By Crewton Ramone.
INTRODUCTION:
“What we have here is a failure to communicate!” ~Cool Hand Luke
I'd say by now, in America today we realize we have a problem with the mathematics.
To quote or paraphrase a president.
“Is our kids learning math?”
The answer is, “No. They isn't.”
Actually to be more accurate, I'd say some of us realize that we have a problem with mathematics in this country. Parents with kids in high school. Parents with kids subject to common core math standards. Corporate executives who can't fill positions with US graduates at either the high school or college level due to sub-standard or nonexistent math skills. Too many students graduating high school can't make change. The average grade for a student in algebra for the first time they take it, is F. That comes with a whole lot of damaged self esteem. It dawned on me recently that there is still a large segment of society that is unaware of the magnitude of this problem. The problem is that a large number of those are the teachers of mathematics themselves, for reasons I'll touch on later but I'll sum up here with this statement: you can get a teaching degree without taking much math, particularly analysis which incidentally is basically how we teach math and these two phrases “A certain percentage have to fail .” and “Boys are naturally better at math than girls are.”
Really?
What If we took this attitude with reading or learning English?
Well, math is just a language and we need to teach it that way. In fact it's my contention that if you can speak English or have command of a language you can learn math—or at least quite a bit of it. But I can fill rooms with volumes of books and papers that document the problems with mathematics education in the USA. And it's not for what would appear to be a lack of trying. We spend plenty of money on math education programs that don't work. And that's when another thing dawned on me after 25 years fooling with mathematics education first hand, tutoring students , teaching parents lecturing and training. The US government has no interest in the masses understanding and being conversant with the mathematics. NONE. This does not serve them. Besides people who do math are notoriously hard to govern. They sure make it sound like it's otherwise though, with common core and STEM and all manner of education initiatives like “No child Left Behind” but all evidence points to the contrary.
If you're reading this book you're probably familiar with John Taylor Gatto and/or Charlotte Thomson Iserbyt. If not, I would suggest you get familiar with their work. They outline and document the systematic dumbing down of the American populace via the public education system. They have both written several books, lectured extensively on the subject and their work is well documented. The bottom line is the government gets what it pays for. And the current state of mathematical education is no accident; which is my focus, but also the sciences, music, the arts, history, English, reading, law, our constitution here in the USA, these things (and that was the short list) are no longer taught well to the masses for obvious reasons. You will find a bibliography of books by them and others on this controversial topic at the end of this book in the appendix. The university system has also been co-opted. People are thoroughly disgusted by what's going on if they are actually paying attention. Many seem to be completely unaware or if confronted with this information are quick to dismiss it. For some of us the situation makes us angry.
In fact it is the dissatisfaction is so great that more and more people are turning to homeschooling; more and more people are finding that what these two and others are saying isn't crazy talk or just conspiracy theory after all and its concerning them greatly, to the point that they are pulling their kids out of free public schools, and taking on the costly and time consuming job of educating their children themselves.
The problem of course, is mathematics, because they find that they may have not have had the best experience with math themselves and are concerned they can't teach it effectively to their own children. Or have found that even though they understand it they have a difficult time imparting it on their own children or students and turning up the volume is of no use at all. And even if they are successful at getting their children to understand math, which they usually confuse with memorization and regurgitating algorithms rather than actual understanding which is again why so many have no idea how to apply the math they have learned to real life problem solving. Even so, there is usually a great deal of pain and suffering that goes along with the experience instead of it being fun and something they looked forward to as children. The problem is you don't know what tools to use or how to use them effectively because chances are you were taught in a manner that, to put it mildly might not have been the most effective and painless way. Further, although you realize that there are problems with the way we teach math from your own personal experience, you might be under the impression that there is no other way, and that it has to be “work” and all about memorization, algorithms, axiom and postulate--and certainly no fun at all.
Well there is a better way. Using base ten manipulatives, is an extremely effective way of making students understand mathematical concepts. In fact, forty years later we have corroborative evidence from universities that say using manipulatives or more sensory input is a superior method for educating students in whatever topic it is, not just mathematics. Until now using math manipulatives was was mostly relegated to addition, subtraction and place value. What I'm showing you how to do you use manipulatives for elucidating counting through calculus concepts including trigonometry and algebra--all starting at a very early age.
The National Council of Teachers of Mathematics has said that using math manipulatives is advised from kindergarten through University level courses. The problem is most people don't know how to use them effectively or properly and can't even identify base ten blocks that are the best to use for ease of presentation and imparting understanding--all base ten blocks are not created equal. Neither are the methods for using them. Believe me I've spent a lot of time on YouTube and the internet, and I've seen quite a few videos were well-meaning teachers do presentations where they use base ten blocks incorrectly—yes, what I'm saying is they're doing it wrong; the blind are leading the blind.
I also find that any student who managed to graduate high school with an A/B average in math assumes everyone else can do simple computation too, and are amazed when it turns out they are the exception not the rule. At this point I have to point out that computation is how we do math it's not the math, but we're failing even to teach computation which should be easy assuming you have the right tools. Again this book is about solutions but will fall on deaf ears if too many of you ask, “solutions to what?” Let me illustrate this point with a few stories .
Once in Utah. We were confronted with the problem of having too much product to store. We didn't have enough space to store it so we went to a storage unit place, Jerry, the man that introduced me to this methodology, and myself were looking for a storage unit that was 10 by 10. We knew what it was we needed because we knew how much product we had, we had we measured how much space it would take and we figured that a 10 by 10 unit would solve our problem. Despite this. he lady at the counter spent quite a bit of time explaining to us about the various sizes; she made it very clear that 5 x 5 was a quarter of a 10 x 10 not half; that if I you bought a 5x5 or a 5x7 or 8x8 how big that was and then went on to explain in great detail the various sizes that they had.
I was going to stop her because Jerry Mortensen was of course standing right there and his ability to do this kind of mathematics was beyond question. He stopped me and let her continue. After she finished her spiel Jerry asked, "why did you go into such detail about the various sizes when the dimensions are printed out right here on this piece of paper?"
"Well," she explained, "most people can't understand these dimensions and I think that, for example, 5 x 5 is half of a 10 x 10 even though clearly it's a quarter. 10 x 10 is 100 square feet are you sure you don't just need 50? Like a 5x10..?"
Jerry looked at me and said, "you know, the problem is worse than I thought." This was in the early 1990's and it has steadily deteriorated since then. I have been watching it from the trenches first hand.
People have a hard time believing that he average person can't make change. Counting up to whatever bill they were given. Next time you are in a retail store ask the person to count back your change. Say you bought something for 36 cents and you paid with a dollar. Rather than just handing you a pile of change, have them count it back for you. 36, and 4 pennies is 40 and a dime is 50 and a fifty cent piece is a dollar or 36, and 4 pennies is 40 and a dime is 50 and a quarter 75 and another quarter makes a dollar. Then give them a problem like, “the bill is 67.83 and I pay with a 100 dollar bill what's my change?” They should be able to just say 32.17 (thirty-two, seventeen) but chances are they'll need you to write it down, and then do it the hard way on paper. And that's just subtraction.
Here's another one.
I'm in a bookstore. A guy is buying some books. And the total comes to $40. Well actually, he is just pricing some books. So, they aren't ringing it up on the cash register. Then the guy wants to know what the total is going to be including the tax.
So, in the normally quiet bookstore one of the cashiers says, "hey, what's the tax going to be?” And somebody else shouts back,"9%". So, then I hear one of the cashiers say, "9% of 40...oh gawd." and he goes over to the cash register. So, I say, "$3 and 60 cents..." Without really thinking about it.
And then the girl punching the cash register says, {punch} “$43 and 60 cents.” right after I do.
And people say, "oh my god, that guy is a math genius."
And I hear people who were in the room and at the table at which I'm sitting nodding and mumbling their agreement. Side note: There's an older gentleman there with gray hair reading a book looking rather erudite behind spectacles. And he kind of just looks at me. But I can't tell from his look whether he is as flabbergasted as I am that people are so impressed by such a simple feat of math where I simply took nine and multiplied it by an even number and came up with $3.60. Or if he was actually adding his approval too by looking at me as if he was quite impressed, but I'm not sure he was impressed by me or the ineptness of the crowd. We shall never know. But the point is that should have been simple and fast for everyone there.
Anecdotal evidence you say? Where are the peer reviewed studies? Try the experiment with regard to making change next time you are out and about. Here's a famous one: 9 out of 100. Is that .9 or .09? You might just ask them to make a decimal out of 9 out of 100 and see what answers you get.
Fact: if they fix the problem the grant money dries up.
Math genius I am not. But I am both persistence and observant. I consider myself a purveyor of mathematics more than an actual mathematician. I don't create math, I just show people how to teach what we already know.
As I've said this book is about solutions. Not about just about problems. I am going to show you that math is a whole lot easier than you think it is or more correctly were taught to think it is. I'm going to show you how to make math easy and even fun. I'll show you what to teach and when to teach it and more importantly how to teach, and back my theory up with practice (and you can watch me do it on video) too.
I'm sure all of you have had experiences with math where math got in the way of something that you wanted to do; for me personally, I didn't have difficulty passing the securities exam or insurance exam. But many of my agents did which is actually how I came into this in the first place. I looked at this as a way to help me get my agents to pass the securities test so that I could pay them because without the passing of these tests they couldn't get a license and without a license they couldn't get paid. And it turned into this whole other thing.
Instead of being an obstacle, what we want to do here is turn that around and make math a vehicle, so that you can accomplish your goals and dreams or whatever desires that you might have; solve the problems that you might need to solve, without math being a hindrance to you and without “post traumatic math disorder.”
I'm going to focus on basic operations. That is, addition subtraction, multiplication, and division. And then fractions and decimals, percentages, a little bit of algebra, a little bit of trigonometry. Some super simple story problems to illustrate some precalculus and calculus concepts. And that's about it. For more detailed explanations about it to go onto the Internet. I have hours and hours of video, and web pages to go along with. Quite a bit of it for free.
I can teach you math but more importantly I can show you how to use simple tools so that you can teach your children math and maybe even have fun doing it. This is basically just how to understand, teach, and learn computation but we've fallen so far, kids, as I have said, are failing at even just that much.
In order to do this, you have to be able to use certain tools and methodologies to their best effect; you just need to have some very basic understanding of some principles and concepts, and you too can teach mathematics, you too can do what I do and be called “a math whisperer.”
Too many say, "oh, you are a genius" or "you are this or that", "oh--you are teacher: you’ve been doing it for 25 years" - "oh you’ve been..." Blah . Blah, blah. Excuses, excuses. If I can do this anybody can. I failed calculus.
Okay, first off, when I was doing this and was two or three years in, people were like "wow! I can’t believe you’ve only been doing this for two or three years!" In fact when I was only about two weeks in professional educators were sure I was an old pro.
I was quite excited to try this out in my mother's classroom. So there I am with a few 2nd graders. Teaching them to factor polynomials on the chalkboard. This back when it was still at chalkboard. Late 80's, 1990 at the latest. They had the blocks on the floor and were gathered around me in a little group.
Unbeknownst to me, the principal of the school had come to my mother's classroom to deliver a message. He saw me doing algebra with little second graders on the board. He stood there silently and watched with his mouth open. (My mother described the scene to me later.) It took quite awhile before I noticed him, I was focused on the task at hand.
Understand these little second graders were having fun, excitedly factoring polynomials. We are probably factoring something like x² + 7x + 12...and they are racing to see who can put it together and tell me the factors first.
Afterward he was sure that I must be professional teacher, and that I had professional training and asked what university I had graduated. Actually, all I was doing was trying out some of the techniques Jerry I showed me using the base ten blocks, and sure enough they worked.
This principal, by the way had degree in mathematics, so he was even more amazed that I was factoring polynomials--something that at that time you just didn't do with 7 year olds. You were supposed to wait until high school. And most people still don't start early enough even though little kids like algebra and ask for it by name once they see how fun it is. You read that correctly. They have since started introducing algebra earlier but they still are symbol based and make it hard and stupid instead of fun and engaging.
By the time you finish reading this book you will be light years ahead of your peers--and that's not hyperbole.
The idea is that Jerry Mortensen had the same problem, everybody was like "oh! Jerry is so special! He created the program--of course he can teach any kid math." or "Maria Montessori she is special because she created the program”—same with Mario Montessori – or whoever it is, right?
They all have a crowd following that says, “they can do it, but I can’t.” or ”they are special, you are different” and what we are all trying to do, or were as the case may be, and Jerry was especially, but myself included, is try to make you understand that YOU can do this also.
Maria Montessori taught her son Mario, he made some improvements, Mario taught Jerry who took the tools and made some improvements as a clinician not a theorist, Jerry taught me and for over 25 years I've been using the methods and refining them also as a clinician in the field working with students and parents and sometimes teachers and occasionally training trainers to teach teachers. Now I'm going to teach you. Not just theory but theory in practice.
Many of you will take to this like fish to water, as soon as you see the method you dive right in, but many are more recalcitrant. Some of you have tried to teach your kids math and had mixed results. Or sent your kids off to school either public or private and found the math education there lacking as evidenced by the child's behavior...usually tears and expletives where “I hate math” is repeatedly heard. I have had child psychiatrists do nothing more than use this method to teach teen age children math because they discovered that teaching math in such fashion as the child understands it causing their grades to improve returns tranquility to the household. Often times though, the average parent cannot afford a child psychiatrist at 100 or more dollars an hour. How about we avoid the problem in the first place and educate the parents, so that they can educate their children? You do most of the teaching of your child's first language naturally and many of you also helped teach your children to read. Math should be no different, it's just nobody ever showed you how and others have tried to beat this natural teaching ability you have out of you on purpose. Some of you may think, “sure, you teach kids English or whatever your mother tongue is, but you don't teach them math. You need a math teacher for that.”
The teachers are there to assist you in the education of your children, not to do it all for you. If you’ve decided that you want to try and help your child with math but you don’t know how or where to start, you are frustrated and you are having a hard time with it; struggling through work books or stale curricula and memorization of formulae and math facts, know that you aren't alone. Some of you don't have these problems. This book is not for you. But if you have struggled with math you are about to be amazed.
Some parents have told me, they can see their kids turning off to math and they know the serious consequences of this. Others may not be having such a hard time but wish there was a better way, or maybe some of your children 'get it' but other siblings don't. There is no telling your personal situation. So I'm going to share some best practices, understanding of basic principles and concepts on how to do math using manipulatives, or base 10 blocks that will make whatever you are doing at whatever level more fun and a lot easier. Promise. You are in the right place. I've had great success at this for years but this was not always the case. I will also show you how to avoid some common pitfalls.
Mathematics is absolutely the gateway to understanding the world around you, to developing reasoning, logic and creative thinking skills and to developing and creating critical thinking skills; mathematical reasoning helps wherever you are, whatever you are doing--math will make you better at it. And certainly the solutions to the problems facing humanity are not going to be found in taxation and political science but in the hard sciences of technology and engineering. We need to generate clean non polluting sustainable energy for example, clean up our water and air, feed growing populations save endangered species, just to name a few challenges. And that's going require a lot more people being conversant with math and problem solving using math. It's also going to require math to get people to understand a lot of those problems already have solutions it's just that some of those solutions threaten the current establishment and their corporation's profits so they make up outlandish stories to get you to believe change is impossible, and because you can't do the math you are prone to believe them.
Look. Mathematics is liberating; education is liberating. Tyrants want to dumb you down and extract as much wealth from you cradle to grave as possible all the while telling you they are actually taking care of you.. Educators want to liberate you and there's nothing more liberating the mathematics.
Too many students are looking at college syllabuses asking, “what kind of degree can I get out of this college or university without taking much math?” This wouldn't be such a problem if children got started right with math from the get go at home. If you are going to wait for superman or government, you are going to wait a long time.
The point is, if your children become poets or journalists, they become a poet or a journalist because they love poetry or journalism not because they washed out of engineering. Maybe they start a band. Not because they failed in the sciences because they couldn't do the math, but because they really love music. (If you can do music you can do math and if you can dance you can count and vis versa.) It frees you to do what you want. Not everyone will become a rocket surgeon. But if what you want to do requires math it won't stop you. Even if like me it's just getting scholarships for college. And an “F” in math in high school does not a full scholarship in college make.
If you are like me, you failed at some point in mathematics. For most people it's right around algebra. For me it was Calculus. (Although I remember fractions throwing me for a loop.) Now you can watch video of me teaching trig to eight year olds. Math isn't hard--all it is is counting. The way we teach it makes it hard. I am going to show you how to use some simple tools to make understanding mathematics fast and easy. Most people just don't know how to count because they weren't given the proper experiences at the proper times. If you would have told me I was going to be teaching people how to teach math after I failed calculus in high school I would have laughed in your face. Now I've had success with just about every kind of student you can imagine from young to old, normal to autistic, blind, kids, deaf kids—name it. You can too.
What I am going to lay out for you is a rough frame work of cutting edge methods and practices you can use to help your children understand mathematics using base ten blocks to level the playing field and make math accessible to all by making math concrete and graspable using base ten blocks as our primary modeling technique. We will also touch on some of the latest brain science because it is important not only to understand mathematics but how we learn mathematics or any subject. The way we learn language at an early age can be applied to learning and understanding math and I'll cover that too.
Just like in days of old, this book has lots of pictures because what we need to do is put the pictures (and reasoning) back into the the mathematics because they are crucial for the understanding of it. Imagine learning to read the word 'cow' without ever seeing a cow. Then the word 'chair' might be confusing because they both have for legs and they both start with 'c'. It's the same in mathematics, the base ten blocks are simply going to help us decode the symbols, keep the operations straight in our minds, and show how to count very quickly, collapsing time frames down to the point where it looks like the fact is memorized when in fact it may be just that the computation was done with lightening speed because a picture can be seen in the mind's eye and be described with words and those words are numbers. A lot of the mathematics gets demystified when you discover what the words and symbols really mean.
You may be thinking that teaching mathematics in someone else's job and that you can't teach your children mathematics because you're not a professional and teaching math requires you being a professional. Well, you teach your children a much more difficult and complicated language: English. And you do it naturally.What this book is going to do is show you how to teach mathematics as naturally as you do English to your children.
Later this fallacy could be used to your advantage as you you offer your skills to parents who would rather hire a professional than do it themselves because they have been conditioned into believing this too.
What I am going to do is show you how to get started with very young children, confident that you can modify the lessons for older students because if young students can get it so can you and so can teen agers. These are proven techniques. I have pages and pages of glowing testimonials from people I've taught now as did Jerry, as did Mario, as did Maria. These methods work. I will teach them to you and even tell you why they work as compared to other techniques.
What many have found is that we are failing at teaching students math, and have been failing at it for so long now that those students have become teachers. Teachers have been trained (not taught) in a manner that isn't as effective as it could be and many of those teachers are either blissfully unaware that there is a huge problem starting a a very young age, or are aware of it but are placed in a bureaucracy where they feel powerless to do anything about it or in fact can't and if they do go against the grain and become 'commando' or 'rouge' teachers they are very quickly identified and either brought back into the fold or eliminated.
Imagine a world where governments and corporations collude not only to withhold cures in medicine, but also to keep you ignorant of the mathematics, and hamstring your logic and reasoning skills which make critical thinking difficult or impossible. The better to extract maximum wealth from you. If at this late date this still sounds like 'conspiracy theory' to you, put the book down. If you have an inkling that what I and others are saying here is true then I invite you to read on.
And basically I go on to tell you that I am not giving you the equipment you already have the equipment, I'm just teaching you how to use the equipment you already have, actually I am not even doing that I'm just explaining to you what others have taught me using base ten blocks, by breaking it down to basic concepts and foundational teaching. Distributive theory is foundational teaching. The difference of two squares is foundational teaching. The definitions of sine cosine and tangent is foundational teaching. So I'm going to put some foundational teaching in the book replete with pictures.
Here is an email exchange that is all too typical. Before we begin let me say none of the little girls pictured are his little girl and this is exactly the time to start teaching math concepts right along with language and motor skills development. But her ability to push a crayon around is not indicative of her ability to understand basic math concepts which, when you think about it are just vocabulary.
I have a 3.5 year old daughter.
