To Be or NOT to Be...
...by Our Kids
in Doing Math?
by Barb Shelton
(Becky, Amy, Rosemary, and Leah)
When talking about Math, the question of
whether or not it's a good idea to allow our kids to use calculators
invariably arises. Here's what one concerned mom ~ who asked,
and got two different answers ~ wrote: "My 14-year-old son is in Saxon Algebra 1/2
and says his friend's mom lets her son use the calculator for the answers. It seemed strange to me, yet I called our local Math store who sells curriculum
and asked them what they thought. They said, 'The real world
uses calculators, so don't worry about it if he wants to use it, let
him.' Again, I was surprised. So I called Saxon,
and they said, 'No, we do not recommend using calculators until Algebra II.' ... What is your view, as I really don't know what is "OK"? I don't want to be a legalist,
yet isn't there something missing when they don't have to
really "figure" out the answer?"
My response to this is... Yes,
something IS missing ~ a lot of time that they could be spending
elsewhere! No, actually I do have some semi-intelligent thoughts on this which I'll share in just a moment. (Don't get your hopes up;
remember I said "SEMI-intelligent"!
In light of all the other concerns about math, this one about
calculators might seem insignificant, but I don't believe it's
insignificant at all! ... I feel that "Hmmm, well,
it depends" is a good answer!
Depends ~ on what? For
it depends on whether or not she knows how to do a particular operation,
has a basic proficiency in calculating, and could do a long problem by hand if she had to. Like, for instance, if all the calculators in the world suddenly self destructed, or, perhaps, were all kidnapped and held for ransom by angry math teachers who did not like the idea of kids using calculators because of all the unsolved (by your child) math problems that would go to waste. You know, something realistic like that.
OK, let's look at this thing logically (which they say is one of the side benefits of learning math: being better able to think logically and solve
problems.) ... If the student does have a basic
proficiency in the basic
operations needed to make it through life (and also to look good to those who actually believe that knowing how to do complicated math problems makes you a better, smarter person), then why in the world would a person NOT use a calculator? Unless you are INTO math and computation is an area you *need* or (actually) WANT to be adept at, then why waste precious time doing a ton of it? (Some,
yes; a ton, no.) Many of the bigger math problems are nothing more
than lots of tiny addition, subtraction, and/or
multiplication problems in the big problem. (Even division is mostly
multiplication and subtraction.) It's just a matter of knowing WHAT
TO DO with the numbers; i.e. the "formula" or procedure.
By formulas, I mean these... the formula for how how to figure a percentage, how to find a price-per-unit, how to compute the area of a flat thing, how to divide a fraction, how to figure the volume of a
three-dimensional thing, how to compute interest, etc. Here's an example...
Let's say the dimensions of a box that your child just HAS to know the volume of (because they're going to fill it with one-inch sugar cubes) is 38 inches wide by 26 inches high by 22 inches deep. (Yes, this is a LOT of very big sugar cubes; that's why they need a BOX to store them in!) As long as they know they need to multiply the three of these numbers: 38 X 26 X 22 to come up with the cubic inches, then I don't feel they need to do all that computation by hand. I can't think of one good reason they'd need to spend precious time doing that, OTHER than "getting faster at math computations" which they have no reason to get faster at since they'll be using calculators all their life! (Cuz, again, the bigger problems are just lots of little ones, *and*, of course, knowing where to place everything in the proper alignment.) I'd rather they got faster at... memorizing scripture, or cleaning their room, or cooking, or doing jobs around the house, or learning the 50 states so that someone won't think they're stupid just because they were homeschooled... You get the picture.) Now this assuming they already know how to multiply and have gotten that skill "up to par." Like, for instance, if you say (in the normal course of a conversation with your child) "Hey, honey, what's 6 times 9?", and they say "Uuuuh... uh... 53? ... No, 59? ... 54!!!" ~ This would *not* qualify as "multipliably functional."
I know that my answer is not what Saxon would say, but, think about it, who would be working at Saxon? Someone who has gone into the math profession!!!
So as long as they know those four
basic math operations and then the formulas for HOW to get an
answer, I say let your kids GO FOR IT with the calculator! And
if my word isn't enough, here are the thoughts of two other
"I let my children use calculators only when they are learning to use the calculator itself, not learning and practicing math concepts. What I mean is, there are ways to figure problems out on the calculator that help when you are at the store, but they DO need to know how to think it through themselves, just in case...I can't count how many times I have gone in a store during a storm or other "computer down time" and the checkers can't even count out the change without their computers or calculators!"
Amy said: "My "take" on calculators is this... My 14-year-old is doing a combination of Singapore
Math and Saxon Algebra 1. I *might* let him use the calculator
a couple of problems per *week*, depending on how he has done in his
math that day... if
his figuring is up to speed, I might choose to let him use the calculator IF
he shows a complete understanding of how the problem is working. If his
figuring (and/or understanding) needs work, I make him *work* on it! My
13-year-old, doing Singapore and Saxon 7/6, is NOT allowed to use the calculator.
That's just my way of making sure (or trying to make sure) they get the
practice they need. My 13-year-old also does every problem in every Saxon set. My 14yo is reviewing
some Algebra 1 concepts before getting up into new stuff, so we are not
only skipping some problems, but also (gasp) skipping LESSONS. When
we get up to the point where he is learning new material, we'll slow
it down. I, too, believe in repetition, but you have to know your
own child. If he's missing several problems, do EVERY one (but maybe
not a whole lesson per day....do1-15 on day 1, and 16-30 on day 2).
If he has the stuff down pat, feel free to move more
quickly...perhaps doing every problem in the first part of the set
(where the "newer" stuff is), and skipping some problems in the
second half. IMHO, Saxon has plenty of repetition built right in,
even with doing odd problems. Again, that's just OUR way of doing
it...not the RIGHT way!
Rosemary, had this to say:
regards to Math, we live in a calculator world. When I was growing
up there were no calculators, and everything needed to be done by
hand. When we got into High School (we use A Beka for Math) in Grade
8, I started letting them use the calculator for percents only.
There were all kinds of different methods for figuring out
percentages and I figured if they didn't know which one to use, it
didn't mater whether they used the calculator or figured them out. I
did not let them uses the % button, but they had to use the decimal
equivalent. It worked well for us. As things got more complicated,
in the higher grades, they had to do a few problems by hand, and if
they knew how to do it, they could then use the calculator...
As I said we live in a different world today then when we were in
school and EVERYBODY uses one today, and I see no harm in letting
them use it."
And to close this discussion of "to
be or NOT to be" allowing our kids use calculators, Leah shared:
the state required homeschool testing in our area. The testing
company lets the kids (homeschool and public schools) use
calculators IF every child in the room has one, or at least has
access to one. (Some parents will just bring one and tell their
child NOT to use it. It can sometimes help keep the peace.)
The children can use the calculators in the "problem solving"
section, but not on the "procedures" section. So, it will show in
the scores if the child REALLY doesn't know how to do basic math."
That sure makes sense to me! In fact,
come to think of it, it's
pretty much exactly what I said to begin with!
And here is a related issue...
Should I let my child
do just every other problem or page?
And let's end with one last related
concern: The issue of whether or not to let the child do every other problem. To which I say: Yes; once they get it.
Becky's response to this question
was "Yes, I do! My
children do every other problem when I know they KNOW the math concept they are practicing. The deal is, if they miss more than 3 problems, they have to go back and do the rest since it seems they need the practice."
I have heard that Saxon recommends they do EVERY problem for the repetitive learning."
To which I say: "Good for Saxon. ;-) Saxon went to a lot of trouble to write up those problems; they don't want them going to waste. (And furthermore... if you could actually get away with doing only half of the problems, and still come out knowing math (whatever math was in that book), then they could theoretically have made the book half the size!!!!!
And they already made it the size it is and, I'm sure, don't want to re-publish it!!! Or have to figure out which math problems to kick out!)
Patti adds: Saxon
good curriculum tool - but it is just that, a tool. Did you know that
almost every math curriculum, including Saxon, was written for a classroom
in which the students must be kept busy so the teacher can help slower
students? They must also have a significant number of practice so that all
students have a chance to master the concept being taught. In a one-on-one
tutoring situation such as homeschool, it is only necessary to do as much
practice as that particular child needs in order to achieve mastery.
And another mom adds further
insights: "In some families, "every other problem" is a good rule of thumb. Sometimes
whole sections can be skipped, or only some refresher problems worked from
time to time. In problem areas, a whole section might be done until that
concept is mastered. Some lessons can be skipped entirely, if appropriate.
In my experience, I have also seen "readiness" as a factor even in older
children. Some concepts we (in my family) have put away for a season
(sometimes weeks, months, and for some things, it has been years). When we
came back to them, it was easily mastered. Seek God's wisdom; that is the
"common sense" you know is best for your child. Don't put on the world's
burdens and weights - the yoke Jesus gives us is easy."
This article was actually an off-shoot of
with Math" - by Barb Shelton
I got the background from
the kids-on-pencils from: