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Visit swithop.com today. - Welcome to Radical Personal Finance, a show dedicated to providing you with the knowledge, skills, insight, and encouragement you need to live a rich and meaningful life now, while building a plan for financial freedom in 10 years or less. On today's show, we continue our series on how to invest in your children at an early age.

This is clearly a very extensive series, and what I'm seeking to do is to persuade you that when you think of investing your money, you ought not first to think of a product that you can buy from a financial product salesman. Rather, you should think broadly about the term.

And I'm developing in detail a thesis that I've had for many years that most of the dollars that parents save to spend and invest in their children, for example, to purchase mutual funds and put them in a 529 account, are probably better off spent in some other form or fashion at an early age into the wellbeing and intelligence of the child.

And so while these are not mutually exclusive, you can do both if you have the money, I wanna encourage you that you're gonna get a better bang for your buck by focusing on these things that I'm talking about. So in this series, we began by talking about your child, preconception of your child and the basic genetic material that your child inheritance, conception and childbirth.

Then we talked about nourishing your child's body, helping him to develop a body that is free of disease, that is vigorous in health, helping him to maximize his genetic potential in terms of height and beauty, et cetera, with good nutrition and a clean environment, lots of exercise, getting stronger, et cetera.

Then we pivoted from the body to the mind. And with regard to the mind, I spent two episodes focusing on literacy. And now in this episode, we're going to turn to numeracy because these two things go hand in hand. Literacy and numeracy are the basics and they're certainly the basics of academics, but I think they're the basic skills of life.

If we had to choose one or the other to focus on, I think literacy would take us farther. Someone who's very good at math, but for some reason can't read is gonna have a harder time absorbing the information that he needs in a practical sense in life. And so if we had to choose between the two, we wanna emphasize literacy, but I don't think we ever have to choose.

I think a strong and healthy mind should be maintaining both of these things together, be both highly literate and highly numerate, and they work together. Now, towards the end of this episode, I'll talk about an appropriate progression because I am not persuaded that numeracy is something that should be emphasized in the youngest of ages.

And while I have titled this series, How to Invest in Your Young Children, I think we should be careful at the age of which we really start to focus on numeracy. But at its core, we want our children to be highly numerate. Why is this important in this context?

Well, at its core, numeracy is a way of making your children smarter. And we wanna have children that are beautiful, that are strong, that are physically dexterous, but we also wanna have children that are very, very smart and well-informed, and we wanna maximize their brain muscles. The brain is a muscle that should be viewed like other muscle groups.

The more it's exercised, the stronger and more powerful it becomes. And we want our children to have large and healthy physical muscles, and we want them to have a large and healthy brain. Interestingly, of course, the physical muscles feed the brain. Exercise is good for your thinking ability because the brain is a muscle, but the brain needs to be exercised not with the lifting of physical weights, but with the manipulation of mental processes.

And this is something that is applicable to you and to me as adults, but also to our children. So we want our children to exercise their brains on a daily basis. I've had this theory for a while about what a perfect brain day would look like for me. You know, how do I make my brain smarter on a daily basis?

Well, I need to exercise it. So what does that look like? Well, ideally, on a daily basis in a perfect world, I'd like to make sure that I read something, that something that I read should be beautiful, it should be attractive, it should inform me, and it should inspire me.

So I want to access something that's beautiful and informative and well-written. So that's gonna involve not just, you know, day-to-day dime store literature, but something that raises me up. I wanna exercise my brain with math. So I wanna do some form of a math workout every day, if at all possible.

And I wanna look at math as a way of strengthening my brain. And so in a perfect world, I should be regularly building my mathematical ability. In an ideal day, I should be making myself smarter with studying and learning and exercising some new language, learning new vocabulary, reading something, expanding my brain.

Multilingualism also is proven to enhance my brain ability. If at all possible, I'd like to engage in some kind of musical activity. So if I can play an instrument or engage in something that's gonna build that skill, that helps me on a daily basis. Something that's aesthetic would be quite valuable.

So if I can draw or paint or just appreciate art, something like that. And of course, we get into all the world of emotions, surrounding myself with the positive emotions of love and a vision and goal setting, et cetera. All these things are good. All of them contribute, and they do some heavy lifting in our brains.

But at its core, the ones that work up our brains the hardest are math and foreign languages. That's where we often have to think, we have to struggle. And it's that exercise of thinking hard that makes the brain harder. There are benefits, of course, to going for a walk.

Many of them, many physical benefits. But if you want to grow your muscular ability, you have to lift heavy weights. And mentally, it's the same thing. There are benefits to just simply going and using and enjoying our brains, right? We all enjoy a relaxing novel or something that's very, very simple.

But in order to grow our brain muscles, we have to challenge it. And one of the fundamentally most useful ways to challenge your brain is quite simply with math. It's extremely valuable to build your brain muscles. Math builds your brain muscles and strengthens them at a measurable level. Think of it as a mental workout, and it makes your brain work more efficiently, more productively, and more effectively.

And this is a really important reason to actually study math, regardless of any practical concepts, meaning regardless of any practicality. I read you a couple of paragraphs from a book called "The Equation for Excellence, "How to Make Your Child Excel at Math" by Arvind Vohra. And in the very first chapter, he talks about why study math.

And I think it's important that you understand this concept. When children ask why they need to study math, the answer usually has something to do with either daily life or applications to science and technology. The problem with the first motivation is that it is an obvious and transparent lie.

The second type of motivation tends to have the opposite of the intended effect. The daily life explanation tells students that they will need math for their daily activities. For example, they will need to calculate the tip in a restaurant or determine how much they should pay for their groceries.

Most students are quick to point out that this problem can be solved by carrying around a calculator. And anyone who is worried about running out of batteries can carry around a spare set of batteries or even two calculators. Even cell phones have built-in calculators. And quick aside, isn't it so funny how antiquated your language can sound when there's a technological change?

This book was published in 2007. And it's ironic because of how antiquated the language sounds when that was a mere 16 years ago. But of course, 2007 was the year that the iPhone, I think it was 7, oh, 7, yeah, pretty sure, is the year the iPhone came out.

So a mere 16 years later, this book just sounds laughably antiquated with that comment. The arguments against the daily life explanation continue. In daily life, you never need to do more than add, subtract, multiply, or divide. Why learn trigonometry? Why study calculus? Why do anything beyond arithmetic? Even math-oriented jobs rarely require any really advanced math.

When I worked as an actuary, the only math I used on the job was multiplication and the occasional exponent. The actuarial profession is one of the most math-oriented professions in the world. The other rationale for studying math focuses on science and technology. We need math to design space shuttles and satellites, to work in laboratories, and to build the newest computers.

In one way, this argument makes sense. Much of that work requires intensive use of advanced math. But very few people work in those areas. Those that work in those areas usually do so because of an internal passion, not because of any external motivation. In fact, from the perspective of most students, there is very little external motivation to be a scientist.

The strongest external motivators for most teenagers are money, fame, power, popularity, and attraction to the opposite sex. None of these powerfully motivate students to pursue careers in science. For every million dollars a scientist makes, the businessmen for whom he works make a billion. For every famous scientist, there are a thousand famous musicians and actors.

The scientists who made the nuclear bomb were not the ones to use it. That power belonged to politicians. And in American culture, scientists have no more popularity or sex appeal than anyone else. Thus, this argument not only fails to motivate students, it actually does the reverse. A student with no interest in being a scientist who hears the technology argument now thinks that advanced math is useful only for scientists.

Thus, he does not need to learn it. If his goal is personal gain, his time is better spent doing almost anything else, studying politics, learning to play the guitar, working out, or thinking of ways to make himself rich. Math becomes just an annoying requirement. So then, why should a student learn math at all?

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In chess, the bishop can move only diagonally. The knight can move in an L shape. A real soldier, on the other hand, can move in any direction. How would studying chess help in any real war? I had, of course, completely missed the point. Strategy has nothing to do with L shapes or diagonals.

A chess player learns to anticipate his opponent. He learns to look for strong positions rather than short-term gains. He learns to make intelligent sacrifices and be wary of the strategic artifices of his opponent. He learns to predict his opponent's future responses to his actions rather than focusing on the immediate gains.

This mental discipline makes his mind sharper and he becomes a much more capable strategist. Similarly, math is important, not because it teaches a student how to use trigonometry to measure the height of a building, but because it develops a student's ability to analyze and solve unfamiliar problems. Math develops concrete reasoning, spatial reasoning, and logical reasoning.

Math does not just develop skills that can be applied to science and technology. When math is taught right, it develops the student's fundamental cognitive architecture, increasing his intelligence. The student will develop the logical reasoning skills that allow a lawyer to analyze a legal situation and to present a coherent and convincing argument.

He will develop the ability essential for any business person to isolate the key components of a system. He will develop mental skills that can be used in any problem-solving situation. His mind will become faster, sharper, and more precise. What lifting weights does for muscles, math does for the mind.

In no sport will an athlete suddenly lie down on his back and lift a weight 10 times. However, the vast majority of athletes do the bench press. Why? It makes them stronger and thus prepares them for athletic endeavors in general. When you teach a child math in the right way, you are giving him the gift of a sharper and more powerful intelligence.

You are helping him actually develop his mind. You are making him smarter. You are giving him the ultimate ability to succeed in the world and to build a happier life for himself. You are not just making him better at math, you are making him better at thinking. I hope you find that encouraging and a little bit inspirational.

When we think about how to make our children smarter, we have to consider the tools at our disposal. And that's what I'm trying to give you. We've talked about the physical tools to make your children's brains work better, things like high fat consumption, lots of exercise, low sugar consumption, et cetera.

But then we pivoted to talking about making your children smarter and more well-informed literacy. And now we wanna make your children smarter in terms of building up not only the physical gray matter of their brain, but also their thinking ability. And mathematics is one of the most consistent tools that we have for that.

I think this is in some ways because math is analogous to a form of a language. I think mathematics could be described quite elegantly as the language of the universe. I am persuaded that as a Christian, I'm persuaded that there's an incredibly useful apologetic for even the existence of God in the unreasonable effectiveness of mathematics.

When you look at how precisely ordered the universe is and how beautifully consistently mathematical, it beggars belief to think that that form of, that language that exists, that is non-physical, that human beings universally can have access to, a universal immaterial reality, such as the language of mathematics, it almost requires a conception that there is a beautiful and elegant design.

And mathematics is a language that as you build fluency in, it just leads to ever increasing opportunities. Now, as a language, I am persuaded that everyone can learn math. And I was gonna talk about this later, but it's important to talk about now. First, as a disclaimer, I myself have never been a math teacher, but I know what it's like to be a struggling student in math and I know the struggles that I myself faced in doing math.

And I know how those struggles can be resolved. So, let's talk about that, because if you are someone, there are many people who have had all of their mathematical appreciation, their love for mathematics chewed up and destroyed by the schooling system that they went through to learn mathematics. And I think that's unfortunate and unnecessary.

I think that if we understand that math is a language, just like any language, it's a language that anyone can speak. When you think about your native language, assuming it's, let's assume it's English for the moment, you can recognize that there are people who genuinely have some form of handicap that will allow them to never master the English language the way that Shakespeare did.

There genuinely are some people who will never attain that level of linguistic ability. But you can also quickly recognize the reason most people don't attain very high levels of linguistic ability is not due to a fundamental handicap or disability. Rather, it's due to not being exposed to high levels to higher levels of language, not being trained in the fundamentals necessary to achieve those high levels of language, and/or not having the time to fully develop their linguistic ability.

Except for a tiny portion of people who are genuinely disabled, anybody can become a master of the English language if given the right materials, the right basic tools, and the fullness of time, and consistent practice and exposure. And the rate at which people advance in the English language or any language depends far more on those basic factors than it does on innate ability.

As you can tell from the previous two episodes, I myself am quite passionate about literacy, high levels of literacy. Anybody who listens to my show understands that I'm a quite literate person. It's one of the things that harms my ability to reach a very broad audience. It's quite simply, I don't speak in a simple or straightforward way.

I don't speak at a fifth grade level. Years ago, I learned a lesson when I was studying copywriting, and the lesson was quite simply that in order to write effective, successful sales copy, sales letters, et cetera, you should never use language that is higher than that of a fifth grader.

And because complex language, when used to write sales letters, causes you to lose vast swaths of your audience and your potential audience. And where I remember this really standing out to me was when I saw in prior to the 2016 presidential election in the United States, I saw at some point an analysis of then candidate Donald Trump, who was running for the office, saying he never used more than fifth grade words, and he never used large vocabulary.

And I thought to myself, 'cause of that connection to sales letters, I thought, boom, this guy understands how to reach people and be an effective politician. And so I necessarily understand that because I use complex language, it limits my ability. My goal is not to reach the highest number of people.

My goal is to reach people that I enjoy talking to and inspiring those who are looking for more. So the world of popular level financial advice is abundantly well-served. I'm seeking to do something more than that. My point is, because I'm so passionate about language, you can see that with my own children and with students that I mentor, et cetera, and even with you, that I'm seeking to help you to achieve a higher level faster than most other people.

We use in our homeschool with a first grader and a fourth, third or fourth, fourth grader, fourth grader, second grader, something like that, with a nine-year-old and a seven-year-old, and a five-year-old, literally read books that are marked as graduate-level texts, as graduate-level in terms of their Lexile scores. That's intentional because the exposure at a young age creates capability, and then that capability has a payoff effect of allowing a student to go much farther, much faster.

But there was a time at which, of course, my children could not read. And it's the same with math. If we use the right techniques and we're skillful about how we introduce math and we establish an appropriate situation, we can help our children to go very, very far in math.

And it should be very rare that a child ever thinks, "Oh, I'm just not good at math." In what I've described in terms of literacy, I've had children that have learned to read at different rates and have struggled with different things. That is normal, but we can and must adapt then what we do to meet the specific needs of our students.

But what we must not do is somehow think that because they have a brain that works slightly differently or because they need a special aid of some kind or they need a little bit longer to learn the basic concepts, that somehow we should stop. We don't stop teaching our children to read just because it takes one child two years instead of two months.

Just like we don't stop encouraging our children to walk just because one child walks at three years old, another child walks at eight months. We're going to continue, you're gonna continue working with your child until he walks. You're going to continue working with your child until he reads. And you must continue working with your child until he is skilled with mathematics.

Mathematics is a language that is accessible to all people. And it doesn't matter the rate at which the language is acquired. What matters is that the language is being progressively acquired. And like languages, languages are one of those things where it's very hard to get worse at languages. Once you have developed linguistic ability, it's very hard to get worse.

Sometimes your progress feels fast, sometimes your progress feels slow, but you don't generally get worse. If you do get worse, right, say you don't use a language at all for five years, when you come back to the language, in very short time, you quickly reach your ability and then move on from there.

So math is a language and it's important to exercise it consistently and ongoing over time. Math is also very useful as a discipline. It's a discipline. Math is generally, for at least for me, and I think for everyone else, math is hard. And hard is something that is good.

Hard is useful. I've talked in past episodes about educational philosophies. And one of the things that I have appreciated over the years is I've appreciated many of the comments that those who maintain the educational philosophy of unschooling, I appreciate the comments and many of the critiques that they make of schooling.

The basic critique would come down to, if you're gonna learn something, you need to actually care about it and want to learn it. Otherwise, you don't really ever learn it. They point out that the things that we learn the most effectively are the things that we want to learn.

And I think that's true. But I myself am not an unschooler, excuse me, I'm not an unschooler because I fear that unschooling does not provide an appropriate structure for character formation. Now, character can be formed in many ways. Generally though, at its core, character is formed by difficulty. And we want to require our children to do difficult things each and every single day of their life in order that they develop the skill of facing and doing difficult things.

A man who does not have the skill of doing things that he doesn't wanna do is a man who will have a very hard time being successful in life. Now, as parents, we go to our toolbox and we say, what tools do I have? Perhaps a man who has a farm or some form of lifestyle where there's heavy physical labor can use that heavy physical labor as the tool for developing the skill set of hard work.

That's certainly something that I think many people notice that can happen well in farming economies. But we no longer live in an agrarian economy. And so that tool is often not very effective for us. Maybe if you live in the frozen north, your tool can be the hard thing we're gonna do every day is go jump in the frozen lake and have cold exposure.

Okay, maybe that's useful. But for many of us in an information age and in an intellectual world, we need something hard and that's probably gonna be something like, it's gonna be something intellectual. And so in order to help our children develop that character skill to do hard things, we need to have something hard to do.

And math is an ideal candidate for that. It's not the only candidate for that. I think that there can be other things. I'm now going to read you an essay from a book called "Climbing Parnassus." And it's called "Climbing Parnassus, a New Apologia for Greek and Latin" by Tracey Lee Simmons.

And this book is trying to encourage people to use Greek and Latin and gain the benefits that many centuries of classically educated students have gained from them. I'm gonna read to you a section here that's talking about the value of the struggle to learn Greek and Latin. I believe though that this applies first to mathematics.

While perhaps there is value in studying Greek and Latin, perhaps, and perhaps this author is completely right, one of the great challenges for many of us is simply we have never gone through that challenge ourselves. I myself was never exposed to Greek and Latin as a child. I didn't have the experience that these authors have.

Nor is it easy for me as a father to find tutors and teachers that can impose this type of disciplined character building structure onto my children. But I believe mathematics can accomplish the same thing. And most of us can impose a disciplined mathematical structure on our children to gain these benefits.

Enjoy this excerpt here from "Climbing Parnassus." You may wish to, you may be inspired and you may wish to use Greek and Latin, but think of mathematics as I read this. W.H. Auden was one of many writers of the last great generation of classically educated men and women, upon whom an early classical training made indelible impressions, intellectual and otherwise.

Those boyish classroom exercises had formed his very sensibility. And he lived to see the stupid, numbing consensus arise that a classical education holds scant value for the modern world. The modern revolt against centering the school curriculum around the study of Latin and Greek is understandable in an age of hyper utilitarianism, he wrote, though it's deplorably mistaken.

It is no doubt a pleasure to read the Greek and Latin poets, philosophers and historians in the original, but very few persons so educated in the past kept up their Greek and Latin after leaving school. The real value of classics though is something quite different. Anybody who has spent many hours in his youth translating into and out of two languages so syntactically and rhetorically different from his own, learns something about his mother tongue, which I do not think can be learned in any other way.

It inculcates the habit, whenever one uses a word, of automatically asking what is its exact meaning. Auden's case for classics was not so much the cultural one, but the case from formation. The pursuit of classics per se is worth all the devotion we can lend it. Classical knowledge provides keys to understanding Western civilization, but the habits Greek and Latin instill are worth at least as much.

The passing of classics from our schools has in fact crippled the larger culture. Here, Auden cast his net far and wide. The people who have really suffered since classical education became undemocratic are not the novelists and poets. Their natural love of languages sees them through. But all those, like politicians, journalists, lawyers, the man in the street, et cetera, who use language for everyday and non-literary purposes.

Among such, one observes an appalling deterioration in precision and conciseness. - Now for a limited time at Delamo Motorsports. Get financing as low as 1.99% for 36 months on Select 2023 Can-Am Maverick X3. Considering the Mavericks taking home trophies everywhere, from King of the Hammers to Uncle Ned's Backcountry Rally, you're not going to find a better deal on front row seats to a championship winner.

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The signs of rot surround us. Nobody, Auden wrote, who had had a classical education could have perpetuated this sentence in "The New Yorker." He, a film director, expresses that dichotomy between man and woman in the images of the bra and dachau. One would hope not. That's the murky self-important lingo emanating from the lit crit sentiment are in English departments.

It doesn't exist to communicate anything to the cultivated mind. It exists to confuse and impress easily bamboozled, uneducated, fee-paying sycophants. It pretends to profundity, but it's tripe. Language like this is not hatched for civilized people. Perhaps we can have culture of a kind without bestowing classical education upon a goodly number of intelligent men and women.

We may doubt whether we can have a literary culture whose roots run deep. Novelist Evelyn Waugh paid tribute to his own classical training. Here we see plainly that the oft-heard cry that students retain little of their Latin misses the point. A classical training, thoroughly conducted along humanistic lines, changes the shape of the mind for the better.

It stays with us. My knowledge of English literature derived chiefly from my home. Most of my hours in the form room for 10 years had been spent on Latin and Greek, history and mathematics. Today, I remember no Greek. I have never read Latin for pleasure and should now be hard put to compose a simple epitaph.

But I do not regret my superficial, superficial for the time perhaps, classical studies. I believe that the conventional defense of them is valid. That only by them can a boy fully understand that a sentence is a logical construction and that words have basic inalienable meanings, departure from which is either conscious metaphor or inexcusable vulgarity.

Those who have not been so taught, most Americans and most women, unless they are guided by some rare genius, betray their deprivation. The old fashioned test of an English sentence, will it translate? Still stands after we have lost the trick of translation. We should note here as well, the starkly limited curriculum.

His schoolmasters might have chosen to clutter the classroom with far shinier objects than it did in the second decade of the 20th century. Commercial French for one thing, or aerodynamics or wood shop. That world was changing after all, true enough. But that didn't mean that the well-constituted mind had changed.

The intellect still required molding. The better schools then, as they ought to be now, were eager primarily to form the student's mind, imparting solid knowledge mainly as a by-product of sound teaching. As with the Greek and Roman schools so many centuries before, the curriculum of Wauw's school was also marked as H.I.

Meru wrote, "By a definite rejection of what it did not include." What it didn't let in was of equal importance to what it did. Any school we might conclude with more than four or five subjects doesn't know what it wants to be. Or we may shudder to think, perhaps it does.

Most public schools in America now strive to be cut rate educational malls for the intellectually lame. Whether or not students first darken the school doors that way. So most of them leave, while even some private schools pose as little more than colorful felt boards for the earnestly shallow, commonly confusing, pious or patriotic piffle with real education.

Neither setup makes for a school any educated human being is bound to respect. Schools of the best kind have always aimed high while keeping feet to the ground. They didn't try to do too much. They tried to do the most important things. Those who ran them knew that we educate ourselves with the tools imparted by good teachers.

All else was up to us. The old schoolmasters didn't profess to teach everything worth knowing. Instead, they professed the opposite. They shaped their curricula narrowly and wisely. Information alone is not knowledge as they knew. Still less is it wisdom. Schools can accomplish much more when they recognize squarely how little they can do.

Yet how much more can be done when our gaze remains steady, our heads sober, our aims high? No results are guaranteed, but the effort pays off. Formed minds and tempered souls are no small gift to the world. Let's see one more example of how good schooling goes bad through wishful thinking pedagogy.

Perhaps the school should be, as we might say now, a challenging place. It should be hard. The work enjoined upon us should help us to develop, not only by its content, but also by its method, the mind capable of teaching itself anything. It's not so much an informed mind we seek, the one full of information for an information age, making us little more than worker bees, but a certain quality of mind, a mind at once agile and civilized, one able to place the society to which it belongs into some scheme of history.

We want not only a well-stored mind, but a well-leavened mind as well. So what of it? This may be a good enough idea as ideas go, yet we must emerge from school doors knowing something, but what should we know? An answer sits at the ready. We should learn how to appreciate the better things of life.

And so we should. The snare here, the snake in the grass waiting to bite, is that this idea has led us down some false paths. Appreciation squares with Renaissance ideals, but as conceived by us moderns, it's miles away from Renaissance methods. Today, we don't lack teachers and theorists wishing to help students pull off an enhanced quality of mind.

Many have tipped their hats to this principle by designing courses whose purpose is to help those students not so much to know, but to appreciate the world around them. Yet this isn't the learning Vittorino da Feltre knew. We don't need under this regime to learn the hard things about poetry or music or art.

We need only to appreciate them as poetry, music, or art. We need only to acknowledge their value. While it's easy to make fun of this attitude, we should recognize that in the ablest hands, the quality of mind sought is a decent goal, and doubtless it's sometimes achieved. Poetry, music, and art were not created after all to provide fodder for tests in school.

Poetry is more than scansion and difficult words, music more than scales and arpeggios, and art more than cracked vases and spatial perspective. All three were made to delight. They were meant to please us in some deep or diverting way. This we must acknowledge. But however good the object of helping young people to take easy the light and the fine things around them, this approach to forming the rough, formless mind is also profoundly wrongheaded.

C.S. Lewis helps us to see why in a little known essay called "The Parthenon and the Optative." "The trouble with these boys," said a grim old classical scholar looking up from some milk and watery entrance papers which he had been marking, "The trouble with these boys is that the masters have been talking to them about the Parthenon when they should have been talking to them about the optative." The optative is one of the moods of the Greek verb.

"Ever since then, I have tended to use the Parthenon and the optative as the symbols of two types of education. The one begins with hard, dry things like grammar and dates and prosody, and it has at least the chance of ending in a real appreciation, which is equally hard and firm, though not equally dry.

The other begins in appreciation and ends in gush. When the first fails, it has, at the very least, taught the boy what knowledge is like. He may decide that he doesn't care for knowledge, but he knows he doesn't care for it and he knows he hasn't got it. But the other fails most disastrously when it most succeeds.

It teaches a man to feel vaguely cultured while he remains, in fact, a dunce. It makes him think he is enjoying poems he can't construe. It qualifies him to review books he does not understand and to be intellectual without intellect. It plays havoc with the very distinction between truth and error.

This is what school has become for us over the haul of three or four generations. It's become not so much about knowledge as it has about experience. The teacher doesn't teach, the teacher facilitates. Instead of providing solid instruction, for instance, about the cathedral at Chartres, about its religious significance and dates and place in French geography and dimensions and Gothic architectural principles, the things that is, we can really know about it, the teacher is now just as likely to stand before a class with a photograph of the cathedral and ask students to respond to it.

What does it make you think of? Would you want to walk into a building like this? Are all these statues beautiful or ugly? Would a woman be comfortable here? Write a paragraph on what you think it must have felt like to stand in front of it. I jest, but only a little.

Here is how we are set on the high road to the Parthenon kind of education, the kind that will, by its very method, allow us later to think we know more than we do. These questions might not make a bad exercise for kindergartners, but they're unfit for anyone older.

One year hence, the students' time will be better spent memorizing Roman numerals. Yet much schooling today, even high schooling, has become every bit as vapid as this whimsical example suggests. Here, before the young can know the dangers of soft teaching or the seductions of ignorance, non-knowledge gets planted and watered, and left unchecked, as it usually is, it will spread like bamboo.

Lewis goes on. And yet education of the Parthenon type is often recommended by those who have and love real learning. They are moved by a kind of false reverence for the muses. What they value, say, in literature, seems to them so delicate and spiritual a thing that they cannot bear to see it, as they think, degraded by such coarse mechanic attendance as paradigms, blackboards, marks, and examination papers.

But there is a profound misunderstanding here. These well-meaning educationalists are quite right in thinking that literary appreciation is a delicate thing. What they do not seem to see is that for this very reason, elementary examinations on literary subjects ought to confine themselves to just those dry and factual questions, which are so often ridiculed.

The questions were never supposed to test appreciation. The idea was to find out whether the boy had read his books. It was the reading, not the being examined, which was expected to do him good. And this, so far from being a defect in such examinations, is just what renders them useful or even tolerable.

Lewis sees learning in a word, objectively. If progress in learning can't be measured for purposes of schooling, we have no way of knowing if it's happening at all. Knowledge can be measured. Appreciation cannot. Furthermore, trying to test pleasure or approval may prove hazardous even to the soul itself. Tell the boy to mug up, which means study up on, tell the boy to mug up a book and then set questions to find out whether he has done so.

At best, he may have learned, and best of all, unconsciously, to enjoy a great poem. At second best, he has done an honest piece of work and exercised his memory and reason. At worst, we've done him no harm, have not pawed and dabbled in his soul, have not taught him to be a prig or a hypocrite, but an elementary examination which attempts to assess the adventure of the soul among books is a dangerous thing.

What obsequious boys, if encouraged, will try to manufacture and clever ones can ape and shy ones will conceal, what dies at the touch of venality is called to come forward and perform, to exhibit itself at that very stage when it's timid, half-conscious stirrings can least endure such self-consciousness. If the tenets of formation ought to guide method in our schools, we also see what content must be.

It must be hard and intractable. It's import significant. It's substance learnable. Content is, in one sense at least, the bar we use to pull ourselves out of ignorance. The formed and forming mind is the muscle we use to pull. Appreciation may be properly valued above solid knowledge. The best kind accompanies us into our sunset years.

Appreciation, inward apprehension and assent touches upon the spiritual in our natures. It is indeed to be sought vigorously. The only real quandary is how to get there. And Lewis, like so many before him, knew that while the long way round, the way of the optative may not guarantee a rival at the port of our desires.

Nonetheless, it is the one way that weather-hardened sea-legged mariners have tested and found to be not only reliable, but given the winds tossing us, safe. Multum non multa. This is the one chart we can trust. Again, I understand that Greek and Latin were the object of that sentence, but I think it's hard to believe that most of us are either desirous or equipped today to go to our children and impose upon them the hard pathway of Greek and Latin and deeply probing the optative.

Most of us are not equipped and we may have other concerns. But I think mathematics provides us with so much of that. And while many of us may be skeptical about Greek and Latin being the core of a child's education, I think far fewer of us are skeptical about mathematics being the core of a child's education.

And so we want to do hard things and we want to use the tools at our disposal. One quote from a different part of the book. "There is a time for play and a time for work. "School can be an enriching, enjoyable place, "and a place some students may look forward "to attending every day.

"Those are fortunate children with fortunate parents. "But children's approval should not be our first concern. "Like a healing doctor, we know this will hurt. "We might as well say so. "School should be a serious place. "Dullards must not set the pace. "Students should be encouraged to develop a sense "of their smallness alongside the world's riches.

"Humility remains a decent aim for the well-educated mind. "Let us not try to do too much. "Those subjects that can be got outside school doors, "things like fashion design, computer training, "and photography should be. "Dissipation of effort can lead to despair. "The world outside will catch up "with the young soon enough.

"School ought to be a training ground for the intellect, "not a clearinghouse for skills. "And if it's to be the latter, we should admit it. "Whatever we decide to teach young people "who will one day step forward to run the world. "And why should we teach anything other than languages, "mathematics, and geography before the age of 13?

"Let's remember as the humanists taught "that we reap as we sow. "These are human beings equipped both with minds and souls. "Bend their twigs, we must, "just so they grow hale and well." Mathematics is perhaps our most useful tool to teach our children discipline so that they can do something hard every single day.

Now, just because it's hard does not mean that we don't want them to succeed. So what is necessary for mathematical success? Well, first, let me share with you my story. I was not good at math when I was younger. The reason I was not good was probably because my math skills were neglected.

My parents tried, I was homeschooled, they did their best. But although I was encouraged and required to learn my math facts, I never really mastered them. I wasn't required to drill them until mastery. When I was younger, I did a math curriculum that was probably fine, and then we switched.

And at one point, I cheated on my math work for months and months. My mom was traveling for a time, my grandmother was overseeing my schooling at one particular time, and I discovered that I could just go and take the answer key from my mom's desk and just copy down the answers.

And I was able to successfully fool my grandmother into thinking that I had done all my work. And my mom eventually figured out that I had just flat out cheated, and I confessed and whatnot, but I got behind. So I got behind. When I went into school in seventh grade into a local, more traditional private school, I was woefully behind.

In fact, my mom had to work hard to try to get them to accept me because I did not pass the math tests sufficiently. My first year in mathematics, I got a D the first semester, so I was barely passing. I was reasonably smart, but I was barely passing.

I didn't get an F, but I was barely passing. So then my dad took me under his wing, and he considered it unacceptable that one of his children should not do that, and he imposed certain requirements on me. I forget all of them, but one of the requirements was that I had to review my homework with him.

I think I had to bring him every test that I went through, and basically, he just took a strong interest in my mathematical abilities. So I got a D the first quarter, a C the next quarter, B the end of that quarter, and then from then, I was able to get Bs.

I kind of caught up Bs and As, and I think I mostly got As, either high Bs or low As, throughout my high school years. But I was never really great at math. I did pass through algebra, trigonometry, geometry, et cetera through to calculus, and I took calculus my senior year in high school.

And I think I did okay on the grade portion, but when it came time to take the AP exam at the end of the year, I got a two on my AP exam, which is a failure on, so I failed my AP exam, never got calculus credit. When I went into college, my freshman year of college, I was required to take a math course, and I, because I had not passed the AP exam, and I figured, well, I'll take calculus again.

And I took calculus, and I passed calculus. I don't know whether I got a B or a C, but to this day, I still have nightmares, and I'm not kidding. I'm not nor am I being hyperbolic. I still have nightmares about math, because that calculus class, I basically just made it up as I went along, and I never really learned it.

I'd never learned calculus. I was able to pass exams enough, but I never learned calculus, and I know I never learned it, because I felt guilty about it, and I knew that I was insufficiently prepared for it. Now, in hindsight, I can look back, and I can see very clearly what went wrong.

And what went wrong was I never did nearly enough math for me to succeed at math. First, I never did nearly enough of the day in, day out, nuts and bolts of arithmetic to master my math facts. Now, I eventually did master them in high school, but that was far too late.

I should have mastered them by third grade. And by master, I mean master them. Math facts, one of the most fundamentally important things for children to succeed in mathematics is that they have absolute and total mastery over math facts. Later in this episode, I'm gonna talk to you about perhaps the inadvisability of doing math too young.

That said, I don't think that there's an age at which it's too young to do math facts. So teaching math facts and ensuring that your children know their math facts, and by math facts, let me define it, in case you're unfamiliar. That means knowing your addition tables, your subtraction tables, your multiplication tables, and your division tables, knowing them cold as just flat out memorized, a memorized body of knowledge, is the most important thing you can do to establish a solid base under your children's later math success.

If you have children who are past, I don't know, third grade, I think third grade age, whatever that is, fourth grade, whatever age that is, basically at that point in time, if your children do not have their math facts known cold, you wake 'em up, shake 'em in the middle of the night and say, "What's eight times six?" Or the hard ones, for me, the hard ones were always nine times seven or things like that.

And if they can't just immediately spit out nine times seven is 63, then you need to do more drilling. So drill them and drill them and drill them and drill them and drill them and drill them and drill them and drill them and drill them until they are known absolutely cold.

So if you're looking to invest in children and if you're looking to invest into your children's brains and to their mathematical abilities, it is your responsibility to make sure that they know their math facts absolutely cold. Go on Amazon, buy a set of math flashcards of math facts, at least up to the 12s, and drill them again and again and again on all the disciplines.

Start, of course, with addition. And introduce it little by little. Just like a language, these need to be done little by little. You can start with your ones and your twos and your threes, but eventually every single one of them needs to be known cold. That's the most important thing to start with.

Now, in looking at my own math career, the next thing that caused major problems was simply I didn't do enough work. I didn't repeat math enough times. In my high school, the curriculum that was used was Saxon math, which was fine. Many people think highly of Saxon math. Of course, it has many critics as well.

I think highly of Saxon math. But what we didn't do was we didn't do all the problems. And we didn't do all the problems because we had to have class time explaining things. And what I now look back and realize clearly was that I almost never benefited from class explanations.

In math, I needed to do problems. And if I needed an explanation, I needed an explanation of a problem that I got wrong until I did it. But I never felt confident. My entire high school and college, very limited college, very limited college math career, I never got confident with my ability in math because I never did enough practice.

They would do things like, okay, you gotta go home and do the evens today, or the odds. We'd always be doing evens or odds. We always skipped half of the problems. And the reason the teacher, the math teacher, did that, of course, was quite simply that there wasn't enough time.

There wasn't enough time to take a class of 20 or 25 or 30 students who were all at various abilities with mathematics, do a 10 to 20 minute lesson, et cetera, and then answer questions of people who don't understand and work those problems and give us enough time. And so when I look back at it, if my math class had simply consisted of my having a room to come into that was quiet and my being expected to read the lesson in the math book and work on it for an hour and then have a teacher or a tutor available to help me if there was something I didn't understand, that would have been far superior for me versus the normal classroom model where you have all the time dedicated to upfront teaching and then you don't have enough time to do the homework.

And so the speed at which a math student proceeds through needs to be slow enough that the student can develop and demonstrate mastery over the material. And so I can see very clearly about how important it would have been for me and was for me to be consistent and to work lots and lots of problems.

Working math problems when you know the material, at least for me, I don't have any way to say for most people, so I'm projecting, but for me is very satisfying. Doing math that you know how to do is very satisfying. It's not boring. The math that we don't like to do is when we don't know how to do it.

And so I don't know if that's a universal experience, but I think it's probably fairly common that if you are coaching your child and your child is not skilled with math, is not succeeding with math, it's probably because your child is not mastering math. And then what happens is you get into this vicious cycle.

Child doesn't understand. Child doesn't understand because he's not done enough problems to understand it, how to do it just instinctively. Because he doesn't understand, the problems are painful. And then because he doesn't wanna do it, he doesn't do enough problems, and you get into this downward cycle where you're just not doing enough of the actual effort.

Think of it like this. Let's use a weightlifting, or let's use a running analogy. If you wanted to be an accomplished runner, you don't become an accomplished runner by once a month going out for a really long run. You become an accomplished runner by doing lots and lots of systematic runs that are well within your ability to build the overall muscular strength and stability and stamina, et cetera, and lung strength, et cetera.

And then you then challenge yourself on occasion, or excuse me, instead of saying on occasion, I say you challenge yourself regularly. So a runner works diligently to build up a solid base under his running, and then he challenges himself with a long run or a fast run, et cetera.

Mathematics should be done on the same principle. There should be lots and lots of consistent putting in the miles, putting in the problems of things that you know, and then there should be challenges where you learn a new concept, it's really challenging, then you do it, do it, do it, do it, do it, and then it becomes old hat, and then you challenge it, et cetera.

And that leads to confidence with mathematics. And so we don't give students generally enough time to do problems. And I understand why. The teacher, how can, if the teacher enforces too many problems, she's gonna complain, but that's the key to doing very, very well. Math mastery comes from doing the work versus just somehow magically understanding it.

Now, this is not, these opinions are not without controversy, but I've read and listened to a lot of people, and I'm reflecting my own insight as a self-aware student who struggled with math, who got better, but who never got as good as he could have become. So what's necessary is consistency and working lots of problems.

Now, to your child's abilities, if you want to help your child succeed, whether your child is in a homeschool environment or in a traditional school environment, one of the best things you can do with his math abilities is to require consistent work from him so that he doesn't go into the summertime slump.

One of the worst things about the way at least the American educational calendar is set up is that you have a school year with a huge long summer break. And what results is that students think that they should only do work five days a week for the 180 days of school.

And then the last couple of weeks are wasted, generally. You have wasted weeks of test prep, and then the first few weeks are wasted trying to catch the child back up. And if math is like a language, it's more important to have daily consistency than it is to have massive levels of work on an ongoing basis.

Meaning if you could only do, if you could only, if you try to study a language for a three-hour stretch, and then you wait a week, you would be better off with just 20 minutes every day or 30 minutes every day, even if your total time invested is less because of the value of consistency.

And I think math has the same basic focus and need. And so I think that if you want your child to develop his brain, regardless of the school environment, you should require as much math as can be practically exercised. And here, I think a good inspirational example would be that of Art Robinson and what he did with his children.

You can read about his story at a website called robinsoncurriculum.com. But the short version of it is that Art Robinson was a, is a scientist, and he and his wife were both research scientists working together. His wife, Lori, they had six children, and they were committed to homeschooling. And then Lori died, developed this illness that killed her in something like 24, 48 hours.

And he was left as a father of six children, including one baby, with no wife, who was desirous and committed to homeschooling while also needing to work. And basically, he applied a very simple system to his own family, and he required his children to learn math facts. Then he wound up accidentally creating a system of self-education for mathematics.

What he would do is he would require his children to learn math facts. Once they had mastered their math facts, then he handed them a Saxon 5-4 book, which is basically the fifth grade book, and they started, and they would just work their way through the problems. And what they did was they did math six days a week, usually about one to two hours a day, and the students were required to teach themselves the lesson and just proceed through the problems.

And if it was going too long, they would lower the problem. Normally, they would do, a Saxon lesson usually has 30 problems on a daily basis, so a 30-problem set would take about an hour to two, one to two hours. If they were going to, if it was too hard for them, they would drop it to 15 problems.

If it was too easy for them, they'd increase it to 45 or 60 problems. But the outcome of this approach led to quite impressive, quite impressive educational results and educational outcomes. He developed a homeschool system that created, that focused on the basics, reading, writing, and arithmetic. In essence, he required his students to do two hours of math a day, to read off of an assigned book list for two hours a day, and then to write a page a day for an essay, which wound up basically being an hour a day.

Following this model, his children all completed calculus at around 14 or 15 years old. Following the study of calculus, they went on and studied physics and chemistry. They all passed AP calculus exams, et cetera. And today, of his six children, it may be all six of them now have PhDs, but four or five of them do.

And you can read more about his story. You can find some old lectures of him lecturing on his homeschooling approach. Very inspirational. In fact, maybe I'll pull in the audio from some of his old lectures and release it to you here in the feed. But very, very inspirational in terms of his story.

And I first read that story before I ever had children, and I have planned since then to do this with my own children, and I'm in the process now of doing it, a couple of modifications. At its core, I wanna emphasize that the key is to do math every day.

And one point that Robinson uses, or used, always used, is that he always required his children to start with math. And his theory on that was you need to, because math is hard, children need to be trained that the first thing you do when you wake up in the morning is you do something hard.

And I am convinced of the value of this. So this is what we do in our homeschool. We get up in the morning. As soon as we start, we start with math, and we start with a hard thing, and we stay at it until we're done. Because at its core, this success skill is something that needs to be developed, and we can use math to develop it in our children.

I don't wanna start my morning with something that's pleasurable or trying to figure out what do I really wanna do first. I wanna start with the hardest thing on my list. Brian Tracy would call this eat that frog, coming from the old saying, maybe attributed to Mark Twain, that if you've gotta eat a frog every day, you know that's gonna be the worst thing that's gonna happen to you.

If you know that you need to eat a frog, that's probably the worst thing that's gonna happen in a day, so you might as well get up and face it and eat the frog, and then you know everything's better from there. So basically the same principle. And so with children, as I see it, this should be a fundamental tool that we use, is we want our children to be smarter, we want them to gain all of the benefits of a rigorous mathematical occasion, education, excuse me.

We want them to gain strict thinking skills, we wanna understand the world very clearly, we want them to have true and fundamental knowledge, not appreciation, and we want them to be trained to do something hard, and to do it first thing every single day. And so mathematics to me seems the ideal way to do it.

The next point though, is that the pace of math progression should be tailored individually to the child. Math, because it is something that involves cumulative knowledge and skills, we don't just try to push the child forward or pull the child back. If the child is struggling with something, we slow down.

We master the concept until the child is no longer struggling, and then we press on. Now I'm fairly young in my own tutoring of this with my children, but I have observed this, and the importance of proceeding at the rate of the student when teaching long division and practicing long division to my eldest child.

Long division is of course a skill that probably for most of us was intimidating at first. It can be difficult, it takes time to develop. And I was tutoring and working, I wasn't requiring an entirely self-taught system at that time, but I was tutoring with my student and working with him, et cetera.

And I realized that it doesn't matter how many problems I help him with. What matters is that I help him until he's able to do it himself, and that he does it himself then until he is confident. I was tempted early in the experience to say, "Well, I'm just gonna help you with a few things, "then you gotta figure it out." But I realized my student is quite young, not at the age yet where I'm willing to be so hardcore.

And I realized it doesn't matter whether a student needs 10 problems of me working them with you, or 110 problems. What matters is that you see the examples and you work the examples and you're helped with it until you master it. And then that you have enough practice examples to master it.

And that's the principle that I think we should all apply with our children, regardless of who their teacher is, regardless of the curriculum, et cetera. Help as much as is necessary until the child's brain grasps it, and then require mastery of the concept. I do believe that requiring the child's brain to figure it out is a tool that we should consistently use.

Back to the book, "Equation for Excellence," chapter four, "Incentive and Struggle, "The Art of Developing the Mind." When taught right, math builds the mind in the way that lifting weights builds the muscles. But not all methods of teaching math do this equally. In fact, some of the more recently adopted methods of teaching math actually do the reverse.

Not only do these methods fail to build cognitive skills, but they actually cause skills that the student has already built to atrophy. Three things cause cognitive skills to develop. The first is age. Even with the worst education available, human biology will make a 16-year-old more intelligent than a two-year-old.

The second thing that causes cognitive skills to develop is exposure. Children who are exposed to interesting ideas and problem types can freely stretch their minds and explore new modes of thought. As a simple example, a child who plays with a Rubik's cube may develop a surer sense of three-dimensional reasoning.

The third consideration is incentive. A child who plays with a Rubik's cube may develop the foundation for strong spatial reasoning. However, without a strong incentive, he may never push his mind to the limit. If he cannot figure out how to solve the Rubik's cube, he will probably just give up.

For the mind to have the incentive to develop, two things are necessary. First, it must encounter a problem that it is unable to do. The process of figuring out how to solve this initially unsolvable problem causes the mind to develop. If a student is only given problems at his current ability level, what incentive does the mind have to improve?

Just as lifting a half-pound weight will not make a person physically stronger, doing an easy math problem will not make a person mentally stronger. Parents and teachers of gifted students often overlook this and just allow them to work at a comfortable pace. The result is that the gifted students never get the opportunity to realize their full potential.

Like natural athletes who never train hard, they end up squandering their innate talents. No matter how smart a student is, he must be given some challenging math problems that he is initially unable to do. If he can solve the problem in five minutes, it is not a real challenging problem.

An appropriate challenging problem should take anywhere from 20 minutes to a week to solve. Once you have a sufficiently challenging problem, the next thing you need is incentive. If the student has no incentive to figure out a difficult problem, he will simply walk away. However, by understanding what motivates your child, you can design the right kinds of incentives.

So we will pause there, but the key is we want the child's brain to struggle with something hard in order for it to grow, just like we want the child to struggle while lifting a heavy weight so that his muscles may grow. When you're looking at math curricula, you may just have one that's exposed to you with your school.

There are a couple of philosophies into which most math curricula are segmented. One is what is called mastery, and the other is what is called spiral. I don't like the word mastery in a name, but let me explain what it means. Basically, the concept is we're going to introduce a concept and we're gonna drill it and drill it and drill it and drill only that concept until the student masters that concept.

Then we're gonna go on to something else and we're gonna drill it, drill it, drill it until the student masters that concept. That's contrasted with, and then we're gonna go on to something else. So the concepts are given as a block and you go through them. That's contrasted with what is often called the spiral approach.

The spiral approach is we're gonna introduce a new concept, you're gonna do some practice problems, and then the next day you're gonna do a couple of problems, but it's gonna be intermixed with everything else. And we're gonna just spiral around going up and up and up and up, and you're gonna master the concept over time because you're doing it a little bit every day.

I've read enough parents' results to recognize that probably both can be fine. It seems like people will go through different math curricula searching for something that works for them. And of course, finding something that works for you is the key. I'm no expert on that field. Right now, we are using the ABECA math curriculum and what I like about it, it's actually for one specific reason.

First, it is a spiral methodology. I'm more attracted to the concept of the spiral methodology 'cause it fits with my concept of math as a language. Introduce something new, learn it, drill it, use it, and don't stop using it. Just continually build, build, build little by little. So I find that attractive, but I would be open to other things.

I just have never needed to try anything else. What I specifically like, the reason we're not using Saxon math, which I appreciate, is that Saxon math being a non-consumable textbook requires the math student to write a significant amount 'cause all the problems have to be copied out on paper.

And the specific hangup that I faced with my eldest is a lack of desire to write. Many young boys are allergic to pencils and we have that disease. Now we make progress in it, good progress over time, but the Abeka math is a very discrete, and I mean that in the mathematical concept, meaning confined, limited, a very discrete thing.

There's a page front and back, and once you're done with the page, you're done. And yet that page seems to fit well, and it doesn't require a lot of writing because the work is done on the page. So that's been a winner for us. I'm impressed with the arithmetic curriculum of the Abeka.

I don't intend to continue at past arithmetic, but time will tell. You go and choose something that you like. I do think there is value in learning concepts of mathematics. And so I have also supplemented the Abeka curriculum with something called Life of Fred. I stumbled into Life of Fred in a very organic manner.

I was actually looking for a high school level personal finance curriculum. I was researching the market on personal finance, trying to understand what was out there. And I stumbled across the Life of Fred personal finance book. And I was browsing the table of contents and the sample book, and I was amazed at the quality of the book as a personal finance curriculum.

I thought to myself, like, this guy's teaching concepts that I'm the only one I know who teaches this stuff, and this is great. So I immediately went and started looking at the rest of his math curriculum. And Life of Fred, the author Stanley Schmidt, something like that, has developed a complete math curriculum that takes a student through from the very basics of arithmetic through and past college level calculus to some of the advanced higher linear, I think he has a linear algebra book.

He might have a differential equation book, I'm not sure. And he does it all in a literary format where he uses this goofy character that kids seem to love, this goofy character. And basically this goofy character has these various adventures, and the various adventures and goofy stories that he goes through require him to develop and exercise math skills.

So it shows the application of the math skills. And he's an experienced math teacher, and my children have loved reading the books. He's very strong on the idea that his math curriculum is the only thing that somebody needs. I'm sure it's maybe so, but I like seeing the output of the Beka, and so we're doing both of them.

But I really love that, and the children really enjoy it. And I like it because it deals with math from an understanding level and in a story way to see the application. And he weaves in all these incredible little extra tidbits of knowledge and fact into his stories, really, really remarkable.

So we've become big fans of Life of Fred. It's not our exclusive curriculum, but we've become big fans of that. And that can be something I think that you may enjoy. So I think that math, what can help with math is learning the concepts, gaining tutoring, et cetera. A narrative approach can help to supplement the drill and kill approach.

Doing math consistently, daily, consistently with shorter breaks, it's fine. I think if your student needs a few weeks off, fine. But I struggle with the idea that students somehow need four months off a year. Doesn't make any sense to me that a student would need four months off at a time.

It does make sense to me that a break, a vacation, is appropriate. So I look at it and say, if I go on vacation, fine. We'll take the family on vacation. That's a good time to have a vacation from school. But the idea that you need four months off from any kind of schooling seems to me a little bit silly.

And so I think that students should at least do math all summer. Even if they just do math and free reading or limited reading. Again, a vacation is fine, but it doesn't need to be a vacation from thinking. We should never have a vacation from thinking. And then lots of consistent work and challenging self-teaching, et cetera, should help a child to be very skilled with mathematics.

Now I want to, I'm not concluding the episode. There's gonna be quite a lot of time after this point. But the last concept I wanna focus on, or the last topic I wanna address with you, is at what age should we start teaching math and how? Because this is important.

And I arrived at my current opinion somewhat on my own. And then I have since found people that agree with me, which helps me to feel increasingly confident. But my comment is basically that formal study of mathematics, I'm not sure that early is better. Now, I'll tell you the story of how I arrived at this conclusion.

First, I have a brother who has a bachelor's degree in mathematics. And his observation and experience of learning mathematics and teaching mathematics is that a whole lot of time is wasted trying to teach math to the young. And that why do we spend a month teaching a concept and drilling a concept for a very young child, when if we just waited a few years, the child could grasp that same concept in a day.

And I have often wondered if he was right. Now, I'm persuaded, I was always persuaded of the idea that we should teach children things at a very young age. But I heard him say that, and I filed that away and paid attention to it. Secondly, I've come across various math teachers who talk about the right age to start learning something like algebra.

And one math teacher who runs a curriculum that I like, and will probably use in high school, he had this comment, he said, "Children shouldn't study algebra until they have hair in their armpits." Basic idea being, your brain needs a certain degree of physical maturity before it can completely and fully is ready for abstract concepts like algebra.

So don't try to teach algebra to your child prodigy and just push, push, push. Just wait until the child is emotionally mature and it'll be easy. And I developed, based on these ideas and hearing various math teachers say things like this, this is why I developed the personal philosophy that our primary focus in the early years should be language because there are disadvantages to many subjects that are taught in school, teaching them at too young of an age.

If the math teachers are correct and a student needs a certain ability with abstract thinking that comes with the maturity of the brain, then our goal is not to get our seven-year-old doing algebra. And similarly, if we look at science, right? I think it's crazy why we spend all kinds of times on kinds of time on science education, quote unquote, for very young children.

I'm personally persuaded that science education should follow math education. Robinson makes this point very heavily. In order for you to do physics, you can't do physics without math, without calculus. Newton invented calculus to do physics or chemistry, et cetera. You need high-level math to do it. Now, many teachers have dumbed it down and taught things without math, but why?

Just wait. Doing science, you should master math and then do science. And it's not that there shouldn't be generalized scientific knowledge, but why? Why spend all this time drilling it? And so I think the primary emphasis with young children should be language because the brain is wired for language acquisition at an early age.

And so for very young children, our academic focus should be language. Our parenting focus should be character, building within them and practicing the skills of character. But from an academic perspective, it should be language. And so it can be your primary language. It can be ancient languages, Greek, Latin, Hebrew, fine.

It can be modern languages. We've done a lot with modern languages and are now doing classical languages. But emphasizing math at an early age doesn't seem super necessary. Rather, mathematical concepts can and should simply be taught in a very straightforward way. So if you go and you look at the Montessori people, if you look at some of the stuff they do with mathematical appreciation, or just playing with your child, teaching your child to count, teaching your child the basic concepts of addition and subtraction and multiplication, et cetera, with physical objects, lots of physical stuff, and not a lot of workbook math at the early years is appropriate.

So last year I was reading a book. I found this fascicle, excuse me, this fascinating book called "Teaching the Trivium, Christian Homeschooling in a Classical Style" by Harvey and Laurie Bluedorn. And I was interested in the book primarily because while I appreciate a lot of what the so-called classical educators have to say, I'm not a big fan of the so-called classical cultures.

I think that Greek thinking has damaged many aspects of our modern world, especially Christianity. Not a big fan of St. Augustine and the Greek thinking that has been applied. I see it as a major problem in much of modern Christianity. And the Roman and Greek societies were just disgusting societies that maybe I appreciate some aspects of the architecture and art and whatnot, but I'm no Hellenist and I'm no Latinist myself.

I'm no Roman. They were disgusting, evil, horrifically sinful societies. But I've always found that if you go into the world of educational pedagogy, you find some of the most serious thinking in this space from classical educators. And so I've never quite figured out how to resolve this conflict. My, I don't wanna be too strong, but my lack of appreciation for Greek and Roman cultures while simultaneously appreciating many of the aspects of classical education.

So I found this title of this book and I bought it not knowing what to expect. And I was blown away by how good it is. Again, it's called "Teaching the Trivium, Christian Homeschooling in Classical Style" by Harvey and Laurie Bluedorn. It's a fairly old book, published in 2001.

So more than 20 years old. But in this book, they included an appendix on math instruction. And so in this book, they talk about basically the philosophy that I've just described to you, which is a philosophy I arrived at independent. And then I came across their thoughtful, well-researched position and it blew me away.

And their basic idea is that children should not start what they call workbook math, which means a formalized workbook-based math curriculum until about the age of 10. And their experience with their children is that their children have been easily able to start their math instruction with basically fifth grade around the age of 10.

So instead of spending hours and hours doing first, second, third, fourth grade stuff, just wait until your children are 10, do informal math instruction through real life living, and then around the age of 10, just start with a fifth grade math book. And that if any of their children, I think they had six children go through this, if any of their children struggled at all, in a few weeks, you can iron out and catch up on anything that was necessary in order to do the fifth grade textbook.

Interestingly, this compares also with Robinson, Art Robinson's experience, his idea about math instruction as a scientist. Just simply have children learn their math facts. When they know their math facts, start with a fifth grade textbook. But they, in this book, include this remarkable appendix, which I think is really beautifully researched.

And I wanna share it with you. Because while I have not chosen to put off intentionally all kind of formalized workbook instruction until fifth grade, I think that if your young children are struggling with math, it should not be a big focus for you if they're seven. I don't think you should expect your seven-year-old to sit down and do two hours of math a day.

And so I wanna share this lengthy appendix with you as a tempering commentary on what I have said, and also something that is perhaps educational as far as some areas where perhaps we are wrong in our modern day on the teaching of math. I'm changing my mind on what I've just said to you.

Looking at how far we are into this episode, I'm going to release this appendix as a separate audio file in the podcast feed here, rather than including it at the end of this episode. If I include it here, too many people will avoid the episode for sake of it being too long.

And I don't want what I've said to be missed. So let me instead sum up this and hope you'll listen to that appendix separately. At its core, we're trying to strengthen our children's minds. We want them to be smarter so that they will be better learners and be able to lead themselves to greater success.

Numeracy, encouraging and developing numeracy is a fundamental way for us to accomplish that. So we want our children to do lots and lots of math. It will grow their gray brain into be a bigger and more powerful muscle. And regardless of whether they ever enter a scientific career or a career in which they use the math, the practice of doing math every day will increase their intelligence.

Frankly, you and I should be doing math every day for these same benefits. And if math is not your thing, doing Sudoku or crossword puzzles or something is key. In terms of staving off dementia, helping us to be smarter, et cetera, we need to be challenging our brain and making it think.

And math is perhaps the best way to do that. So don't force too much math on your children. If your children are young and they're not doing well with math, back off. Focus on language at an early age rather than mathematics. But as your children get into math, require them to do math every day so that they will develop the character of doing hard things first thing every day, and so that they will become deeply numerate and become smarter, more accomplished, better educated individuals who know how to teach themselves the things that matter.

- Big Boyz Comedy Kings is coming to Yamava Resort and Casino Saturday, December 9th with D.L. Hughley. ♪ That sweater so tight, look like a snap between the legs ♪ - Cedric the Entertainer. - Once we stop running, I'll find out what it was we was running about. - And Paul Rodriguez.

- What is it about old Mexican men? They could be missing a leg, they still wanna get into a fight. - Hosted by my man Eric Blake in a special performance by Mario. Big Boyz Comedy Kings, December 9th at Yamava Resort and Casino tickets can be purchased at axs.com.

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