What I am seeing seems to be that dependence on the calculator has short circuited the learning of math and the development of analytical skills. Most students who take high school algebra are not going to be scientists, mathematicians or engineers. These skills are the most important things they should take from their math courses. The computational and analytical skills learned in math often can be applied to a host of everyday problems in business, personal finance, etc. (boldface mine--Darren)
What truly drives me nuts is when students get wrong answers because they don't know how to use the very calculator they brought to class! Then, during a test, they want me to teach them how to use their calculators! It's insanity, truly.
My solution, keeping in mind that I teach pre-calculus and below:
- Algebra I, no calculators except for square roots. And you can bet we go over those square root tables in the back of the book, too!
- Algebra II, you can use it, but it won't help you much. Factoring, conic sections, logarithms--I'll make sure you understand the underlying concepts, and you'll understand them without a calculator.
- Pre-calc, no graphing calculator allowed, unless it has No. 2 stenciled on it near the eraser. You need to understand where those sin/cos/tan numbers your calculator gives you are coming from.
Our calculus teachers, and some others, think I should teach and promote graphing calculator usage in my pre-calc classes. I'd be amenable to it if there were a reason to use a graphing calculator above and beyond solving problems that are best solved by graphing, like sin x = cos x + tan x or something equally silly.
Will this debate ever go away?
9 comments:
The teaching of math is a pet peeve of mine.
My daughter just finished 4th grade. I found out when she was in 3rd grade that the teachers were not allowed to teach multiplication tables by rote, as it doesn't "empower" the children to learn anything. They learned skip counting instead. Which meant that at the end of 3rd grade, she knew none of her times tables. But she did have a nifty little book she'd made with the skip-counts colored in -- 2,4,6,8, etc colored in on the skip counting page for 2. This, I was told, was TERC math, the approved method of teaching math in our local school district. Her teacher confessed to me at a conference that the previous year she got into trouble for sending home practice worksheets of the time tables because she didn't get approval from the district for covering "off topic material."
WHAT????
I also found out that some teachers tell the kids not to worry, when they get to higher math they'll be able to use calculators all the time.
Now, when the kids enter 6th grade-middle school, they are expected to know their times tables. WITHOUT a calculator. So what is elementary school preparing them for???
With such a lack of prep at the lower levels, it's no wonder kids at the higher levels can't add sums to greater than 10 without taking off their shoes to assist in the counting.
I can remember not being allowed to use calculators on algebra, geometry, or pre-calc tests - we were expected to know how to manipulate those numbers. In fact, through most of high school and college, the only time I remember being allowed to use a calculator was in chemistry & physics.
How did we get our daughter to learn her times tables? Schoolhouse Rock, which enabled her to sing them, and within a few short weeks, she knew them without singing them.
People forget that the brain is a much more powerful calculator than anything Texas Instruments ever created - after all, it was a brain that was able to invent a calculator to begin with!
I'm a social studies teacher, but situations will arise inside and outside the classroom where I need to do some quick simple math in my head. I have no problem doing this, but even my brightest students seem incapable of it. Although I'm no math teacher, your ideas about limiting the use of calculators sound solid to me.
Hear hear to both of you!
No! No calculators! They are the spawn of the devil! The only calculators my students are allowed to use are their fingers.
Yes, I do teach my students how to do math on their fingers - especially multiplication and division. (Not just the 9s-trick... ALL multiplication/division.) I find it very sad that I know many 11th graders who don't know even know how to *multiply*.
It's not that difficult to do multivariable calculus without a calculator, so algebra shouldn't be a problem. (Incidently, you don't get a calculator for the CSETs 'cept for the geo. section - which I didn't use, because I couldn't afford one of the 'approved' ones. My calculator was too old.) The only exception I make to this is the 'wierd' numbers (multiplication that involves lots of decimal numbers, trig functions of random angles, etc.)
Square roots you can do by factoring - and I always insist that my students NOT give me a decimal number unless we're using the table in the back.
Bah humbug. Calculators. *sniff*
I teach junior high reading and I am amazed at what simple math the students cannot do! Where I live rote memorization of the times tables is not taught. Note to many in high level administrative positions, first we learn it by rote, then we integrate it into our brain with practice and then apply it to the higher level. At least that is how I learned LOTS of things I still use.
When did rote memorization become a crime? Oh yes, I remember, when somebody decided that schools needed to focus on "higher level" thinking skills. But doesn't one usually build a foundation and walls before putting on the roof, metaphorically speaking of course!
As a math teacher I see a clear use for the graphing calculators.
But, I truly believe that the curriculum can often drive the use of calculators. Do elementary math books call for or direct teachers and students to use them? As far as I can tell (please correct me if I am wrong) they do.
I am often puzzled why elementary schools don't have a "math specialist" on staff or a travelling one. My students tell me that their elementary teachers couldn't teach fractions or other concepts. The topic of estimation seems to have been lost. Finding factors by using the nearest square root as well.
I encourage my students to use their calculators on the SAT's when they are feeling fear - basic math concepts seem to vanish. I focus on using the TI's lists, plots, and other conceptual abilities.
Overall, though, I wonder why the calculators even appear in elementary school. That is quite puzzling.
I do note though, Darren, that the article you quoted from did state at the end that there is a place for calculators.
Of course there's a place for them. The debate is where.
Calculators are actively discouraged in the lower grades in California's K-12 Math Standards. In fact, I don't think the word calculator is used at all until 6th grade (don't have the standards in front of me, but that's my recollection), and I can't even remember why it would be then.
As for using a calculator when students feel fear, when math concepts vanish--they won't vanish when students have mastered them. That's kinda the definition of mastery!
I had a lengthy discussion with a parent on this topic this afternoon. I'll write a post about it at a later date.
Elaine S., in my classes I refer to the calculator as a "devilbox" or as a "boxo del Diablo".
Seriously, I do.
When my oldest child hit third grade, around 12 years ago, I was appalled that instead of using rote memorization, multiplication was taught as a three week unit. Sure, the concept can be taught, but in life there are such things as social security numbers, addresses, alphabets, and phone numbers which must be learned by memory. I was one of the guinea pigs for "New Math". We did multiplication tables writing one a day while the teacher took up lunch money. To this day I can multiply and divide in my head. My own kids have to use a calculator for EVERYTHING. It's great to check facts for accuracy or for balancing a chemistry or physics equation, but honestly, most people should be able to calculate a 15% tip without using one.
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