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Comment by michaelmcdonald | Hacker News Reader

Change is hard. When computers were first introduced to schools there were similar arguments and complaints. When calculators were brought in instead of the slide rule we heard it would be the end of actually "knowing" math. Teachers who are great find ways to use technology and tools available to inspire their students and create engaging lessons. This teacher just sounds resistant to change.

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Two counter-points... 1. Computers in classrooms have rarely, if ever, been deployed to entire classrooms in the way that tablets can be. Typically, you'll see one or two PCs in a class, plus a computer lab. PCs don't distract in the same way iPads can.

2. Calculators do make people worse at math. I saw this first-hand with my son. As he went through school, they used calculators for everything. Students began to rely on the calculators for simple arithmetic and took the answers provided as gospel, not realizing that garbage in = garbage out. He, along with many of his peers, never really developed the fluency in math to say to themselves "hmm, that answer looks suspect. Let me try again."

But you as a parent could easily fix that. Schools don't have a monopoly on education.

Of course, and we did. But, I continue to believe that allowing calculators on ALL mathematics work from a young age does the student a disservice. Calculators certainly have their place, but elementary school arithmetic is not that place.

Agreed. So I taught my eldest arithmetic at home and discouraged the schools from giving him more calculators until the sums involved more than two digits and other operators than the basic four. After the third calculator they got the message. Interesting aside: the teacher couldn't do anything beyond single digit arithmetic without reference to a calculator either. Pretty sad affair, and I really wonder how someone who does not understand the basics gets to be a teacher.

Counter anecdote to your calculator anecdote. I grew up using calculators all through school and excelled in knowing math. Using a calculator did not inhibit my ability to question the result of the calculator whatsoever. I don't think calculators are necessarily to blame here.

Change also doesn't just happen because you dumped a computer in a room. I personally haven't seen a computer used effectively in a classroom, in a large part because the teachers don't know how to integrate them into their lessons. They were given devices and then given no instruction on how to use them.

Education is just barely starting to come out of what I call the "... but on a computer!" [1] era, which is when you try to do exactly the same thing you did before, but now it's on a computer (or a tablet in this case).

There's basically no advantage to taking existing classroom practices, but sticking them on a computer. You'll have to rewrite the entire education process to figure out how to harness computers.

Let me give a concrete example. I am now a fantastic speller, of a language that is one of the harder languages to spell. Am I fantastic because I'm just that awesome? No! Am I fantastic because I have spent years studying lists of words and taking spelling tests? Hell no! I'm fantastic now because every major text input I use now has the red-squiggly line, and the instant I misspell a word and hit space, bam, red line. Backspace & correct. Right-click and select if I really, really can't work it out. (But with backspace & correct actually being way faster, I prefer that.) With instant feedback comes a high rate of learning. I can tell this isn't "cheating", because when I do function in an environment where I don't have this functionality, I retain my spelling skill, the golden standard of whether a skill exists in the tools or the brain. In fact I write many of my blog posts in emacs with no spelling support on, and while I still scan over my posts with a spell checker before posting them, I routinely experience writing several thousand words without a single misspelling, because I have harnessed solid technology to train my brain. I also spell well with handwriting.

This is unbelievably fantastic technology for teaching spelling so efficiently and so effectively that it hardly even need be explicitly taught; sit students down in front of this technology and have them simply write and let the red squiggly handle the spelling training. (You'll still need vocabulary training, but, again, let the red squiggly handle the spelling of the vocabulary while the vocabulary training focuses on meanings.)

By contrast, doing spelling tests "but on a computer" is a terrible way of doing business! First of all, if the students have to "turn in" the test before they get feedback, you've already missed the sub-second feedback rate that would have been so much better anyhow, but second of all, the fact that you're having a spelling test at all is a huge waste of their time. That's the sort of second-order effect we need to be harnessing with computers in the classroom, and we are only at the very, very beginning of that road.

My first grader is just starting spelling tests. He's not quite computer savvy enough to start writing on a computer yet, but you can believe I'll be setting him up with a red squiggly as soon as is practicable.

I still believe computers are going to rewrite education from top-to-bottom, but I find it is proving to be one of the most entrenched, hidebound, nearsighted, and even perhaps terrified of real change elements of society we can possibly imagine. We're so scare of what bad things might happen if we don't stuff a conventional education into our children's heads (moreso than ever, thanks to ever-more test-based education) that we're terrified of experimenting with anything new, and the only acceptable change to the "conventional" education is to precommit even more time to it, making it that much harder to work any experimentation into the system. There are major religions that treat their holy texts as more flexible than the way our culture treats the official line of How Children Are Taught.

[1]: http://www.jerf.org/iri/post/2916

What you're describing as the "but on a computer" era is also known in education as the first stage of the SAMR model: Substitution, Augmentation, Modification, and Redefinition.

This is a well known pitfall in technology integration. I don't think a lot of people in this thread are giving due credit to educators - it's their job, and there's a lot of smart people in education who have just as much common sense as the armchair teachers who think otherwise.

http://www.emergingedtech.com/2015/04/examples-of-transformi...

Educators have their hands tied. We've centralized everything, and the central bureaucracy has decided it doesn't matter how innovative educators can be because the central bureaucracy already knows everything about the best way to teach, and if you deviate from it, you're fired. (A couple of intermediate steps through failing test scores and the consequences, but that's the effect.)

Until the educators get the central bureaucracy off their backs, it doesn't matter what they are capable of.

If you'd like to read my point as being that the central bureaucracy is "the most entrenched, hidebound, nearsighted, and even perhaps terrified of real change" part of the system, I'm perfectly comfortable with that.

This is the number one reason I love static analysis tools like ReSharper for coding. I write a piece of dodgy code, and it tells me "Hey, this could result in trying to access a null pointer", or, "Hey, dummy, this conditional is logically inconsistent and the block below can never get executed" or "Hey, you can rewrite this great big loop with a simpler LINQ statement." Then after a few times of doing this, I internalize the rules, and start doing it on my own.

Yes, very freequent use of computers in classrooms are linked to significantly worse outcomes[0]

0: http://www.keepeek.com/Digital-Asset-Management/oecd/educati...

But calculators actually did negatively impact basic arithmetic skills.

The number of people that can't do 9x14 without reaching for a calculator is scary.

The number of people who need to do 9x14 when they have no access to a calculator is pretty much zero.

To be fair though, that's the math version of "I don't need to know JavaScript at all because I will always have jQuery." Technically accurate but lazy.

Javascript or 9x14 is not the kind of knowledge that's valuable for its own sake. http://unreasonable.org/Feynman_and_the_map_of_the_cat

That doesn't mean it isn't a valuable skill. Mental arithmetic can also improve other brain skills.

No? As an Asian student I have seen countless people try to push their children to exercise arithmetic skills because they believe that does good to their brains. However, it only misleads children to hate "math" and sometimes even their lives based on this the most important subject again and again. Moreover, children would wholly waste their exercised brain on the ruined confidence because some of them just cannot "recite" the patterns well among questions in tests, because you're required to answer too much questions during too short time, which means if you cannot recite the solution patterns from textbook and calculate the answers right at first time, you barely have no chance to try it again. Even those who did excellently in those high-school tests will face another crash at the beginning of university, because the "real math" no matter cares your arithmetic skills, but your abstract thinking and the feeling to grab and deduct rules from axiom. After all, except those real geniuses can conquer these two very different requirements and continuously get payback from that, I don't see any benefits from focusing on arithmetic with so high-strength training.

That's too application focused. The primary value of arithmetic is that it forces you to exercise parts of your mind in a way which would otherwise be difficult.

The same can be said of general mathematics, and literary analysis, etc.

Hum, basic arithmetics is mechanical repetition. There may be some benefit to the brain in doing it, but I'm doubting it until I get evidence.

The main benefit is that knowing arithmetics well makes higher mathematics easier to learn. That's because one won't get distracted doing calculations. That's still true on the calculator era, just a bit less so, thus I do think it's important to learn arithmetics... It just the "it improves your brain" that I find highly suspect.

To this point is there an easier way to do this than mentally do (9x10)+(9x4), which is what I've done since I was in elementary school (29 now)?

Hmm that's interesting - I'd tend to round one of the numbers, whichever is closest to a '5' or '10', to make an 'easier' multiplication, then add / subtract the extra value lost / gained by rounding.

Example 9 x 14 = (<10> * 14) - ([1] * 14) = 140 - 14 = 126

key: <> easier rounded number [] deal with rounding 'error'

I've done that before too, but for whatever reason my mind just defaults to adding two numbers rather than subtracting. Probably either habit or I just find it easier.

Weird, I did it the other way - 9x10 + 9x4 = 90 + 36 = 126

I do the same. However, recognizing you can do that is part of learning arithmetic and problem solving in general. I learned that method at an early age and it taught me that most big, scary problems in general are really just a bunch of small problems that can be identified and solved more easily.

10 times 14 - 14.

(9* 7) * 2 :)

I find (10x14) - (1x14) = 140 - 14 = 126 slightly quicker and less error prone than carrying the ten across the hundred boundary with 9x10 + 9x4 = 90 + 36 = 126, I'm not an educator though so there may be better ways taught now.

But this is wildly off topic, and in reality I'd rather someone knew how to use their calculator or excel or Python to do this sum than know how to do this sum in their heads.

It's important they know the rough answer in terms of scale and shape, so that any mistype or error is quickly recognised, but I don't think it is important to actually know how to quickly do long multiplication in one's head.

You only have two sig figs at best for an engineering estimate you could get close by rounding up to 10x15 which is 150. The error on both terms is gonna round to about ten so subtract both error factors from the 1st order estimate and get about 150-10-10 aka a decent engineering estimate done in the head to two sig figs is 130. Thats not too far from a calculated answer, only a couple percent off, which is smaller than the measurement error.

The most important estimating still, after manipulation of sig figs is knowing which way to bend for the overall system. So say I'm tiling a kitchen floor or buying paver bricks for a modest sized patio. Well, some raw material is going to be too ugly to use and I'm going to screw up some of the trimming and cutting and I'm going to drop some, and the cost of the gasoline and time to drive out to the home center and buy one more (mismatched) tile or brick is very high, so in that scenario I'd buy the 10x15=150 tiles and hope thats enough (I'm feeling lucky today). On the other hand if I had 9 steel chains each rated (by whom? Static or dynamic loads? Point concentrations or perfectly (LOL) distributed?) to 1400 pounds each, I would round way down for safety's sake and not suspend more than 10 x 10 or 10000 pounds on that platform. Even if the chains are rated properly I only need to screw up or fail four of them and the thing crashes down.

Anyway for engineering purposes 9x14 is somewhere around 100 to 150.

This is how arithmetic is starting to be taught in elementary schools now, which unfortunately has resulted in those big Facebook blow ups about how "common core" math homework doesn't make sense anymore.

The number of people who can do it quickly in their head, maybe. I don't know a single adult who would look at that problem and say they don't know how to solve it.

Math is a perishable skill. You get slow at it if you don't use it.

It is just a matter of remembering the tricks. (9x10) + (9x4)

But calculators actually did negatively impact basic arithmetic skills.

Sure, but the interesting question is if they negatively impacted math skills.

Depends what kind of math skills are you looking for.

I remember my classmate, 1st year at university, that passed one of his classes just because his calculator was capable of precise enough numeric integration.

Next semester he was required to construct proofs as well and he flunked the class.

I do 9 x 14 in my head by breaking it down. I assume others do this too. Anyone should be able to break a problem down (pre or post tech generation) and do the small parts, then put them together to answer the bigger question.

In general, that's the essence of learning. If we stop teaching that, then we're all in trouble ;)

9 x 10 = 90

9 x 4 = 36

90 + 36 = 126

Ha, very interesting, I do something very similar, although for multiplication by 9 I would multiply by 10(since it requires no mental effort, you just add a zero at the end) then subtract one. So:

14 x 10 = 140

140 - 14 = 126

> negatively impact basic arithmetic skills

Yep and that skill was rendered completely obsolete. Always remember being told "you won't always have a calculator with you!!" because I couldn't be bothered showing my working on my maths work.

How did that work out... oh everyone now always has calculators with them. Glad I didn't waste my time memorising multiplication tables.

  > When calculators were brought in instead of the slide rule
  > we heard it would be the end of actually "knowing" math.

Plato argued in Phaedrus that literacy would be the end of anyone actually "knowing" anything. Why learn if you can just google^H^H^H^H^H^H read it? Same shit, different millennium.

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