Starting Algebra Young...and Forgetting Arithmetic

[SierraNevada]

As I was browsing through DSs current math book- LOF Decimals and Percents, I saw that the author was telling students that this was the last book in which they wouldn't be allowed to use a calculator. Then it dawned on me that if DS finishes all of elementary math (not that soon as we are going deeper with multiples cirriculms) in the next year or so that traditionally he will entered the "Calculator Use Okay" zone. Then it scared me that after so few years of doing long math he might be more prone to forget it. I admit I had to quickly review long division before I taught him as well as long division with two decimals. But I had three times as many years drilling that stuff into me at his age.

 

So the question is-- do you allow your very young algebra ready children to use a calculator? I just fear that math fact fluency would really suffer as well as algorithm memory.

[Crimson Wife]

No, I do not allow calculator use prior to Algebra 2 with limited exceptions. Talent search testing (EXPLORE, SAT) I allow calculators and have my student practice by working through some of the Singapore CWP problems. Also, there are certain really tedious calculations where I allow calculator use after the student shows me that he/she knows what to do (arithmatic means, calculations involving higher-power exponents, certain roots problems, compound interest, etc.)

[mom2bee]

If you use a calculator then you could continue to do a few review problems long hand on a regular basis. So, maybe 3x a week, do 5-15 long arithmetic problems by hand and show your work. Do one or two addition, subtraction, multiplication and division problems. Then throw in some arithmetic with fractions and decimals and a couple of word problems.

 

[Dmmetler]

AOPS is designed so that if you think a calculator will help, you're going down the wrong path, and most math competitions don't allow calculators, so DD rarely uses one. She could for LOF, I guess, which she does on her own, but she usually doesn't bother to find the thing. It's actually been somewhat a problem in the other direction-that on the EXPLORE, when she's allowed to use one, she often does things by hand that would have been quite amenable to calculator use and would have taken much less time.

 

 

 

[boscopup]

I don't allow a calculator. I also have my son do elementary CLE Math to keep stuff fresh. He's currently working through the 5th grade CLE while doing AoPS Prealgebra (and AoPS is designed for no calculator use needed... if you need to divide two large, unwieldy numbers, there is an easier method to find).

 

The CLE lesson takes him about 10-15 minutes to complete. He likes having that "easy" part of his day, and it's helping him stay automatic with the basics.

[regentrude]

There is absolutely no reason to permit children to use a calculator for algebra 1.

My DD has not needed a calculator through calculus, except for a very rare few problems and for her high school physics and chemistry, and for a few problems on the SAT.

Any math curriculum that emphasizes calculator use is doing a students a great disservice. I see calculator dependence in my college students all the time, and yes, they forget basic arithmetic.

The best thing you can do for your kids long term math mastery is to hold off on calculator use for several more years and select a program that is designed to teach math without a calculator. AoPS works very well for that; in fact, if the student feels the need to use a calculator with AoPS it is a sure sign that he is on the wrong track.

[quark]

DS is self teaching calc now and so far no calculator use for math unless when he is curious (or I am curious) and then he uses geogebra but he doesn't do that for assigned problems. We allowed calculator use for algebra-based physics (some problems not all) the year after he finished algebra 1 just because he was handling 4 math-related subjects at the time and it helped with speed and reduced some of the computation frustration. He otherwise mentally calculates or hand computes and hand draws all graphs...takes him a long time sometimes (he wasn't a perfectionist until he started drawing graphs lol) but it's so worth it. Only disadvantage I can think of is that he forgot he could use the calculator for Explore and it might have helped him beat the clock if he had, plus he had to be reminded several times that he could use the calculator for SAT practice tests despite reading the instructions that said he could do so. He has said numerous times that it feels like cheating to use the calculator. But really no biggie so far. This is my slow-working, fine-motor challenged boy whose handwriting speed is not at all reflective of his mental processing speed.

[lewelma]

No calculator use here.  In fact, we skip the limited calculator-specific sections in Singapore Discovering Maths because my younger has found that once he uses the calculator for a few days he hates having to go back and do it by hand.  Better to not have the comparison, and make the hand calculating more palatable while he is still mastering it.  It was ds who suggested skipping the calculator sections.

 

Ruth in NZ

[SierraNevada]

I'm so glad to hear of everyone forgoing the calculator.  I didn't know that AOPS was designed for use without one. I am thrilled to hear that. 

[EndOfOrdinary]

I only allow my son to use a calculator for chemistry work. It is applied algebra, so I don't know if you count that. He gets to use it because many of the problems in Apologia are designed to require fairly annoying decimal computation which are then rounded to a few decimal places. Since in chemistry I want him to understand the concepts and how to work with them, he gets to use a calculator on a few problems so he does not get bogged down.

 

We use AoPS so no calculator in math.

[EKS]

I allowed a calculator starting in Algebra I, but I also made my son do a Big Huge Review of arithmetic with ALEKS at the same time.  That was much more difficult that it would have been not using the calculator for algebra.

[Gil]

You can get through all of highschool (possibly undergrad) math and science with out using a calculator. Certainly not using one so much that it effects your mental/written math abilities. Some curriculums specifically build in calculator questions and exercises but you could excise them easily enough. You should not need a calculator for algebra 1 or even most of 2. You might find it handy in PreCalculus (or which ever class you do a ton of graphs and applications in) but...it is 100% optional for the core skills that those subjects require.

[raptor_dad]

I only allow my son to use a calculator for chemistry work. It is applied algebra, so I don't know if you count that. He gets to use it because many of the problems in Apologia are designed to require fairly annoying decimal computation which are then rounded to a few decimal places. Since in chemistry I want him to understand the concepts and how to work with them, he gets to use a calculator on a few problems so he does not get bogged down.

 

We use AoPS so no calculator in math.

 

When I was back in school taking undergrad biochem courses around a decade ago, no calculators were allowed on exams. You had to be able to do arithmetic and other basic math like approximating logs and such for *many* of the problems. This was an issue for some students.

 

I think calculators are fine but they shouldn't become a crutch.

[Kerileanne99]

When I was back in school taking undergrad biochem courses around a decade ago, no calculators were allowed on exams. You had to be able to do arithmetic and other basic math like approximating logs and such for *many* of the problems. This was an issue for some students.

 

I think calculators are fine but they shouldn't become a crutch.

Funnily enough, hubby teaches chemistry at Uni level, and I tutor it...the students are allowed calculators (in fact I have not seen any who did not use them.) The problem the students have is rarely the chemistry, but the math. They practice plugging the numbers into the calculator but have no idea what they are doing. They might be trying to calculate a mole of carbon and be off by orders of magnitude...and not even realize.

I think using calculators, even in chemistry, actually decreases the understanding because students get used to 'plugging and chugging' and don't stop to think. It leads to a total disconnect, even if they are reasonably good in math.

 

And I cannot tell you how many students have paid me, at $30-$40 per hour, to teach them how to do log math in chem...same for hubby. Students have no idea what to do and don't even want to know, other than which buttons they have to push to get the answer if an exponent or log show up on their exams.

[EndOfOrdinary]

When I was back in school taking undergrad biochem courses around a decade ago, no calculators were allowed on exams. You had to be able to do arithmetic and other basic math like approximating logs and such for *many* of the problems. This was an issue for some students.

 

I think calculators are fine but they shouldn't become a crutch.

  

Funnily enough, hubby teaches chemistry at Uni level, and I tutor it...the students are allowed calculators (in fact I have not seen any who did not use them.) The problem the students have is rarely the chemistry, but the math. They practice plugging the numbers into the calculator but have no idea what they are doing. They might be trying to calculate a mole of carbon and be off by orders of magnitude...and not even realize.

I think using calculators, even in chemistry, actually decreases the understanding because students get used to 'plugging and chugging' and don't stop to think. It leads to a total disconnect, even if they are reasonably good in math.

And I cannot tell you how many students have paid me, at $30-$40 per hour, to teach them how to do log math in chem...same for hubby. Students have no idea what to do and don't even want to know, other than which buttons they have to push to get the answer if an exponent or log show up on their exams.

Oh, he will not always be able to use them. Right now there is just a disconnect still occurring between his conceptual ability and desire to learn versus his ability to quickly divide by complex decimals. For right now, the calculator allows him to progress at a pace that works until his speed of computation increases enough to carry him through. It is much like how I scribed his narrations when he first began composing essays. My writing allowed him enough time to catch up on the physical act of writing, while still being able to progression his knowledge of composition.

[Kerileanne99]

 

Oh, he will not always be able to use them. Right now there is just a disconnect still occurring between his conceptual ability and desire to learn versus his ability to quickly divide by complex decimals. For right now, the calculator allows him to progress at a pace that works until his speed of computation increases enough to carry him through. It is much like how I scribed his narrations when he first began composing essays. My writing allowed him enough time to catch up on the physical act of writing, while still being able to progression his knowledge of composition.

I am positive you are well-aware of what your kiddo needs and am sure you would never allow your child to use it as a crutch:) I absolutely wasn't directing this at you, but rather a complaint about calculators I general. My kid is very young and I have already learned that lots of adaptations/concessions must be made to allow them to continue to learn whilst their bodies and endurance have a chance to mature! There is a big difference between that and kids who spend their high school years learning to push buttons rather than learn math, lol!

[Dmmetler]

How does this compare to statistics? My DD is playing with it now, and her bio mentors have actually encouraged use of R and stat calculators to play with it now, since she doesn't yet have the math to necessarily do all the calculations herself, but is trying to understand what research is showing.

 

 

 

[Kerileanne99]

How does this compare to statistics? My DD is playing with it now, and her bio mentors have actually encouraged use of R and stat calculators to play with it now, since she doesn't yet have the math to necessarily do all the calculations herself, but is trying to understand what research is showing.

Ha! The thought of trying to do stats computations without a calculator is actually high up there in the realm of real torture for me. That is one area of math I can't imagine doing without a calculator:)

My stats prof in college actually had us work them by hand the first couple in each new area, then allowed calculator use so we would appreciate/understand more.

Easier things like mean, mode, simpler calculations fine, a calculator is not necessary...but R data analysis? Ugh!

[raptor_dad]

Funnily enough, hubby teaches chemistry at Uni level, and I tutor it...the students are allowed calculators (in fact I have not seen any who did not use them.) The problem the students have is rarely the chemistry, but the math. They practice plugging the numbers into the calculator but have no idea what they are doing. They might be trying to calculate a mole of carbon and be off by orders of magnitude...and not even realize.

I think using calculators, even in chemistry, actually decreases the understanding because students get used to 'plugging and chugging' and don't stop to think. It leads to a total disconnect, even if they are reasonably good in math.

 

And I cannot tell you how many students have paid me, at $30-$40 per hour, to teach them how to do log math in chem...same for hubby. Students have no idea what to do and don't even want to know, other than which buttons they have to push to get the answer if an exponent or log show up on their exams.

 

 I totally agree. At UWashington, the med school departments like biochem do a great job teaching their undergrad courses. But, the professors really hate dealing with the undergrad issues like grade grubbing and cheating. The calculator ban is mostly to prevent cheating, since on high end calcs and devices you could load in notes, etc. Rather than try to manage what types of devices are allowed it is easier to just ban them. So, the takeaway isn't that you shouldn't use a calculator on homework or in lab. It is that there may be times when you need to be able to do all the work w/o a calculator.