Thanks.  You must be a speed reader.  You replied to the post almost as soon as I put it up.

What really excites me about this work is the synergistic effect of using good techniques from various fields like rapid mental calculation, speed reading, and memory training.   The amazing thing is that teaching these skills takes less time than an ordinary curriculum would take.  The time spent teaching rapid learning is more than made up for because a child learns, say, the times tables in a few weeks instead of a few years giving them ample time to go on to more advanced levels of mathematics and/or expand their interests into other fields. 

It find it very stimulating all the things Brillkids parents have worked with and I often follow up on their posts to buy books or check out links or methods they recommend.  Never fail to learn something new.  I wish public education displayed that kind of dynamism.

PokerDad,

This is a fascinating thread!  I have studied Smith's book in detail but have never read Matthew Syed's book Bounce.  I will have to get it.  Thanks for the reference.

 I teach rapid mental mathematics for kids of all ages in our Jones Geniuses materials and I have accomplished that by studying many of the methods of the great mental calculators and simplified them so that even young children can learn them.  You may not want to teach your child to do the 10th root of 30 digit numbers but deriving the cube roots of numbers up to one million is quite simple, square roots are only a bit more complex to derive. Everyone should know this as powers and roots are the core of higher math and those used the most are squares & cubes.  So don't worry about the esoteric heights of mental math calculation but don't ignore the practical levels that can be scaled rather easily.  Usually these mental calculation methods will not be taught in school which seems wedded to paper, pencil, and calculators.  Typical long multiplication is right to left so you do not have to retrace your steps and change numbers when sums are carried over.  Mental math starts to the left with the biggest product in a multiplication then adds the smaller products to it one by one keeping a running total in their head while doing the next multiplication.  It takes a little concentration but anyone can do it. Concentration is perhaps the most valuable skill we can teach.   Everyone should be able to do 2 digit by 2 digit multiplication mentally.  You came up with a great observation that all mental calculators proceed left to right.  Here were your excellent observations:

prodigies learned math early; they learned about numbers in many cases before they learned their alphabet
prodigies spent a lot of time by themselves; the time alone was spent doing mental math
prodigies lacked distractions, or pretty much stuff that you'd find in a common home (such as television and toys)
in some cases, prodigies actually became less proficient as they got older
prodigies did not learn their skill in school, and most (but certainly NOT all) learned before going to school
rarely did prodigies begin to excel in their early teens, but it did happen.
almost every prodigy calculates from left to right.

Most calculating prodigies did indeed start early, pre-school age.   It is not essential to learn numbers first before the alphabet.  However, many famous stage calculators were illiterate shepherds like Mondeux, Mangiamele, Pierini, and Inaudi.  Yes, clearly their massive amounts of free time plus the need to constantly count the animals in their charge stimulated some of them to a fascination with numbers.  Bidder was taught by his brother putting pellet shot arranged into squares to practice multiplication which is why he recommends it.  It is a good technique but not essential.  Prodigies tend to lose their skills, much of which is subconscious, when they begin to attend school and all their time is taken up with mundane tasks in literacy and mathematics that are far beneath them but occupy all their time so they regress in their skills quite dramatically over time.  This happens in reading as well as math so beware of putting your child into the public school mill unless you want them homogenized. Idiot savants, usually autistics, simply do mental math all the time because they find it comforting.  Anyone who does mental math a lot will get good at it. 

For every child who develops these skills spontaneously, thousands if not millions, can develop rapid mental calculation when taught the skills competently.  After Mozart's father published a book on how he developed his son's musical ability there suddenly appeared hundreds of musical prodigies worldwide.  George Bidder did not have a father who was a prodigy but he did go on to pass his abilities down to his children and grand children.  There is a meme out there (ala Doman) that only children can do these things but this is quite untrue.  There are notable cases of adults like Millie Osaka and Maurice Dagbert who learned prodigious math calculation skills as adults.  Plus, think about it, many geniuses like Richard Feynman are the product of a gradual acquisition of skill over a lifetime.

The point is that current math education and materials are typically so lacking that calculation skills that are essential cannot even be taught well, like the times tables and fractions.  Lack of skill in fractions is mainly caused by a lack of underlying skill in factoring.  Factoring is called the Fundamental Principle of Mathematics it is so important.  It is quite easy with only a little practice and knowledge (you must know the factors and primes of all numbers to 100) to do seemingly amazing feats.

PokerDad, you mentioned the number 7551 in your factoring discourse.  It took me about a minute to work it out.  7551 is divisible by 3 since all the digits add up to a multiple of 3, so we divide it by 3 to get 3 x 2517 which is also divisible by 3, so we now have 3 x 3 x 839.  839 is a prime number.  I know this because we teach our kids to memorize all the primes to 1000.  It is crucial to know high primes (at least to 1000) in calculation.  For example, if this were a fraction denominator you would be stuck there not knowing if it could be simplified further.  With memory training it is not a difficult task to memorize the primes to 1000, takes an hour or two.  We use picture mnemonics, very simple once you know the basics of memory training.  If you had asked to factor a much bigger number with zeros like 7,551,000 it would have been just as easy:  2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 839  (each zero is a ten - its factors are 2 x 5 so with 3 zeros add three 2s & 5s).

Why do this when we have calculators?  That is the question really.   Number one, there is nothing wrong with using calculators.   I just recommend using them to expand the mind rather than replace it.  Neurophysiological development is dependent upon doing pushups for the brain.  Mathematical ability forms a key part of the structure of thought, our ability to comprehend the world we live in (how many people don't much recognize the exponential difference between the government spending a million dollars or a billion dollars versus a trillion dollars).  It is all just fuzzy zeros.  Brain research is quite explicit that exercising our, and our children's, minds mathematically makes them smarter.  Number two, doing metal math up to a certain level is much faster than being calculator dependent and builds number sense that prevents errors.  Those who can do mental calculation (for example of SAT type problems) are typically 3 to 5 times faster that those with calculators!  This is the difference between the engineer (or carpet salesman) who can think on his feet, do the calculation in his head and see right through to the solution to the problem versus the guy who has to go crunch the numbers for half a day.  Time is money. The defining qualities of a professional are SAS - Speed, Accuracy, and Skill.   That is why you pay the accountant $100 an hour rather than hire someone at minimum wage to do your books. 

Anyway, do not despair!  There are many simple, effective mental calculations that can and should be taught to great effect. And they should be taught far earlier than they are.  Unfortunately you won't fine them in math textbooks.  (Never say never, but rarely)   Our kids will spend massive amounts of time learning arithmetic, algebra, geometry just for starters;  might as well make it easy and enjoyable for them.  Kids tend to like doing things they can do well and tend to not like doing things they cannot do well.  Sort of like us adults.  Once they get fascinated with a subject like mathematics they may choose to fly very high indeed.  We need people who can do that. 

 

Mandab,

I agreed with 90% of what the Crain article said.  Most of us who work on the practical level with our children are not purists.  We understand instinctively the need to use the whole brain rather than focus on only half of it.  Forgive me, having been through the education mill I know its weaknesses inside out.  Too often, the education "experts" are not even classroom teachers and some have never been.  They spin theories.  These theories usually sound good but frequently do not survive their first encounter with reality. 

In any case, I have been thinking lately that the overwhelming emphasis on "holistic" learning usually ends abruptly when you enter serious academics.  I think that is what you were referring to when you said more left brain discrete learning and memorization is required later on.  My daughter is taking an Anatomy class for medical training.  There will be little flexibility in this course.  Students will learn the massive data base or they will not be nurses or doctors.  Would we have it any other way? The same can be said of advanced mathematics or other technical disciplines.

Your comments made me think.  I have always done it contrary to your scenario.  Early left brain skills like phonics and math operations are essential to open the door to understanding in reading and mathematics, higher order thinking.  The stronger, and broader, the foundation of basic skills the higher the pyramid of higher order thinking can be built.    I am not saying you are wrong it just seems a new way of thinking of it for me.  I have known moms who have done a fabulous job in teaching their children very effectively, and almost exclusively, via right brain learning and arrived at the point where they knew their phonics, numbers, and facts.  So I know it is possible.  However, having worked with so many children myself I know they are not all alike.

This throws off many mothers whose first child may have learned to read like falling off a log.  Just put a book into their hands and read it to them pointing to the words and they were off and running.  For their next child however that may not work at all.  The first was an instinctive right brain learner, the second an instinctive left brain learner.  He demands to understand the mechanics of the process.  He wants to know the sounds and how they are put together.  If we approach it as if all (early) learning "should" be right brained then this child gets let out.  In my estimation and from studying the research, about half of kids can learn to read without direct instruction in phonics.   The others require direct instruction step by step, letter-sounds, sounding out, reading connected discourse in stages from simple to complex, etc.  Two points here, these left brained kids who need direct instruction are no less intelligence.  In fact, they may be more intelligent demanding to understand the process thoroughly not glossing through it.  Second, the right brained kids may, not always, have trouble later when they get out of the range of their normal speaking vocabulary, words which they can guess and into longer, more technical words that they cannot guess.  Here their lack of word attack skills may handicap them.  Many public school kids plateau around fifth grade reading skill.  Usually this will not happen with a home school mom because she is on top of it and will do things to bring their skills along.  Because a child is instinctively right brained or left brained is no reason to cater exclusively to that learning style.  They also need strength in the other way of processing to be an effective learner.  To take a physical example, should we ignore development of one leg because the child instinctively favors the other.  I hope not.

Your description of math skills "doing enough equations that they know the answers" is really a definition of left brain (rote) learning rather than right brain (holistic) learning.  Right brain is more conceptual which is essential as well.  A lack of higher order thinking is like having to do a jigsaw puzzle without the picture of it complete.  However, holistic activities if not well thought out can take too much time for the results obtained.  Color the two bananas yellow and the three apples red and write down below how many fruit there are.   In that period of time my students have practiced 400 math problems.  There has to be a balance though.  Too much poorly planned left brain practice can lead to burn out.  Too little can simply close the doors to many interesting, challenging, well-paid professions later on in life because a sufficient knowledge data base, that old demon of "rote" learning, has never been built.   The conventional wisdom is that one can always bone up later when they become motivated to be a doctor or a jet pilot, but I have found achieving that to be the exception not the rule.  The layers of skill, or lack of them, have already been laid down long ago.  The knowledge pyramid must be completely rebuilt.   

Mandab,

That was a great post on Right Brain Learning Tips.  Many very good principles and concepts for teaching effectively.
I did want to point out that Right Brainers like the authors of the article you are quoting often marginalize or even demonize
left brain learning like direct instruction of discrete skills and rote learning.  The article advised to "avoid rote learning".
Our school system has been destroyed by this type of approach.  Students do not know phonics or the multiplication
tables and since teachers are restrained from teaching these things, by rote that is, many students remain stuck there
and no amount of "holistic" learning succeeds in correcting that situation.

There is a ton of research backing up the fact we need to utilize both sides of the brain, discrete left brain skills that
result in assimilating a data base of information and holistic right brain skills that put the puzzle together in context.
I am always leery of "Best Practices" type of lists because they oftentimes give information that is contraindicated
by research.  They are usually not research-based although the author seems to think they are but are more often
a checklist for ideological correctness.  There are vicious wars going on in education between Right Brainers and
Left Brainers.  It is easy to get caught up in it.

It was a great article tho.  Thanks for the feedback.

DadDude & PokerDad,

Glad to see you are stilling dedicated to working the memorization methods.  I wanted to ask you for input.  I downloaded Mnemosyne and found it unsatisfactory.  I am studying Hebrew and it could not handle the diacritical markings copied into it.  Also I was unable to make the print larger.  Small print is a killer for me and would also be for a young child whose visual acuity is not well developed yet.  Do SuperMemo or Anki have these same problems?  Mnemosyne is a free download however and would work for most things I imagine.

As for testing, absolutely the next step is to move away from passive reception to active recall and explanation.  You might try a Cloze test.  It is very easy.  When the material is repeated just leave a blank where the details you want remembered are.  Columbus sailed the ocean blue in _______.   That sort of thing.  It works greats for remembering discrete detail.  The final stage is being able to express a more or less "comprehensive" understanding of the event.  A three year olds understanding will not be the same as a seven year olds, etcetera so adjust accordingly. 

Dear cokers4life,

Glad to see you starting Jones Geniuses Early Learning.  One good thing about living in the times we do is that there are many options, quite a few of them are very good.  I just reviewed ZooPhonics which is an excellent early learning program for learning sounds.   Unfortunately, it is limited to only teaching sounds and is not suited or designed to teach sounding out words.   Conceptually it is almost exactly like our program at that stage.  I have no idea if they used our program as a template for theirs.  However, our Threshold to Reading program is different since we seamlessly go on to sounding out words and reading connected discourse.  Generally, your child ends up at a second grade reading level after finishing Threshold to Reading and the primer 100 Easy Lessons (takes months not years).  In general, I find it too easy for parents to spend a lot of money on many things that deliver too little in the way of results, a program for colors, one for shapes, etc.  It all adds up.  Prioritize your objectives.  Focus like a laser on letter-sounds and digit-quantities.  Those are the keys that open the door to the universe of knowledge.

My son is three, and I am going to be starting Jones Genius.  I like their program because it allows you to progress as fast or as slow as you want (I prefer fast).  It says the program can have your child performing at least algebra by the time they are 8 or 9 years old.   It appears simple and easy enough and begins at the very beginning with simple learning 1-1 concept and how to write your numbers.  They now have it where you can get a digital copy making it easy for international customers to obtain the program.   Plus, the organization is a non-profit.  There is like three or four levels, and as they advance through the levels they learn to do mental math (which is important to me). 

I found this review very helpful.  http://grhomeschooling.blogspot.com/2010/09/jones-geniuses-matrix-math-review-ages.html

 

Tanvi,

Absolutely, although I am not expert with the abacus I have looked into the research results of those practicing mathematics this way and they are very good.  I find it to be especially effective for being able to visual place value so well and consequently being able to visual math calculations in a way that paper and pencil methods are not conducive to.  We are planning to add abacus practice into our Math Two program which follows Matrix Math which is Math One. Math Two is a program still at the planning stage.  Hope to have it available this years.

 Lead the way Tanvi !  Keep us posted on your results.

Chris,

The kids learn the first, second, and third powers of the digits 0-9 as a part of learning their Factor Table (multiplication table).  Third power products are not in the multiplication table but we will immediately proceed to doing powers and roots once mult & div are mastered.  Once they are grounded in powers we proceed to derivation of roots.  Second and third power are the ones used the most often so we concentrate on doing those calculations quickly.

I could set up a free online demo that would focus on the use of animal mnemonics to teach letter sounds.  Would that be useful?

PokerDad,

Surely that is true, different parents will have different values.  I taught my daughter languages.  Amy Chua taught her daughters piano and violin.
Many black parents in the inner city will focus their children on sports, a significant avenue of success for many inner city kids.

Granted the basics are behavior, reading, math.  How high do we set the bar on these and where do we go afterward. 
The selection, order, and pacing of skills either serve to enhance learning or restrict and retard them. 
From my perspective as a specialist in accelerated learning I feel strongly we should, from the start, teach speed reading, memory training,
and rapid mental calculation skills.  These are not normally taught but they result in a vast improvement in learning & processing ability.

You may have read the post on Peter Wozniak who invented SuperMemo and has carried on Ebbinghaus work on natural memory:

http://www.wired.com/medtech/health/magazine/16-05/ff_wozniak?currentPage=all

It is a bit depressing because the work on natural memory via recall and review of material on a regular basis concludes that we forget
most of what we learn (80%) and there does not seem to be much we can do about it.  So what does that say about our quest for
encyclopedic knowledge?

One need not be limited to natural memory.  We know how to train memory.   

Tanvi,

I must apologize.  You started this thread and I have yet to respond to your question because so many others seem to have weighed in very ably.
We are now recognizing that activation of the cerebral cortex can and does occur much earlier than the average 2 years old as listed on our materials.
Matrix Math is now used effectively with children only a few months old.  I do not know about LM (Little Math, I presume) so I cannot really comment or compare.
To answer one of your questions, JG Math would work very well in conjunction with abacus training.

I can tell you what the major pitfalls are that most early learning materials fall into that we have tried to avoid with JG Matrix Math.
 They often do not prioritize objectives.  For example, I have seen many programs that cheerily promise to teach colors and shapes etc.,
and they do... for a price.  If you want to spend a high price to teach your child colors and shapes fine.  There is so much to learn you
will be broke soon.  Doman is bad about not prioritizing.  Babies are learning about impressionistic paintings and wild birds.
 I have no problem with any of that but are wild birds rather than letter-sounds or digit-quantities really the priority?

Second early learning programs typically take way too long with each stage of the process which is a function of their understanding
of how fast children are capable of progressing.  Kindergarten and first grade math workbooks are very beautifully illustrated with lots of
cool coloring and math activities for the kiddos to do.  In a year's time the child will never advance beyond the most complicated problem
in the book, usually in the range of 7 + 5 (a two digit answer perhaps but seldom if ever larger than the teens). 

Third they are often totally right brained activities treating the child as incapable of learning anything.  Basic math facts and phonics
must be intuited because only a right brain orientation "should" be used.  Left brain skills are subtly discouraged or in some cases
condemned or even demonized.  This is needless nonsense.  It is like two carpenters arguing over whether you build a house with a hammer or a saw.

Matrix Math focus on connecting the quantity with the digits by using a matrix of dots placed on the numbers providing for rapid advancement to addition and subtraction.
We then build up their concentration and knowledge of math facts via practice eventually getting them off the dot matrix once they have memorized the matrix.
It is a great program that can get a 5 or 6 year old to mastery of addition and subtraction often within a few weeks.  For younger children it takes longer but
it is still very effective as long as you apply the program consistently and have fun bonding with your child.  If it is a chore to you, it will be a chore to them too.
Progress is determined by a set of 10 steps rather than a timeline.  It is a process, it takes whatever time the process takes.  Just follow the steps to success.
All the materials are provided so you don't have to make anything yourself.  The process is explained in detail in the text and on the DVD. 

Chris1,

Yes, you are right the children must know the cubes of the one digit numbers to calculate the roots of six digit numbers.  Most mathematics is a combination of memorized data interacting with calculating skill.  You memorize the multiplication table and can multiply vast quantities because of it as long as you are facile with the procedure.  It is no different for our kids.

You definitely have a point that demonstration problems are typically chosen because of their apparent difficulty but actual ease of calculation.  Dead time in a public demonstration is fatal.
People lose interest.   However that kind of misses the point that many apparently difficult problems are really very easy if you have the proper prerequisite skills.  Why shouldn't all kids have the mastery that permits rapid mental calculation of large numbers whenever possible.  We focus on those types of computations that are used the most. 

We do not neglect the necessary mathematical calculations children need to know just because they don't provide good fodder for public demonstration.  Fractions for example are a must for entry into higher math.  An addition of fractions problem is really a series of operations and may take some10 seconds to do.  That is too long for demonstration purposes. However, Fraction Master is a prerequisite to entering into our algebra course.  We do not let students enter algebra that do not have their Fraction Master award.  (not a very commercial approach, frankly)

Weakness in mastery of basic math facts to some degree is almost universal even among adults because of poor teaching methodology (what is 9 x 12 = ?).  The next level is factoring, knowing the prime factors at least of the numbers up to 100, some students haven't even heard of it although it is the Fundamental Principle of Mathematics, so weakness in basic facts typically grows into often massive ignorance of factoring.   The third and equally essential skill level is fractions.  If you are good at factoring, fractions are a piece of cake even though there are eight operations with fractions you must master.  Many parents seem to be fooled that their kids are competent with fractions because they can intuit 1/2 + 1/4.   

All of these operations need to be paired with applications such as word problems to teach the higher order thinking  that allows them to connect their calculation skill up with the reality of the world we live in.

Mom2bee,

If you want to teach Jones Geniuses I would love to have you on board.  Math Seven is the level we train teachers in.  Once they have mastered the same skills we are asking the students to master they are capable of teaching anything at or below that level except for Matrix Math.  Matrix Math takes a little special training.  However, if you have done it with your child you would be more than competent to teach it to others.  There is only the one assessment regardless of level because we are going to start by cleaning up basic skills and this assessment is amazing at telling us where the student is concerning their math abilities. 

Matrix Math starts off by teaching numeration concepts, digit shapes and quantities using dots placed on each digit in a pattern, thus the name Matrix Math.  The child learns a handful of very basic and crucial skills: how to count forward and backward from 0 to 20, counting the matrix on the digits, memorizing the matrix on the digits, connecting the dots to make the digits, counting forward and backward from each number tween 0 and 20.  Rather quickly they are able to add by counting the dots forward, and subtract by counting the dots backward.  After they have memorized the matrix they no longer need the special worksheets that have the dots on them.  First they work with very large manipulatives then once they get the idea we move to paper.  The first worksheet has 4 problems in addition on one side and 4 problems in subtraction on the other in very large print.  There are five versions of each level of worksheet so they do not simply memorize the answers.  They will then move up to 12 on a page then to 24 then to 50 on a page.  Then they go off the dots.  It works really well and does not take long.  Of course, the younger the child the more time you will typically need to spend with them on it but they will get it.

Feel free to contact me at [email protected] and I will be happy to help get you the training and materials to find out if you want to teach or not.

You know you can probably think of a simpler device to make a rope run.  There seem to be plenty of metal pieces out there with regularly spaced holes in them like shelving supports maybe.  I remember Doman trying to figure out how to make a device that increased the CO2 in the child's lungs to provoke the auto response to breathe deeply.  He figures what it would take to change the CO2 content of a small room.  He thought of a lot of complicated, and expensive, things.  Eventually he realized that breathing into a paper bag for a few minutes would do the trick.

I mentioned a couple of days ago I am doing a free online seminar "Formula for Guaranteed Success in Any Subject".  It will be Friday March 23 from 1-2 pm CST.
All participants will receive a free eBook "Formula for Guaranteed Success in Any Subject".  (I had put the wrong date down in a previous post, my apologies)
It does focus on motivation as one of the primary elements of guaranteed success so it relates very strongly to our subject of encyclopedic knowledge.
In any case, to register for the free online seminar:  email [email protected].   

We will send the free eBook to anyone who requests it (email [email protected]) but we are not releasing it before the online seminar next Friday.
The next online seminar "Natural Memory Versus Trained Memory" will take place on the following Friday, March 30 from 1-2 pm CST.  This is also a part of
our exploration of encyclopedic knowledge that I feel strongly is a must, training the memory.  Anyway, there are limited places so you do need to register,
just drop a line to Chris and he will send you the link.  I am working on a free eBook to go with that one as well.  These are listed on the Brillkids announcements.

Via my non-profit institute I am trying to give away as much as I can of the valuable insights and materials I have developed over the years.  Short seminars,
short eBooklets to accompany them that people can grasp quickly and implement right away to good advantage.
 Please help me give stuff away by referring anyone who is interested to participate.