Hand-held calculators are 40 years old, reports the Washington Post.

Educators are deadlocked over whether calculators are helping create a more numerate society capable of claiming the next technological breakthrough or making students technology-dependent and mathematically insecure.

The United States lags in international math exams. Top performers, including Singapore and China, put more emphasis on mental math and memorization and introduce calculators to the curriculum later than the United States does, said Tom Loveless, director of the Brown Center on Education Policy at the Brookings Institution, who has researched how calculators affect student achievement.

Calculator defenders say students can skip “repetitive, drill-based learning” in favor of “creativity and curiosity.”

“We can jump past the grunt work and get to more sophisticated levels of analysis,” said James M. Rubillo, executive director of the National Council of Teachers of Mathematics.

Even NCTM, which recommends using calculators in kindergarten, now says students should learn “mental math” skills.

I once tutored a student who could calculate rapidly in his head but had trouble understanding math concepts. His response to any problem was to multiply every number in sight, because that he could do. I never came across a kid who could understand concepts but couldn’t add or multiply without a calculator. Are there such students?

“I never came across a kid who could understand concepts but couldnâ€™t add or multiply without a calculator. Are there such students?”I’d wager to say “no”, just as I’d wager to say there are no clarinet students who can play expressively without knowing their fingerings. It just doesn’t happen that way. When students are struggling to keep the basics straight in their head, there’s no mental capacity left to grasp any higher order concepts.

“I never came across a kid who could understand concepts but couldnâ€™t add or multiply without a calculator. Are there such students?”

No, but that’s because of the way you phrase the question.

There are many students who understand math concepts but don’t add or multiply very well.

â€œI never came across a kid who could understand concepts but couldnâ€™t add or multiply without a calculator. Are there such students?â€

My dyslexic daughter catches on to concepts very quickly, scores very high on standardized tests, and was in the TAG program. She has an amazing ability to figure things out intuitively. But she is terrible at computation. We’ve done Kumon, drills, special software programs, and worksheets ad nauseum. She understands the mechanics fine, but her accuracy is terrible. Unfortunately, she doesn’t think she’s good at math, because she usually gets the wrong answer.

I know a number of dyslexic kids with the same problem. I don’t know how common it is, but these kids are definitely out there.

When you administer the Woodcock Johnson III Tests of Achievement as often as I do as part of a special ed diagnosis, and then see the final scores–oooh, yeah, there are *definitely* kids out there who struggle with computation but who *do* grasp the mechanics and concepts.

Most of the kids on my caseload who are identified as having a disability in math can understand the mechanics and, surprisingly, do quite well in figuring out the processes of story problems. There’s nothing wrong with their ability to reason in Math. Math Calculation, or Math Fluency, however…I have one student whose parent told me that they had spent hours with flash cards, tapes, posters…everything to get this child to memorize the math tables…and the child couldn’t retain the information.

Quincy’s answer was correct–for the pre-calculator era. I was one of those kids who struggled with the math facts, and calculation interfered with understanding. What we’re seeing now are probably the kids who would not have made any progress in understanding higher math concepts in the past, because they’d still be stuck back in calculation.

I understand the concepts well but the elderly postal worker at my post office can do sums in his head much faster than I can. I became dependent on my calculator in middle school and never learned to add quickly in my head. I can do it but am painfully slow.

The bright side is that I am getting faster with practice. By the way, I have a BS in Mechanical Engineering and an MS in Computer Science. Pathetic, I know.

I think calculators become a crutch to students and they lose the ability (or never get it) to do mental arithmetic reasonably fast.

I also have a dyslexic child who has a strong conceptual grasp of math and weak computation skills. He’s 10 and has completed level 6 of Singapore Math but still adds with his fingers. We use the calculator sparingly.

I never came across a kid who could understand concepts but couldnâ€™t add or multiply without a calculator. Are there such students?”

I have never in all my years of teaching found a college student who could function well with a broad range of mathematical concepts and not add and multiply by hand – including fractions

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Calculators are a blessing if they ae used properly. The TI-83 will invert a 10×10 matrix. I would not advocate teaching the square root algorithm to every student in middle school. The teaching of trigonometry has been revolutionized – my high school text was 50% tables and computations.

But the temptation always exists to take the easy way out in math instruction and people do rather than face the hard truth.

OTOH, there are people with cognitive disabilities who can do things with calculators that they could never learn to do by hand.

Calculators are tools. Treat them as such.

You wouldn’t try to build a house without tools but at the same time there are home repairs that can be accomplished much faster without having to use a tool.

Why is this so hard to grasp?

Perhaps it’s not unlike saying “no need to learn grammar or spelling — the spellchecker catches it for me.”

moreover, the important skill of estimating and checking to see if you’ve not hit the wrong key is critical, if the calculator is to be a useful tool. Missed keys are not qiute catastrophic whlie tpying, (apart the shudder of journalists and editors) but a similar keystroke error on a calculator can send students deep into the land of error (or send the satellite into Mars).

My high school algebra 2 and trig teacher wouldn’t let us use calculators on our tests. It was infuriating at the time, but I sure learned the concepts well!

I agree that calculators should be tools not crutches. Unforunately I see too many kids whose mental math skills are not even close to what they should be.

My sons both did K-5 at a school where the only time calculators were used were on the state mandated End of Grade (and the calculators are mandated for the test) They were regularly drilled in math facts and while I don’t think they do mental math as well as they should, they know their facts better than many of their peers. At their current school both their math teachers (6th & 8th grades) have sent home notes regarding the lack of mastery of the math facts for most of the students.

On the relationship of calculators and dyslexis — my older son is dyslexic and it was thought not to impact his math. However for the past 2 years his teachers and I have been after him for all the “careless mistakes” he would make on his tests. He knew his facts and he understood the concepts but he regularly got incorrect answers due to what appeared to be careless mistakes. However this spring when we went through his re-evaluation for the LD services for his reading/written output it jumped out at me that the transposition and pattern issues he has there might also be manifesting themselves as “careless mistakes” in math. I asked the psychologist if that was possible and she agreed that it was likely. However as his problem relates to transposition, I’m not sure if the calculator does more harm than good as he can still transpose going from calculator to paper.