Should our kids use pencils or keyboards?

In Montreal, most kids have to write on paper using a pencil. They have paper dictionaries. My kids have spent an enormous amount of time learning to write in cursive using pencils, and no time at all (in school) learning to touch type with a keyboard.

I do have pens, that I use to take notes on post-its. But that is about all. All my notes are in electronic form, they are searchable, and I have an integrated spell-check everywhere. I expect that anyone who writes all day solely using pencil and paper is either an artist or someone close to retirement.

On this note, my kids swear that most of their teachers can’t touch type (type on a keyboard without looking at it) while they have been able to touch type before they could write in cursive.

When I was a kid, I owned a typewriter, and later a computer (a TRS-80). Whenever I could, I would do my assignments on a typewriter or computer. The result was invariably nicer looking and more reusable. Typing used to be a skill limited to a few secretaries, but it is now ubiquitous in all walks of life. I never imagined that 30 years later, my kids would still have to write long texts using pencil and paper.

I should qualify this statement: students with diagnosed learning disabilities, and that’s a sizeable fraction of all students these days, can use a computer and a keyboard in class. My kids are envious. Why can’t they use a computer? Why indeed!

They are now learning to do algebra, by hand, as if you couldn’t trivially solve algebraic equations on a computer. I am a computer scientist and I was trained as a mathematician, but I never solve quadratic equations on paper. The risk of mistake is too high. I rely on a computer. Literally, anyone can go to WolframAlpha, enter an equation, and get instantly the correct answer back. The challenge in modern-day mathematics is elsewhere. The dirty error-prone algebra is better done by computers. No engineer or accountant could remain employed and forbid the use of computers, the last engineers and accountants that worked without computers have long ago retired.

There may come a time when our computers stop working but if you think it is likely, you should learn to fight and hunt, not to do mathematics the way people did in 1920.

I could comment at length on what they are learning. Computing the height of a cone given its total area and apothem was a recent problem one of my kids had to solve. And the teachers are eager to set the total area to a nice value like 405.112. Just so that it will look more boring and intimidating. I swear that the problems are so artificial that you’d think these instructors live in another dimension. Who has ever had to compute the height of a cone given that its total area is 405.112. Who?

Before algebra, they had to learn to do long divisions. I had an argument with a teacher about it, when I pointed out that no adult ever does a long division. She pointed out that, sure, they will use calculators, but they need to know how the calculator does it. I objected that computers and calculators do divisions using circuits, that these circuits could be taught… but that it had little to do with doing long divisions by hand.

In any case, I am not alone in thinking that schools are out of touch. Many people are asking schools to become more modern.

In Montreal, a famous education professor, the kind of professors who consult with the government to decide what kids will do, wrote an essay to oppose such reforms. He cites some of my close colleagues who are building up the resistance.

I answered back on Twitter, with some of my usual objections. If educators want to claim that they are in sync with the rest of society, let us at least move beyond the pencil and the paper.

I was offered back a famous study reading texts on paper helps comprehension (as opposed to reading text on computers). I guess that the plan is to raise the new generation of kids of print out all they facebook feeds before reading them? Because let us face it: if you cannot read and understand electronic text you are handicapped, anywhere but in a school.

The fact is that you have to understand text on a screen. There is no choice. I find it scary that the people in charge of our kids would reject screens as a medium for text.

The typical belief of reactionary anti-science educators is that technology is bad for your brain. You will hear stories about mobile phone, the Internet or video games making kids stupid. We can only be saved with paper books and dictionaries. Before that, television was going to destroy us. Long ago, some philosophers thought that books were disastrous: only their voice could carry their wisdom. Successive layers of technology are fought back. That’s fine. What is not fine is the fabrication out of thin air of “facts” to support this gut-driven rejection.

What do more recent studies show? They show that eager students who are given time to become familiar with screens, there is no benefit to paper over screens. Other studies question the superiority of paper: Subrahmanyam et al. found reading the texts on paper did not make a significant difference, compared with computer conditions. Some researchers found that Boys and reluctant readers prefer screens. Porion et al. find that provided we meet all the paper versus computer presentation conditions (text structure and length, screen size, several types of questions measuring comprehension and memory), on-screen reading performances can be improved, and even become comparable to paper-based reading performances. Fesel et al. find that reading hypertext may foster deeper understanding in children.

I could have kept going but as you can see, it is far from an objective truth that people learn better on paper than on a screen. What is certain, however, is that many teachers are unfamiliar with computer technology and prefer to use paper.

How much of the ongoing focus on pencil and paper is a reflection on the preferences and biases of teachers and parents?

What about typing?

Cochran-Smith (1991) showed that when students have to type their documents, they produce fewer spelling errors and produce longer text. This was reaffirmed in more recent meta-analyses by Goldberg et al. (2003) and Graham et al. (2012). A key determinant of success is that students must be good trained to type: don’t compare students who have 12 years of training with pen and paper with students who hardly ever touched a keyboard. Christensen (2004) also found that typing produced better narratives.

Ouellette and Tims (2014) found no difference on a word‐recognition and spelling test between the typing and handwriting conditions. Masterson and Apel (2006) found no difference in quality of spelling between the handwriting and typing conditions.

What about paper dictionary versus electronic dictionary? Chen found that there are no significant differences between electronic dictionaries and paper dictionaries use in comprehension, production and retention of vocabulary although the speed of the former is significantly faster than the latter.

I did about one hour of research for this blog post. The scientific evidence seems clear to me. If you account for various factors, including skills and familiarity, there is no inherent superiority of the pencil over the keyboard, of the paper over the screen. The fact that schools in Montreal provide keyboards and screens to the many students with learning disabilities also supports the non-superiority view.

And yet I am told by teachers all around, by education researchers and professors that, obviously, we use pencil and paper because it is better for the students. It seems to me to be merely a reflection of their own preferences.

They invoke some mysterious knowledge, some untold studies. They dismiss my own survey made entirely of peer-reviewed scientific papers. They argue from authority. We are the educators, we know what is best. They evoke neuroscience, biology, psychology, but without ever sticking to precise falsifiable (scientific) claims.

Yes, we urgently need to reconnect schooling with reality. People use computers to do mathematics or they get fired. People use computers to type and publish documents or they never find work. We spell-check using computers, not with a paper dictionary. We no longer write letters with pen and paper.

Reactionary education experts are not fooling young boys like mines. They know you are disconnected. They know you can’t touch type. They know you can’t find answers outside of books and conferences.

Yes we also need to teach kids about entrepreneurship because they are not going to have factory jobs where they have to write reports on paper. Many of them are going to be self-employed.

Yes, we need to teach them about critical thinking because the hierarchical world of experts is gone and fakenews is everywhere.

But that’s a bit scary, isn’t it? What if the kids start asking for the scientific evidence against using screens to read? What if they actually go through it all? What if they question the conclusions that the reactionary educators have?

No, you don’t need to teach all of them about trigonometry and the volume of a cone. Is that the best you have? It is not good enough. You are failing our kids.

Enforcing the use of paper dictionaries in schools for pedagogical reasons in 2019 is as scientific as rejecting vaccination for fear of autism.

Published by

Daniel Lemire

A computer science professor at the University of Quebec (TELUQ).

26 thoughts on “Should our kids use pencils or keyboards?”

  1. In Italy is pretty much the same, and most of Europe (probably Finland is the only known exception).

    I have also kids in school, and yes, they do long division etc.
    But this striked me: “Yes, we urgently need to reconnect schooling with reality”.

    Well, I understand your point, but which is our connection to reality? I am a full-time SW developer, I’ve worked in a lot of different environments (from Computer Graphics to TLC /Network handling currently Test Automation) but I am pretty aware that I am disconnected from reality, since most of my “reality” is a computer screen, with some information on it.

    My kids (and yours too) are already “disconnected” quite a bit with youtube bizarre stuff/apps/whatever. The question also is “is this the reality we want our kids have?”.

    I agree that we need our schools to teach computing as well (hey my son has enrolled coder dojo!). But we need also (especialy at younger ages) to use the real thing, i.e. drawing with pencil, getting dirty with ink, this kind of thing. Yes, long division is quite boring. Yes, I’ve re-studied it in order to understand if my son is doing it correctly, I’ve forgotten totally them. But all of this gives you a bit of practical wisdom that on-screen does not have.

    So, fine getting computers on school. Fine at using it, but don’t throw away the pencil, and use it for a drawing, for making physical thing looking better, making your (real) world better.

    Yes, school programs should be updated, they are (mostly) the same as mine after > 25 years. But wisely.

    1. There are skills you learn to do well as an adult in this world. These skills do not include “long divisions and writing 5-page essays on paper”.

      That is, I don’t pretend to know what should be taught, but I can quite certainly say that what is getting taught right now is not credibly relevant.

      1. L’apprentissage d’une langue ne se limite pas à écrire des travaux scolaires ou des rapports. C’est une notion liée aux référents culturels, à la langue maternelle, à la communication, à l’individu lui-même. Ça dépasse le cadre strictement utilitaire auquel vous le confinez, et c’est d’ailleurs là que votre propos dérape : un ordinateur est une machine avec un immense espace de stockage. Il suffit de stocker et d’aller chercher l’information selon les besoins. Le cerveau ne fonctionne pas ainsi, n’est pas qu’un outil, n’est pas une machine.

  2. I strongly disagree, of course it’s idiotic to write long texts to paper but for short notes (as you do actually) nothing beats pencil and paper and this can be done ANYWHERE in any context, so mastering handwriting is a must.
    Furthermore, call me an old goat but I cannot really “think” about code on screen despite having a 23″, when faced with a nasty problem I print a few pages to examine the point leisurely.

    1. Yes, short notes are fine, but that is not what high school kids are taught to do. They have to write long-form compositions, with paper dictionaries.

      Printing things out on paper to examine them, to draw on them is fine. But that’s not what schools near me do… they do the reverse: everything is on paper, and only exceptionally is it in computer form. (Except for the students with learning disabilities.)

      I don’t know about you, but coding using pen and paper only would be damn hard for me.

    1. You are correct. I am guessing that educators are worried about what might happen if all computers in the world stop working and we urgently need to do long divisions. My take is that if the zombie apocalypse does come, a better skill to have will be hand-to-hand combat.

  3. My kids have spent an enormous amount of time learning to write in cursive using pencils, and no time at all (in school) learning to touch type with a keyboard.

    Combien de temps estimez-vous nécessaire la maîtrise des touches d’un clavier d’ordinateur? Quel cours préconisez-vous? Savez-vous que la clavier est une assez vieille invention? Que ce ne sont que les lettres de l’alphabet disposés dans un autre ordre?

    I do have pens, that I use to take notes on post-its. But that is about all.
    C’est l’expérience que vous avez. Merci de la partager, mais veuillez comprendre qu’elle n’est pas universelle.

     I expect that anyone who writes all day using pencil and paper is either an artist or someone close to retirement.
    Autrement dit : complètement dépassé, tandis que vous, vous êtes merveilleusement en phase avec la société contemporaine. Et si l’école ne l’est pas, c’est forcément parce que les instituteurs ne sont pas aussi intelligents ni aussi au fait des avancées technologiques que vous.

    On this note, my kids swear that most of their teachers can’t touch type (type on a keyboard without looking at it) while they have been able to touch type before they could write in cursive.
    Si vos enfants le disent, ça doit être vrai. Les enfants ne mentent ni ne se trompent jamais. Moi-même, j’écris présentement ce billet laborieusement avec mes pieds sur une vieille machine à écrire parce que je ne comprends pas trop comment fonctionne un ordinateur. Je vais le numériser après.

    The risk of mistake is too high. I rely on a computer.
    Traduction libre : vous dépendez d’un ordinateur et vous vous êtes délibérément atrophié d’un savoir utile, de sorte que vous n’êtes plus entièrement autonome de ce point de vue.

    Just so that it will look more boring and intimidating.
    Voilà l’argument le plus courant des technophiles (qui n’ont aucune, et j’insiste, aucune notion de ce qu’est enseigner; de ce qu’est une langue; de ce qu’est écrire; de ce qu’est l’apprentissage d’une langue ou d’un système complexe de signes) : c’est plus motivant sur un ordinateur parce que les jeunes aiment ça (faux), y sont habitués (comprenez plutôt : en ont marre, sont saturés de technologie). C’est un des clichés les plus répandus par les gens qui n’ont pas d’expérience d’enseignement.
    I answered back on Twitter, with some of my usual objections. If educators want to claim that they are in sync with the rest of society, let us at least move beyond the pencil and the paper.
    Erreur de perspective : l’école n’a pas à être en phase avec la technologie justement. L’école enseigne des savoirs, pas des outils. L’école enseigne la langue, son fonctionnement, sa grammaire, sa syntaxe, son lexique.

    Because let us face it: if you cannot read and understand electronic text you are handicapped, anywhere but in a school.

    Voilà, on tombe dans parfait délire : sur quoi fondez-vous l’idée saugrenue qu’un jeune élève aura du mal à lire sa page Face de bouc (voilà déjà un exemple d’activité qui n’a pas sa place à l’école) s’il n’a appris à lire que sur du papier? Sérieux? Vous êtes conscient, j’espère, que c’est le cas de toutes les personnes nées avant les années 2000 environ? Vous n’êtes pas conscient par contre, visiblement, que si votre hypothèse est farfelue et carrément délirante, l’inverse, c’est-à-dire que la lecture sur écran donne de moins bons résultats, a par contre été démontré par des études sérieuses, plus sérieuses en tout cas que les nombreuses opinions qui ne se fondent que sur des spéculations et des hypothèses ni vérifiées, ni vérifiables. On appelle ça, chez les profs, des gérants d’estrade. Du genre qui essaie de contredire un philosophe de l’éducation qui réfléchit à la question depuis trente ans.
    Que certains élèves préfèrent lire sur écran n’étonnera personne. Mais c’est absolument sans importance. On ne fonde pas une pédagogie sur ce que veulent les élèves, pas plus qu’on élève des enfants par sondage auprès d’eux.

    I could have kept going but as you can see, it is far from an objective truth that people learn better on paper than on a screen. What is certain, however, is that many teachers are unfamiliar with computer technology and prefer to use paper.
    Vos préjugés vous appartiennent. Des études sérieuses existent (il ne suffit pas d’en lire des résumés sur la toile), qui montrent que ce n’est pas une question d’opinion mais de configuration du cerveau. L’évolution physiologique est un processus très lent et pour l’instant, le cerveau fonctionne encore comme celui de nos parents. On verra ce qu’il en est dans deux ou trois générations, mais de même que le cerveau multi-tâche est un mythe utile aux techolâtres, de même, la lecture et l’écriture sont des procédés beaucoup plus complexes que la caricature que vous en donnez.

    Education experts are not fooling young boys like mines. They know you are disconnected. They know you can’t touch type. They know you can’t find answers outside of books and conferences.
    Merci de mépriser ma profession aussi candidement, de faire dire ce que vous voulez aux études que vous citez, d’ignorer ce que disent les sciences cognitives et les neuro-psychologues et de vous positionner en tant que grand spécialiste de sujets que vous ne maîtrisez visiblement pas.

  4. It’s easier to cheat with ^C^V than with pen and pencil.
    There are people who do algebra all day long, for example carpenters and computing cone size on the fly, without tools other than plain calculator is relevant.
    To read a book you need to use something like 100 muscles. For screen reading that’d be 30. Ancient Greeks (in Peripatetic scool) already knew that brain works better when you’re moving more muscles. Paper books give better cadence – in computers we’ve lost the invention of codex book over scrolls. Not to mention Dots Per Inch, kerning, Frames Per Second and other technicalities which stumble in a way.
    Paper dictionaries are worse than computer ones because dictionaries are used to quickly find relevant definition or translation and carry on with the proper work. Latency matters here.
    Recently US marines reintroduced compulsory celestial navigation because one cannot trust GPS. Be weary of computer optimism.
    ,,There are skills you learn to do well as an adult in this world. These skills do not include “long divisions and writing 5-page essays on paper”” – I’d say it helps in the Darwinian sense when you write a letter to your girlfriend by hand 😉
    All in all I strongly agree that schools should revamp their curricula, but not if favor of screentime. For example: instead of protozoa it should learn how medicines work. Instead of abstract math, do tangible “let’s compute size of Earth by watching sunset” or “when we’d suffocate if we sealed the classroom well”.

    1. I doubt the ability of most adults, including carpenters, to figure out by hand (with or without a school calculator) the correct height of a cone given its apothem and total area. I’d be very nervous when working with a carpenter that does not use software to solve such problems. And the carpenters that I have seen don’t have calculators. They have Internet-connected smartphones. They take pictures and they share them. They use web applications.

      I suppose that if a carpenter has to regularly solve the cone-height problem, then he will have the formula worked out in advance. Even so, they will be far better off relying on a computer to solve it. Human beings make mistakes too easily when applying algorithms. We are just not as good as computers at that.

      Regarding the benefits of paper books… The evidence from the several papers I have cited is that once you account of greater familiarity and subjective taste, there is no substantive benefit to the paper book over the electronic documents. And if you are using electronic documents for work, you know that they have massive benefits: a common task, search for occurences of a term, is much easier with electronic documents, we can carry and transmit electronic documents much more easily. The era of paper reports and books is gone. We all have to work with electronic documents (except maybe retirees, artists, and some teachers). If schools are to prepare kids for the real world, then they have to adopt electronic documents.

      I find it interesting that people fear dependence on computers. Yet they somehow do not fear our dependence on cars. That is, we do not teach kids of handle horses and carts. We don’t train them to walk long distance with goods to sell. We are fine with assuming that they will enjoy modern means of transporations.

      I think we have to equally assume that connected computers are here to stay.

      Yes. Some people are trained to handle horses, do celestial computations. Some people need to do these things. Someone needs to know about long divisions. Someone needs to know how to hunt with a primitive bow.

      But let us not be fooled: you don’t forbid software dictionaries for neurobiological reasons. You are forbid them because you are a reactionary, a luddite.

  5. I have (more or less as a hobby) decided to learn a lot of “ancient” arts, such as horse riding and handling, basic farming techniques, the use of antique black powder firearms (that I could in a pinch make my own powder and ammunition), and the use of various formula and methods of computation., which is strange considering I write software for a living (and have done so for over 30 years).

    That said, I love my kobo e-reader, and I hate writing anything beyond a brief note in cursive. If anything, I would like to have an e-ink tablet/typewriter with a touch surface for instant note taking and serious writing. Sadly, the e-ink typewriters out there are either not yet there, very expensive, or very slow.

    None of this takes away from your thesis – that educators are way behind. Some teachers know that. They are as frustrated as you are. However, a note of caution is necessary – one of my kids schools took the plunge by way of introducing iPads to all kids. These are expensive, and come with little in the way of supportive software and infrastructure. I think the cheaper Chromebook, with its well thought out educational support ecosystem is a far better choice and should be in all schools from an early age.

    1. These are expensive, and come with little in the way of supportive software and infrastructure.

      Schools in Quebec have benefited from overly generous funding for technology… smart whiteboards are found nearly everywhere in primary schools. My youngest boy has an iPad from the school.

      Throwing computers and fancy hardware in the classroom does not make it up-to-date.

  6. Re those carpenters: cone computations are rare although sometimes needed, but Pythagorean theorem is used every day. If they didn’t know Euclidean geometry exists or specific equations, they’d do random cuts here and there until it fits. Or reinvent ancient math.

    Re paper vs. digital books: there are different use cases. Sometimes latency, searching, browsing and indexing is the key and then digital wins. Sometimes it’s ease of immersion, flow, focus, memorizing, making short notes – then paper wins. The scientific research on that matter is in field of psychology, made in the middle of reproducibility crisis so I would be reluctant to rely on it.

    Re dependency on computers vs. dependency on cars: we do teach our kids how to crawl, walk, run and bike. And we encourage them to prefer that rather than being a car passenger or later a car driver. First natural mobility, then artificial mobility.

    All the above arguments put the problem in wrong light and leads us to wrong divisions. I also believe that schools should be modernized but I’d rather see the problem not in conservatism but in the very old spirit of enlightenment entangled with absolutism and scientific reductionism (in other words: give them tools and be a moderator of socialized work, rather than one-to-many ivory tower guardian for single academic specialization).

    1. Carpenters, machinists, engineers, architects and even many artists know about Pythagore, and it is fine to discuss Pythagore’s theorem in class. But that is very much not what I was stating. I am willing bet good money that very few carpenters could compute the height of a cone given the total area of the cone and the apothem, especially if the total area is something like 405.112. This is the exam question my son got in third year of high school last week. It is quite a bit harder because it is the total area of the cone.

  7. I believe the point is not about pencils VS keyboards, it’s about change. Most people are reluctant to change, or even afraid of it. Change means that your knowledge and expertise will go away, maybe your job, and why not your life-long purpose too? You must start from scratch, you’re probably less nimble or have less time to learn new things, etc

    Professors are just not different from most people.

    My opinion is that schools should focus on teaching methodologies to learn (whatever it is), how to observe, analyse and validate, how to adapt. Also I strongly believe that all schools should not teach the same things in the same way, in order to have a more resilient Educational program.

  8. So I do a lot of writing directly in Latex when working out equations. All the same, there are times when picking up a pen and writing a whole bunch of paragraphs + simple diagrams cannot be replaced.

    I encourage my daughter to pick up her drawing book and sketch whatever her heart desires. She can also create amazing drawings on an IPad, but only a high end IPad with a high end stylus.

    I figure, encourage the analogue, as there will always be time for digital.

    Now I admit I am enjoy a bit a red wine while listening to analogue records, and will read the full article+comments. 🙂

  9. Still drinking red wine and working my way through the article …

    Years ago I worked out the cubic polynomial expansion in the interval 0-3 using pen and paper. Was this silly? Maybe. Perhaps I could have looked up the answer. But assuming the interval 0-3 simplified the algebra. And so I coded up the result with Doppler shifts on the interval 0-3. Pen and paper sometimes precedes the digital.

  10. I haven’t done long division in years, but I’m sure I can still do it. Only because I forgot how ever summer in elementary school and had to relearn it. Is that an essential skill? Maybe not. But I think it is a usefull example that teaches our analogue brains how to think.

  11. So I leave you with another example …

    We have our daughter enrolled in Spanish immersion even though my scientific brain thought this was inefficient and pointless. In my case, afterall, I would have been lost trying to learn math in Spanish.

    But…

    The school district swears that language immersion helps students develop in intangible ways. They catch up to the English students in English after a couple of years, afterall. Pen and paper is a skill that needs to be learned, just like any other skill. There is also no apparent point to learning music, and creating art in an ensemble. There is more to life than the digital.

    –Matt

    1. The school district swears that language immersion helps students develop in intangible ways. They catch up to the English students in English after a couple of years, afterall.

      My understanding of the litterature is that kids who skip grades for whatever reasons, quickly catch up, and kids who retake a year basically see little benefit. Home-schooled students, students who skip schools, basically outdo school-educated students in college, after you have accounted for all variables you could. (https://www.tandfonline.com/doi/abs/10.1080/15582159.2015.998963)

      What does that tell you about the value of the education provided by schools… that you can basically skip it and do just as well or better?

  12. Indeed our “education” system is hardly more than slightly inconvenient day care, that serves mostly to create a lowest common denominator of pliant worker-bot for yesterday’s industry.

    The problem is not so much that this is so – it is that we are not in absolute disgust at it – or even willing to take an honest look at it.

  13. Educational research has moved on. A couple of references to study:

    See “Four-Dimensional Education: The Competencies Learners Need to Succeed” from the Center of Curriculum Redesign, which provides a comprehensive framework for what skills the 21st century learner needs:
    https://curriculumredesign.org/our-work/four-dimensional-21st-century-education-learning-competencies-future-2030/

    From Transcend, guidelines for schools:
    https://static1.squarespace.com/static/55ca46dee4b0fc536f717de8/t/5be841ac4d7a9c5e1eeea528/1541948239807/Designing+for+Learning+Primer+Transcend.pdf

    From Summit schools, guidelines for content and teachers:

    https://summitps.org/wp-content/uploads/2018/09/The-Science-of-Summit-by-Summit-Public-Schools_08072017-1.pdf

  14. My personal experience is that writing somehow enables some parts of my brain and I can focus, think and store knowledge better.
    I am proficient at touchless writing yet I always prefer to take written notes on courses, trainings, meetings etc.
    Same with quick and dirty sketches at job, whiteboard is so much better and faster than computer diagrams.

    I would say I “think by writing”, if I swap out a problem from memory to paper/whiteboard, it is easier for me to come up with a solution.

    When I was a child I had no computer at home yet my after-hours with computer at school were the most efficient and intense time because I always come with a TODO list, sketches etc. on paper and reached flow state easily.

    As for division, I think it doesn’t matter people do not divide by hand anymore. It is just a way of introducing idea of basic algorithm that solves hard problem by following strict set of rules and by reducing a larger problem to a sequence of simpler, already known operations.

    I agree paper dictionary makes little sense today. It is a basic key-value lookup and it is faster to just google it.
    But when I think more about it, searching in a paper dictionary actually teaches a kid how to efficiently search through a lot of alphabetically sorted text.

  15. It’s not about doing long divisions by hand for practical purposes, it’s about understanding how they work. Same for quadratic equations. If you don’t understand these basic things, then you can’t, for example, become a mathematician. It’s like a carpenter who never learnt how to use a hammer and a screwdriver.

    That’s what school should be about: Understanding how things work, and you’re not going to if you have a piece of software do everything for you. The teacher might as well give you the answer of problems right away.

    Think about it, as someone who was trained as a mathematician, you understand those quadratic equations and can write a solver program for them. You can’t do that if you don’t know how they work.

    1. It’s not about doing long divisions by hand for practical purposes, it’s about understanding how they work.

      If this was the goal, you’d think that students would be asked to derive the long division algorithm from first principles, or to prove that it is correct using a proof. Of course, this does not happen. The general trend is to go toward “directed instructions” which involves simply memorizing the process without any reasoning whatsoever. This is the general trend because it works: if your goal is to apply the long division, then you do not want to be thinking too hard about why it works, you want to focus on rote execution.

      If you don’t understand these basic things, then you can’t, for example, become a mathematician

      You can also say that you cannot be an accountant if you do not understand two-entry tables. Yet we do not teach two-entry tables in schools.

      Why don’t we teach two-entry tables?

      I could go on. There are many ideas that are foundational to our civilization (including two-entry tables) that are not taught in schools.

      You refer to software… My favorite story is how this teacher I met taught that learning about long division would help you understand how calculators do a division. But, of course, calculators do not do a long division, they use a circuit-based approach… and students are not taught about circuit design.

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     [This is not a link](http://example.com)

To create not a block, but an inline code span, use backticks:

Here is some inline `code`.

For more help see http://daringfireball.net/projects/markdown/syntax