons. I believe that doing multi-digit multiplication for instance is the practice that is needed to finally get the multiplication table memorized solidly. I too was a high-school math teacher frustrated by students who had to reach for a calculator to divide both sides of an equation by 3.

[wapiti]

I want to add another comment based on what I see from my boys' school classes.  Unfortunately, the problems are written such that it would take much longer to come to an answer without the calculator.  There is no attempt by the text writers to select less-tedious numbers or select numbers that would motivate a student to practice manipulating numbers to further develop number sense.  (ETA, yeah, I miss AoPS)

Edited April 17, 2016 by wapiti

[Laurie4b]

I want to add another comment based on what I see from my boys' school classes.  Unfortunately, the problems are written such that it would take much longer to come to an answer without the calculator.  There is no attempt by the text writers to select less-tedious numbers or select numbers that would motivate a student to practice manipulating numbers to further develop number sense.  (ETA, yeah, I miss AoPS)

 

I've seen this, too. It's one thing I dislike about Khan Academy. When introducing a new concept, they don't give kids easy numbers first until they get the hang of it. So calculator has to come out right away. 

[Arcadia]

I've seen this, too. It's one thing I dislike about Khan Academy. When introducing a new concept, they don't give kids easy numbers first until they get the hang of it. So calculator has to come out right away.

Khan Academy is favored towards test prep. Tests favored use of calculators for maximum scores unless the child has fast computation speeds. My oldest is faster mentally then pressing the calculator most of the time while my younger use the calculator to beat the clock for timed tests. Like I said earlier, the calculator is a means to an end. What needs to improve is teacher's math education.

 

If you want to avoid using a calculator, singapore primary math and MEP for K-6th can be done without calculator. AoPS and singapore additional math requires minimal use of the scientific calculator. Old calculus textbooks requires scientific calculator only.

The current public school textbooks from algebra and up have sections on using graphing calculator in most chapters. You can always skip those exercises which are for practicing the use of graphing calculators.