A few words about unschooling math
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A few words about unschooling math
A Few Words about Unschooling Math
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FREEDOM TO CHOOSE
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 Fingers & toes, pattern blocks, two by two, 4x4, tape measure, #, scale, $, save, interest, model, profit (loss), earn, spend, checkbook, recipe, batting average, Captain May I? third base,  thirty love, fault, par, birdie, strike, spare, first down and ten to go, penalty box, map, scale of miles, compass, Pokémon, Candyland, Monopoly, Go, Chess, Sorry! dominoes, dice, poker chips, Bridge, Crazy Eights, charts,Â
              Origami, knit 1 purl 2, weigh + pulley, ratio, chances, statistics,  average, more or less, even, odd, yards, N scale, area, score, speed limit, braking distance, fourth dimension, sixth sense, Indy 500, build, plan, rate,  estimate.
              Predict, revise, depth, angle, trade, straight, spiral, high tide, low ball, tempo, %, quarter note, half pound, forecast, budget, half price, plus tax,  longitude, light years, escape velocity, precession of the equinoxes (oh Best Beloved) ?, range, set,Â
               Stitch, sort, size, plot, dozen, $, gain, lose, exact, income, allowance, loan, knots, beads, gear ratio, minutes, degrees, fathoms, grid,   meters,  Anno, The Number Devil, half pipe, quarter turn, full bore,  turning radius, stacking, nesting, measure up, @, scale down, abacus, debit, infinity, first class, equal share, short shrift, waxing, waning, rhythm, balance, cycle,  value, graph, perigee, frequency,      Â
              Pennies, double helix, £, time zone, millennium, program,  binary, generation, epoch, era, nano second, code, puzzle, fiscal year, progression, midpoint, watts, lumens, ?,  horsepower, ohms, Great Circle Route, 52 Pickup, ‘55 Chevy, Hundredth Monkey, altitude, Lego, Tangrams,  Fibonacci series, height, width, length, volume, output, Eureka! displacement, schedule, time limit,  add up, count down, four score, last full measure, census, Are we there yet? a bushel and a peck, postage, efficient operation, elegant solution, gigabytes, google,Â
               Powers of Ten, increase, < >, decrease, supply & demand, links, contour lines, Great Divide, Bingo! count down, stock market, daily log, rent, discretionary income, arc, geometric proportions,   geologic time, navigation, 16 mm,   Stonehenge, ¢, grams/ounces, f stop, low bid, dot-to-dot, orienteering, etc.
Â
FREEDOM TO CHOOSE
Â
 Fingers & toes, pattern blocks, two by two, 4x4, tape measure, #, scale, $, save, interest, model, profit (loss), earn, spend, checkbook, recipe, batting average, Captain May I? third base,  thirty love, fault, par, birdie, strike, spare, first down and ten to go, penalty box, map, scale of miles, compass, Pokémon, Candyland, Monopoly, Go, Chess, Sorry! dominoes, dice, poker chips, Bridge, Crazy Eights, charts,Â
              Origami, knit 1 purl 2, weigh + pulley, ratio, chances, statistics,  average, more or less, even, odd, yards, N scale, area, score, speed limit, braking distance, fourth dimension, sixth sense, Indy 500, build, plan, rate,  estimate.
              Predict, revise, depth, angle, trade, straight, spiral, high tide, low ball, tempo, %, quarter note, half pound, forecast, budget, half price, plus tax,  longitude, light years, escape velocity, precession of the equinoxes (oh Best Beloved) ?, range, set,Â
               Stitch, sort, size, plot, dozen, $, gain, lose, exact, income, allowance, loan, knots, beads, gear ratio, minutes, degrees, fathoms, grid,   meters,  Anno, The Number Devil, half pipe, quarter turn, full bore,  turning radius, stacking, nesting, measure up, @, scale down, abacus, debit, infinity, first class, equal share, short shrift, waxing, waning, rhythm, balance, cycle,  value, graph, perigee, frequency,      Â
              Pennies, double helix, £, time zone, millennium, program,  binary, generation, epoch, era, nano second, code, puzzle, fiscal year, progression, midpoint, watts, lumens, ?,  horsepower, ohms, Great Circle Route, 52 Pickup, ‘55 Chevy, Hundredth Monkey, altitude, Lego, Tangrams,  Fibonacci series, height, width, length, volume, output, Eureka! displacement, schedule, time limit,  add up, count down, four score, last full measure, census, Are we there yet? a bushel and a peck, postage, efficient operation, elegant solution, gigabytes, google,Â
               Powers of Ten, increase, < >, decrease, supply & demand, links, contour lines, Great Divide, Bingo! count down, stock market, daily log, rent, discretionary income, arc, geometric proportions,   geologic time, navigation, 16 mm,   Stonehenge, ¢, grams/ounces, f stop, low bid, dot-to-dot, orienteering, etc.
We are coordinators of Unschoolers Unlimited, support group for self directed learners. Email us to request a free information packet & our latest newsletter.
wow...thoughtful
THAT was quite a list...THANKS! (From a new homeschooling family who has yet to pick a curriculum beyond "real life.")
JMommer
JMommer
Search Engines
The search engines probably like this post, which is the reason it exists. 

Moti Levi
www.LearningByYourself.com
www.LearningByYourself.com
Re: Search Engines
Moti wrote:The search engines probably like this post, which is the reason it exists.
Actually, I wrote this before I knew about search engines. It was a response to people who said they were "unschooling except for a couple of pages of math every day." Folks find it hard to believe you can learn math by living life and I wanted to give just a few ideas.
Luz
We are coordinators of Unschoolers Unlimited, support group for self directed learners. Email us to request a free information packet & our latest newsletter.
An Apology
Then I apologize for my post. It is a common method for attracting search engines (smile) and I misunderstood your post.
Yes, you can learn Math from life but like much of unguided learning it can be chaotic and bring about solutions/algorithms/methods that apply in narrow situations but are used incorrectly in other situations as a result. It has to do with how we learn, and how we make deductions.
That said, for non-mathematicians, if Math has no relevancy to life that the student also knows and understand, it becomes a meaningless exercise, as the case is often when Math is taught in school.
Yes, you can learn Math from life but like much of unguided learning it can be chaotic and bring about solutions/algorithms/methods that apply in narrow situations but are used incorrectly in other situations as a result. It has to do with how we learn, and how we make deductions.
That said, for non-mathematicians, if Math has no relevancy to life that the student also knows and understand, it becomes a meaningless exercise, as the case is often when Math is taught in school.
Re: An Apology
Moti wrote:Then I apologize for my post. It is a common method for attracting search engines (smile) and I misunderstood your post.
Yes, you can learn Math from life but like much of unguided learning it can be chaotic and bring about solutions/algorithms/methods that apply in narrow situations but are used incorrectly in other situations as a result. It has to do with how we learn, and how we make deductions.
That said, for non-mathematicians, if Math has no relevancy to life that the student also knows and understand, it becomes a meaningless exercise, as the case is often when Math is taught in school.
Allow me to make some comments:
1. Usually one CAN learn arithmetics and basic calculation from life (unless he or she, of course is Carl Gauss

2. Math IS relevant pretty much to everything in life--another matter how one wants to describe this life around him (her) self and that is where the real problem lies--MATH IS not easy (I would agree) and unlike literature (which we may or may not like) requires a little bit different mental organization and approach. But will we make a conclusion about American literature without reading Hemingway and Steinbeck, or about German one without Heine or Schiller??? Not if we are thoughtfull, i would guess

Warmest Regards
Re: An Apology
babaika wrote:
Allow me to make some comments:
1. Usually one CAN learn arithmetics and basic calculation from life (unless he or she, of course is Carl GaussIn 99% of the cases, however, it will not be "math". Enough to mention that dear to everyone issues of annuities or compound interest are related to the fundamental issues of numerical sequences or properties of a power respectively (to name a few concepts) and understanding of those requires a little bit more than just hands on experience
Of course that it won't be mathematics as we study in the university, i.e. the theory of math and not applied. As trained as such I should know

2. Math IS relevant pretty much to everything in life--another matter how one wants to describe this life around him (her) self and that is where the real problem lies--MATH IS not easy (I would agree) and unlike literature (which we may or may not like) requires a little bit different mental organization and approach. But will we make a conclusion about American literature without reading Hemingway and Steinbeck, or about German one without Heine or Schiller??? Not if we are thoughtfull, i would guess
Math is indeed pretty much relevent to everything in life. BUT, not all math studied in school is relevant to what people would encounter. Take all the trigonometry proofs required [based on trig identities]. Why on earth do 99% of people need to be able to do those?<br>
You could argue that it developes logic and organization skills, but there are much better ways of doing so. In fact, all those "proofs", which are nothing but a sequence of exchanges of one term with another, can be done without thinking at all and just by a basic search approach.
Let me explain "Easy" as I mean it. Math (school, not Mathematics) is Easy. It is so because it can be done without abstract thought and has no open questions. It only requires a good mastery of the knowledge base, a systematic approach, and no fear to try. I know because I taught hundreds of students all of school's math in 3.5 months (about two 4 hours class a week), starting with 1+1 [I swear that was the first thing I wrote on the board] and ending with calculus. Can I say that they understood Mathematics? No way. Did they get high grades? Yep. The average grade was above 90%! [national standardized test]. Of course, they did understand the basic ideas of "Math". But not the real abstract ideas behind it.
So, Math is easy. Mathematics is not

Re: An Apology
Moti wrote:Of course that it won't be mathematics as we study in the university, i.e. the theory of math and not applied. As trained as such I should knowBut given the discussion about school (elementry - high) math I was using "math" as such and not as mathematics. And of course, to understand some basic finance requires a much deeper understanding of mathematics that is even taught in schools [option trading would require stochastic processes and such for example].
Math is indeed pretty much relevent to everything in life. BUT, not all math studied in school is relevant to what people would encounter. Take all the trigonometry proofs required [based on trig identities]. Why on earth do 99% of people need to be able to do those?
You could argue that it developes logic and organization skills, but there are much better ways of doing so. In fact, all those "proofs", which are nothing but a sequence of exchanges of one term with another, can be done without thinking at all and just by a basic search approach.
Let me explain "Easy" as I mean it. Math (school, not Mathematics) is Easy. It is so because it can be done without abstract thought and has no open questions. It only requires a good mastery of the knowledge base, a systematic approach, and no fear to try. I know because I taught hundreds of students all of school's math in 3.5 months (about two 4 hours class a week), starting with 1+1 [I swear that was the first thing I wrote on the board] and ending with calculus. Can I say that they understood Mathematics? No way. Did they get high grades? Yep. The average grade was above 90%! [national standardized test]. Of course, they did understand the basic ideas of "Math". But not the real abstract ideas behind it.
So, Math is easy. Mathematics is not
Yes and No at the same time


Warmest Regards
I agree
that the FLOW of material is critical. I believe I said it somewhere in this forum as it is the principles of my teaching philosophy when I write the books (or teach); namely that with the correct flow [and some other required elements] math can be easy. BUT, as I said, I differentiate between proving (and understanding of course) La Grange's theorem and being able to understand its idea and apply it.
I agree with you that almost all (some exceptions but much, much fewer than people think) can understand Math. However, to understand the higher level, that of the full theory development and concepts, relatively few can. Exactly like most can learn to play the piano. Few can be Motzart
I agree with you that almost all (some exceptions but much, much fewer than people think) can understand Math. However, to understand the higher level, that of the full theory development and concepts, relatively few can. Exactly like most can learn to play the piano. Few can be Motzart

Re: I agree
Moti wrote:that the FLOW of material is critical. I believe I said it somewhere in this forum as it is the principles of my teaching philosophy when I write the books (or teach); namely that with the correct flow [and some other required elements] math can be easy. BUT, as I said, I differentiate between proving (and understanding of course) La Grange's theorem and being able to understand its idea and apply it.
I agree with you that almost all (some exceptions but much, much fewer than people think) can understand Math. However, to understand the higher level, that of the full theory development and concepts, relatively few can. Exactly like most can learn to play the piano. Few can be Motzart
Agree!!!


Warmest Regards
Agree as well
(smile) it seems we do agree on much. In fact, my view is that because fo the flawed approach and books math is studied at too slow a pace. Especaily in the "concpet/theory" sense. For example, when I talk to 4th/5th graders I introduce the "Achiles and the Turtle" paradox [it did get solved recently] by playing it as a game. Few are quick to figure it out and EVERYONE gets it. From there we introduce the idea of infinitely small (which is the basis for calculus) and the idea of infinity in general. Even learn to compare countable sets vs. real numbers [a string with pins in it do wonder to show it
]. And the chess riddle [large numbers, leading to the infinite idea] and progression of such. Many BIG ideas in an hour, and they LOVE it and they get it!
So, yes, I do agree even big parts of mathematics, at least concept wise, are Easy. That said, using those concept and being formal about them is much more difficult and out of reach for most. But using them, and figuring out the applied proofs [meaning: not the real general theorems] is within almost all's reach, if done in correct flow, and explanation.

So, yes, I do agree even big parts of mathematics, at least concept wise, are Easy. That said, using those concept and being formal about them is much more difficult and out of reach for most. But using them, and figuring out the applied proofs [meaning: not the real general theorems] is within almost all's reach, if done in correct flow, and explanation.
Re: Agree as well
Moti wrote:(smile) it seems we do agree on much. In fact, my view is that because fo the flawed approach and books math is studied at too slow a pace. Especaily in the "concpet/theory" sense. For example, when I talk to 4th/5th graders I introduce the "Achiles and the Turtle" paradox [it did get solved recently] by playing it as a game. Few are quick to figure it out and EVERYONE gets it. From there we introduce the idea of infinitely small (which is the basis for calculus) and the idea of infinity in general. Even learn to compare countable sets vs. real numbers [a string with pins in it do wonder to show it]. And the chess riddle [large numbers, leading to the infinite idea] and progression of such. Many BIG ideas in an hour, and they LOVE it and they get it!
So, yes, I do agree even big parts of mathematics, at least concept wise, are Easy. That said, using those concept and being formal about them is much more difficult and out of reach for most. But using them, and figuring out the applied proofs [meaning: not the real general theorems] is within almost all's reach, if done in correct flow, and explanation.
Well, turtle problem is a classic example of increment and a slope within system of linear functions

This is an illustration of what and how is required for students to understand the concept in order to solve simplest problems on this topic. And this one, as well as hundreds of others, is not a situation when say gaming methods will do any good. Good (correct) answer at this stage is just merely means to an end, which is HOW to do this--and that is what will matter a great deal down the road. Well, I should say--spending all this Saturday with my daughter on-line, preparing (reviewing) her for the math test for Business School in UW. Approaches are virtually the same--needless to say, the test included problems on (for obvious reasons) Marginal Revenues and Costs (and whatever else--hate economics



Warmest Regards
Did you read my bio on my website?


The point of it is that college education is not what you think anymore. It deteriorated strongly [due to SRTEs that make sure that professors would want to make the students happy, not knowledgable, and students who are used to being spoon fed in school, and of course the horrible multiple choice questions all tests use now].
Anyway, I agree with your first paragraph - I was a physics major as well [I started a dual degree in Math and Phsyics but then decided to focus on math and move to Operations Research].
And don't tell you daughter what I said - as long as she believes she needs to learn deeply, she would

And how can you hate economics? It's mostly math...[My research included lots of economic modelling

Re: Did you read my bio on my website?
Moti wrote: I was a physics major as well [I started a dual degree in Math and Phsyics but then decided to focus on math and move to Operations Research].
And don't tell you daughter what I said - as long as she believes she needs to learn deeply, she would
And how can you hate economics? It's mostly math...[My research included lots of economic modelling]
I Will not



Warmest Regards
Re: Did you read my bio on my website?
Moti wrote:And how can you hate economics? It's mostly math...[My research included lots of economic modelling]
Because my degree is in....naval engineering




PS. Although--once in a while I love to crack my skull over some economics problems. But those are mostly on differentiation (extrema).
Warmest Regards
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