2023-02-27_How_to_Invest_in_Your_Children_at_a_Very_Young_Age_Part_6-Catalyze_Numeracy_in_Your

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00:01:00.920 | - Welcome to Radical Personal Finance,

00:01:02.160 | a show dedicated to providing you with the knowledge,

00:01:03.760 | skills, insight, and encouragement you need

00:01:06.100 | to live a rich and meaningful life now,

00:01:08.600 | while building a plan for financial freedom

00:01:10.100 | in 10 years or less.

00:01:11.800 | On today's show, we continue our series

00:01:13.900 | on how to invest in your children at an early age.

00:01:17.780 | This is clearly a very extensive series,

00:01:19.680 | and what I'm seeking to do is to persuade you

00:01:22.380 | that when you think of investing your money,

00:01:24.180 | you ought not first to think of a product

00:01:27.980 | that you can buy from a financial product salesman.

00:01:32.980 | Rather, you should think broadly about the term.

00:01:36.140 | And I'm developing in detail a thesis

00:01:39.300 | that I've had for many years that most of the dollars

00:01:42.620 | that parents save to spend and invest in their children,

00:01:46.660 | for example, to purchase mutual funds

00:01:48.500 | and put them in a 529 account,

00:01:50.460 | are probably better off spent in some other form

00:01:54.060 | or fashion at an early age into the wellbeing

00:01:59.060 | and intelligence of the child.

00:02:02.460 | And so while these are not mutually exclusive,

00:02:06.820 | you can do both if you have the money,

00:02:09.020 | I wanna encourage you that you're gonna get a better bang

00:02:11.020 | for your buck by focusing on these things

00:02:13.100 | that I'm talking about.

00:02:14.140 | So in this series, we began by talking about your child,

00:02:18.140 | preconception of your child and the basic genetic material

00:02:21.380 | that your child inheritance, conception and childbirth.

00:02:24.340 | Then we talked about nourishing your child's body,

00:02:27.860 | helping him to develop a body that is free of disease,

00:02:30.740 | that is vigorous in health,

00:02:32.140 | helping him to maximize his genetic potential

00:02:34.940 | in terms of height and beauty, et cetera,

00:02:37.060 | with good nutrition and a clean environment,

00:02:39.940 | lots of exercise, getting stronger, et cetera.

00:02:42.540 | Then we pivoted from the body to the mind.

00:02:44.980 | And with regard to the mind,

00:02:47.900 | I spent two episodes focusing on literacy.

00:02:51.580 | And now in this episode, we're going to turn to numeracy

00:02:55.380 | because these two things go hand in hand.

00:02:58.460 | Literacy and numeracy are the basics

00:03:01.420 | and they're certainly the basics of academics,

00:03:03.620 | but I think they're the basic skills of life.

00:03:05.980 | If we had to choose one or the other to focus on,

00:03:09.620 | I think literacy would take us farther.

00:03:11.740 | Someone who's very good at math,

00:03:14.860 | but for some reason can't read

00:03:17.300 | is gonna have a harder time absorbing the information

00:03:20.420 | that he needs in a practical sense in life.

00:03:24.860 | And so if we had to choose between the two,

00:03:28.380 | we wanna emphasize literacy,

00:03:30.580 | but I don't think we ever have to choose.

00:03:32.100 | I think a strong and healthy mind

00:03:34.420 | should be maintaining both of these things together,

00:03:37.300 | be both highly literate and highly numerate,

00:03:40.180 | and they work together.

00:03:41.820 | Now, towards the end of this episode,

00:03:43.460 | I'll talk about an appropriate progression

00:03:46.420 | because I am not persuaded that numeracy

00:03:49.380 | is something that should be emphasized

00:03:51.020 | in the youngest of ages.

00:03:54.060 | And while I have titled this series,

00:03:56.500 | How to Invest in Your Young Children,

00:03:58.500 | I think we should be careful at the age

00:04:00.380 | of which we really start to focus on numeracy.

00:04:05.060 | But at its core,

00:04:06.220 | we want our children to be highly numerate.

00:04:09.740 | Why is this important in this context?

00:04:12.760 | Well, at its core,

00:04:14.340 | numeracy is a way of making your children smarter.

00:04:18.780 | And we wanna have children that are beautiful,

00:04:21.180 | that are strong, that are physically dexterous,

00:04:24.980 | but we also wanna have children

00:04:26.140 | that are very, very smart and well-informed,

00:04:28.460 | and we wanna maximize their brain muscles.

00:04:31.500 | The brain is a muscle that should be viewed

00:04:33.940 | like other muscle groups.

00:04:35.900 | The more it's exercised,

00:04:37.820 | the stronger and more powerful it becomes.

00:04:40.940 | And we want our children to have

00:04:42.700 | large and healthy physical muscles,

00:04:45.220 | and we want them to have a large and healthy brain.

00:04:48.940 | Interestingly, of course,

00:04:49.980 | the physical muscles feed the brain.

00:04:52.240 | Exercise is good for your thinking ability

00:04:54.360 | because the brain is a muscle,

00:04:55.940 | but the brain needs to be exercised

00:04:57.860 | not with the lifting of physical weights,

00:05:00.260 | but with the manipulation of mental processes.

00:05:03.420 | And this is something that is applicable

00:05:05.220 | to you and to me as adults,

00:05:07.820 | but also to our children.

00:05:09.460 | So we want our children to exercise their brains

00:05:12.200 | on a daily basis.

00:05:13.620 | I've had this theory for a while

00:05:15.500 | about what a perfect brain day would look like for me.

00:05:19.060 | You know, how do I make my brain smarter on a daily basis?

00:05:22.340 | Well, I need to exercise it.

00:05:23.420 | So what does that look like?

00:05:24.300 | Well, ideally, on a daily basis in a perfect world,

00:05:29.100 | I'd like to make sure that I read something,

00:05:32.260 | that something that I read should be beautiful,

00:05:35.220 | it should be attractive,

00:05:36.620 | it should inform me, and it should inspire me.

00:05:39.940 | So I want to access something that's beautiful

00:05:43.260 | and informative and well-written.

00:05:46.340 | So that's gonna involve not just, you know,

00:05:49.400 | day-to-day dime store literature,

00:05:52.280 | but something that raises me up.

00:05:55.360 | I wanna exercise my brain with math.

00:05:58.000 | So I wanna do some form of a math workout every day,

00:06:02.240 | if at all possible.

00:06:03.520 | And I wanna look at math as a way of strengthening my brain.

00:06:07.600 | And so in a perfect world,

00:06:09.840 | I should be regularly building my mathematical ability.

00:06:13.640 | In an ideal day, I should be making myself smarter

00:06:16.480 | with studying and learning and exercising

00:06:19.200 | some new language, learning new vocabulary,

00:06:22.000 | reading something, expanding my brain.

00:06:23.840 | Multilingualism also is proven to enhance my brain ability.

00:06:28.640 | If at all possible, I'd like to engage

00:06:30.580 | in some kind of musical activity.

00:06:33.800 | So if I can play an instrument or engage in something

00:06:37.800 | that's gonna build that skill,

00:06:39.400 | that helps me on a daily basis.

00:06:41.600 | Something that's aesthetic would be quite valuable.

00:06:44.920 | So if I can draw or paint or just appreciate art,

00:06:49.740 | something like that.

00:06:50.580 | And of course, we get into all the world of emotions,

00:06:52.200 | surrounding myself with the positive emotions of love

00:06:55.240 | and a vision and goal setting, et cetera.

00:06:57.180 | All these things are good.

00:06:58.960 | All of them contribute,

00:07:00.060 | and they do some heavy lifting in our brains.

00:07:04.160 | But at its core, the ones that work up our brains

00:07:07.580 | the hardest are math and foreign languages.

00:07:11.880 | That's where we often have to think, we have to struggle.

00:07:14.360 | And it's that exercise of thinking hard

00:07:17.880 | that makes the brain harder.

00:07:20.520 | There are benefits, of course, to going for a walk.

00:07:23.000 | Many of them, many physical benefits.

00:07:25.200 | But if you want to grow your muscular ability,

00:07:28.120 | you have to lift heavy weights.

00:07:30.280 | And mentally, it's the same thing.

00:07:32.320 | There are benefits to just simply going

00:07:34.080 | and using and enjoying our brains, right?

00:07:37.040 | We all enjoy a relaxing novel

00:07:39.440 | or something that's very, very simple.

00:07:41.160 | But in order to grow our brain muscles,

00:07:43.320 | we have to challenge it.

00:07:44.880 | And one of the fundamentally most useful ways

00:07:48.000 | to challenge your brain is quite simply with math.

00:07:51.960 | It's extremely valuable to build your brain muscles.

00:07:56.960 | Math builds your brain muscles

00:07:59.600 | and strengthens them at a measurable level.

00:08:03.880 | Think of it as a mental workout,

00:08:05.740 | and it makes your brain work more efficiently,

00:08:09.040 | more productively, and more effectively.

00:08:11.880 | And this is a really important reason

00:08:13.760 | to actually study math, regardless of any practical concepts,

00:08:18.760 | meaning regardless of any practicality.

00:08:21.640 | I read you a couple of paragraphs

00:08:23.000 | from a book called "The Equation for Excellence,

00:08:25.680 | "How to Make Your Child Excel at Math" by Arvind Vohra.

00:08:29.000 | And in the very first chapter,

00:08:30.880 | he talks about why study math.

00:08:33.680 | And I think it's important that you understand this concept.

00:08:38.300 | When children ask why they need to study math,

00:08:40.300 | the answer usually has something to do

00:08:41.860 | with either daily life

00:08:43.020 | or applications to science and technology.

00:08:45.960 | The problem with the first motivation

00:08:47.540 | is that it is an obvious and transparent lie.

00:08:51.960 | The second type of motivation

00:08:54.160 | tends to have the opposite of the intended effect.

00:08:57.340 | The daily life explanation tells students

00:08:59.780 | that they will need math for their daily activities.

00:09:02.340 | For example, they will need to calculate the tip

00:09:04.120 | in a restaurant or determine how much they should pay

00:09:06.140 | for their groceries.

00:09:07.540 | Most students are quick to point out

00:09:08.820 | that this problem can be solved

00:09:09.960 | by carrying around a calculator.

00:09:11.620 | And anyone who is worried about running out of batteries

00:09:13.640 | can carry around a spare set of batteries

00:09:15.700 | or even two calculators.

00:09:17.240 | Even cell phones have built-in calculators.

00:09:19.660 | And quick aside, isn't it so funny

00:09:21.500 | how antiquated your language can sound

00:09:24.700 | when there's a technological change?

00:09:26.380 | This book was published in 2007.

00:09:28.620 | And it's ironic because of how antiquated

00:09:32.500 | the language sounds when that was a mere 16 years ago.

00:09:36.100 | But of course, 2007 was the year that the iPhone,

00:09:38.540 | I think it was 7, oh, 7, yeah, pretty sure,

00:09:40.660 | is the year the iPhone came out.

00:09:42.340 | So a mere 16 years later,

00:09:44.060 | this book just sounds laughably antiquated

00:09:46.660 | with that comment.

00:09:47.580 | The arguments against the daily life explanation continue.

00:09:52.040 | In daily life, you never need to do more

00:09:53.820 | than add, subtract, multiply, or divide.

00:09:56.620 | Why learn trigonometry?

00:09:58.380 | Why study calculus?

00:09:59.840 | Why do anything beyond arithmetic?

00:10:02.260 | Even math-oriented jobs rarely require

00:10:04.940 | any really advanced math.

00:10:06.700 | When I worked as an actuary,

00:10:08.120 | the only math I used on the job was multiplication

00:10:10.580 | and the occasional exponent.

00:10:12.440 | The actuarial profession is one of the most

00:10:14.140 | math-oriented professions in the world.

00:10:16.380 | The other rationale for studying math

00:10:18.100 | focuses on science and technology.

00:10:20.420 | We need math to design space shuttles and satellites,

00:10:23.220 | to work in laboratories, and to build the newest computers.

00:10:26.420 | In one way, this argument makes sense.

00:10:28.580 | Much of that work requires intensive use of advanced math.

00:10:32.300 | But very few people work in those areas.

00:10:34.400 | Those that work in those areas usually do so

00:10:36.420 | because of an internal passion,

00:10:38.200 | not because of any external motivation.

00:10:41.200 | In fact, from the perspective of most students,

00:10:43.140 | there is very little external motivation to be a scientist.

00:10:46.680 | The strongest external motivators for most teenagers

00:10:49.740 | are money, fame, power, popularity,

00:10:52.180 | and attraction to the opposite sex.

00:10:54.380 | None of these powerfully motivate students

00:10:56.380 | to pursue careers in science.

00:10:58.420 | For every million dollars a scientist makes,

00:11:00.420 | the businessmen for whom he works make a billion.

00:11:03.180 | For every famous scientist,

00:11:04.460 | there are a thousand famous musicians and actors.

00:11:07.080 | The scientists who made the nuclear bomb

00:11:08.900 | were not the ones to use it.

00:11:10.320 | That power belonged to politicians.

00:11:12.460 | And in American culture, scientists have no more popularity

00:11:15.900 | or sex appeal than anyone else.

00:11:18.120 | Thus, this argument not only fails to motivate students,

00:11:20.580 | it actually does the reverse.

00:11:22.380 | A student with no interest in being a scientist

00:11:24.780 | who hears the technology argument

00:11:26.780 | now thinks that advanced math is useful only for scientists.

00:11:30.300 | Thus, he does not need to learn it.

00:11:32.380 | If his goal is personal gain,

00:11:33.940 | his time is better spent doing almost anything else,

00:11:36.680 | studying politics, learning to play the guitar,

00:11:39.220 | working out, or thinking of ways to make himself rich.

00:11:42.280 | Math becomes just an annoying requirement.

00:11:45.700 | So then, why should a student learn math at all?

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00:12:19.700 | Kings used to play chess to learn military strategy.

00:12:23.800 | When I first heard this at age 10,

00:12:27.020 | the idea struck me as unbelievably stupid.

00:12:30.380 | In chess, the bishop can move only diagonally.

00:12:33.540 | The knight can move in an L shape.

00:12:35.780 | A real soldier, on the other hand,

00:12:37.260 | can move in any direction.

00:12:38.940 | How would studying chess help in any real war?

00:12:42.840 | I had, of course, completely missed the point.

00:12:44.820 | Strategy has nothing to do with L shapes or diagonals.

00:12:48.540 | A chess player learns to anticipate his opponent.

00:12:51.420 | He learns to look for strong positions

00:12:53.500 | rather than short-term gains.

00:12:55.260 | He learns to make intelligent sacrifices

00:12:57.500 | and be wary of the strategic artifices of his opponent.

00:13:00.740 | He learns to predict his opponent's future responses

00:13:03.220 | to his actions rather than focusing on the immediate gains.

00:13:07.300 | This mental discipline makes his mind sharper

00:13:09.760 | and he becomes a much more capable strategist.

00:13:13.060 | Similarly, math is important,

00:13:14.980 | not because it teaches a student how to use trigonometry

00:13:17.660 | to measure the height of a building,

00:13:19.380 | but because it develops a student's ability

00:13:21.180 | to analyze and solve unfamiliar problems.

00:13:24.420 | Math develops concrete reasoning,

00:13:26.700 | spatial reasoning, and logical reasoning.

00:13:29.600 | Math does not just develop skills

00:13:31.660 | that can be applied to science and technology.

00:13:34.300 | When math is taught right,

00:13:35.580 | it develops the student's

00:13:36.580 | fundamental cognitive architecture,

00:13:39.140 | increasing his intelligence.

00:13:41.220 | The student will develop the logical reasoning skills

00:13:43.700 | that allow a lawyer to analyze a legal situation

00:13:46.300 | and to present a coherent and convincing argument.

00:13:49.540 | He will develop the ability essential

00:13:51.380 | for any business person to isolate

00:13:53.060 | the key components of a system.

00:13:55.060 | He will develop mental skills that can be used

00:13:57.300 | in any problem-solving situation.

00:13:59.540 | His mind will become faster, sharper, and more precise.

00:14:03.580 | What lifting weights does for muscles,

00:14:05.780 | math does for the mind.

00:14:07.660 | In no sport will an athlete suddenly lie down on his back

00:14:10.700 | and lift a weight 10 times.

00:14:12.640 | However, the vast majority of athletes do the bench press.

00:14:16.260 | Why?

00:14:17.100 | It makes them stronger and thus prepares them

00:14:19.020 | for athletic endeavors in general.

00:14:21.300 | When you teach a child math in the right way,

00:14:23.420 | you are giving him the gift of a sharper

00:14:25.380 | and more powerful intelligence.

00:14:27.420 | You are helping him actually develop his mind.

00:14:30.420 | You are making him smarter.

00:14:33.020 | You are giving him the ultimate ability

00:14:34.820 | to succeed in the world

00:14:36.440 | and to build a happier life for himself.

00:14:38.820 | You are not just making him better at math,

00:14:41.380 | you are making him better at thinking.

00:14:45.020 | I hope you find that encouraging

00:14:47.540 | and a little bit inspirational.

00:14:49.840 | When we think about how to make our children smarter,

00:14:52.540 | we have to consider the tools at our disposal.

00:14:55.700 | And that's what I'm trying to give you.

00:14:58.300 | We've talked about the physical tools

00:14:59.900 | to make your children's brains work better,

00:15:02.540 | things like high fat consumption, lots of exercise,

00:15:06.060 | low sugar consumption, et cetera.

00:15:08.680 | But then we pivoted to talking about

00:15:10.720 | making your children smarter

00:15:11.940 | and more well-informed literacy.

00:15:13.660 | And now we wanna make your children smarter

00:15:15.980 | in terms of building up

00:15:17.420 | not only the physical gray matter of their brain,

00:15:20.020 | but also their thinking ability.

00:15:22.020 | And mathematics is one of the most consistent tools

00:15:24.440 | that we have for that.

00:15:26.660 | I think this is in some ways

00:15:28.100 | because math is analogous to a form of a language.

00:15:33.100 | I think mathematics could be described quite elegantly

00:15:36.060 | as the language of the universe.

00:15:38.680 | I am persuaded that as a Christian,

00:15:40.900 | I'm persuaded that there's an incredibly useful apologetic

00:15:44.820 | for even the existence of God

00:15:46.420 | in the unreasonable effectiveness of mathematics.

00:15:49.540 | When you look at how precisely ordered the universe is

00:15:53.060 | and how beautifully consistently mathematical,

00:15:57.100 | it beggars belief to think that that form of,

00:16:01.880 | that language that exists, that is non-physical,

00:16:06.260 | that human beings universally can have access to,

00:16:09.740 | a universal immaterial reality,

00:16:12.340 | such as the language of mathematics,

00:16:14.300 | it almost requires a conception

00:16:17.300 | that there is a beautiful and elegant design.

00:16:20.660 | And mathematics is a language

00:16:22.860 | that as you build fluency in,

00:16:24.940 | it just leads to ever increasing opportunities.

00:16:28.380 | Now, as a language,

00:16:30.060 | I am persuaded that everyone can learn math.

00:16:33.200 | And I was gonna talk about this later,

00:16:36.940 | but it's important to talk about now.

00:16:39.020 | First, as a disclaimer,

00:16:41.060 | I myself have never been a math teacher,

00:16:45.100 | but I know what it's like to be a struggling student in math

00:16:49.980 | and I know the struggles that I myself faced in doing math.

00:16:54.980 | And I know how those struggles can be resolved.

00:16:59.120 | So, let's talk about that,

00:17:02.320 | because if you are someone,

00:17:05.260 | there are many people who have had

00:17:07.360 | all of their mathematical appreciation,

00:17:11.740 | their love for mathematics chewed up and destroyed

00:17:16.700 | by the schooling system

00:17:18.460 | that they went through to learn mathematics.

00:17:21.140 | And I think that's unfortunate and unnecessary.

00:17:26.060 | I think that if we understand that math is a language,

00:17:30.540 | just like any language,

00:17:33.100 | it's a language that anyone can speak.

00:17:36.600 | When you think about your native language,

00:17:39.200 | assuming it's, let's assume it's English for the moment,

00:17:42.000 | you can recognize that there are people

00:17:47.160 | who genuinely have some form of handicap

00:17:52.040 | that will allow them to never master the English language

00:17:56.720 | the way that Shakespeare did.

00:17:59.540 | There genuinely are some people

00:18:01.320 | who will never attain that level of linguistic ability.

00:18:06.320 | But you can also quickly recognize

00:18:11.220 | the reason most people don't attain

00:18:15.560 | very high levels of linguistic ability

00:18:18.920 | is not due to a fundamental handicap or disability.

00:18:23.920 | Rather, it's due to not being exposed to high levels

00:18:30.620 | to higher levels of language,

00:18:33.120 | not being trained in the fundamentals necessary

00:18:36.520 | to achieve those high levels of language,

00:18:39.300 | and/or not having the time

00:18:41.320 | to fully develop their linguistic ability.

00:18:44.520 | Except for a tiny portion of people

00:18:46.920 | who are genuinely disabled,

00:18:48.880 | anybody can become a master of the English language

00:18:54.120 | if given the right materials,

00:18:58.400 | the right basic tools, and the fullness of time,

00:19:02.960 | and consistent practice and exposure.

00:19:04.980 | And the rate at which people advance

00:19:08.960 | in the English language or any language

00:19:12.440 | depends far more on those basic factors

00:19:16.440 | than it does on innate ability.

00:19:19.120 | As you can tell from the previous two episodes,

00:19:22.300 | I myself am quite passionate about literacy,

00:19:26.440 | high levels of literacy.

00:19:28.400 | Anybody who listens to my show

00:19:30.000 | understands that I'm a quite literate person.

00:19:33.200 | It's one of the things that harms my ability

00:19:35.840 | to reach a very broad audience.

00:19:38.040 | It's quite simply, I don't speak

00:19:39.800 | in a simple or straightforward way.

00:19:42.440 | I don't speak at a fifth grade level.

00:19:44.620 | Years ago, I learned a lesson

00:19:46.080 | when I was studying copywriting,

00:19:48.180 | and the lesson was quite simply

00:19:49.600 | that in order to write effective, successful sales copy,

00:19:53.320 | sales letters, et cetera,

00:19:55.080 | you should never use language

00:19:57.680 | that is higher than that of a fifth grader.

00:20:01.000 | And because complex language,

00:20:05.080 | when used to write sales letters,

00:20:08.000 | causes you to lose vast swaths of your audience

00:20:11.960 | and your potential audience.

00:20:13.360 | And where I remember this really standing out to me

00:20:19.240 | was when I saw in prior to the 2016 presidential election

00:20:22.800 | in the United States, I saw at some point an analysis

00:20:26.400 | of then candidate Donald Trump,

00:20:28.680 | who was running for the office,

00:20:29.760 | saying he never used more than fifth grade words,

00:20:32.400 | and he never used large vocabulary.

00:20:35.120 | And I thought to myself,

00:20:36.400 | 'cause of that connection to sales letters,

00:20:38.400 | I thought, boom, this guy understands how to reach people

00:20:41.960 | and be an effective politician.

00:20:43.800 | And so I necessarily understand

00:20:47.160 | that because I use complex language,

00:20:51.360 | it limits my ability.

00:20:53.200 | My goal is not to reach the highest number of people.

00:20:57.120 | My goal is to reach people that I enjoy talking to

00:20:59.640 | and inspiring those who are looking for more.

00:21:01.600 | So the world of popular level financial advice

00:21:04.800 | is abundantly well-served.

00:21:06.560 | I'm seeking to do something more than that.

00:21:09.520 | My point is, because I'm so passionate about language,

00:21:13.300 | you can see that with my own children

00:21:15.720 | and with students that I mentor, et cetera,

00:21:17.440 | and even with you,

00:21:18.800 | that I'm seeking to help you

00:21:21.120 | to achieve a higher level faster than most other people.

00:21:25.600 | We use in our homeschool with a first grader

00:21:28.000 | and a fourth, third or fourth, fourth grader,

00:21:29.880 | fourth grader, second grader, something like that,

00:21:31.640 | with a nine-year-old and a seven-year-old,

00:21:34.120 | and a five-year-old,

00:21:35.720 | literally read books that are marked

00:21:38.680 | as graduate-level texts,

00:21:40.880 | as graduate-level in terms of their Lexile scores.

00:21:44.160 | That's intentional because the exposure at a young age

00:21:48.000 | creates capability,

00:21:49.320 | and then that capability has a payoff effect

00:21:51.680 | of allowing a student to go much farther, much faster.

00:21:55.080 | But there was a time at which, of course,

00:21:57.640 | my children could not read.

00:21:59.320 | And it's the same with math.

00:22:01.560 | If we use the right techniques

00:22:03.880 | and we're skillful about how we introduce math

00:22:07.160 | and we establish an appropriate situation,

00:22:10.560 | we can help our children to go very, very far in math.

00:22:14.560 | And it should be very rare that a child ever thinks,

00:22:19.560 | "Oh, I'm just not good at math."

00:22:22.280 | In what I've described in terms of literacy,

00:22:24.760 | I've had children that have learned to read

00:22:26.480 | at different rates and have struggled with different things.

00:22:29.040 | That is normal, but we can and must adapt then what we do

00:22:34.040 | to meet the specific needs of our students.

00:22:40.640 | But what we must not do is somehow think

00:22:44.560 | that because they have a brain

00:22:46.840 | that works slightly differently

00:22:48.320 | or because they need a special aid of some kind

00:22:52.040 | or they need a little bit longer

00:22:53.240 | to learn the basic concepts,

00:22:55.360 | that somehow we should stop.

00:22:57.160 | We don't stop teaching our children to read

00:22:59.680 | just because it takes one child two years

00:23:03.280 | instead of two months.

00:23:04.840 | Just like we don't stop encouraging our children to walk

00:23:07.760 | just because one child walks at three years old,

00:23:09.960 | another child walks at eight months.

00:23:12.160 | We're going to continue,

00:23:14.480 | you're gonna continue working with your child

00:23:16.400 | until he walks.

00:23:18.100 | You're going to continue working with your child

00:23:19.880 | until he reads.

00:23:21.480 | And you must continue working with your child

00:23:25.240 | until he is skilled with mathematics.

00:23:29.040 | Mathematics is a language that is accessible to all people.

00:23:33.280 | And it doesn't matter the rate

00:23:35.860 | at which the language is acquired.

00:23:38.080 | What matters is that the language

00:23:39.800 | is being progressively acquired.

00:23:43.800 | And like languages,

00:23:45.800 | languages are one of those things

00:23:46.860 | where it's very hard to get worse at languages.

00:23:49.500 | Once you have developed linguistic ability,

00:23:53.440 | it's very hard to get worse.

00:23:55.260 | Sometimes your progress feels fast,

00:23:57.320 | sometimes your progress feels slow,

00:23:59.640 | but you don't generally get worse.

00:24:02.420 | If you do get worse, right,

00:24:04.960 | say you don't use a language at all for five years,

00:24:07.320 | when you come back to the language,

00:24:08.960 | in very short time, you quickly reach your ability

00:24:11.640 | and then move on from there.

00:24:13.740 | So math is a language

00:24:15.740 | and it's important to exercise it

00:24:17.960 | consistently and ongoing over time.

00:24:20.820 | Math is also very useful as a discipline.

00:24:25.760 | It's a discipline.

00:24:27.040 | Math is generally, for at least for me,

00:24:30.600 | and I think for everyone else, math is hard.

00:24:33.120 | And hard is something that is good.

00:24:37.320 | Hard is useful.

00:24:39.140 | I've talked in past episodes

00:24:43.000 | about educational philosophies.

00:24:44.780 | And one of the things that I have appreciated over the years

00:24:49.200 | is I've appreciated many of the comments

00:24:50.880 | that those who maintain the educational philosophy

00:24:54.720 | of unschooling, I appreciate the comments

00:24:59.000 | and many of the critiques that they make of schooling.

00:25:01.800 | The basic critique would come down to,

00:25:04.000 | if you're gonna learn something,

00:25:05.040 | you need to actually care about it and want to learn it.

00:25:07.500 | Otherwise, you don't really ever learn it.

00:25:09.900 | They point out that the things

00:25:11.120 | that we learn the most effectively

00:25:12.540 | are the things that we want to learn.

00:25:14.120 | And I think that's true.

00:25:15.620 | But I myself am not an unschooler, excuse me,

00:25:19.440 | I'm not an unschooler because I fear

00:25:23.400 | that unschooling does not provide

00:25:25.960 | an appropriate structure for character formation.

00:25:31.560 | Now, character can be formed in many ways.

00:25:34.440 | Generally though, at its core,

00:25:37.880 | character is formed by difficulty.

00:25:42.120 | And we want to require our children

00:25:46.080 | to do difficult things each and every single day

00:25:50.720 | of their life in order that they develop the skill

00:25:55.480 | of facing and doing difficult things.

00:25:58.860 | A man who does not have the skill

00:26:01.740 | of doing things that he doesn't wanna do

00:26:04.460 | is a man who will have a very hard time

00:26:06.340 | being successful in life.

00:26:08.260 | Now, as parents, we go to our toolbox

00:26:11.640 | and we say, what tools do I have?

00:26:13.460 | Perhaps a man who has a farm or some form of lifestyle

00:26:18.460 | where there's heavy physical labor

00:26:20.060 | can use that heavy physical labor as the tool

00:26:22.860 | for developing the skill set of hard work.

00:26:26.300 | That's certainly something that I think many people

00:26:28.380 | notice that can happen well in farming economies.

00:26:31.900 | But we no longer live in an agrarian economy.

00:26:34.260 | And so that tool is often not very effective for us.

00:26:37.620 | Maybe if you live in the frozen north,

00:26:39.420 | your tool can be the hard thing we're gonna do every day

00:26:41.700 | is go jump in the frozen lake and have cold exposure.

00:26:44.620 | Okay, maybe that's useful.

00:26:46.520 | But for many of us in an information age

00:26:49.540 | and in an intellectual world, we need something hard

00:26:52.320 | and that's probably gonna be something like,

00:26:56.660 | it's gonna be something intellectual.

00:26:58.340 | And so in order to help our children develop

00:27:02.180 | that character skill to do hard things,

00:27:05.300 | we need to have something hard to do.

00:27:06.800 | And math is an ideal candidate for that.

00:27:09.580 | It's not the only candidate for that.

00:27:11.900 | I think that there can be other things.

00:27:14.200 | I'm now going to read you an essay

00:27:15.740 | from a book called "Climbing Parnassus."

00:27:19.740 | And it's called "Climbing Parnassus,

00:27:22.780 | a New Apologia for Greek and Latin" by Tracey Lee Simmons.

00:27:26.780 | And this book is trying to encourage people

00:27:30.220 | to use Greek and Latin and gain the benefits

00:27:34.300 | that many centuries of classically educated students

00:27:37.820 | have gained from them.

00:27:39.740 | I'm gonna read to you a section here

00:27:41.280 | that's talking about the value of the struggle

00:27:44.060 | to learn Greek and Latin.

00:27:46.300 | I believe though that this applies first to mathematics.

00:27:51.700 | While perhaps there is value

00:27:53.340 | in studying Greek and Latin, perhaps,

00:27:55.620 | and perhaps this author is completely right,

00:27:58.260 | one of the great challenges for many of us

00:28:00.020 | is simply we have never gone through that challenge

00:28:03.820 | ourselves.

00:28:04.660 | I myself was never exposed to Greek and Latin as a child.

00:28:10.060 | I didn't have the experience that these authors have.

00:28:13.940 | Nor is it easy for me as a father to find tutors

00:28:17.860 | and teachers that can impose this type

00:28:20.540 | of disciplined character building structure

00:28:23.460 | onto my children.

00:28:25.300 | But I believe mathematics can accomplish the same thing.

00:28:29.340 | And most of us can impose a disciplined

00:28:32.780 | mathematical structure on our children

00:28:34.460 | to gain these benefits.

00:28:36.580 | Enjoy this excerpt here from "Climbing Parnassus."

00:28:39.780 | You may wish to, you may be inspired

00:28:41.900 | and you may wish to use Greek and Latin,

00:28:43.480 | but think of mathematics as I read this.

00:28:46.820 | W.H. Auden was one of many writers

00:28:49.740 | of the last great generation

00:28:51.020 | of classically educated men and women,

00:28:52.860 | upon whom an early classical training

00:28:55.540 | made indelible impressions, intellectual and otherwise.

00:28:59.540 | Those boyish classroom exercises

00:29:01.780 | had formed his very sensibility.

00:29:03.740 | And he lived to see the stupid, numbing consensus arise

00:29:07.620 | that a classical education holds scant value

00:29:10.060 | for the modern world.

00:29:11.820 | The modern revolt against centering the school curriculum

00:29:14.140 | around the study of Latin and Greek is understandable

00:29:16.740 | in an age of hyper utilitarianism, he wrote,

00:29:19.340 | though it's deplorably mistaken.

00:29:21.620 | It is no doubt a pleasure to read the Greek and Latin poets,

00:29:24.820 | philosophers and historians in the original,

00:29:27.420 | but very few persons so educated in the past

00:29:30.140 | kept up their Greek and Latin after leaving school.

00:29:33.240 | The real value of classics though

00:29:35.340 | is something quite different.

00:29:36.940 | Anybody who has spent many hours in his youth

00:29:38.980 | translating into and out of two languages

00:29:42.540 | so syntactically and rhetorically different from his own,

00:29:45.900 | learns something about his mother tongue,

00:29:48.740 | which I do not think can be learned in any other way.

00:29:51.700 | It inculcates the habit, whenever one uses a word,

00:29:55.020 | of automatically asking what is its exact meaning.

00:29:58.460 | Auden's case for classics was not so much the cultural one,

00:30:03.140 | but the case from formation.

00:30:05.340 | The pursuit of classics per se

00:30:07.140 | is worth all the devotion we can lend it.

00:30:09.620 | Classical knowledge provides keys

00:30:11.220 | to understanding Western civilization,

00:30:13.540 | but the habits Greek and Latin instill

00:30:16.060 | are worth at least as much.

00:30:18.340 | The passing of classics from our schools

00:30:20.300 | has in fact crippled the larger culture.

00:30:22.740 | Here, Auden cast his net far and wide.

00:30:26.220 | The people who have really suffered

00:30:27.540 | since classical education became undemocratic

00:30:30.580 | are not the novelists and poets.

00:30:32.860 | Their natural love of languages sees them through.

00:30:35.860 | But all those, like politicians, journalists, lawyers,

00:30:39.060 | the man in the street, et cetera,

00:30:40.620 | who use language for everyday and non-literary purposes.

00:30:44.540 | Among such, one observes an appalling deterioration

00:30:47.540 | in precision and conciseness.

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00:31:20.260 | - How ironic that those democratic fears of elitism

00:31:25.020 | should ensure that those born without the privileges

00:31:27.740 | of the educated classes will remain permanently disabled,

00:31:31.500 | victims of others' good intentions.

00:31:34.220 | The signs of rot surround us.

00:31:36.820 | Nobody, Auden wrote, who had had a classical education

00:31:40.780 | could have perpetuated this sentence in "The New Yorker."

00:31:44.420 | He, a film director, expresses that dichotomy

00:31:47.980 | between man and woman in the images of the bra and dachau.

00:31:51.620 | One would hope not.

00:31:53.780 | That's the murky self-important lingo

00:31:55.820 | emanating from the lit crit sentiment are

00:31:58.300 | in English departments.

00:31:59.900 | It doesn't exist to communicate anything

00:32:01.900 | to the cultivated mind.

00:32:03.460 | It exists to confuse and impress easily bamboozled,

00:32:07.860 | uneducated, fee-paying sycophants.

00:32:11.180 | It pretends to profundity, but it's tripe.

00:32:15.660 | Language like this is not hatched for civilized people.

00:32:19.980 | Perhaps we can have culture of a kind

00:32:22.660 | without bestowing classical education

00:32:24.780 | upon a goodly number of intelligent men and women.

00:32:27.420 | We may doubt whether we can have a literary culture

00:32:30.100 | whose roots run deep.

00:32:32.020 | Novelist Evelyn Waugh paid tribute

00:32:33.780 | to his own classical training.

00:32:35.300 | Here we see plainly that the oft-heard cry

00:32:38.420 | that students retain little of their Latin

00:32:40.300 | misses the point.

00:32:41.700 | A classical training,

00:32:42.820 | thoroughly conducted along humanistic lines,

00:32:45.060 | changes the shape of the mind for the better.

00:32:47.460 | It stays with us.

00:32:49.540 | My knowledge of English literature

00:32:50.900 | derived chiefly from my home.

00:32:53.100 | Most of my hours in the form room for 10 years

00:32:55.660 | had been spent on Latin and Greek,

00:32:57.540 | history and mathematics.

00:32:59.460 | Today, I remember no Greek.

00:33:01.420 | I have never read Latin for pleasure

00:33:02.900 | and should now be hard put to compose a simple epitaph.

00:33:06.180 | But I do not regret my superficial,

00:33:08.940 | superficial for the time perhaps, classical studies.

00:33:12.020 | I believe that the conventional defense of them is valid.

00:33:15.060 | That only by them can a boy fully understand

00:33:17.620 | that a sentence is a logical construction

00:33:19.900 | and that words have basic inalienable meanings,

00:33:23.340 | departure from which is either conscious metaphor

00:33:25.980 | or inexcusable vulgarity.

00:33:28.580 | Those who have not been so taught,

00:33:30.620 | most Americans and most women,

00:33:32.340 | unless they are guided by some rare genius,

00:33:34.660 | betray their deprivation.

00:33:36.700 | The old fashioned test of an English sentence,

00:33:39.460 | will it translate?

00:33:40.620 | Still stands after we have lost the trick of translation.

00:33:44.940 | We should note here as well,

00:33:47.900 | the starkly limited curriculum.

00:33:50.660 | His schoolmasters might have chosen to clutter the classroom

00:33:53.460 | with far shinier objects

00:33:54.900 | than it did in the second decade of the 20th century.

00:33:57.700 | Commercial French for one thing,

00:33:59.140 | or aerodynamics or wood shop.

00:34:02.340 | That world was changing after all, true enough.

00:34:05.820 | But that didn't mean

00:34:06.940 | that the well-constituted mind had changed.

00:34:09.820 | The intellect still required molding.

00:34:12.740 | The better schools then, as they ought to be now,

00:34:15.180 | were eager primarily to form the student's mind,

00:34:17.780 | imparting solid knowledge mainly

00:34:20.380 | as a by-product of sound teaching.

00:34:23.060 | As with the Greek and Roman schools

00:34:24.780 | so many centuries before,

00:34:26.260 | the curriculum of Wauw's school was also marked

00:34:29.100 | as H.I. Meru wrote,

00:34:30.420 | "By a definite rejection of what it did not include."

00:34:34.900 | What it didn't let in was of equal importance

00:34:36.900 | to what it did.

00:34:38.220 | Any school we might conclude

00:34:39.540 | with more than four or five subjects

00:34:41.340 | doesn't know what it wants to be.

00:34:43.580 | Or we may shudder to think, perhaps it does.

00:34:47.740 | Most public schools in America now strive

00:34:49.740 | to be cut rate educational malls

00:34:51.580 | for the intellectually lame.

00:34:53.340 | Whether or not students first darken

00:34:54.980 | the school doors that way.

00:34:56.660 | So most of them leave,

00:34:58.180 | while even some private schools pose

00:35:00.060 | as little more than colorful felt boards

00:35:02.100 | for the earnestly shallow, commonly confusing,

00:35:04.980 | pious or patriotic piffle with real education.

00:35:08.060 | Neither setup makes for a school

00:35:09.900 | any educated human being is bound to respect.

00:35:13.460 | Schools of the best kind have always aimed high

00:35:16.100 | while keeping feet to the ground.

00:35:18.020 | They didn't try to do too much.

00:35:20.380 | They tried to do the most important things.

00:35:23.500 | Those who ran them knew that we educate ourselves

00:35:26.540 | with the tools imparted by good teachers.

00:35:29.460 | All else was up to us.

00:35:31.420 | The old schoolmasters didn't profess

00:35:33.300 | to teach everything worth knowing.

00:35:35.460 | Instead, they professed the opposite.

00:35:37.980 | They shaped their curricula narrowly and wisely.

00:35:42.020 | Information alone is not knowledge as they knew.

00:35:44.820 | Still less is it wisdom.

00:35:47.300 | Schools can accomplish much more

00:35:48.860 | when they recognize squarely how little they can do.

00:35:51.860 | Yet how much more can be done when our gaze remains steady,

00:35:55.180 | our heads sober, our aims high?

00:35:58.180 | No results are guaranteed, but the effort pays off.

00:36:01.900 | Formed minds and tempered souls

00:36:04.220 | are no small gift to the world.

00:36:06.780 | Let's see one more example of how good schooling goes bad

00:36:09.540 | through wishful thinking pedagogy.

00:36:11.740 | Perhaps the school should be, as we might say now,

00:36:14.740 | a challenging place.

00:36:16.500 | It should be hard.

00:36:18.180 | The work enjoined upon us should help us to develop,

00:36:21.740 | not only by its content, but also by its method,

00:36:25.580 | the mind capable of teaching itself anything.

00:36:29.140 | It's not so much an informed mind we seek,

00:36:32.860 | the one full of information for an information age,

00:36:35.580 | making us little more than worker bees,

00:36:37.980 | but a certain quality of mind,

00:36:41.500 | a mind at once agile and civilized,

00:36:44.540 | one able to place the society to which it belongs

00:36:47.180 | into some scheme of history.

00:36:49.540 | We want not only a well-stored mind,

00:36:53.100 | but a well-leavened mind as well.

00:36:56.500 | So what of it?

00:36:57.580 | This may be a good enough idea as ideas go,

00:37:00.100 | yet we must emerge from school doors knowing something,

00:37:03.100 | but what should we know?

00:37:04.740 | An answer sits at the ready.

00:37:07.140 | We should learn how to appreciate the better things of life.

00:37:11.820 | And so we should.

00:37:13.140 | The snare here, the snake in the grass waiting to bite,

00:37:15.980 | is that this idea has led us down some false paths.

00:37:20.100 | Appreciation squares with Renaissance ideals,

00:37:23.020 | but as conceived by us moderns,

00:37:25.420 | it's miles away from Renaissance methods.

00:37:29.140 | Today, we don't lack teachers and theorists

00:37:31.460 | wishing to help students pull off

00:37:33.140 | an enhanced quality of mind.

00:37:35.140 | Many have tipped their hats to this principle

00:37:37.100 | by designing courses whose purpose is to help those students

00:37:40.100 | not so much to know,

00:37:41.460 | but to appreciate the world around them.

00:37:44.700 | Yet this isn't the learning Vittorino da Feltre knew.

00:37:48.020 | We don't need under this regime

00:37:49.980 | to learn the hard things about poetry or music or art.

00:37:53.660 | We need only to appreciate them as poetry, music, or art.

00:37:57.820 | We need only to acknowledge their value.

00:38:00.300 | While it's easy to make fun of this attitude,

00:38:01.860 | we should recognize that in the ablest hands,

00:38:04.420 | the quality of mind sought is a decent goal,

00:38:07.140 | and doubtless it's sometimes achieved.

00:38:09.220 | Poetry, music, and art were not created after all

00:38:11.700 | to provide fodder for tests in school.

00:38:14.260 | Poetry is more than scansion and difficult words,

00:38:17.460 | music more than scales and arpeggios,

00:38:19.740 | and art more than cracked vases and spatial perspective.

00:38:23.380 | All three were made to delight.

00:38:26.060 | They were meant to please us in some deep or diverting way.

00:38:29.740 | This we must acknowledge.

00:38:31.540 | But however good the object of helping young people

00:38:33.780 | to take easy the light and the fine things around them,

00:38:36.500 | this approach to forming the rough, formless mind

00:38:39.220 | is also profoundly wrongheaded.

00:38:41.580 | C.S. Lewis helps us to see why in a little known essay

00:38:44.500 | called "The Parthenon and the Optative."

00:38:48.500 | "The trouble with these boys,"

00:38:49.980 | said a grim old classical scholar

00:38:51.740 | looking up from some milk and watery entrance papers

00:38:54.460 | which he had been marking,

00:38:55.940 | "The trouble with these boys is that the masters

00:38:57.980 | have been talking to them about the Parthenon

00:39:00.260 | when they should have been talking to them

00:39:01.660 | about the optative."

00:39:03.460 | The optative is one of the moods of the Greek verb.

00:39:06.900 | "Ever since then, I have tended to use the Parthenon

00:39:09.540 | and the optative as the symbols of two types of education.

00:39:13.940 | The one begins with hard, dry things

00:39:16.740 | like grammar and dates and prosody,

00:39:19.740 | and it has at least the chance of ending

00:39:21.460 | in a real appreciation, which is equally hard and firm,

00:39:24.260 | though not equally dry.

00:39:26.140 | The other begins in appreciation and ends in gush.

00:39:31.020 | When the first fails, it has, at the very least,

00:39:33.220 | taught the boy what knowledge is like.

00:39:35.940 | He may decide that he doesn't care for knowledge,

00:39:38.340 | but he knows he doesn't care for it

00:39:40.380 | and he knows he hasn't got it.

00:39:42.580 | But the other fails most disastrously

00:39:44.620 | when it most succeeds.

00:39:48.460 | It teaches a man to feel vaguely cultured

00:39:51.700 | while he remains, in fact, a dunce.

00:39:54.100 | It makes him think he is enjoying poems he can't construe.

00:39:57.940 | It qualifies him to review books he does not understand

00:40:00.900 | and to be intellectual without intellect.

00:40:04.660 | It plays havoc with the very distinction

00:40:07.140 | between truth and error.

00:40:09.740 | This is what school has become for us

00:40:12.700 | over the haul of three or four generations.

00:40:15.260 | It's become not so much about knowledge

00:40:17.420 | as it has about experience.

00:40:21.180 | The teacher doesn't teach, the teacher facilitates.

00:40:25.620 | Instead of providing solid instruction, for instance,

00:40:28.420 | about the cathedral at Chartres,

00:40:30.540 | about its religious significance and dates and place

00:40:33.180 | in French geography and dimensions

00:40:35.420 | and Gothic architectural principles,

00:40:37.860 | the things that is, we can really know about it,

00:40:41.540 | the teacher is now just as likely to stand before a class

00:40:44.500 | with a photograph of the cathedral

00:40:46.140 | and ask students to respond to it.

00:40:50.420 | What does it make you think of?

00:40:52.740 | Would you want to walk into a building like this?

00:40:55.660 | Are all these statues beautiful or ugly?

00:40:59.260 | Would a woman be comfortable here?

00:41:01.740 | Write a paragraph on what you think it must have felt like

00:41:04.700 | to stand in front of it.

00:41:06.140 | I jest, but only a little.

00:41:09.340 | Here is how we are set on the high road

00:41:11.580 | to the Parthenon kind of education,

00:41:14.060 | the kind that will, by its very method,

00:41:16.300 | allow us later to think we know more than we do.

00:41:20.420 | These questions might not make a bad exercise

00:41:23.140 | for kindergartners, but they're unfit for anyone older.

00:41:28.100 | One year hence, the students' time

00:41:29.620 | will be better spent memorizing Roman numerals.

00:41:32.260 | Yet much schooling today, even high schooling,

00:41:35.500 | has become every bit as vapid

00:41:38.540 | as this whimsical example suggests.

00:41:41.660 | Here, before the young can know the dangers

00:41:43.860 | of soft teaching or the seductions of ignorance,

00:41:46.900 | non-knowledge gets planted and watered,

00:41:49.900 | and left unchecked, as it usually is,

00:41:52.740 | it will spread like bamboo.

00:41:54.520 | Lewis goes on.

00:41:57.060 | And yet education of the Parthenon type

00:41:59.240 | is often recommended by those

00:42:00.620 | who have and love real learning.

00:42:02.700 | They are moved by a kind of false reverence for the muses.

00:42:07.220 | What they value, say, in literature,

00:42:09.140 | seems to them so delicate and spiritual a thing

00:42:12.860 | that they cannot bear to see it, as they think,

00:42:16.100 | degraded by such coarse mechanic attendance

00:42:19.320 | as paradigms, blackboards, marks, and examination papers.

00:42:24.320 | But there is a profound misunderstanding here.

00:42:27.580 | These well-meaning educationalists

00:42:29.620 | are quite right in thinking that literary appreciation

00:42:32.580 | is a delicate thing.

00:42:34.220 | What they do not seem to see is that for this very reason,

00:42:37.580 | elementary examinations on literary subjects

00:42:40.340 | ought to confine themselves to just those dry

00:42:44.260 | and factual questions, which are so often ridiculed.

00:42:49.060 | The questions were never supposed to test appreciation.

00:42:52.540 | The idea was to find out

00:42:53.900 | whether the boy had read his books.

00:42:56.340 | It was the reading, not the being examined,

00:42:58.840 | which was expected to do him good.

00:43:01.060 | And this, so far from being a defect in such examinations,

00:43:05.680 | is just what renders them useful or even tolerable.

00:43:09.780 | Lewis sees learning in a word, objectively.

00:43:14.500 | If progress in learning can't be measured

00:43:16.680 | for purposes of schooling,

00:43:18.380 | we have no way of knowing if it's happening at all.

00:43:20.980 | Knowledge can be measured.

00:43:22.780 | Appreciation cannot.

00:43:24.660 | Furthermore, trying to test pleasure or approval

00:43:27.740 | may prove hazardous even to the soul itself.

00:43:30.700 | Tell the boy to mug up, which means study up on,

00:43:34.140 | tell the boy to mug up a book

00:43:36.520 | and then set questions to find out whether he has done so.

00:43:39.580 | At best, he may have learned,

00:43:41.020 | and best of all, unconsciously, to enjoy a great poem.

00:43:44.540 | At second best, he has done an honest piece of work

00:43:46.780 | and exercised his memory and reason.

00:43:49.180 | At worst, we've done him no harm,

00:43:50.860 | have not pawed and dabbled in his soul,

00:43:53.340 | have not taught him to be a prig or a hypocrite,

00:43:56.340 | but an elementary examination which attempts to assess

00:43:59.820 | the adventure of the soul among books is a dangerous thing.

00:44:03.940 | What obsequious boys, if encouraged,

00:44:06.240 | will try to manufacture and clever ones can ape

00:44:09.260 | and shy ones will conceal,

00:44:10.860 | what dies at the touch of venality

00:44:13.140 | is called to come forward and perform,

00:44:16.180 | to exhibit itself at that very stage when it's timid,

00:44:19.840 | half-conscious stirrings

00:44:21.380 | can least endure such self-consciousness.

00:44:25.920 | If the tenets of formation ought to guide method

00:44:28.580 | in our schools, we also see what content must be.

00:44:32.820 | It must be hard and intractable.

00:44:36.120 | It's import significant.

00:44:37.820 | It's substance learnable.

00:44:40.540 | Content is, in one sense at least,

00:44:42.680 | the bar we use to pull ourselves out of ignorance.

00:44:46.360 | The formed and forming mind is the muscle we use to pull.

00:44:50.940 | Appreciation may be properly valued above solid knowledge.

00:44:55.560 | The best kind accompanies us into our sunset years.

00:44:58.420 | Appreciation, inward apprehension and assent

00:45:01.540 | touches upon the spiritual in our natures.

00:45:03.940 | It is indeed to be sought vigorously.

00:45:06.280 | The only real quandary is how to get there.

00:45:09.180 | And Lewis, like so many before him,

00:45:11.500 | knew that while the long way round,

00:45:13.700 | the way of the optative may not guarantee a rival

00:45:17.500 | at the port of our desires.

00:45:19.420 | Nonetheless, it is the one way

00:45:21.620 | that weather-hardened sea-legged mariners

00:45:24.220 | have tested and found to be not only reliable,

00:45:27.500 | but given the winds tossing us, safe.

00:45:31.780 | Multum non multa.

00:45:34.980 | This is the one chart we can trust.

00:45:37.960 | Again, I understand that Greek and Latin

00:45:43.940 | were the object of that sentence,

00:45:46.100 | but I think it's hard to believe that most of us

00:45:50.340 | are either desirous or equipped today

00:45:54.860 | to go to our children and impose upon them

00:45:58.260 | the hard pathway of Greek and Latin

00:46:02.260 | and deeply probing the optative.

00:46:05.180 | Most of us are not equipped and we may have other concerns.

00:46:08.760 | But I think mathematics provides us with so much of that.

00:46:14.820 | And while many of us may be skeptical about Greek and Latin

00:46:19.220 | being the core of a child's education,

00:46:22.060 | I think far fewer of us are skeptical about mathematics

00:46:26.300 | being the core of a child's education.

00:46:29.780 | And so we want to do hard things

00:46:32.100 | and we want to use the tools at our disposal.

00:46:36.980 | One quote from a different part of the book.

00:46:40.900 | "There is a time for play and a time for work.

00:46:44.300 | "School can be an enriching, enjoyable place,

00:46:47.060 | "and a place some students may look forward

00:46:48.880 | "to attending every day.

00:46:50.500 | "Those are fortunate children with fortunate parents.

00:46:53.720 | "But children's approval should not be our first concern.

00:46:57.200 | "Like a healing doctor, we know this will hurt.

00:46:59.860 | "We might as well say so.

00:47:01.660 | "School should be a serious place.

00:47:05.100 | "Dullards must not set the pace.

00:47:08.240 | "Students should be encouraged to develop a sense

00:47:10.700 | "of their smallness alongside the world's riches.

00:47:13.900 | "Humility remains a decent aim for the well-educated mind.

00:47:18.140 | "Let us not try to do too much.

00:47:20.440 | "Those subjects that can be got outside school doors,

00:47:23.320 | "things like fashion design, computer training,

00:47:25.220 | "and photography should be.

00:47:27.260 | "Dissipation of effort can lead to despair.

00:47:30.300 | "The world outside will catch up

00:47:31.760 | "with the young soon enough.

00:47:33.420 | "School ought to be a training ground for the intellect,

00:47:37.600 | "not a clearinghouse for skills.

00:47:41.180 | "And if it's to be the latter, we should admit it.

00:47:43.540 | "Whatever we decide to teach young people

00:47:45.640 | "who will one day step forward to run the world.

00:47:48.580 | "And why should we teach anything other than languages,

00:47:53.360 | "mathematics, and geography before the age of 13?

00:47:57.980 | "Let's remember as the humanists taught

00:47:59.680 | "that we reap as we sow.

00:48:01.400 | "These are human beings equipped both with minds and souls.

00:48:05.980 | "Bend their twigs, we must,

00:48:09.080 | "just so they grow hale and well."

00:48:13.420 | Mathematics is perhaps our most useful tool

00:48:18.420 | to teach our children discipline

00:48:22.400 | so that they can do something hard every single day.

00:48:28.240 | Now, just because it's hard does not mean

00:48:33.120 | that we don't want them to succeed.

00:48:34.500 | So what is necessary for mathematical success?

00:48:38.580 | Well, first, let me share with you my story.

00:48:41.400 | I was not good at math when I was younger.

00:48:45.560 | The reason I was not good was probably

00:48:49.440 | because my math skills were neglected.

00:48:52.440 | My parents tried, I was homeschooled, they did their best.

00:48:56.600 | But although I was encouraged

00:48:58.700 | and required to learn my math facts,

00:49:01.560 | I never really mastered them.

00:49:03.900 | I wasn't required to drill them until mastery.

00:49:07.200 | When I was younger, I did a math curriculum

00:49:09.560 | that was probably fine, and then we switched.

00:49:12.480 | And at one point, I cheated on my math work

00:49:15.040 | for months and months.

00:49:16.720 | My mom was traveling for a time,

00:49:18.320 | my grandmother was overseeing my schooling

00:49:20.320 | at one particular time, and I discovered

00:49:23.200 | that I could just go and take the answer key

00:49:25.400 | from my mom's desk and just copy down the answers.

00:49:30.400 | And I was able to successfully fool my grandmother

00:49:32.800 | into thinking that I had done all my work.

00:49:34.280 | And my mom eventually figured out

00:49:35.720 | that I had just flat out cheated,

00:49:37.000 | and I confessed and whatnot, but I got behind.

00:49:39.540 | So I got behind.

00:49:40.840 | When I went into school in seventh grade

00:49:43.200 | into a local, more traditional private school,

00:49:46.800 | I was woefully behind.

00:49:48.760 | In fact, my mom had to work hard

00:49:50.880 | to try to get them to accept me

00:49:52.280 | because I did not pass the math tests sufficiently.

00:49:56.000 | My first year in mathematics,

00:49:58.760 | I got a D the first semester, so I was barely passing.

00:50:03.760 | I was reasonably smart, but I was barely passing.

00:50:06.640 | I didn't get an F, but I was barely passing.

00:50:09.440 | So then my dad took me under his wing,

00:50:12.160 | and he considered it unacceptable

00:50:14.120 | that one of his children should not do that,

00:50:16.040 | and he imposed certain requirements on me.

00:50:18.160 | I forget all of them, but one of the requirements

00:50:21.600 | was that I had to review my homework with him.

00:50:25.280 | I think I had to bring him every test that I went through,

00:50:28.280 | and basically, he just took a strong interest

00:50:29.760 | in my mathematical abilities.

00:50:31.840 | So I got a D the first quarter, a C the next quarter,

00:50:34.400 | B the end of that quarter, and then from then,

00:50:36.760 | I was able to get Bs.

00:50:37.760 | I kind of caught up Bs and As,

00:50:39.680 | and I think I mostly got As, either high Bs or low As,

00:50:43.120 | throughout my high school years.

00:50:44.940 | But I was never really great at math.

00:50:49.480 | I did pass through algebra, trigonometry, geometry, et cetera

00:50:53.160 | through to calculus, and I took calculus

00:50:55.200 | my senior year in high school.

00:50:57.280 | And I think I did okay on the grade portion,

00:51:02.280 | but when it came time to take the AP exam

00:51:04.840 | at the end of the year, I got a two on my AP exam,

00:51:07.520 | which is a failure on, so I failed my AP exam,

00:51:09.960 | never got calculus credit.

00:51:11.760 | When I went into college, my freshman year of college,

00:51:14.240 | I was required to take a math course,

00:51:16.000 | and I, because I had not passed the AP exam,

00:51:19.040 | and I figured, well, I'll take calculus again.

00:51:21.380 | And I took calculus, and I passed calculus.

00:51:24.740 | I don't know whether I got a B or a C,

00:51:26.760 | but to this day, I still have nightmares,

00:51:29.080 | and I'm not kidding.

00:51:30.180 | I'm not nor am I being hyperbolic.

00:51:32.640 | I still have nightmares about math,

00:51:37.080 | because that calculus class,

00:51:38.440 | I basically just made it up as I went along,

00:51:40.320 | and I never really learned it.

00:51:42.160 | I'd never learned calculus.

00:51:44.360 | I was able to pass exams enough,

00:51:46.860 | but I never learned calculus,

00:51:48.320 | and I know I never learned it,

00:51:50.080 | because I felt guilty about it,

00:51:51.480 | and I knew that I was insufficiently prepared for it.

00:51:55.880 | Now, in hindsight, I can look back,

00:51:57.500 | and I can see very clearly what went wrong.

00:52:00.480 | And what went wrong was I never did nearly enough math

00:52:03.240 | for me to succeed at math.

00:52:05.320 | First, I never did nearly enough of the day in, day out,

00:52:08.600 | nuts and bolts of arithmetic to master my math facts.

00:52:11.560 | Now, I eventually did master them in high school,

00:52:15.640 | but that was far too late.

00:52:16.840 | I should have mastered them by third grade.

00:52:18.920 | And by master, I mean master them.

00:52:20.980 | Math facts, one of the most fundamentally important things

00:52:26.000 | for children to succeed in mathematics

00:52:28.820 | is that they have absolute and total mastery over math facts.

00:52:33.820 | Later in this episode, I'm gonna talk to you

00:52:35.580 | about perhaps the inadvisability of doing math too young.

00:52:39.140 | That said, I don't think that there's an age

00:52:43.740 | at which it's too young to do math facts.

00:52:46.580 | So teaching math facts and ensuring

00:52:48.780 | that your children know their math facts,

00:52:51.580 | and by math facts, let me define it,

00:52:52.900 | in case you're unfamiliar.

00:52:54.020 | That means knowing your addition tables,

00:52:56.580 | your subtraction tables, your multiplication tables,

00:52:59.140 | and your division tables,

00:53:00.780 | knowing them cold as just flat out memorized,

00:53:05.780 | a memorized body of knowledge,

00:53:08.340 | is the most important thing you can do

00:53:11.820 | to establish a solid base

00:53:13.420 | under your children's later math success.

00:53:16.220 | If you have children who are past, I don't know,

00:53:19.660 | third grade, I think third grade age, whatever that is,

00:53:22.140 | fourth grade, whatever age that is,

00:53:23.980 | basically at that point in time,

00:53:25.580 | if your children do not have their math facts known

00:53:29.380 | cold, you wake 'em up, shake 'em in the middle of the night

00:53:32.620 | and say, "What's eight times six?"

00:53:34.340 | Or the hard ones, for me, the hard ones

00:53:36.100 | were always nine times seven or things like that.

00:53:38.660 | And if they can't just immediately spit out

00:53:40.500 | nine times seven is 63,

00:53:41.700 | then you need to do more drilling.

00:53:45.060 | So drill them and drill them and drill them

00:53:47.300 | and drill them and drill them and drill them

00:53:48.900 | and drill them and drill them and drill them

00:53:50.620 | until they are known absolutely cold.

00:53:55.620 | So if you're looking to invest in children

00:53:58.340 | and if you're looking to invest into your children's brains

00:54:02.380 | and to their mathematical abilities,

00:54:04.820 | it is your responsibility to make sure

00:54:07.260 | that they know their math facts absolutely cold.

00:54:11.380 | Go on Amazon, buy a set of math flashcards of math facts,

00:54:16.380 | at least up to the 12s,

00:54:18.100 | and drill them again and again and again

00:54:21.660 | on all the disciplines.

00:54:22.780 | Start, of course, with addition.

00:54:24.100 | And introduce it little by little.

00:54:25.860 | Just like a language,

00:54:27.500 | these need to be done little by little.

00:54:29.140 | You can start with your ones and your twos and your threes,

00:54:32.420 | but eventually every single one of them

00:54:35.260 | needs to be known cold.

00:54:36.840 | That's the most important thing to start with.

00:54:39.860 | Now, in looking at my own math career,

00:54:41.940 | the next thing that caused major problems

00:54:44.900 | was simply I didn't do enough work.

00:54:48.660 | I didn't repeat math enough times.

00:54:51.940 | In my high school, the curriculum that was used

00:54:56.140 | was Saxon math, which was fine.

00:54:59.900 | Many people think highly of Saxon math.

00:55:01.860 | Of course, it has many critics as well.

00:55:04.020 | I think highly of Saxon math.

00:55:06.320 | But what we didn't do was we didn't do all the problems.

00:55:09.380 | And we didn't do all the problems

00:55:10.980 | because we had to have class time explaining things.

00:55:14.020 | And what I now look back and realize clearly

00:55:16.220 | was that I almost never benefited from class explanations.

00:55:20.140 | In math, I needed to do problems.

00:55:23.980 | And if I needed an explanation,

00:55:25.900 | I needed an explanation of a problem

00:55:27.700 | that I got wrong until I did it.

00:55:30.020 | But I never felt confident.

00:55:31.940 | My entire high school and college,

00:55:34.740 | very limited college, very limited college math career,

00:55:37.620 | I never got confident with my ability in math

00:55:41.140 | because I never did enough practice.

00:55:43.360 | They would do things like,

00:55:44.280 | okay, you gotta go home and do the evens today,

00:55:46.740 | or the odds.

00:55:47.580 | We'd always be doing evens or odds.

00:55:49.340 | We always skipped half of the problems.

00:55:51.300 | And the reason the teacher, the math teacher,

00:55:53.460 | did that, of course, was quite simply

00:55:56.180 | that there wasn't enough time.

00:55:57.860 | There wasn't enough time to take a class

00:55:59.540 | of 20 or 25 or 30 students

00:56:02.020 | who were all at various abilities with mathematics,

00:56:07.020 | do a 10 to 20 minute lesson, et cetera,

00:56:10.260 | and then answer questions of people who don't understand

00:56:12.900 | and work those problems and give us enough time.

00:56:15.500 | And so when I look back at it,

00:56:18.780 | if my math class had simply consisted

00:56:21.340 | of my having a room to come into that was quiet

00:56:24.780 | and my being expected to read the lesson in the math book

00:56:27.780 | and work on it for an hour

00:56:29.340 | and then have a teacher or a tutor available to help me

00:56:31.900 | if there was something I didn't understand,

00:56:33.820 | that would have been far superior for me

00:56:35.900 | versus the normal classroom model

00:56:37.940 | where you have all the time dedicated to upfront teaching

00:56:41.740 | and then you don't have enough time to do the homework.

00:56:45.140 | And so the speed at which a math student proceeds through

00:56:49.500 | needs to be slow enough that the student can develop

00:56:53.140 | and demonstrate mastery over the material.

00:56:58.020 | And so I can see very clearly

00:57:00.040 | about how important it would have been for me

00:57:02.940 | and was for me to be consistent

00:57:04.980 | and to work lots and lots of problems.

00:57:07.020 | Working math problems when you know the material,

00:57:10.820 | at least for me, I don't have any way to say

00:57:15.120 | for most people, so I'm projecting,

00:57:17.300 | but for me is very satisfying.

00:57:19.220 | Doing math that you know how to do is very satisfying.

00:57:22.500 | It's not boring.

00:57:25.660 | The math that we don't like to do

00:57:27.180 | is when we don't know how to do it.

00:57:29.220 | And so I don't know if that's a universal experience,

00:57:32.580 | but I think it's probably fairly common

00:57:34.900 | that if you are coaching your child

00:57:37.060 | and your child is not skilled with math,

00:57:40.220 | is not succeeding with math,

00:57:42.580 | it's probably because your child is not mastering math.

00:57:45.760 | And then what happens is you get into this vicious cycle.

00:57:49.120 | Child doesn't understand.

00:57:50.840 | Child doesn't understand

00:57:51.840 | because he's not done enough problems to understand it,

00:57:56.200 | how to do it just instinctively.

00:57:59.200 | Because he doesn't understand, the problems are painful.

00:58:02.120 | And then because he doesn't wanna do it,

00:58:03.520 | he doesn't do enough problems,

00:58:04.480 | and you get into this downward cycle

00:58:05.880 | where you're just not doing enough of the actual effort.

00:58:09.600 | Think of it like this.

00:58:10.800 | Let's use a weightlifting, or let's use a running analogy.

00:58:15.360 | If you wanted to be an accomplished runner,

00:58:17.220 | you don't become an accomplished runner

00:58:19.520 | by once a month going out for a really long run.

00:58:23.380 | You become an accomplished runner

00:58:25.300 | by doing lots and lots of systematic runs

00:58:28.660 | that are well within your ability

00:58:30.840 | to build the overall muscular strength and stability

00:58:35.620 | and stamina, et cetera, and lung strength, et cetera.

00:58:38.100 | And then you then challenge yourself on occasion,

00:58:42.480 | or excuse me, instead of saying on occasion,

00:58:44.520 | I say you challenge yourself regularly.

00:58:46.840 | So a runner works diligently

00:58:49.380 | to build up a solid base under his running,

00:58:52.160 | and then he challenges himself with a long run

00:58:54.800 | or a fast run, et cetera.

00:58:57.040 | Mathematics should be done on the same principle.

00:59:00.120 | There should be lots and lots of consistent

00:59:02.760 | putting in the miles,

00:59:04.000 | putting in the problems of things that you know,

00:59:06.040 | and then there should be challenges

00:59:07.720 | where you learn a new concept, it's really challenging,

00:59:10.020 | then you do it, do it, do it, do it, do it,

00:59:11.760 | and then it becomes old hat,

00:59:12.800 | and then you challenge it, et cetera.

00:59:14.880 | And that leads to confidence with mathematics.

00:59:18.220 | And so we don't give students generally

00:59:20.840 | enough time to do problems.

00:59:23.160 | And I understand why.

00:59:24.840 | The teacher, how can, if the teacher enforces

00:59:27.360 | too many problems, she's gonna complain,

00:59:29.160 | but that's the key to doing very, very well.

00:59:32.920 | Math mastery comes from doing the work

00:59:36.640 | versus just somehow magically understanding it.

00:59:39.920 | Now, this is not, these opinions are not without controversy,

00:59:43.200 | but I've read and listened to a lot of people,

00:59:45.480 | and I'm reflecting my own insight

00:59:48.760 | as a self-aware student who struggled with math,

00:59:51.520 | who got better, but who never got as good

00:59:53.720 | as he could have become.

00:59:55.740 | So what's necessary is consistency

00:59:57.960 | and working lots of problems.

01:00:00.360 | Now, to your child's abilities,

01:00:02.520 | if you want to help your child succeed,

01:00:04.920 | whether your child is in a homeschool environment

01:00:07.300 | or in a traditional school environment,

01:00:09.480 | one of the best things you can do with his math abilities

01:00:12.720 | is to require consistent work from him

01:00:15.900 | so that he doesn't go into the summertime slump.

01:00:20.040 | One of the worst things about the way

01:00:21.800 | at least the American educational calendar is set up

01:00:24.840 | is that you have a school year

01:00:26.980 | with a huge long summer break.

01:00:29.120 | And what results is that students think

01:00:31.620 | that they should only do work five days a week

01:00:33.920 | for the 180 days of school.

01:00:35.880 | And then the last couple of weeks are wasted, generally.

01:00:39.360 | You have wasted weeks of test prep,

01:00:41.920 | and then the first few weeks are wasted

01:00:43.560 | trying to catch the child back up.

01:00:45.920 | And if math is like a language,

01:00:48.160 | it's more important to have daily consistency

01:00:51.840 | than it is to have massive levels of work

01:00:56.280 | on an ongoing basis.

01:00:57.460 | Meaning if you could only do,

01:00:59.300 | if you could only, if you try to study a language

01:01:03.040 | for a three-hour stretch, and then you wait a week,

01:01:06.960 | you would be better off with just 20 minutes every day

01:01:09.720 | or 30 minutes every day,

01:01:11.680 | even if your total time invested is less

01:01:14.240 | because of the value of consistency.

01:01:16.280 | And I think math has the same basic focus and need.

01:01:21.280 | And so I think that if you want your child

01:01:24.080 | to develop his brain,

01:01:25.460 | regardless of the school environment,

01:01:28.480 | you should require as much math

01:01:31.960 | as can be practically exercised.

01:01:34.660 | And here, I think a good inspirational example

01:01:38.240 | would be that of Art Robinson

01:01:40.600 | and what he did with his children.

01:01:43.280 | You can read about his story

01:01:44.720 | at a website called robinsoncurriculum.com.

01:01:48.440 | But the short version of it is that Art Robinson

01:01:51.080 | was a, is a scientist,

01:01:53.880 | and he and his wife were both research scientists

01:01:56.300 | working together.

01:01:57.140 | His wife, Lori, they had six children,

01:01:59.440 | and they were committed to homeschooling.

01:02:01.560 | And then Lori died, developed this illness

01:02:05.040 | that killed her in something like 24, 48 hours.

01:02:07.400 | And he was left as a father of six children,

01:02:11.000 | including one baby, with no wife,

01:02:13.440 | who was desirous and committed to homeschooling

01:02:16.600 | while also needing to work.

01:02:19.040 | And basically, he applied a very simple system

01:02:24.640 | to his own family,

01:02:27.820 | and he required his children to learn math facts.

01:02:31.340 | Then he wound up accidentally creating a system

01:02:35.460 | of self-education for mathematics.

01:02:39.020 | What he would do is he would require his children

01:02:40.900 | to learn math facts.

01:02:41.900 | Once they had mastered their math facts,

01:02:44.380 | then he handed them a Saxon 5-4 book,

01:02:48.080 | which is basically the fifth grade book,

01:02:50.300 | and they started,

01:02:51.340 | and they would just work their way through the problems.

01:02:54.340 | And what they did was they did math six days a week,

01:02:58.320 | usually about one to two hours a day,

01:03:00.580 | and the students were required

01:03:02.820 | to teach themselves the lesson

01:03:04.380 | and just proceed through the problems.

01:03:06.820 | And if it was going too long,

01:03:08.340 | they would lower the problem.

01:03:09.340 | Normally, they would do,

01:03:10.420 | a Saxon lesson usually has 30 problems on a daily basis,

01:03:13.420 | so a 30-problem set would take about an hour to two,

01:03:16.060 | one to two hours.

01:03:17.080 | If they were going to,

01:03:18.660 | if it was too hard for them,

01:03:21.700 | they would drop it to 15 problems.

01:03:23.140 | If it was too easy for them,

01:03:24.100 | they'd increase it to 45 or 60 problems.

01:03:26.820 | But the outcome of this approach

01:03:31.100 | led to quite impressive,

01:03:33.740 | quite impressive educational results

01:03:38.660 | and educational outcomes.

01:03:40.020 | He developed a homeschool system

01:03:42.660 | that created,

01:03:45.100 | that focused on the basics,

01:03:46.580 | reading, writing, and arithmetic.

01:03:48.460 | In essence, he required his students

01:03:50.000 | to do two hours of math a day,

01:03:52.180 | to read off of an assigned book list for two hours a day,

01:03:54.980 | and then to write a page a day for an essay,

01:03:56.940 | which wound up basically being an hour a day.

01:04:00.280 | Following this model,

01:04:01.340 | his children all completed calculus

01:04:02.980 | at around 14 or 15 years old.

01:04:05.940 | Following the study of calculus,

01:04:07.340 | they went on and studied physics and chemistry.

01:04:10.060 | They all passed AP calculus exams, et cetera.

01:04:12.620 | And today, of his six children,

01:04:14.200 | it may be all six of them now have PhDs,

01:04:16.340 | but four or five of them do.

01:04:18.420 | And you can read more about his story.

01:04:20.380 | You can find some old lectures of him lecturing

01:04:23.620 | on his homeschooling approach.

01:04:26.340 | Very inspirational.

01:04:27.260 | In fact, maybe I'll pull in the audio

01:04:28.620 | from some of his old lectures

01:04:29.980 | and release it to you here in the feed.

01:04:32.100 | But very, very inspirational in terms of his story.

01:04:35.860 | And I first read that story before I ever had children,

01:04:38.940 | and I have planned since then

01:04:41.020 | to do this with my own children,

01:04:42.260 | and I'm in the process now of doing it,

01:04:44.700 | a couple of modifications.

01:04:46.380 | At its core, I wanna emphasize

01:04:49.060 | that the key is to do math every day.

01:04:52.820 | And one point that Robinson uses,

01:04:56.060 | or used, always used,

01:04:57.580 | is that he always required his children to start with math.

01:05:01.380 | And his theory on that was you need to,

01:05:04.580 | because math is hard, children need to be trained

01:05:08.580 | that the first thing you do when you wake up in the morning

01:05:11.200 | is you do something hard.

01:05:13.120 | And I am convinced of the value of this.

01:05:15.700 | So this is what we do in our homeschool.

01:05:17.460 | We get up in the morning.

01:05:18.860 | As soon as we start, we start with math,

01:05:20.980 | and we start with a hard thing,

01:05:22.100 | and we stay at it until we're done.

01:05:23.940 | Because at its core, this success skill

01:05:28.120 | is something that needs to be developed,

01:05:29.860 | and we can use math to develop it in our children.

01:05:32.980 | I don't wanna start my morning

01:05:34.260 | with something that's pleasurable

01:05:35.860 | or trying to figure out what do I really wanna do first.

01:05:38.460 | I wanna start with the hardest thing on my list.

01:05:41.120 | Brian Tracy would call this eat that frog,

01:05:43.140 | coming from the old saying,

01:05:44.700 | maybe attributed to Mark Twain,

01:05:46.300 | that if you've gotta eat a frog every day,

01:05:48.540 | you know that's gonna be the worst thing

01:05:49.900 | that's gonna happen to you.

01:05:51.100 | If you know that you need to eat a frog,

01:05:53.400 | that's probably the worst thing

01:05:54.340 | that's gonna happen in a day,

01:05:55.880 | so you might as well get up and face it and eat the frog,

01:05:58.300 | and then you know everything's better from there.

01:06:00.940 | So basically the same principle.

01:06:02.740 | And so with children, as I see it,

01:06:05.140 | this should be a fundamental tool that we use,

01:06:08.420 | is we want our children to be smarter,

01:06:10.060 | we want them to gain all of the benefits

01:06:11.900 | of a rigorous mathematical occasion, education, excuse me.

01:06:15.580 | We want them to gain strict thinking skills,

01:06:17.620 | we wanna understand the world very clearly,

01:06:19.700 | we want them to have true and fundamental knowledge,

01:06:22.220 | not appreciation,

01:06:24.020 | and we want them to be trained to do something hard,

01:06:26.660 | and to do it first thing every single day.

01:06:29.860 | And so mathematics to me seems the ideal way to do it.

01:06:33.960 | The next point though,

01:06:37.380 | is that the pace of math progression

01:06:41.220 | should be tailored individually to the child.

01:06:46.380 | Math, because it is something

01:06:48.220 | that involves cumulative knowledge and skills,

01:06:51.900 | we don't just try to push the child forward

01:06:54.020 | or pull the child back.

01:06:55.820 | If the child is struggling with something, we slow down.

01:06:59.120 | We master the concept

01:07:00.300 | until the child is no longer struggling,

01:07:01.960 | and then we press on.

01:07:03.700 | Now I'm fairly young in my own tutoring of this

01:07:08.220 | with my children,

01:07:10.180 | but I have observed this,

01:07:13.300 | and the importance of proceeding at the rate of the student

01:07:18.300 | when teaching long division

01:07:20.260 | and practicing long division to my eldest child.

01:07:24.140 | Long division is of course a skill

01:07:25.680 | that probably for most of us was intimidating at first.

01:07:28.220 | It can be difficult, it takes time to develop.

01:07:31.180 | And I was tutoring and working,

01:07:32.740 | I wasn't requiring an entirely self-taught system

01:07:35.860 | at that time,

01:07:36.820 | but I was tutoring with my student

01:07:38.980 | and working with him, et cetera.

01:07:40.840 | And I realized that it doesn't matter

01:07:43.880 | how many problems I help him with.

01:07:47.000 | What matters is that I help him

01:07:49.920 | until he's able to do it himself,

01:07:51.600 | and that he does it himself then until he is confident.

01:07:54.900 | I was tempted early in the experience

01:07:58.320 | to say, "Well, I'm just gonna help you with a few things,

01:08:00.000 | "then you gotta figure it out."

01:08:01.520 | But I realized my student is quite young,

01:08:03.400 | not at the age yet where I'm willing to be so hardcore.

01:08:06.440 | And I realized it doesn't matter

01:08:09.280 | whether a student needs 10 problems

01:08:12.000 | of me working them with you,

01:08:13.560 | or 110 problems.

01:08:15.660 | What matters is that you see the examples

01:08:18.480 | and you work the examples

01:08:20.000 | and you're helped with it until you master it.

01:08:22.760 | And then that you have enough practice examples

01:08:25.340 | to master it.

01:08:26.520 | And that's the principle that I think

01:08:27.920 | we should all apply with our children,

01:08:29.400 | regardless of who their teacher is,

01:08:31.540 | regardless of the curriculum, et cetera.

01:08:35.760 | Help as much as is necessary

01:08:37.960 | until the child's brain grasps it,

01:08:40.880 | and then require mastery of the concept.

01:08:43.840 | I do believe that requiring the child's brain

01:08:48.200 | to figure it out is a tool

01:08:51.440 | that we should consistently use.

01:08:54.680 | Back to the book, "Equation for Excellence,"

01:08:56.880 | chapter four, "Incentive and Struggle,

01:08:59.120 | "The Art of Developing the Mind."

01:09:02.240 | When taught right, math builds the mind

01:09:04.080 | in the way that lifting weights builds the muscles.

01:09:06.160 | But not all methods of teaching math do this equally.

01:09:09.080 | In fact, some of the more recently adopted methods

01:09:11.360 | of teaching math actually do the reverse.

01:09:13.720 | Not only do these methods fail to build cognitive skills,

01:09:16.840 | but they actually cause skills

01:09:19.360 | that the student has already built to atrophy.

01:09:23.060 | Three things cause cognitive skills to develop.

01:09:26.380 | The first is age.

01:09:28.140 | Even with the worst education available,

01:09:30.160 | human biology will make a 16-year-old

01:09:32.420 | more intelligent than a two-year-old.

01:09:34.760 | The second thing that causes cognitive skills to develop

01:09:37.720 | is exposure.

01:09:39.560 | Children who are exposed to interesting ideas

01:09:42.060 | and problem types can freely stretch their minds

01:09:44.600 | and explore new modes of thought.

01:09:46.840 | As a simple example, a child who plays with a Rubik's cube

01:09:49.680 | may develop a surer sense of three-dimensional reasoning.

01:09:53.320 | The third consideration is incentive.

01:09:56.180 | A child who plays with a Rubik's cube

01:09:57.920 | may develop the foundation for strong spatial reasoning.

01:10:01.240 | However, without a strong incentive,

01:10:02.880 | he may never push his mind to the limit.

01:10:05.280 | If he cannot figure out how to solve the Rubik's cube,

01:10:07.920 | he will probably just give up.

01:10:09.880 | For the mind to have the incentive to develop,

01:10:12.080 | two things are necessary.

01:10:13.880 | First, it must encounter a problem that it is unable to do.

01:10:18.880 | The process of figuring out how to solve

01:10:24.320 | this initially unsolvable problem

01:10:27.620 | causes the mind to develop.

01:10:30.240 | If a student is only given problems

01:10:32.720 | at his current ability level,

01:10:34.640 | what incentive does the mind have to improve?

01:10:37.800 | Just as lifting a half-pound weight

01:10:40.000 | will not make a person physically stronger,

01:10:42.540 | doing an easy math problem

01:10:44.280 | will not make a person mentally stronger.

01:10:47.400 | Parents and teachers of gifted students often overlook this

01:10:50.160 | and just allow them to work at a comfortable pace.

01:10:52.700 | The result is that the gifted students

01:10:54.520 | never get the opportunity to realize their full potential.

01:10:57.600 | Like natural athletes who never train hard,

01:10:59.880 | they end up squandering their innate talents.

01:11:02.840 | No matter how smart a student is,

01:11:04.760 | he must be given some challenging math problems

01:11:07.480 | that he is initially unable to do.

01:11:10.120 | If he can solve the problem in five minutes,

01:11:11.800 | it is not a real challenging problem.

01:11:13.920 | An appropriate challenging problem

01:11:15.600 | should take anywhere from 20 minutes to a week to solve.

01:11:19.520 | Once you have a sufficiently challenging problem,

01:11:23.360 | the next thing you need is incentive.

01:11:26.300 | If the student has no incentive

01:11:27.640 | to figure out a difficult problem,

01:11:29.160 | he will simply walk away.

01:11:30.920 | However, by understanding what motivates your child,

01:11:33.840 | you can design the right kinds of incentives.

01:11:37.600 | So we will pause there, but the key is

01:11:40.880 | we want the child's brain to struggle with something hard

01:11:45.780 | in order for it to grow,

01:11:47.720 | just like we want the child to struggle

01:11:51.180 | while lifting a heavy weight so that his muscles may grow.

01:11:55.620 | When you're looking at math curricula,

01:11:58.980 | you may just have one that's exposed to you

01:12:01.420 | with your school.

01:12:03.860 | There are a couple of philosophies

01:12:05.440 | into which most math curricula are segmented.

01:12:09.160 | One is what is called mastery,

01:12:11.640 | and the other is what is called spiral.

01:12:14.440 | I don't like the word mastery in a name,

01:12:16.460 | but let me explain what it means.

01:12:17.720 | Basically, the concept is we're going to introduce a concept

01:12:20.760 | and we're gonna drill it and drill it and drill it

01:12:22.360 | and drill only that concept

01:12:23.840 | until the student masters that concept.

01:12:26.000 | Then we're gonna go on to something else

01:12:27.580 | and we're gonna drill it, drill it, drill it

01:12:28.920 | until the student masters that concept.

01:12:31.320 | That's contrasted with,

01:12:32.880 | and then we're gonna go on to something else.

01:12:34.080 | So the concepts are given as a block

01:12:38.960 | and you go through them.

01:12:40.180 | That's contrasted with what is often called

01:12:42.320 | the spiral approach.

01:12:43.500 | The spiral approach is we're gonna introduce a new concept,

01:12:46.480 | you're gonna do some practice problems,

01:12:48.240 | and then the next day you're gonna do a couple of problems,

01:12:50.640 | but it's gonna be intermixed with everything else.

01:12:53.080 | And we're gonna just spiral around

01:12:54.760 | going up and up and up and up,

01:12:55.960 | and you're gonna master the concept over time

01:12:58.280 | because you're doing it a little bit every day.

01:13:01.240 | I've read enough parents' results to recognize

01:13:05.380 | that probably both can be fine.

01:13:07.800 | It seems like people will go through

01:13:09.320 | different math curricula searching for something

01:13:11.760 | that works for them.

01:13:13.480 | And of course, finding something that works for you

01:13:15.400 | is the key.

01:13:17.320 | I'm no expert on that field.

01:13:25.600 | Right now, we are using the ABECA math curriculum

01:13:29.600 | and what I like about it,

01:13:32.480 | it's actually for one specific reason.

01:13:34.880 | First, it is a spiral methodology.

01:13:36.960 | I'm more attracted to the concept of the spiral methodology

01:13:39.800 | 'cause it fits with my concept of math as a language.

01:13:43.400 | Introduce something new, learn it, drill it, use it,

01:13:45.640 | and don't stop using it.

01:13:46.960 | Just continually build, build, build little by little.

01:13:49.920 | So I find that attractive,

01:13:51.480 | but I would be open to other things.

01:13:53.080 | I just have never needed to try anything else.

01:13:55.440 | What I specifically like,

01:13:56.840 | the reason we're not using Saxon math,

01:13:59.120 | which I appreciate,

01:14:00.440 | is that Saxon math being a non-consumable textbook

01:14:05.440 | requires the math student to write a significant amount

01:14:11.240 | 'cause all the problems have to be copied out on paper.

01:14:13.920 | And the specific hangup that I faced with my eldest

01:14:18.720 | is a lack of desire to write.

01:14:21.380 | Many young boys are allergic to pencils

01:14:24.040 | and we have that disease.

01:14:25.280 | Now we make progress in it, good progress over time,

01:14:27.840 | but the Abeka math is a very discrete,

01:14:31.240 | and I mean that in the mathematical concept,

01:14:32.840 | meaning confined, limited, a very discrete thing.

01:14:35.880 | There's a page front and back,

01:14:37.480 | and once you're done with the page, you're done.

01:14:39.000 | And yet that page seems to fit well,

01:14:40.880 | and it doesn't require a lot of writing

01:14:42.480 | because the work is done on the page.

01:14:44.080 | So that's been a winner for us.

01:14:45.960 | I'm impressed with the arithmetic curriculum of the Abeka.

01:14:48.720 | I don't intend to continue at past arithmetic,

01:14:51.440 | but time will tell.

01:14:53.160 | You go and choose something that you like.

01:14:56.460 | I do think there is value

01:14:58.520 | in learning concepts of mathematics.

01:15:02.220 | And so I have also supplemented the Abeka curriculum

01:15:06.660 | with something called Life of Fred.

01:15:09.640 | I stumbled into Life of Fred in a very organic manner.

01:15:13.480 | I was actually looking for a high school level

01:15:15.960 | personal finance curriculum.

01:15:17.200 | I was researching the market on personal finance,

01:15:19.040 | trying to understand what was out there.

01:15:20.840 | And I stumbled across the Life of Fred personal finance book.

01:15:25.240 | And I was browsing the table of contents

01:15:27.440 | and the sample book,

01:15:28.840 | and I was amazed at the quality of the book

01:15:31.800 | as a personal finance curriculum.

01:15:33.720 | I thought to myself, like, this guy's teaching concepts

01:15:35.820 | that I'm the only one I know who teaches this stuff,

01:15:37.800 | and this is great.

01:15:39.040 | So I immediately went and started looking

01:15:40.560 | at the rest of his math curriculum.

01:15:43.360 | And Life of Fred, the author Stanley Schmidt,

01:15:45.720 | something like that,

01:15:47.000 | has developed a complete math curriculum

01:15:50.100 | that takes a student through

01:15:52.320 | from the very basics of arithmetic

01:15:55.280 | through and past college level calculus

01:15:58.520 | to some of the advanced higher linear,

01:16:00.280 | I think he has a linear algebra book.

01:16:02.440 | He might have a differential equation book, I'm not sure.

01:16:05.040 | And he does it all in a literary format

01:16:08.000 | where he uses this goofy character

01:16:12.120 | that kids seem to love, this goofy character.

01:16:17.560 | And basically this goofy character

01:16:20.380 | has these various adventures,

01:16:22.340 | and the various adventures and goofy stories

01:16:24.980 | that he goes through require him to develop

01:16:28.700 | and exercise math skills.

01:16:30.680 | So it shows the application of the math skills.

01:16:33.900 | And he's an experienced math teacher,

01:16:37.620 | and my children have loved reading the books.

01:16:40.420 | He's very strong on the idea that his math curriculum

01:16:43.800 | is the only thing that somebody needs.

01:16:46.260 | I'm sure it's maybe so,

01:16:47.920 | but I like seeing the output of the Beka,

01:16:52.920 | and so we're doing both of them.

01:16:54.820 | But I really love that, and the children really enjoy it.

01:16:57.660 | And I like it because it deals with math

01:16:59.660 | from an understanding level

01:17:01.300 | and in a story way to see the application.

01:17:05.200 | And he weaves in all these incredible

01:17:07.620 | little extra tidbits of knowledge and fact

01:17:10.100 | into his stories, really, really remarkable.

01:17:12.260 | So we've become big fans of Life of Fred.

01:17:14.580 | It's not our exclusive curriculum,

01:17:16.020 | but we've become big fans of that.

01:17:17.180 | And that can be something I think that you may enjoy.

01:17:20.020 | So I think that math, what can help with math

01:17:22.100 | is learning the concepts, gaining tutoring, et cetera.

01:17:25.300 | A narrative approach can help to supplement

01:17:29.700 | the drill and kill approach.

01:17:31.900 | Doing math consistently, daily,

01:17:35.060 | consistently with shorter breaks, it's fine.

01:17:38.900 | I think if your student needs a few weeks off, fine.

01:17:41.840 | But I struggle with the idea that students

01:17:43.620 | somehow need four months off a year.

01:17:47.460 | Doesn't make any sense to me that a student

01:17:49.460 | would need four months off at a time.

01:17:51.740 | It does make sense to me that a break,

01:17:53.740 | a vacation, is appropriate.

01:17:55.540 | So I look at it and say, if I go on vacation, fine.

01:17:58.700 | We'll take the family on vacation.

01:17:59.800 | That's a good time to have a vacation from school.

01:18:01.620 | But the idea that you need four months off

01:18:03.820 | from any kind of schooling seems to me a little bit silly.

01:18:07.620 | And so I think that students should

01:18:09.720 | at least do math all summer.

01:18:12.520 | Even if they just do math and free reading

01:18:14.760 | or limited reading.

01:18:16.920 | Again, a vacation is fine, but it doesn't need

01:18:18.760 | to be a vacation from thinking.

01:18:20.080 | We should never have a vacation from thinking.

01:18:22.300 | And then lots of consistent work

01:18:23.920 | and challenging self-teaching, et cetera,

01:18:25.580 | should help a child to be very skilled with mathematics.

01:18:29.260 | Now I want to, I'm not concluding the episode.

01:18:32.200 | There's gonna be quite a lot of time after this point.

01:18:34.600 | But the last concept I wanna focus on,

01:18:36.680 | or the last topic I wanna address with you,

01:18:39.300 | is at what age should we start teaching math and how?

01:18:42.520 | Because this is important.

01:18:45.660 | And I arrived at my current opinion somewhat on my own.

01:18:50.660 | And then I have since found people that agree with me,

01:18:58.020 | which helps me to feel increasingly confident.

01:19:00.620 | But my comment is basically

01:19:02.660 | that formal study of mathematics,

01:19:06.240 | I'm not sure that early is better.

01:19:08.180 | Now, I'll tell you the story

01:19:09.480 | of how I arrived at this conclusion.

01:19:10.860 | First, I have a brother

01:19:12.860 | who has a bachelor's degree in mathematics.

01:19:17.000 | And his observation and experience of learning mathematics

01:19:20.980 | and teaching mathematics is that a whole lot of time

01:19:25.560 | is wasted trying to teach math to the young.

01:19:28.980 | And that why do we spend a month teaching a concept

01:19:33.180 | and drilling a concept for a very young child,

01:19:35.780 | when if we just waited a few years,

01:19:37.540 | the child could grasp that same concept in a day.

01:19:40.240 | And I have often wondered if he was right.

01:19:44.580 | Now, I'm persuaded, I was always persuaded of the idea

01:19:47.840 | that we should teach children things at a very young age.

01:19:50.500 | But I heard him say that,

01:19:51.900 | and I filed that away and paid attention to it.

01:19:54.540 | Secondly, I've come across various math teachers

01:19:57.700 | who talk about the right age

01:19:58.980 | to start learning something like algebra.

01:20:01.260 | And one math teacher who runs a curriculum that I like,

01:20:04.860 | and will probably use in high school,

01:20:07.180 | he had this comment, he said,

01:20:09.060 | "Children shouldn't study algebra

01:20:11.100 | until they have hair in their armpits."

01:20:13.300 | Basic idea being, your brain needs a certain degree

01:20:16.120 | of physical maturity before it can completely and fully

01:20:21.120 | is ready for abstract concepts like algebra.

01:20:26.020 | So don't try to teach algebra to your child prodigy

01:20:29.060 | and just push, push, push.

01:20:30.460 | Just wait until the child is emotionally mature

01:20:33.980 | and it'll be easy.

01:20:35.720 | And I developed, based on these ideas

01:20:38.940 | and hearing various math teachers say things like this,

01:20:42.180 | this is why I developed the personal philosophy

01:20:46.140 | that our primary focus in the early years should be language

01:20:50.300 | because there are disadvantages to many subjects

01:20:53.140 | that are taught in school,

01:20:54.180 | teaching them at too young of an age.

01:20:55.980 | If the math teachers are correct

01:20:57.540 | and a student needs a certain ability with abstract thinking

01:21:01.020 | that comes with the maturity of the brain,

01:21:03.940 | then our goal is not to get our seven-year-old

01:21:06.040 | doing algebra.

01:21:07.720 | And similarly, if we look at science, right?

01:21:09.960 | I think it's crazy why we spend all kinds of times

01:21:12.960 | on kinds of time on science education, quote unquote,

01:21:16.360 | for very young children.

01:21:17.500 | I'm personally persuaded that science education

01:21:20.280 | should follow math education.

01:21:21.680 | Robinson makes this point very heavily.

01:21:24.700 | In order for you to do physics,

01:21:25.820 | you can't do physics without math, without calculus.

01:21:28.880 | Newton invented calculus to do physics

01:21:31.320 | or chemistry, et cetera.

01:21:32.500 | You need high-level math to do it.

01:21:34.580 | Now, many teachers have dumbed it down

01:21:36.320 | and taught things without math, but why?

01:21:39.520 | Just wait.

01:21:40.720 | Doing science, you should master math and then do science.

01:21:45.720 | And it's not that there shouldn't be

01:21:47.560 | generalized scientific knowledge, but why?

01:21:50.120 | Why spend all this time drilling it?

01:21:52.000 | And so I think the primary emphasis with young children

01:21:55.200 | should be language because the brain

01:21:59.120 | is wired for language acquisition

01:22:01.920 | at an early age.

01:22:03.440 | And so for very young children,

01:22:05.280 | our academic focus should be language.

01:22:08.080 | Our parenting focus should be character,

01:22:11.280 | building within them and practicing the skills of character.

01:22:16.100 | But from an academic perspective, it should be language.

01:22:18.360 | And so it can be your primary language.

01:22:21.400 | It can be ancient languages, Greek, Latin, Hebrew, fine.

01:22:25.880 | It can be modern languages.

01:22:27.440 | We've done a lot with modern languages

01:22:29.840 | and are now doing classical languages.

01:22:31.740 | But emphasizing math at an early age

01:22:34.480 | doesn't seem super necessary.

01:22:37.560 | Rather, mathematical concepts can and should

01:22:40.880 | simply be taught in a very straightforward way.

01:22:44.240 | So if you go and you look at the Montessori people,

01:22:47.360 | if you look at some of the stuff they do

01:22:49.160 | with mathematical appreciation,

01:22:50.320 | or just playing with your child,

01:22:51.920 | teaching your child to count,

01:22:53.160 | teaching your child the basic concepts of addition

01:22:55.760 | and subtraction and multiplication, et cetera,

01:22:57.680 | with physical objects, lots of physical stuff,

01:23:00.280 | and not a lot of workbook math

01:23:01.960 | at the early years is appropriate.

01:23:04.220 | So last year I was reading a book.

01:23:06.380 | I found this fascicle, excuse me,

01:23:08.580 | this fascinating book called "Teaching the Trivium,

01:23:11.640 | Christian Homeschooling in a Classical Style"

01:23:13.800 | by Harvey and Laurie Bluedorn.

01:23:15.920 | And I was interested in the book primarily

01:23:18.460 | because while I appreciate a lot

01:23:20.860 | of what the so-called classical educators have to say,

01:23:24.620 | I'm not a big fan of the so-called classical cultures.

01:23:28.800 | I think that Greek thinking has damaged many aspects

01:23:32.400 | of our modern world, especially Christianity.

01:23:35.320 | Not a big fan of St. Augustine

01:23:36.920 | and the Greek thinking that has been applied.

01:23:38.800 | I see it as a major problem in much of modern Christianity.

01:23:42.380 | And the Roman and Greek societies

01:23:44.520 | were just disgusting societies

01:23:47.040 | that maybe I appreciate some aspects

01:23:50.320 | of the architecture and art and whatnot,

01:23:52.080 | but I'm no Hellenist and I'm no Latinist myself.

01:23:54.480 | I'm no Roman.

01:23:55.460 | They were disgusting, evil, horrifically sinful societies.

01:24:00.200 | But I've always found that if you go

01:24:02.160 | into the world of educational pedagogy,

01:24:05.680 | you find some of the most serious thinking

01:24:07.960 | in this space from classical educators.

01:24:13.360 | And so I've never quite figured out

01:24:14.800 | how to resolve this conflict.

01:24:16.640 | My, I don't wanna be too strong,

01:24:20.920 | but my lack of appreciation for Greek and Roman cultures

01:24:25.920 | while simultaneously appreciating many

01:24:28.540 | of the aspects of classical education.

01:24:31.140 | So I found this title of this book

01:24:32.880 | and I bought it not knowing what to expect.

01:24:34.420 | And I was blown away by how good it is.

01:24:35.800 | Again, it's called "Teaching the Trivium,

01:24:37.460 | Christian Homeschooling in Classical Style"

01:24:39.100 | by Harvey and Laurie Bluedorn.

01:24:40.420 | It's a fairly old book, published in 2001.

01:24:44.060 | So more than 20 years old.

01:24:49.060 | But in this book, they included an appendix

01:24:52.760 | on math instruction.

01:24:54.960 | And so in this book, they talk about basically

01:24:58.440 | the philosophy that I've just described to you,

01:25:00.080 | which is a philosophy I arrived at independent.

01:25:02.520 | And then I came across their thoughtful,

01:25:03.960 | well-researched position and it blew me away.

01:25:06.360 | And their basic idea is that children should not start

01:25:11.360 | what they call workbook math,

01:25:13.560 | which means a formalized workbook-based math curriculum

01:25:16.520 | until about the age of 10.

01:25:18.440 | And their experience with their children

01:25:21.280 | is that their children have been easily able to start

01:25:26.040 | their math instruction with basically fifth grade

01:25:29.160 | around the age of 10.

01:25:31.000 | So instead of spending hours and hours doing

01:25:34.600 | first, second, third, fourth grade stuff,

01:25:36.680 | just wait until your children are 10,

01:25:38.440 | do informal math instruction through real life living,

01:25:42.360 | and then around the age of 10,

01:25:43.200 | just start with a fifth grade math book.

01:25:46.280 | And that if any of their children,

01:25:48.040 | I think they had six children go through this,

01:25:49.360 | if any of their children struggled at all,

01:25:51.560 | in a few weeks, you can iron out and catch up

01:25:53.760 | on anything that was necessary

01:25:55.240 | in order to do the fifth grade textbook.

01:25:57.280 | Interestingly, this compares also with Robinson,

01:25:59.680 | Art Robinson's experience,

01:26:00.920 | his idea about math instruction as a scientist.

01:26:04.160 | Just simply have children learn their math facts.

01:26:06.720 | When they know their math facts,

01:26:07.720 | start with a fifth grade textbook.

01:26:09.340 | But they, in this book, include this remarkable appendix,

01:26:13.000 | which I think is really beautifully researched.

01:26:15.280 | And I wanna share it with you.

01:26:16.960 | Because while I have not chosen to put off intentionally

01:26:21.640 | all kind of formalized workbook instruction

01:26:25.440 | until fifth grade,

01:26:27.000 | I think that if your young children

01:26:28.720 | are struggling with math,

01:26:30.380 | it should not be a big focus for you if they're seven.

01:26:35.880 | I don't think you should expect your seven-year-old

01:26:37.680 | to sit down and do two hours of math a day.

01:26:39.760 | And so I wanna share this lengthy appendix with you

01:26:43.200 | as a tempering commentary on what I have said,

01:26:46.680 | and also something that is perhaps educational

01:26:50.880 | as far as some areas where perhaps we are wrong

01:26:54.320 | in our modern day on the teaching of math.

01:26:56.400 | I'm changing my mind on what I've just said to you.

01:26:59.920 | Looking at how far we are into this episode,

01:27:03.080 | I'm going to release this appendix as a separate audio file

01:27:07.600 | in the podcast feed here,

01:27:08.800 | rather than including it at the end of this episode.

01:27:10.960 | If I include it here, too many people will avoid the episode

01:27:13.560 | for sake of it being too long.

01:27:15.400 | And I don't want what I've said to be missed.

01:27:16.840 | So let me instead sum up this

01:27:19.720 | and hope you'll listen to that appendix separately.

01:27:23.000 | At its core, we're trying to strengthen

01:27:25.040 | our children's minds.

01:27:27.200 | We want them to be smarter

01:27:29.400 | so that they will be better learners

01:27:31.400 | and be able to lead themselves to greater success.

01:27:34.840 | Numeracy, encouraging and developing numeracy

01:27:38.760 | is a fundamental way for us to accomplish that.

01:27:42.520 | So we want our children to do lots and lots of math.

01:27:47.000 | It will grow their gray brain

01:27:49.120 | into be a bigger and more powerful muscle.

01:27:51.640 | And regardless of whether they ever enter

01:27:54.920 | a scientific career or a career in which they use the math,

01:27:58.800 | the practice of doing math every day

01:28:01.960 | will increase their intelligence.

01:28:04.240 | Frankly, you and I should be doing math every day

01:28:06.440 | for these same benefits.

01:28:08.560 | And if math is not your thing,

01:28:11.760 | doing Sudoku or crossword puzzles or something is key.

01:28:16.560 | In terms of staving off dementia,

01:28:19.400 | helping us to be smarter, et cetera,

01:28:21.240 | we need to be challenging our brain and making it think.

01:28:24.480 | And math is perhaps the best way to do that.

01:28:26.880 | So don't force too much math on your children.

01:28:30.320 | If your children are young

01:28:31.440 | and they're not doing well with math, back off.

01:28:33.480 | Focus on language at an early age rather than mathematics.

01:28:38.040 | But as your children get into math,

01:28:39.920 | require them to do math every day

01:28:42.720 | so that they will develop the character

01:28:45.480 | of doing hard things first thing every day,

01:28:48.440 | and so that they will become deeply numerate

01:28:51.360 | and become smarter, more accomplished,

01:28:54.320 | better educated individuals

01:28:56.120 | who know how to teach themselves the things that matter.

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2023-02-27_How_to_Invest_in_Your_Children_at_a_Very_Young_Age_Part_6-Catalyze_Numeracy_in_Your_Children