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Thread: Might Kids do better if?

  1. #1 Might Kids do better if? 
    Forum Senior chero's Avatar
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    Might kids do better in math through out their educational path and future career paths if the basics of math were taught with out paper? instead of writing the problems down, students as young as 5 to as old as 12 would rely on observing and calculating quick operations purely in their heads. paper could be introduced as a helper for longer and more demanding equations.


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    Well, the Koreans (East Asia somewhere if I'm wrong on that) certainly used to do that in the very early years.

    It's a very good way for learning tables, number families and the basic calculation arithmetic. Even two step problems. But it really shouldn't be pushed beyond that.

    At some stage everyone has to learn, no matter how clever or skilled they are, that problems must be written down. They should be written down clearly and the steps used to solve the problem must be set out in standard format. It's better that you have that particular skill taught, then learned and mastered, so that it is automatic long before you have to work with algebraic expressions.


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    Forum Radioactive Isotope cosmictraveler's Avatar
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    Why not allow the use of computers so that they could just remember what formulas to use then "plug in" the numbers to get the answers? It seems that today there's few people using a pencil and paper in many fields any longer and are only using the PC to do work on.
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    I don't think the struggle in math lies in paper or writing. Many need to be able to see and study the problem before they can easily do it in their heads. The text books help as well. More mistakes are likely to happen if they rely on their memories. I don't know if they're learning much if a computer does it all for them. Nevertheless, the higher you go in math, the more a calculator is encouraged. Even the top mathematicians in the world still needs to write things down with the accompanment of a calculator. Improvement on focus is at least a step in the right direction and kids are hard enough to keep still.
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    Why not allow the use of computers so that they could just remember what formulas to use then "plug in" the numbers to get the answers? It seems that today there's few people using a pencil and paper in many fields any longer and are only using the PC to do work on.
    Where would students get their "feel" for numbers from. Maths is not mindless application of formulae. How does someone who's "learned" maths this way know, more or less instinctively, that the answer shown on a machine is more like the distance between earth and the sun, rather than earth and the moon? (And therefore the number displayed is more about a typo than it is an answer to the set problem.)

    I have a lot of trouble getting percentages and orders of magnitude through the resistant skulls of students whose previous maths learning has been on this formulaic basis. I wouldn't want it to become the accepted or acceptable standard. Just ask anyone who has to put first year university students through remedial maths to see what they think.
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  7. #6  
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    Quote Originally Posted by adelady View Post
    Why not allow the use of computers so that they could just remember what formulas to use then "plug in" the numbers to get the answers? It seems that today there's few people using a pencil and paper in many fields any longer and are only using the PC to do work on.
    Where would students get their "feel" for numbers from. Maths is not mindless application of formulae. How does someone who's "learned" maths this way know, more or less instinctively, that the answer shown on a machine is more like the distance between earth and the sun, rather than earth and the moon? (And therefore the number displayed is more about a typo than it is an answer to the set problem.)

    I have a lot of trouble getting percentages and orders of magnitude through the resistant skulls of students whose previous maths learning has been on this formulaic basis. I wouldn't want it to become the accepted or acceptable standard. Just ask anyone who has to put first year university students through remedial maths to see what they think.
    Not to mention, what happens when the power goes out and you have to use math to figure out how to get the power back on. You can't fixed a broken computer if you don't know the math. And to create a math program, a human still has to know the math to write the program. Computers are only as smart as the people programming them. And in some cases, only as smart as the idiot at the keyboard.
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    PhDemon - absolutely!

    The thing I hate about watching this happen is seeing the passive helplessness of students when faced with a technological device that "gives" arithmetic/ mathematical answers. It looks like when the machines are switched on, something inside the student is switched off.
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  9. #8  
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    Pen and paper is pretty much necessary in order to learn Algebra, and in today's day and age none of the earlier maths really matter anyway. (You can use a hand calculator to do arithmetic.)

    So you might as well get the kids used to writing stuff down as early as possible.
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    Quote Originally Posted by cosmictraveler View Post
    Why not allow the use of computers so that they could just remember what formulas to use then "plug in" the numbers to get the answers?
    That's some of the problem and why kids and many adults think math sucks and is too hard....they think math is about remembering formula; IT ISN'T. It's about math sense and patterns that match the world around us. I'm not a traditional direct teacher + drill and kill teacher. Kids learn well if there's a good amount of cooperative learning, inductive thinking using examples from the real world and not shy about using a calculator or computer to save time doing thing kids already know how to do.
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    It doesn't help that U.S. students are saddled with a system of measurement units put together by random accumulation. I well remember my college days when given any problem in physics or engineering with quantities given in "English" units, one first converted everything to metric, solved the problem, then converted everything back to "English" units. Too many people in this country utterly fail to grasp how hard it is to get students to grasp the relationships between quantities like mass, force, and velocity when the whole measurement system is so crude it almost entirely eliminates any sense of such a relationship.
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    It doesn't help that U.S. students are saddled with a system of measurement units put together by random accumulation
    I have a lot of sympathy for that view - and we've moved to a metric system yonks ago, but ....

    I also have good memories of kids of distinctly average ability able to move smoothly between multiplying and dividing by a variety of numbers for a variety of purposes. Remember, we had pounds, shillings, pence (and the always relevant guineas) to deal with as well. It was a great opportunity for students to easily see the equivalence where 40 sixpences (or 80 threepences) equals 2 10 shilling notes equals one pound note. We gained a lot with metric conversion, but we did lose something useful in the process. For those of better than average ability, moving to other base number systems was not much of a chore with that already varied background.
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    Quote Originally Posted by danhanegan View Post
    It doesn't help that U.S. students are saddled with a system of measurement units put together by random accumulation.
    It probably doesn't hurt as much as we think it might. Most of the English units are natural (why they were developed) and I've watched kids blaze through estimations, which is a powerful tool for number sense, because of it. I concede it might slow kids down later.

    You remind me though of an article from a couple years back though, a study that suggest that languages which include the odd number naming conventions such as our use of "eleven" instead of "onesy-one" (like 21 = twenty one, 31 = thirty one) delayed math and math vocabulary by at least six months in young people.
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    Forum Masters Degree LuciDreaming's Avatar
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    Various studies from Theresa Nunes show that children can do some quite complicated math in their heads that they can't solve on paper. For example children making a living selling things on the streets can complete basic calculations/fractions/percentages when it concerns the fair division of profits or goods. The difficulties they have on paper are largely due to misunderstanding/not understanding the operands and symbols. She has also done some excellent work showing how the Piagetian idea of staged development in mental faculties is largely incorrect in that it is the representation and context that is the key to children understanding a problem (mathematical or otherwise). For example she showed that you can teach the concept of mass and density to a child of 11 years through representing the problem physically with water and floating/non-floating objects. Piagetian theory suggests you cant teach abstract concepts to a child until they are about 12 years and above.
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    Forum Masters Degree LuciDreaming's Avatar
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    (I seem unable to start new paragraphs so I'll break the post up.....). There is a type of staged learning in children but it is their understanding of the world that determines how they learn. Children up to the ages of 12 ish think largely in the physical world - they like doing stuff, football, singing, whatever. They understand other people in terms of what they like doing - "Jack is my best friend cos he likes football...." that sort of thing. If you want to teach them an abstract concept like maths they have the ability to understand it if you ground it in the physical. So I don't think pen and paper is the best way to start. Refs: Nunes - Learning mathematics, perspectives from everyday life. Schools, Mathematics and the world of reality pp61-78 1993. Nunes, Schliemann and Carraher - Street Mathematics and School Mathematics. 1993. Nunes, Bryant, Pretzlik and Hurry, Childrens understanding of intensive qualities. British Educational Research Association 2002
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    Forum Masters Degree LuciDreaming's Avatar
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    As a by the by, we are not much different as adults. We learn by doing, whatever it is, physics, maths, needlework. Until you actually make some sort of physical movement you haven't learned anything.
    "And we should consider every day lost on which we have not danced at least once. And we should call every truth false which was not accompanied by at least one laugh" Nietzsche.
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    Piagetian theory suggests you cant teach abstract concepts to a child until they are about 12 years and above.
    I think he worked on 11 to 16. But you can still use Piagetian concepts in teaching. We always worked on simple principles in tuition.

    From known to unknown.
    From concrete to abstract.
    From specific to general.
    From local to global.
    From simple to complex.

    Which is a pretty good summation of his ideas. But. We used that structure regardless of a student's age - because their learning gaps indicated that they'd probably missed those steps at the "appropriate" age.
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    Might kids do better in school if adults weren't such rubbish educators........ Sugata Mitra: Build a School in the Cloud | Video on TED.com
    "And we should consider every day lost on which we have not danced at least once. And we should call every truth false which was not accompanied by at least one laugh" Nietzsche.
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    Japanese elementaries often teach abacus - not sentimentally but as a cunning and proven way to hijack parts of the brain normally devoted to eye/motor coordination, to serve instead as high-speed arithmetic engines. With proper training, the student develops a working inner model of the abacus, and can fire back answers like an idiot savant. Some people still twiddle their fingers or jiggle their eyeballs during the split-second calculation.
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    I learnt abacus at school in the Soviet Union. And mathematics where we did not use paper. At university (in Australia) we used Mathematica on Macintosh computers for learning. But throughout all this there were paper-based exercises. I think limiting exercises to one media is folly.

    These days, however, you would do well to get people to use paper. And not a tablet.
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  21. #20  
    has lost interest seagypsy's Avatar
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    Quote Originally Posted by pyoko View Post
    I learnt abacus at school in the Soviet Union. And mathematics where we did not use paper. At university (in Australia) we used Mathematica on Macintosh computers for learning. But throughout all this there were paper-based exercises. I think limiting exercises to one media is folly.

    These days, however, you would do well to get people to use paper. And not a tablet.
    Remember the old days when the word "tablet" referred to a pad of paper? lol. old days being like 10 years ago.
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    Might kids do better in school if adults weren't such rubbish educators
    It's a bit like the description of democracy - it's the worst form of government apart from every other form of government we've ever tried.

    Much the same for education. Some people are rotten educators, some school systems make it harder for good educators to do their stuff. But every technological innovation which was lauded at its introduction because it 'could' replace the always unreliable human teacher - radio, films, television, calculators, whiteboards replacing blackboards, computers, interactive whiteboards, phones - never did so. The reason these devices are so easy to sell to school systems is the eternal hope of administrators that they can now, finally, get rid of some/ many/ all those pesky teachers. The money would often be better applied to adding a teacher or two to the staff to make the job easier and better and more relevant to the needs of the real live students in those schools.

    In the end, there is no substitute for teachers. We prefer good, well-trained teachers. But teachers nevertheless. Teachers are the worst way to deliver education - apart from every other method anyone's ever tried.
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    I don't think Sugata Mitra intended for teachers to be replaced but to show how kids educate themselves given the right questions and tools. I don't think teachers are the worst way to educate (I cant think who else would educate except teachers) and fully appreciate that there are good and bad teachers (....?) but I didn't say teachers are rubbish educators - I said adults are. We forget what its like to be children and stifle them-we mistake play for being naughty and expect them to sit still for long periods of time. As adults we are all responsible for the education of our children and we haven't made a good job of it for the majority. I certainly never got a decent education learning the "three r's" method at school or the "because I said so" method of most adults and in England anyone who makes it to the top of the tree in almost any profession has come from a private school and/or a moneyed background.

    Pong - I read somewhere that there are some children in these Abacus schools who can do some complicated multi digit calculations at the same time as completing a language puzzle - something like; complete this sentence or does this word rhyme with another word, that sort of thing. They think the reason they can do it is because the mathematical puzzle is represented mentally as a picture rather than symbols and the word puzzle is represented as symbols - so they can effectively do the two puzzles simultaneously because they utilise different areas of the brain. I'll see if I can find the article if you are interested.
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    but I didn't say teachers are rubbish educators - I said adults are. We forget what its like to be children and stifle them
    It's not so much stifling them, as forgetting what it's like - or never knowing if you were the sort of kid who learned things easily - how to break things down to the steps necessary to learn them. John Mighton's The Myth of Ability is an outstanding example. He focuses on maths, fractions in particular, but the concept is applicable to lots of subject matter. There's no need to go all the way with his army of volunteers approach. A teacher or parent who absorbs his message can become a much better teacher of children.

    in England anyone who makes it to the top of the tree in almost any profession has come from a private school and/or a moneyed background.
    And most of those schools use highly structured "old-fashioned" teaching and testing methods. I'll never forget the shock we got one day. We'd discovered an old 2nd hand algebra text - the first edition was in 188x - (we like collecting old textbooks) and we were using it for tutoring because the many examples were meticulously graduated for difficulty. You could judge where a student was up to with the concept and choose a dozen examples of exactly the right level of difficulty both for practice and for stepping up the pace. Along comes one of our students who happened to attend our most expensive (10-15k per term) private school. Who pulled out his school maths work at the time - a page photocopied from the very same book, but it was the 1914 edition.
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    After retiring as a naval officer, my father pursued a second career as a schoolteacher. After completing a bachelor's degree in accounting he wound up teaching math courses to 7th graders. He felt a bit intimidated by his fellow teachers, some of whom had many years of experience and advanced degrees. He also wanted to become tenured, which is crucial in the American education system. So he tried to just do what he thought was expected of him, teaching the recommended curriculum out of the recommended textbook.

    These books were full of theories and techniques he had little familiarity with, what is known in America as "new math." But Dad was a quick study, he read a couple of chapters ahead and made sure he understood what the text was driving at before actually trying to teach the material. However, as is inevitable, some of the students had trouble understanding. Sometimes he would get frustrated, pull out a stick of chalk, and begin a supplementary lecture with the words, "well, this is how they taught me to do it when I was your age." (Dad was in the 7th grade when world war 2 was being fought.) Often, the students found his old-timey techniques much easier to understand and work with than the "official" methods presented in the textbook.

    Inevitably students would ask "why didn't you just show us that in the first place?" Dad had no answer, because he couldn't really understand why the text avoided his old fashioned "tried and true" methods either.
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    Quote Originally Posted by adelady View Post
    how to break things down to the steps necessary to learn them.
    Most people can learn even the most complex concepts if they are started at the right point and have things broken down into enough steps for them. This really is a pretty basic concept that we see all the time yet it seems people don't always grasp it's simplicity. Education systems around the world follow the same progessional path, you start off at the beginning and step by step you improve your skills and knowledge as you work your way up the grades. The learning process is broken down into easy bite size chunks that follow on from each other.

    The way in which people learn at school following this method is learn move on, learn move on, this process is constantly repeated. Now this works fine where pupils are actually learning and enjoying learning. The problem here though is not everyone learns at the same rate and if students are struggling with some steps then it will hold them back from learning further steps, they stop enjoying it then struggle even more because they arn't acheiving the sames rewards of success of their fellow classmates.

    Generally success leads to further success, the reward comes in the fact that we all natuarally enjoy things we are good at. So when we stop succeeding things seem harder and we become less interested thus a cycle forms which needs to be broken. One of the best methods to achieve this is more steps. Most students will struggle at some stage and it's important not to let this become a cycle which holds them back, so giving them extra steps that really break down the area that they are struggling with helps.

    Again it's a straight forward approach whilst ever the student is struggling more steps are added and if they are still struggling with these then those steps are also broken down in further steps, at each stage the steps are being broken down into less complicated concepts. Eventually the students will begin to understand the concept and work their way back up the complexity ladder, also the added steps will give them back the rewards of success from understanding and completing the extra steps.

    This type of approach can be applied to many areas with similar success because it is focused on enabling people to acheive their objectives and progressing.
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    Quote Originally Posted by seagypsy View Post
    Quote Originally Posted by pyoko View Post
    I learnt abacus at school in the Soviet Union. And mathematics where we did not use paper. At university (in Australia) we used Mathematica on Macintosh computers for learning. But throughout all this there were paper-based exercises. I think limiting exercises to one media is folly.

    These days, however, you would do well to get people to use paper. And not a tablet.
    Remember the old days when the word "tablet" referred to a pad of paper? lol. old days being like 10 years ago.
    Hah. I thought he meant a tablet of paper, and wondered what the advantage of separate sheets of paper would be.
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    Most people can learn even the most complex concepts if they are started at the right point and have things broken down into enough steps for them. This really is a pretty basic concept that we see all the time yet it seems people don't always grasp it's simplicity.
    For people who never had much difficulty learning stuff themselves, it really isn't so simple. Understanding exactly how many steps and assumed concepts are implicit in something as "simple" as equivalent fractions, for example, is a big task for someone who's never thought about it before.

    For a teacher or parent it's always a matter of finding the right balance between enough explanation and boring a student rigid with detail they don't need because they just "get it". And then there's the further problem with some students who struggle interminably with one apparently simple concept, like money or measurement, but who have no difficulty at all with something most students find challenging at first, like adding or multiplying fractions. I've used maths for illustration, but the same thing applies to other subjects - but not necessarily in such clear-cut ways.
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    With math, I usually find the ones who struggle are about 90% right in their reasoning process, but missing one tiny detail. Instead of telling them they're wrong and repeating all the information to them, I get them to tell me their process in detail. I listen until I hear the error, then keep listening until they finish. Then I tell them they were basically right except one thing, and that if they correct that one thing they will have gotten it.

    It's important, when doing so, however, that you yourself are not depending on wrote memory. You've got to be open to all the possible ways the right reasoning process could take form. Not just listening for one set of words.

    It's ironic, but it seems that remedial teaching is mostly about listening. I've done a fair amount of tutoring "hopeless" students with success.
    Some clocks are only right twice a day, but they are still right when they are right.
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