Homeschool World Forum

[Ned & Luz]

A Few Words about Unschooling Math
 
FREEDOM TO CHOOSE
 
 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, 
                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, 
                 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,       
                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, 
                 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.
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[JMommer]

THAT was quite a list...THANKS! (From a new homeschooling family who has yet to pick a curriculum beyond "real life.")

JMommer

[Moti]

The search engines probably like this post, which is the reason it exists.
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Moti Levi
www.LearningByYourself.com

[Ned & Luz]

[Moti]

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.
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Moti Levi
www.LearningByYourself.com

[babaika]

[Moti]

[babaika]

[Moti]

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
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Moti Levi
www.LearningByYourself.com

[babaika]

[Moti]

(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.
_________________
Moti Levi
www.LearningByYourself.com

[babaika]

[Moti]

or you would have seen I am [well, until the end of this June] a Professor in a Business School [in Penn State, Graduated from Wharton] so I KNOW what business school ask for. Alas, the majority of courses do not ask for deep understanding of concepts (and I taught at Wharton, at Tulane, and at my position now). In fact, the biggest problem I had in my courses was that I did make them really think and understand the concepts and they were not used to it. Even in college now the approach is "here's a formula, can you spit it back at us on the test?" At both Tulane and Penn State, which are highly ranked business schools [in fact, my dept at PSU was ranked #1 for undergrads...] I asked (because they needed to know it to use in a case in my course) them about NPV [Net Present Value] which is a BASIC concept in finance. So basic that if a student who finishes a business school doesn't know it, s/he should not be hired in my mind. Uniformly they didn't know it, could not really explain it, and didn't even know how to use it [though they probably knew how to press the NPV function in Excel and get the result, well, maybe not even that ].

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 ]
_________________
Moti Levi
www.LearningByYourself.com

[babaika]

[babaika]