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(and a Fun Invitation…)

by Oliver DeMille

Spring Fever Reader

canstockphoto-momandsonreading When springtime comes, it’s more difficult to keep the kids in their classrooms. They might be there physically, but their minds are increasingly outside in the sunshine, running amidst the flowers, listening to the sounds of birds, and feeling the warm breeze.

And actually – the adults aren’t immune to this pull, either!

In the little town where I grew up, nine months of the year were spent attending school, and three months were not. But the months of April and May were, somehow, clearly understood as a “halfway place”. Yes, we had to stay in school for a few more weeks, but we were encouraged to lean into summer—meaning that our focus on summer things could increasingly take a higher priority than school.

And what, exactly, was summer about? Not school, certainly. It was about: Playing. Working. Sports. Swimming. Vacation. Fun. All of this was part of it—certainly. But summer, at least in my family, was mainly about Reading.

Not the kind of reading that was assigned by teachers, but the kind you did on your own, for fun, for interest, for excitement.

Jumping In

beware the anti-readers DeMille-Great Minds read, read, read

Perhaps not all families approach summer that way…but why not? They could. Maybe even should! :)

Think about it. There’s nothing more effective for learning than reading a good book in the shade, getting lost for long, hot hours in stories and ideas that bring smiles and deep thoughts.

So, with summer ahead, isn’t it time to jump in and get some spring reading done?

For our family that’s exactly what it’s about. And, this year, we want to invite you to join our family in reading four really great books in the days, weeks, and months just ahead.

You can read others of course, but here are some awesome (and fun) spring and summer classics we’re going to tackle this year, in 2015:

APRIL: The Fourth Turning by Strauss & Howe

This is a powerful book about the world we live in, how it is changing in some very important ways, and what it’s likely to look like in the next ten years. Once you read it, you’ll never view the world the same. It’s an easy read, full of important ideas. And if you have any older children or youth in your family (ages 8-18, for example), it teaches about four personality types (based on generations) that will help you understand your kids better—and help them understand you! The discussions you’ll have with them will priceless. Plus, it’s a really fun book. Of all the books I’ve quoted over the years, I think this one is at the top of the list, right along with Pride and Prejudice.

MAY: Anne of Green Gables

This is one of the best books ever written on how to mentor girls. If you have a girl in your home (ages 1-18), this is a must! It’s deep, and it’s fun. It’s easy reading, and very enjoyable. The chapters are short—perfect for a quick read in the warm evenings, or read together with your kids for a few minutes during hot afternoons after lunchtime. If you’ve read this book before, you know that it’s so worth re-reading! And if you’ve never read it, now’s the time! It’s a great book. If you are a teacher of any kind, including children’s main teachers (parents), this is a truly excellent read for you.

JUNE: Bendigo Shafter by Louis L’Amour

This is one of the best books you’ll ever read about how to mentor young men (ages 1-18). It is a fun story, fast paced and full of action. The romance is very sweet and compelling, and it will engage the women and girls as well as boys and men. If you are a dad, this book is a great way to connect with your son(s). It teaches a man’s way of getting a great education, growing up, and raising a boy into a man—making it fun for dads. It will teach dads to really mentor their boys more effectively. In fact, it will do the same for moms by helping you get inside your boys’ heads and really understanding them. A powerful book! Don’t miss it! If you are a teacher of any kind, reading Anne and Bendigo will improve your ability to inspire young people.

JULY: Little Men

This is another great classic, and it builds on Anne of Green Gables and Bendigo Shafter to help parents and teachers mentor both boys and girls. What really works in helping our kids get a great education? And what are the powerful things we can do to create the right environment in our home—the kind of environment that naturally reduces family conflicts and encourages love, support, and positive relationships to flourish? This book is a must read! It’s truly enjoyable, fun, and great—for you as an individual, or read as a family together in the heat of summer!

DeMille-Great Readingy Why and Where

We are reading these specific four books together for a reason: they teach us how to be better parents and mentors, and that’s a great focus for summer!

So let me invite you now to make these books part of your great 2015 spring. They will bring a higher sense of life, excitement, and increased learning to your year. Those who read them will experience an improved, more effective learning year than those who don’t read such great classics—and we’ve seen year after year that it will translate to your whole home and family. Join us for this 4-book 2015 reading fiesta. It’s going to be a blast!

In my little hometown growing up, my three favorite places to spend summer were the town library (picking out books to read), the city park (reading on the grass in the shade during the hot afternoons), and our back porch (reading on the couch, into the evening and long after dark). We’re going to repeat such fun spring and summer reading this year with our family, using these four great books, and we invite you along on this exciting journey through these books!

Action Items:

  • Own your copy of the book! These are great additions to your family library, and worth returning to over and over.
  • Read with a pen in hand, and a question, concern or goal in mind. Write in the margins with little symbols (! / ??? / :) ) and underline, circle, star in line with the txt.
  • In the blank pages and spaces at the back of the book (and in the front as well, as needed) keep a running record of important ideas, listed by page number, such as “64: why relationships fail; 72: little girls’ greatest dreams; 99: watch the character rationalize a bad decision
  • Share what you’re reading by blogging, discussing or reading passages aloud that may be of interest to your family

iStock_news It’s no coincidence that these same 4 titles are the upcoming events for our Mentoring in the Classics series!

If you’d like to go in depth and enjoy mentoring and discussion with others who are reading these titles as well, come join us for Mentoring in the Classics >>


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What is TJEd?

Published on 14. Apr, 2015 by in Basic TJEd, Blog



What is TJEd?

by Oliver and Rachel DeMille

The Purpose of Learning Since TJEd places such high value on parents leading out and personalizing in their homes, the answer to this question can vary quite a bit; and there are some principles that are constant.

Here is the TJEd philosophy in a nutshell:

Every student has inner genius, and the best educational results are usually attained when a mentor continually assesses what the individual student needs and tries to help deliver it.

That’s it. The rest is just possible ways to do this.

Standing on their Shoulders

Think of the best teacher you ever had… What made him or her so great?

  • Did he truly care about you? Did she give you a vision of who you could become? Did he love the topic so much that it was inspiring?
  • Did she challenge you to be more?
  • What other things made your best teacher so good?

Leadership Education-Greatness and Goodness Whatever your answer, all of these are part of the Thomas Jefferson Education philosophy. It all boils down to a mentor taking stock of what each student really needs most, and then helping him get it.

This means different things for different students, so TJEd is always individualized. It also means different things for the same student at different times, because any student will need different things at age 7 than at age 16, for example.

The central points of TJEd can be summed up as follows. You might want to stop and think about each of these as you read:

  • Every student has areas of inner genius and/or potential greatness.
  • The purpose of education is to help the student find and develop such areas of inner genius, along with obtaining general knowledge and skills that will be helpful in the student’s life and help the student really flourish personally and improve society through dedicated service.
  • Students typically find their areas of genius by pursuing studies they are passionate about.
  • Great mentors can help students get passionate about new areas.
  • The focus of great mentors (parents, teachers, coaches, etc.) is learning, not educational systems or bureaucracy.
  • Part of great education is identifying one’s life purpose or potential life missions and preparing for them through the learning process. Even when a student’s plans change, as they often do, the enthusiasm generated by pursuing learning for a life purpose usually translates into further passion for later missions.
  • Mentors can help students expand their areas of passion outside their comfort zone, but the passion should be “pilot” and the other things should take a supportive role.
  • Great education nearly always flows naturally from great teaching and mentoring.
  • The simplest way for a mentor to start being a great mentor is to identify the greatest teachers, coaches and mentors from his or her own life experiences, clarify in his mind what made these teachers so great, and seek to emulate the best things about these great teachers—always with an eye toward the personalized needs of an individual student.
  • The role of education mentors and teachers is to inspire students, by example and by whatever is personally inspirational to each individual.
  • The responsibility of getting a great education is that of the student, not the mentors, parents or teachers. Mentors inspire, students study and learn.
  • Parents are the only true experts on their homes and children; teachers are the only true experts on their classroom.

great education is inspired education Perhaps the greatest support to this TJEd philosophy is the methodology, which is summarized by the 7 Keys of Great Teaching.

Again, the 7 Keys are not the philosophy, but they are a powerful methodology that mentors can use, modify, or not use, as needed to best help the individual student learn most effectively at a given time.

Want to learn more?

If TJEd is calling to you, I would not recommend “winging” it. Don’t just mimic a friend, or browse and guess. You’ll feel so much more confident and empowered when you do your homework. There are lots of freebies available on this site to help you get a “feel” for whether TJEd is a fit for you. Check out the links at the end of this post! :)

Once you’re past that point, and feel like it is a fit – the 7 Keys Certification is set up specifically to help you become a self-guided learner, design your ideal family education culture, become conversant in the language of the classics, and really *own* the principles of Leadership Education so you can be your own expert. Check it out!

think read 1 http://tjed.org/7-keys-certification/ (It’s on deep discount right now with Coupon Code SIMPLEBONUS13)

And please, do join the discussion about how to apply TJEd in your home and classroom. There are thousands of inspiring and supportive parents mentors on our Facebook group sharing daily in the dialog, with ideas on how to, which resources, when this-or-that, etc.

With Rachel DeMille as the moderator and dozens of ad-hoc mentors who go out of their way to be helpful, you’re sure to find answers to your questions!

Join now >>

Resources to Learn More:


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A Major Revolution in Teaching Math

(Are You Using It Yet? It’s So Much Easier and More Effective!)

by Oliver DeMille

Old and New

mommy math Have you heard about the new way of teaching math? It’s revolutionary, because it works so effectively. If you do this, teaching (and learning) math will be so much easier, so much more fun, than other ways to help your students study mathematics.

Actually, this new way is a very old way. It’s the classic way. The way effective parents and teachers used to do it. But we’ve mostly lost it in modern educational circles and curricula, so it’s new to us.

By way of introduction, there are 7 important levels of teaching math—and modern math instruction usually only teaches 1 of these levels. This puts our kids, and their teachers and parents, at a distinct disadvantage.

And to be clear, the other 6 levels don’t make it harder – they make it easier! Why teach only 1 level, when the other 6 are essential parts of math, make math more meaningful, relatable and fun?

Solvings and Solutions

The answer is that the national multiple-choice exams like the ACT and SAT only test one level—so, naturally, most teachers and schools ignore the other levels. They consider them unimportant.

But they aren’t. All 7 levels are vital to genuine math understanding. We need to teach them all. Otherwise, we get a few kids who can ace the tests but don’t really understand that depth of the mathematical principals, and, worse, we get around 80% of the kids who can’t even excel on the exams. They simply don’t click with the one level of math we teach.

But almost all of them would click with one of the other 6 levels, as teachers who use all 7 levels experience routinely. And when a student clicks with 1 level, the other levels become easier, more simple, and frankly, more interesting.

Each of the 7 levels is very important to any authentic and lasting understanding of the mathematical field.

[For help in internalizing, personalizing and applying these levels, try our free class that incorporates these 7 Steps >>]

Sir Cumference Dragon of Pi 1. Stories

Discover stories about math and the mathematicians (historical and also in current life) who use, study, and love it.

Want ideas? Here are a few:

2. Shapes, Patterns, Symbols, Numbers, etc.

huff-kid-parabola Fall in love with shapes, patterns, numbers, symbols, etc. Students who skip this step are always going to feel some sense of disconnect with math – like it’s a foreign language, and they don’t have a dictionary. This is true even of many students who learn to do well on the tests.

Many of the math games in our home were found in thrift stores and yard sales. Keep you eyes open – opportunities will come your way! Want ideas? Here are a few:

3. Math-Loving Mentor

math-clock Nothing can beat an in-person connection with a math-loving mentor! Find a math-loving math mentor who cares for you, who can pass on a love of math to you. And, when you read and study math, make sure you do it from someone who LOVES math, and shares it with creativity and delight.

For example, check out these authors, who are simply amazing in their ability to help math-phobics learn and love math:

4. Spreadsheets

spreadsheet_canstockphoto25236565 Use and understand spreadsheets, business plans, and other mathematically-based technologies in everyday life and tasks.

A sort of a cross between a Word document and a calculator, spreadsheets are valuable for everything from capturing lists and data (like Christmas card lists, to-do lists, book lists, classroom performance data, etc.) to calculating “what-if?” scenarios for budgeting, debt management, business planning, etc.

What can you use spreadsheets for?

  • Profit and Loss
  • Budgets
  • Inventories
  • Charts and Graph
  • Using as database
  • Invoicing
  • Working out loan interests

Want help with the basics?

5. Math Classics

Read math and mathematically-based classics (e.g. the great mathematicians such as Euclid, Newton, Einstein, etc.). This brings relevance to the topic. Students who do this simply never ask, “how am I ever going to use math in real life?” It’s already become part of their life experience. Sound counter-intuitive? Just wait until you read a math classic. The masters themselves tie math to myriad other subject areas and every-day life.

See our lists of math classics (Not exhaustive! Just some great ideas on where to start…):

do-the-math_canstockphoto6130675 6. Do the Math

Study and master math problems, techniques, language, proofs, and testing skills from basic arithmetic through algebra, geometry, trigonometry and calculus. You can even study higher fields of math like Conic Sections or Dynamics.

7. Math Classics in Depth

Study the great mathematicians on a higher level than # 5, by really going deep in your math readings. Learn to truly think mathematically. This is a great source of fun and personal improvement for many math teachers. And parents can learn to love it as well. Of course, Level 7 really only works after you’ve spent time on the earlier levels.

Leona-Tai_Fun-with-fibonacci-parabola Once you are ready to try level 7, here are a few books to get you started:

Math Problems and Life Problems

math-study-hourglass-steps The truth is that some students can jump around from level to level, because they grasp one kind of logical process even without understanding the foundations upon which it is built. But without such foundations, they’ll often run into a wall in their learning.

And even some of the best “Level 6” math students will learn to emphasize facts over morals, details over people, and rote processes over creative thinking or genuine reasoning and application.

Also, the problem with this list of 7 levels differs for those who are naturally “good at math” versus other types of learners. All 7 of these levels are valuable and very important for anyone learning (or teaching) math. For children and youth (and adults) to whom math doesn’t come quite so naturally, levels 1-5 will make learning Level 6 much, much easier and more fun.

Yet, sadly for most students, few adults help them realize how much levels 1-5 can help them. And few teachers understand how much they’ll benefit by engaging Level 7 in addition to the other 6.

Thus most students in nearly all schools are directed to Level 6 and receive very little of the other levels. But this is a mistake. These other levels take nothing away from Level 6; in fact, they broaden the young person’s Level 6 abilities, skills, interest, engagement and effectiveness.

Likewise, if a child or youth tends toward high literary, artistic, or athletic successes, experiencing the natural creativity of Levels 1-5 can be very inspiring when he or she studies Level 6.

Skipping and Starting

Again, parents and math teachers will do well to closely review—even memorize—the 7 Levels outlined above. Write them down, post them on your mirror, and keep them in mind as you work with your youth during his or her teen years and beyond. Skipping the first 5 levels will reduce his educational experience and overall development.

For more resources and training on how to use this 7-Level approach to math excellence, we have developed a mini-course, offered free here >>

Do the Math (not just the math, you know?)

multiplechoice If you plan to teach math or science to others, including in your home or beyond, knowing the other levels besides Level 6 (Level 6 is arithmetic, algebra, geometry, trigonometry, calculus, etc.) will also help you relate to and work with students who aren’t natural mathematical learners.

If you are a natural math learner yourself and also a teacher, this is incredibly helpful because it will help you speak more fluently with students who aren’t natural math lovers.

Of course, natural math learners don’t just learn math and science using mathematical-style thinking, they tend to learn everything this way. If you are parent or teacher helping such a student, the key is to make sure he or she gets enough exposure to Levels 1-5. This is so important.

And it will significantly upgrade the student’s math success. I can’t imagine why anyone would try to teach or help their kids learn math with only one level. That’s like trying to play Ping-Pong with the paddle in your mouth and both hands tied beyond your back. It can be done, but why on earth would you limit yourself that way?



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important Now, for the week of 3/31/15 – 4/7/15, get our award-winning MIC for just $10/month and our exciting new BBF subscription for just $8/month!

(promotional rate on BBF only available to subscribers of MIC >>)

March Madness pricing It must be spring fever!!

For the week of March 31 – April 7, 2015, we’re offering our premium subscriptions at a deep discount! Just $18 per month total for both our award-winning Mentoring in the Classics AND our exciting new Black Belt in Freedom! Jump in now for maximum savings.

WAIT! If the deep discount isn’t compelling enough to make you leap in, consider this: Even if you’re not planning to participate fully in the study plan right now, here’s why you should subscribe now ANYWAY:

  1. The audios are a convenient and easy way to keep your mind enriched and your heart inspired. Even without the readings, you’ll be amazed at what listening to these audios does for your sense of empowerment, confidence and vision, as well as the mood and rhythm in your home!
  2. Even if you just “bank” the content for later, it’s totally worth the cost of the subscription! This is *you* building a library of resources that you can return to again and again, and that will be a blessing to your family, long-term!

Is This You??

Have you passed on Mentoring in the Classics or Black Belt in Freedom because you don’t feel you can keep up? Let me talk you down off that ledge, please. Read on…

When you pay the little bitty bit to subscribe to MIC or BBF (or both), the content is yours to keep FOREVER. No expiration, no due date. Think of it like buying a set of books, one each month.

We’ve all seen offers like that for encyclopedias or classics or wildlife cards, recipes, Dr. Seuss or Disney or whatever. BBF and MIC are simply monthly acquisitions for you to put on your shelf.

The value never decreases, and you can use them on your own timeline. The price is so low right now, it’s worth it! Bank them. Listen to the audios for inspiration even if you’re not reading the texts right now, for whatever life-season reason you have. It’s okay! Just do it. Get what benefit from them makes sense for you right now, and bank them for later. I bet you won’t ever be sorry!

Don’t let this opportunity pass you by. Here are the links to sign up using our No-fooling April pricing. But act now — these prices are going to buzz off soon. March 31 – April 7 is your window period, so don’t miss out!

Learn about and/or subscribe to Mentoring in the Classics >>

Learn about and/or subscribe to Black Belt in Freedom >>


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(in 3 very short Acts)

by Oliver DeMille

Act I

Baby playpen Enter a child and a youth.

*In 2014 the article by Hanna Rosin entitled “The Overprotected Kid” was the most frequently read magazine story for the whole year on Atlantic.com. (The Atlantic, March 2015, 15) It really struck a chord. Why does this generation of parents worry that many of their youth are “overprotected”?

  • The term “Helicopter Parents” is now used to describe those who hover around their children closely watching and often over-programming their lives.
  • TIME magazine wrote about today’s generation of children whose parents and adult teachers and guides are so involved that the kids “are desperate to carve out a space of their own” and “teens need a place to make mistakes.”

Exit the child and youth.

Act II

Enter the parents.

  • Brigid Schulte wrote in her book Overwhelmed: “This is how it feels to live my life: scattered, fragmented, and exhausting. I am always doing more than one thing at a time and I feel I never do any one particularly well. I am always behind…with one more thing and one more thing and one more thing…” (cited in Lev Grossman, TIME, March 24, 2014, 58)
  • Why is feeling “scattered, fragmented and exhausted” the “quintessentially modern and increasingly universal experience” for most parents nowadays? (Ibid.)
  • As one article put it, “…you’re too busy to do things like read books” and your days too often “consist of…multitasking snippets.” (Ibid.)

But why? Is this just the way things are today? Or do we have a choice?

Exit the parents.


Enter the chorus.

“A generation of kids with helicoptering parents.

“A generation of mothers and fathers frazzled,
pulled in many directions, always hurrying to the next thing.

“Always hurrying. Always tired…”


Fairytale-Simplicity copy Enter the children, teens, and parents.

“I just returned from living for a year in the south Pacific for my husband’s work,” she said. “It was really fun. For the whole family.”

“How so?” I asked.

“Well,” she grasped for the right words… “For one thing, we only ate fresh fruit and organic-style meats and vegetables. No processed food at all.”

She paused. “I’m not sure how to explain why this made such a difference. I’ve never been very concerned with health, so at first I didn’t realize it was even happening. But after a few months all our normal aches and pains went away. The fog in my head just suddenly cleared up. We all stopped moping. Everyone in the family walked around smiling, happy. We had so much energy. We played and ran every chance we got. And we hugged every time we saw each other. It was…amazing.”

I could tell there was more to the story, so I waited.

“We also walked a lot. I mean, a lot. I felt in such good shape, the best shape of my life actually.”

I nodded with interest.

“But that was just the beginning.

The Meaning of Real

“The really important thing is that we spent pretty much every evening together. All of us—my husband after work, myself, the little kids, and our two teenagers. Every night we sat around together and read books aloud and talked about them…”

Tears began running down her cheeks and she fought for composure. “It was…”

This time she really couldn’t find the words.

Real life?” I asked.

She smiled and nodded. Still the tears ran. Fairytale-yearn copy

“What else?” I finally asked.

“Nothing. That’s it,” she gulped. “That’s the whole thing. It was so simple. And it changed everything. I got my teens back. And the littler kids…well, we all bonded. It was just so incredible…”

Her voice drifted off.

“How long since you got back to the States?”

“Three months.”

“It must be nice to be home, even though you loved your time there.”

Her face took on a confused expression. “Maybe.”

“What does that mean?” I chuckled.

What Makes the Difference

She pondered, then replied, “Well, the aches and pains have come back. And the foggy brain. I didn’t realize how much background stress my body used to feel. And I hardly ever walk anywhere now.”

“Ah…” I sighed. “That makes sense. What about reading together every night?”

Her shoulders slumped a bit, and she shook her head sadly.

AA006003 I asked, “Are the kids moping again?”

“A little.” She paused. Then she said, “Too much.”

I smiled slowly. “You know, they have books here in the States. And evenings too.”

She was surprised at my words, and her head snapped up. She looked me right in the eyes. I could see the battle taking place behind them.

Then she grinned.

“We also have fruits and vegetables here,” she added, pensively. “Lots of them.”

Her shoulders squared again, and she set her jaw. “You’re right, of course. I’m not going to just let the old bad habits control us. We can still eat right, walk a lot, smile more, and read together every evening. It might be more challenging, given our complex work and activity schedules, but we can carve out time to read most nights.”

“It’s the little things,” I said. “Always the little things that really make the difference.”


Whatever your life and your family’s life

is like right now,

there are 2 or 3 little things that would make it
drastically, incredibly better—immediately.

What are they?

Brainstorm. Ponder. Pray. Find out.

And do them.

This very small thing will make ALL the difference
for your whole family.


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Homeschool and Testing, Part II

(The Huge Problem With Multiple Choice Exams)

by Oliver DeMille

(Note: if you haven’t read Homeschool and Testing Part I, please read it here,)

Question: What is the problem with multiple choice tests?

Answer: Well, it depends…

Child with learning difficulties Really. That’s the best answer. Nearly always. “It depends…”

C.S. Lewis taught in The Abolition of Man that all schooling has a design, meaning that each curriculum and testing arrangement is designed to bring about certain results. And many great educational thinkers from all sides of the education debates have agreed with this idea—from Dewey to Montessori, and from Adler to Jacques Barzun, for example.

So, to get straight to the point, what are multiple choice exams designed to do to (and for) students? To explore this question, let’s use a little comparison.

How and What to Test

Oral exams naturally focus on what the student has learned, and how effectively he or she thinks. Oral examiners ask a question, listen to the answer, and then respond with further follow-up questions. In Socratic form, they notice an area of hesitation in the student’s response, a clear error, or a potential weakness. And so they follow up with additional questions to see if this is really a lack of knowledge and understanding, or if perhaps the student simply misspoke.


Likewise, the examiners witness a strength, or even a talent, and ask the student to share more of it. In this way, oral exams can very effectively arrive at an overview and outline of what the student knows and doesn’t know, cares about or doesn’t, has prepared for or not. Most of all, this format allows the examiner to see if the student can think creatively and independently, and how well he can do both.

To a lesser extent (because it isn’t as interactive), an essay exam can discover a great deal about what the student knows about a topic. I used to schedule three-day exams for college students and ask essay questions like:

“Write everything you know about the Federalist Papers. List all 85 and comment on each. Take your time. Be thorough.”


“List every year from 1776 to the present year, and write at least one major event (what happened, why it was important, how it influenced later events, etc,) for each year.”

The results often ran to forty or more handwritten pages of solid, excellent summary, annotation, commentary, and thinking. Essay exams test knowledge where oral exams more effectively test a combination of knowledge, understanding, wisdom, and the ability to think.

Multiple Choices

think read 2 Projects, reports, research papers, and other such assignments are other forms of examination (though not always considered so in the United States). Depending on the specifics of the project, they test different things. In general, such individual or even group assignments test the ability to understand what is expected, plan and work to deliver it, and then implement the plan and follow through. This naturally tests one’s initiative, innovation, work ethic, delivery, and tenacity. All vitally important skills.

In short, and this is my first major point in this article, the best education includes all of these modes of testing (especially between ages 15 and 25). Why not learn all these lessons? Why leave any out? In fact, we should include multiple choice tests in this overall model.

At their best, multiple choice exams are designed to assess precision, rote memorization, and the ability to dialectically narrow down options to a single correct response. These are essential skills.

Schooling, Experts, and Purpose

My second point is that while multiple choice exams are a good part of a youth’s overall educational experience, in modern education they are often overdone—at the expense of the other types of testing and their important lessons. Why not do fewer multiple choice exams and more of the others? Why not reach for a meaningful balance that increases excellence?

Rear view of class raising hands

The problem with this is that too many schools teach to the tests—too often. This is backed by legislatures, administrators, departments, experts, policies, and mandates, so it is difficult to reform. But it should be reformed, nonetheless. And the sooner, the better.

Teaching to the tests puts schooling ahead of learning, and this is literally the same as putting the cart before the horse. It simply doesn’t work very well. When the means become more important than the goals, something is awry, and quality always suffers under such circumstances. Our schools deliver mediocrity and failure much more often than they would if their focus was learning—rather than schooling.

Schooling is supposed to support learning, and it absolutely can. But on the issue of testing, particularly standardized multiple choice testing, schooling frequently harms learning. It harms teaching. It harms studying. It harms thinking.

None of this is good for education.

Flawed Logic

The Purpose of Learning Third, and this is my main thesis, while multiple choice exams do teach effectively in some fields, as a national standardized system they are a very bad idea—because their design is actually based on a flawed logic that is unknown to most people and deeply hurts our society.

What do I mean? Well, in fields where the answers to questions are very much a matter of thinking, not rote memorization, multiple choice exams pit the “expert” answer against the student’s natural tendency to think and reason. This may in fact separate the scores of students who have learned to please the experts (usually labeled “good” students) from those who don’t care what the experts think (often called “bad” students), but it leaves a third group: those who care, but disagree; those who are thinking on their own (e.g. the natural leaders).

In short, in many cases multiple choice exams—whatever academic subject they test and however the student scores—leave the following lessons imprinted on many test-takers:

  1. If you get the right answer, you’re smart
  2. If you get the wrong answer, you’re not smart
  3. The experts determine the answer — so your purpose isn’t to think, it’s to agree with the experts
  4. Smart people agree with the experts
  5. Your independent thinking isn’t smart

Are there logical leaps in this progression? Certainly. But the flawed lessons are there as well. And there is at least as much logic supporting any of these statements as rejecting them. How can a young mind not wonder: “Why else would the adults put so much value and weight on these tests? Obviously, agreeing with the experts is the path to success.”

Testing the Test

Let’s consider this same point from another angle, using different words and examples. Imagine you take the following test, in a highly emotional, competitive schooling environment where you are repeatedly told by those in authority that such tests will determine your success, status, progress, earning levels, and to a large extent your happiness in life. In this emotionally charged state, you sit and try to answer the following:

  1. How many truly excellent ways are there to test students?
    1. One
    2. Two
    3. Three
    4. More than Three
    5. None of the Above
    6. All of the Above
    7. It Depends
  2. Which is the best way to test students?
    1. Multiple Choice Questions
    2. Essay Questions
    3. Assignments/Projects/Reports
    4. Oral Questions
    5. None of the Above
    6. All of the Above
    7. Two of the Above
    8. It Depends

Of course, these exact questions aren’t really on any test that I know about. Thankfully. But they are implicit in every multiple choice test any student ever takes. Think about this for a moment. This is huge!

This form of testing is a good example of many actual exams in which, ironically, the only possible correct answer differs according to an unwritten code.

This is a serious problem. How is one to know when the “code” is in play, and when it isn’t? What, in fact, is the code?

Why is there an unwritten code in the first place?

Exploding the Code

To address these concerns, let’s back up to the first time a child takes a multiple choice exam. A number of things are going on when this happens. For example, the child has no idea there is a “code.” Nor does the child have any idea what the code actually is. Nor has the child ever pondered that the code is designed to reward those who conform to the views of the experts and simultaneously “put in their place” those who think in other ways. So, as a result, the child takes the exam, guided by nothing except his or her innate senses and any instructions given by an adult.

For some children, this turns out to be a victory. Their good memory helps, but ultimately it is their innate sense of pleasing authority that helps them mark the answers they’ve heard from the adults in their life. They are quickly labeled the “good” students. (Assuming, of course, that the parent or teacher uses an exam designed “of the experts, by the experts, and for the experts”—as most modern multiple choice exams are.)

Learning Styles Matter-Mentors failure But for other children this seminal event is much less promising. Let’s say, for example, that the student’s innate senses are much more attuned to reasoning things out in his own mind, or taking in the evidence from her personal experiences and applying them to each question on the exam, or even doodling on the side of the exam because he innately feels happier and learns more when he activates what pop psychology would call his “right brain creativity.”

Such students will very likely get poor marks on the test. As a result, parent-teacher conferences will be held, adults will worry about and plan for these children, and the kids may even sense from a whisper, a glance, or a word that something has changed in how the adults now think of them.

Of course, the opposite will occur if the teacher or parent chooses, or by simple accident uses, an exam designed to test the child’s reasoning ability—not his attunement to the “right” answers so highly valued by the experts. In such a situation, the first group will feel the sense of loss while the latter groups will be told they are smart.

Certainly the reality is much more complex than this little example. But over time, test after test after test, grade after grade, the child learns to either run with his initial tendencies or find ways to suppress them. He is, inevitably, taught to accept the “expert” approach to learning if he wants to succeed in most schools.

And whether he comes from Group One or Group Two above, he learns that “good,” “smart,” “gold star” students take multiple choice tests the “expert” way, by turning off their thinking, creative, independent, innovative brains and focusing on the rote, accepted, repetitive, expert way of arriving at answers. Not every test is necessarily part of this system, but most are.

Questions and Failure

The great tragedy is that this choice bleeds into other aspects of the young person’s life. How could it not? If tests are so important—and all the adults are loudly affirming that this is inarguably the case—then certainly the world is made in the image of such tests. Right?

beware institutionalism-beware 2 The pathway to success is obvious in such a world: rote, repetitive, risk averse, non-creative, dependent but safe, trusting without really challenging assumptions; and, most importantly, truly applying yourself, working very hard to excel, and doing these things better than anyone else does them! Get the rote, safe, accepted answer more frequently than your peers. In fact, get it every time. Get it without fail. Be a truly great student.

Never fail. Failure is…failure.

Don’t learn from failure, just don’t fail. Don’t risk; just do better at what the experts want. This is the way to good grades, scholarships, acceptance, success, advancement, promotion. Even in programs that promote multi-lane thinking, like law schools, such thinking is still expected to conform to clearly delineated norms established by teams of experts.

The fact that such paths usually lead to what has been called “high-class drone work” or “highly-paid repetitive careers” isn’t the point. Or, more accurately: it’s the whole point! The goal. The objective. The plan. The definition of a successful life.

The difficulty is that the answer to these test questions should be “It Depends.” Every time. On every multiple choice test.

That’s a bold statement. But just consider:

  1. How many truly excellent ways are there to test students?
    1. One
    2. Two
    3. Three
    4. It Depends
  2. Which is the best way to test students?
    1. Multiple Choice Questions
    2. Essay Questions
    3. Assignments/Projects/Reports
    4. Oral Questions
    5. None of the Above
    6. All of the Above
    7. It Depends
  3. Solve the problem: 1 + 1 = _________. Mark the correct answer:
    1. 2
    2. 3
    3. 1
    4. All of the Above
    5. None of the Above
    6. x
    7. It Depends

Now, to repeat, here’s the kicker: The best answer to all three of these exam questions is “It Depends.”


Not for the reasons you might think.

“It Depends”

First of all, “it depends” is the best answer because it is the most interesting answer. In fact, it’s the only interesting answer of those provided. And that’s the point: When the answer has to be one of those provided by the experts, the creative and independent part of the student’s thinking automatically shuts down—at least a little. And frequently a lot.

connections Yet the best answers, the great answers, any groundbreaking or truly innovative answers, will always come when no solution is provided and you have to use your initiative, innovation, and thinking to come up with something excellent.

Think about it. The student who sincerely answers these questions with “It Depends” is thinking.

In other words, in giving the answer “It Depends” to a question like 1 + 1 = _____, the respondent is telling us something amazing about himself. He is “out the box.” He can see other alternatives. (Too many people trained in the multiple choice era simply don’t see any alternatives, or are fully trained at dismissing them.)

He isn’t dependent on someone’s list of options. He can innovate. He isn’t bound by the so-called “right” answer provided by the experts. In all the years of training and schooling and being told the “right” answers and the “right ways” to find the right answers, and even to “show his work” to prove how he got the right answers in the “approved” way, he has kept a bit of himself apart from the conveyor belt, aloof from pleasing the experts, and independent of doing things just to fit in.

Moreover, by not just marking “2” he is saying that he does not, in fact, care about impressing you—whoever you are who is administering the test—more than about thinking, pondering, considering, and looking beneath the surface. To the world “of experts, by experts, and for experts,” he may be seen as a rebel.

Good. Where thinking and innovating are concerned, we need more rebels. By definition, if you are doing things the accepted, normal way—the way sanctioned and outlined by the experts—you aren’t actually innovating. We need more who think outside the box. More leaders, more trailblazers, more inventors, more artists, more who deeply challenge assumptions and seek for better ways—our world hungers for these. Schoolhouse meme

Excellent Sheep

Our current societal decline is, at least in part, a result of our sad deficiency of originality, initiative, innovation, independent thinking, and chutzpah. And multiple choice tests are designed to decrease such traits even more broadly in the general population. They naturally train “excellent sheep” as William Deresiewicz wrote in his challenging book by that title. Allan Bloom referred to this very trend as “the closing of the American mind.”

The educational battle has in most circles become a competition to win the contest of The Top Rote Learner, The Best Expert Pleaser, and The Superior Elite-Drone Careerist. And multiple choice tests are essential to this model. They aren’t its only feature, to be sure, but without them this system would dwindle. They are part of its glue, its ether, its essence.

They may, in fact, be its essence. The self-chosen name of this system is “the meritocracy,” and what would it be without standardized, nationalized, multiple choice exams? Literally: nothing. It would collapse.

This isn’t to say that a meritocratic essay or oral exam system would be any better. These would simply wend their way directly back to aristocracy. Any one-size-fits-all system of schooling will always underperform in genuine learning and create a funnel to credentialist elitism at the top.

That’s not the answer. The ideal is something much better, a truly educated populace, where all are independent, creative, deep learners and thinkers. Adults as well as students.

Too idealistic? Maybe. But this goal is worth fighting for. And the solution to the current “rote-conveyor-belt/drone-work-careers/excellent-sheep-meritocracy” model is true educational diversity: Let every family ponder, study, consider and choose wisely the best educational path for each individual child and youth—depending on various different, and constantly changing, needs. Let the market respond accordingly.

1 + 1 = ?

A huge surprise-Freedom Works Freedom actually works. We should give it a chance in the field of learning. To the extent that we do, learning will overtake schooling—to the huge benefit of all society.

But, before we go on, there’s one more thing. There’s a second reason that the most accurate solution to 1 + 1 = ________ is “it depends.” What is it? Well, in fact, “it depends” is actually the most accurate sum. It really is.

What does this mean? For most people trained on the conveyor belt system of modern education, the rote method has trained them to think that 1 + 1 is 2. And it can be, under certain circumstances. But what the large majority of people educated in this era of rote factory-style learning were never taught is that 1 + 1 = 2 has never been proven. Why? Because no mathematician has ever been able to prove that 1 = 1.

In fact, 1 = 1 is an unproven axiom, meaning that it is an assumption that mathematicians just accept even though they can’t prove it. There is a long history of great mathematicians and scientists who tried to prove that 1 = 1, and that therefore 1 + 1 = 2, but the best they could come up with is to start their mathematics with the postulate:

“Let” 1 = 1

Then they built everything else, including 1 + 1 = 2, on top of this foundational assumption. But the foundation is still unproven.

In fact, it has been widely disproven. For example, if you are talking about apples, 1 never equals 1. There are no 2 apples that are truly the same.

The only way they are identical is numerically, meaning in our mathematical minds or what Plato called “The Ideal.” Not in physical reality. So, yes, if you are only working a math problem, then 1 + 1 might equal 2 because humans long ago decided to “Let 1 + 1.”

But there are many times in the real world where 1 doesn’t equal 1. In fact, the only place 1 = 1 is in theoretical mathematics. So, if the question is posed as it was above (“Solve the problem: 1 + 1 = _________”), the truly most accurate answer, mathematically and otherwise, is “it depends.” If you are using theoretical math and you have defined your terms based on “Let 1 = 1”, the answer is 2. If you are not, the answer is “it depends.”

But since the question above didn’t specify, then it depends. Period.

In short, the student who marked “it depends” got it right while all those who marked “2” got it wrong. The ones who chose “2” weren’t just trying to please the experts; most of them actually don’t understand the mathematics. Thus the sheep aren’t all that “excellent” after all. And that’s a huge problem in our educational system, because many multiple choice questions on our nationalized exams (in all subjects) are this way. Many!

The Power of Many

believe-children Again, we need more than one kind of testing to get it right, because not every student is the same—any more than your 1 apple is the same as any other 1 apple. And while the number 1 can be used numerically in theoretical mathematics, when we are talking about children we need something much more serviceable. We need to help each one of them get a superb education, and that means that one size doesn’t fit everyone.

Let there be many kinds of schools, and many kinds of tests. Some will prove beneficial to great learning, while others will not. And over time those most effective will flourish and grow. But all will be available to the individual student who needs one or two of them to really flourish.

This kind of educational buffet only thrives in a free system. And right now, homeschooling is a leader in this charge. Let there be as many kinds of testing as there are children with different educational needs, goals, talents and dreams. Let the variety of tests grow so there is a truly excellent testing model to match each student.

That’s great education. Nothing else comes close.

Is this kind of truly personalized education and testing for every single important student even possible at a national level? Perhaps. Perhaps not. But it is certainly possible in most homes and families.

Starting with yours.


Are you ready for an upgrade to your family education culture? Check out the 7 Keys Certification, available free right now with the purchase of one of our Homeschool Bundles >>

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[Scroll down to download free math course…]

This is it.

This is how to teach math, even if you stink at it. Even if you hate math.

And even if you don’t.

pick1 math 300x121 Back to School Bonus Issue   Top Picks and New Science Recommendations by Rachel DeMille, TJEd.org

The math-project images in this post are from real families, friends of mine, who have given permission for them to be used here. Most were created with a sense of authentic wonder that math-love at this level was even possible!

masarik-shapes2 The study of math has lost its soul in the past century. We have become so obsessed with our comparative lack of math proficiency that we have over-compensated on the side of learning skills without drawing meaning from the study of math. It was not always so: In ancient times math was strongly tied to music, philosophy and other “practical” pursuits.

The net result of this lack of vision is that today’s learners (and teachers!) are uninspired to explore math; they believe they are no good at math, and ultimately, that math has nothing to do with anything they care about. Or, they excel at the techniques of math study and evaluation, and generally lack the ability to explore and create mathematically.

Thank goodness for a surge of great resources, with an ever-expanding field, to help today’s learners with the elegance and titillation of mathematical study. We are relearning the language of math in the 21st century!

masarik-shape1 Inspirational Math

For some parents and teachers — especially homeschoolers it seems — teaching math and science is the greatest worry. As TJEders, those of us who aren’t math-inclined find this especially challenging: How do you “Inspire and not Require” when you don’t like math? How do you use “Classics, not Textbooks”? And Omigoodness, what of “You, not Them” in math studies? Must I really???

Never fear. As with everything else, your change of heart and new-found inspiration in math (suggestions to discover this new-found inspiration follow below…) will infuse your home and classroom with a dynamic and enthusiastic Love of Learning that leads to a successful Scholar- and Depth-approach to mathematics.

As with everything worthwhile, “there ain’t no quick fix”; even so, you’ll be amazed at how much you have to offer as a mentor and educator when you find yourself having “a-ha’s” and epiphanies, and when you start to daydream and ponder in the wee hours about the mathematical thoughts, readings and projects that are spinning in your creative mind! Sound impossible? It’s not! This has been my experience. What have you got to lose?

masarik-mandala1 Your goal: to inspire your students to love math and to become life-long students of math.

Your strategy: You, not Them. Inspire, not Require. Classics, not Textbooks.

Your tactic: come face-to-face with greatness, experiencing the works of others who love math and are life-long math students.

It works! It will work for you!!!

Math, Mentored by Math-Lovers

Huff-parabola1 In our award-winning Mentoring in the Classics subscription, we recently took on math with Schneider’s ground-breaking A Beginner’s Guide to Constructing the Universe. We are delighted to report that math lovers found new levels of enjoyment, while math-phobics rescripted their thinking and found that they’re not math-stupid after all!

This was so successful that we want to now share it freely with everyone, and invite all who are willing to join in the revolution! So here, below, is the mentoring content prepared for Mentoring in the Classics.



huff-parabola2 Welcome to Mentoring in the Classics: Schneider’s A Beginner’s Guide to Constructing the Universe

This post contains:

  • The introductory mentoring content, including audio and Study Guide I
  • The debriefing mentoring content, including Enhanced Study Guide I & II

Please scroll down to access your download links.


How This Class Works

To gain the most from your mentoring experience, we encourage you to use the following order: huff-parabola3

  1. Listen to the audio introduction, available to download from the links below.
  2. Review the Study Guide (PDF download, linked below)
  3. Read the book, pen in hand, utilizing tips and prompts from the Study Guide and Intro Audio
  4. Discuss with your local book group, family members, online community, etc.
  5. Post blog articles and other creative responses to the work, and share them!
  6. Review the Debriefing Audio mentoring, and the updated Study Guide (including parts I & II) – all linked below.

Introductory Audio Mentoring

This month’s Introduction features Oliver DeMille.

Here are your options to download the audio file (identical audio is available in two download options), and the Study Guide: huff-kid-parabola

See below** for instructions on saving your audio.


Debriefing Audio Mentoring and Study Guide

This month’s Debriefing features Oliver and Rachel DeMille, Ian Cox (25) and Emma DeMille Cox (22), Oliver James DeMille (23) and Sara DeMille (21).

We made special efforts to confine our discussion to the topics that would be best represented in audio – so some of the “mathier” stuff that totally fascinated us was not included. Too confusing without a whiteboard to demonstrate!

However, we DID enhance the Study Guide with TONS of new stuff. You’re going to love it!
Here are your options to download the Debriefing Audio and Enhanced Study Guide:

See below** for instructions on saving your audio.

Study Guide, Parts I & II:

Schneider’s A Beginner’s Guide to Constructing the Universe

Prepared by Rachel DeMille

This Month’s Mentoring Content, Part I

west-concentric The Introductory Mentoring Audio, (click here to listen** >>), consists of a small-group tutoring session including Oliver, Rachel, and daughters Emma (22) and America “Meri” (11).

Please take a moment to download your audio content to your computer immediately so you have uninterrupted access to it!  

1: Ideas for Writing or Discussion:

  • What is “math”?
  • How does your definition of “math” differ after reading this book?
  • Which of the 7 Steps of math study have you emphasized most in your life?
  • Which step are you utilizing most with those you teach and mentor?
  • Which step are you planning to emphasize most in the next while, in your own studies? In your teaching?
  • What math terms do you use in everyday language? Candiss_west_mangala

o What’s the difference?
o The “solution” is “relatively”simple.”
o You’ve got a big “problem!”
o There are “more”factors” than you’re admitting.
o The “sum” of the “parts” is “great than” the “whole.”
o A “lesser” man would never have endured that.

  • How can using math terms in your everyday language enhance your thinking, and help your children/students develop more fluency with the language of math? (exponential, rounded, fraction, dividend, quarter, equal, tangent, ….?)
  • Have you found yourself thinking more about math during/since the time you have spent reading this book?
  • What new patterns and problems have you noticed or entertained in your mind?

2: Resources for Additional Study: math-clock

3: Article: What’s Math Got To Do With It?

Love_math_1 I’ve often said that the “Why” we teach something informs the “How.”

Years ago Oliver wrote an introduction to a math course. He articulated “Why” we learn and teach math, and I think having this vision is not only inspiring and motivating, but really helps us focus our approach and methods.

He created a list of “values” that clearly articulates the meaning and purpose of math education, and (along with the introductory paragraphs written by the course instructor, Troy Henke) I share it here with you:

“Mathematics is an integral part of a statesman’s education . . . . Math teaches a person to think in a way that no other field does. As a person studies math, he learns to: Apples Addition

  1. Seek and recognize patterns
  2. Explore the relationship between things
  3. See similarities and also distinctions
  4. Analyze logically but with a deep sense that there is a right answer and a set ideal worth detecting
  5. Compare and contrast
  6. See things in black and white
  7. See infinite shades of grey and therefore avoid jumping to conclusions
  8. Seek evidence for conclusions and check opinion with first-hand research
  9. Put his own pen to paper before accepting what society tells him
  10. Seek for absolutes
  11. Remain open to surprising new information which makes past conclusions limited though perhaps still accurate

“Now, clearly, the practical art must also be mastered—
we want you to be able to pass any standardized test with the highest marks.

“But more importantly, we want you to be able to think like
an Archimedes, a Descartes, a Newton, a Sophie Germain, an Einstein.”


4: Concepts- How to Learn and Teach Math:  

1. Discover stories about math, and those who use, study and love it.  
2. Fall in love with shapes, patterns, numbers, etc.  
3. Be, or find, a close example of a math-loving math student  
4. Use spreadsheets in every-day life  
5. Read Math Classics  
6. Study math problems, skills, techniques, language and testing  
7. Study the Greats on a higher level


6: Level 5 Mentor Prompt on A Beginner’s Guide to Constructing the Universe:

  • Using a pen in the margins and endsheets, or a separate notebook, record the conversation that occurs between Michael Schneider and yourself.
  • Capture your epiphanies and questions, and make a note of the things you want to share with others.


7: Read, with pen in hand, A Beginner’s Guide to Constructing the Universe, and review the above Study Guide prompts for more study ideas and activities.

8: Study Guide, Part II

Now that you’ve heard the Mentor Debriefing Audio, check out these additional resources!

[This section will include images shared by class participants of the “math fun” that was prompted by their study this month!]

Leona-Tai_Fun-with-fibonacci-parabola Best books to get you loving math:

Best books to get your kids loving math:

Geometric Solid Christmas Ornaments

Geometric Solid Christmas Ornaments

More Resources:

Here is a diagram of Rachel’s “7 Pattern” (referenced in the audio):

7 Pattern RD

Math Fun!

Movie Math problems

 Check or submit your answers in the comments here >>

Ian’s Notes on…

A Beginner’s Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science A Voyage from 1 to 10, by Michael Schneider

Prepared by Ian Cox

This section will feature images submitted by class members of the projects they did at home, inspired by this book!

Note: This is by no means a complete list of all the experiments and hands—on exercises found in this book. Have fun finding and doing the “To Do’s” Throughout this book!

To Do:

Candiss-spyrograph Monad: Wholly One

1. Page 17 Half of a circle has the same area as a rolling circle within it.
a. Compare and contrast different shapes to a circle. Circles with the same perimeter cover more area.

Dyad: It Takes Two to Tango

2. Pg. 32 Doodle with the dyad.

Triad: Three—Part Harmony

3. Pg. 51 Construct a set of Borromean Rings. They only overlap while none interlock.
4. Pg. 53 Light is a mixture of colors. Ex White = Red, Green and Blue-Violet. Additive vs. Subtractive Colors.

Tetrad: Mother Substance

5. Pg. 61 How to bring depth to the universe. Construct the tetrahedron
6. Pg. 62 Tetrahedral wire frame and soap solution to make bubbles.
7. Pg. 67 Fill a jar with soil, water and air then shake it to discover the natural order of the elements.
8. Pg. 70-71 Two ways to construct a square.
9. Pg. 73 Construct square with a square etc.
10. Pg. 80 Salt in bowl of water crystallizes as the water evaporates. tools-math
11. Pg. 81 Rubber ball and chalk to draw five elements.
12. Pg. 83 Construct the five elemental shapes.
13. Pg. 84-85 Two ways to construct a cube. Create a cube with wire and put it in bubble solution.
14. Pg. 86 Construct deltahedra.
15. Pg. 87 Construct Icosahedra.
16. Pg. 88 Construct a tetrahedron, octahedron, and an icosahedron.
17. Pg. 94 Self-discovery

Pentad: Regeneration

18. Pg. 102 Cut an apple and pear at its equator to see their star/pentagon formation.
19. Pg. 103 Tie your shoes. You just made a “goo luck” pentagon.
20. Pg. 105 Classic Puzzle.
a. And how to cut out a star.
21. Pg. 111-112 Doodle and experiment with pentagons an pentagrams with paper construction.
22. Pg. 113 Inscribe life forms with pentagons and stars.
23. Pg. 119 The Golden Mean: Divide a Graph to get approximately 1.62 of the Fibonacci sequence. 1/89 = Fibonacci sequence.
24. Pg. Experiment with any two numbers, divide them, and see the sequence approach pi (Ф).
25. Pg. 121 How to divide a line at the Golden Mean.
26. Pg. 122-123 Constructing Golden Mean calipers.
27. Pg. 124-126 Explore Golden Mean ratios in nature with the human body.
28. Pg. 130 Aesthetics of Ф, look around at common house items (3×5, 5×8)
29. Pg. 131 Construct a Golden Rectangle.
30. Pg. 132 Construct a 3-D Golden Frame.
31. Pg. 135 Find the Golden Mean with calipers on Notre Dame. Geo_solid-Gaulin
a. Pg. 136 On a Sarcophagus
32. Pg. 140 Spirals: Doodle some! Construct as well as compare and contrast the Archimedean Spiral vs. the Golden Spiral
33. Pg. 142 Construct a Golden Spiral.
34. Pg. 145 The Golden Triangle and Spiral.
35. Pg. 148 Self-replicating balance: Another way to see this principle of balance through change is to bend a piece of wire into a golden spiral and balance it by a pencil of straw through the eye.
36. Pg. 158 Observe streams, ponds, rowboats, etc.
37. Pg. 161 Observe clouds, weather, fire, flags, etc.
38. Pg. 165 See plants as energy.
39. Pg. 169 Look at leaves from the perspective of the sun.
40. Pg. Build a plant replica.

Hexad: Structure‐Function‐Order

41. Pg. 179 Ponder Hexad: Stucture-Function-Order
42. Pg. 183 Construct the Hexagon
43. Pg. 184 Observe symmetry’s
44. Pg. 185 Designs and patterns.
45. Pg. 186 Hexagonal knot.
46. Pg. 187 Circumference relations.
47. Pg. 187 Musical Hexagon
48. Pg. 191 Doodle Hexagons.
49. Pg. 197 Construct Dodekagon
50. Pg. 199 Thirteen clay balls, twelve circle the one.
51. Pg. 205 Trace the Great Seal of the United States of America with a Hexagon.
52. Pg. 213 “Square the Circle”
53. Pg. 216 Geometry of Stonehenge.

Heptad: Enchanting Virgin

Wells-solids1 54. Pg. 225 Divide 360 degrees by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
55. Pg. Construct approximate heptagon.
56. Pg. 228 Doodle with Athena’s web
57. Pg. 229 Make a heptagon audible.
58. Pg. 230 Construct a heptagon with knotted string, paper knot, and tooth picks.
59. Pg. 237 Experiment with music.
60, Pg. 242 Construct a Lyre of Apollo
61. Pg. 247 Tracing paper over painting.
62. Pg. 252 View rainbow with each eye individually.
63. Pg. 253 View color TV with a magnifying glass.
64. Pg. 263 Focus on “the heart” chakra.

Octad: Periodic Renewal

65. Pg. 267 Try to fold a piece of paper in half eight times.
66. Pg. 270 Create and octagon.
wells-solids3 67. Pg. 271 Hear proportions
68. Pg. 273 Trace octagons on creatures to see symmetry.
69. Pg. 274 Construct the breath of the compassionate.
70. Pg. Guitar strings and periodic recurrence.
71. Pg. Resonance, or vibrations, of a car.
72. Pg. 283 Doubling relations in the body.

Ennead: The Horizon

73. Pg. 308 Casting out nines in multiplications chart.
74. Pg. 312 How many symmetric shapes do nine coins make? Or, can you make?
75. Pg. 313 Create a labyrinth.

Dekad: Beyond Number

76. Pg. 337 Birth of Decagon and internal patterns.
77. Pg. 340 Construct Islamic Tiling Pattern.
78. Pg. 342 “Paradise” art geometry.
79. Pg.344 Geometry of St. John the Divine Cathedral.

Epilogue: Now That You’ve Constructed the Universe..

80. Pg. 348 What characters of geometry does this vegetable have?

 “Take note of that which comes comes from without and that which comes from within.”

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Homeschool and Testing, Part I

by Oliver DeMille

Lessons and Differences

notimetolearn I was halfway through my meal in a crowded Los Angeles restaurant when it happened. I glanced up and noticed a man staring at me from the next table. I wondered what he was staring at, so I smiled. He grinned back, then began scrutinizing his napkin. Yes…his napkin.

I was so surprised that I watched him for a minute, and I soon realized what was going on. His napkin was spread out on the table like a large place mat. In fact, his whole family had their napkins arranged as place mats, with their plates, cups, and utensils all on top of the napkins. Together their napkins covered the whole table in a makeshift tablecloth.

The man had seen me using my napkin on the corner of my mouth—and it had shocked him. I imagine him thinking: “What kind of people use their place mats on their mouth?”

By this point he was explaining the situation to his family members, all of whom were pointing around the room at other people using their napkins as…well, napkins. Not place mats. They were speaking in a foreign language I don’t understand, so I couldn’t tell what they were saying about their new discovery.

Soon they began laughing, and somewhat sheepishly they lifted their cups and plates, moved the napkins from their position laid out on the table, and put them in their laps like napkins. It was clear that they considered this a very strange custom. When Rachel returned to the table, I related to her the goings-on, and she chuckled, “Well, either one or both of you is really weird – depending on who’s doing the evaluation.”

My thoughts returned to her comment later that day, when she asked me what I would say to people who wonder why elementary and high school age homeschoolers who take standardized exams often test way above average in some areas but well below them in others. I thought it was a poignant question, and it brought to mind a friendly conversation I once had with a school principal.

Who Lands Where

We served on a charitable committee together, and one day in a moment of waiting he mentioned that homeschoolers in his district who for whatever reason take the district’s standardized tests nearly all test “off the charts” high in Language Arts and Social Studies, but well under the curve in Science and Math.

Then he cocked his head to one side and said, “Except for two homeschooling families in the district whose kids test the exact opposite—very high in Math and Science, and quite low in Language Arts and Social Studies.” He wondered why this trend was so prominent. Why didn’t they all test to the averages, like most of the schools?

I had just about the same reaction to him that I did to the man in the restaurant with his family’s napkins under their plates. How do you tell somebody from one culture what a very different culture is like? Certainly not easily, simply, or quickly. There’s more to it than that.

Still, I tried. First I referred him to national statistics that show the average of public school students (tested across the board on academic topics) in the 50th percentile, private school students in the eighties, and homeschoolers in the nineties.

As I remember it, he shook his head and said: “I’ve researched all those statistics, and they don’t hold up because the public school numbers represent all students in public school while not all homeschoolers decide to take such tests. If we made the same tests voluntary in public schools, we’d get much higher results too—because most of those who would take them would be well prepared.”

That made sense to me, so I tried another response. “Good point. The truth is that many homeschoolers don’t really respect multiple choice testing. It’s not the best way to know what students have really learned. Essay exams are much better. And oral exams are even more effective. You can really explore a student’s learning with oral exams.”

The High and The Low

He nodded his head vigorously. “I agree. But that isn’t an option for most public schools. We are required by law to use standardized tests, most of which are multiple choice. Parents, teachers, and administrators have little say about that. And we spend a lot our time teaching to the mandated tests.”

I asked, “Do you think you could greatly improve testing and learning if you and your teachers could design the tests yourselves instead of having to teach to those mandated?”

“Absolutely!” he suddenly got passionate about the topic.

I replied: “Well, that’s exactly what many homeschooling parents are doing. They are designing the kind of assessment they think best measures what they want to emphasize in their kids’ education. That’s why some families excel in Math and others in Language Arts, because they have different values, goals, and objectives.”

He pondered, then nodded. “That makes sense. But what about the students who don’t do well in certain important subjects, like Math? What do homeschoolers do about this?”

“Well, what do public schools do with students who don’t do well in Math, Science, or some other topic?” I asked. “Or do all public school students excel in every subject?”

He grinned good-naturedly. “Touché,” he said. Then his face turned serious. “But at least we try. When a student is behind in a field of study, we work hard to help the student catch up. Do homeschoolers do this?”

I laughed. Still chuckling, I replied, “No, not at all. Homeschoolers tell their kids to avoid subjects like Math and English and never try to learn such topics under any circumstances…” I struggled for the right way to finish my joke.


He chuckled before I could complete my thought. “Of course they try. I didn’t mean to offend. It’s just that my main experience with homeschoolers comes when a family stops homeschooling and their kids enter public school—and their assessment tests show them low in some area.”

I nodded. “That would be frustrating. But like you said earlier, they are usually very high in some other topics, right?”

“Yes, nearly always.”

think read 2 I responded: “But homeschoolers aren’t the only ones like that, right? I mean, do you have students who have been in public school their whole life, who test high in one or two topics and low in others?”

He smiled and sighed. “I see your point. Of course many students test high in some subjects and low in others.”

“I bet certain students test high in most or even all subjects, and some test low in all topics. And many test in the middle on everything. Right?”

“Yes, of course,” he replied.

“So, really, it’s exciting when any student tests high in anything, right? So you should be really happy with any homeschooler or public schooler, or private schooler, who comes into your school testing high in anything. Right?”

He laughed. “Conservatively optimistic, yes,” he said. “But we would like them all to test high in everything.”

“So would pretty much all homeschooling parents, I think,” I said. “But a lot of homeschoolers are more interested in their students truly excelling and learning ‘off the charts’ in some important topics, so they may spend more time on those areas of focus. That would explain the high scores in subjects they care about a lot.”

Meeting It

We both nodded. Then I chuckled again, and said, “Maybe the homeschoolers who test low in Math and Science should take classes at public school and the public school students who test low in Language Arts and Social Studies should attend some of the local homeschools.”

He grinned widely. “I’d have a hard time selling that one.”

“So would I,” I replied.

We both laughed.

It was an interesting conversation. I felt like I really understood his views on the topic much better than before, and I think he understood mine as well. In fact, it was a lot like the man’s napkin at the restaurant in L.A.

The truth is, those nice cloth napkins really did make good place mats. How sad it would have been if I’d started criticizing using the “napkin” that way and the man had started lecturing me on using my “place mat” wrongly. I’m glad we both smiled and understood each other instead—even with the cultural divide.

We each had different goals with those napkins, but they both worked. We both met our goals.

And that’s the real issue, after all. If a public school meets a given family’s goals for a certain child, excellent! Who is anybody else to tell those parents they should make changes? Or if a homeschool plan meets your goals for a child, why should anyone else have the right to change your way of doing things? They shouldn’t.

And this brings us to the deeper problem.

Napkins or Place Mats?

The real challenge: Do you know your family’s educational goals for each child? If not, that’s a real problem.

That’s where the “Brainstorm a Blank Page” habit comes in, as discussed in our book The 5 Habits of Successful Homeschoolers. We call it “Blank Page Mentoring” in this post.

This really matters. If you know the right individual goals and objectives for your children and youth this week, and every week, you’ll know how to make excellent decisions regarding their education. If not, you won’t. Knowledge really is power.

And let’s be clear: Testing is secondary, or more accurately, tertiary, to learning. Learning is the real goal of quality education. And different kinds of learning naturally resonate with different kinds of testing. But the starting point isn’t testing. Not at all. It’s knowing what the right objectives are right now for each child’s education.

Knowing these objectives—really knowing them—will tell you how he or she should learn and how his or her learning can be most effectively tested or assessed. This is the key place to start the education of every child, and it is the sole responsibility of each child’s parents. Period.

think read 1 Some parents delegate this duty or just leave it to someone else. But we should all celebrate parents who don’t delegate this profound role in society. We need many more such parents.

In fact, here’s a powerful standardized test we might offer all parents in our modern world:

“How well do you carry out the great responsibility to always know the right individualized educational goals and objectives for each of your children—each week, every week? And, knowing them, how well do you implement them? Or, to what extent do you delegate—or simply leave—this vital parental duty to others?”

How do you score? How can you improve? Will you start today, right now?

What a great exam.

So, finally, which is best: Napkins or place mats? It all depends on your goals. The key is to make sure that as a parent you really know and embrace the right goals for each child—every week. Nobody can do this as well a loving, dedicated, focused parent.

Once you know this, and live it, selecting the right kind of testing will come naturally and easily.

(Watch for the sequel to this article, entitled “Homeschool and Testing Part II,” next week.)

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Article Correction: Thanks to Bill Peavoy and his friends for pointing out an error in the original posting of this article. Instead of 72% trust of public schools in 1975, the number was actually 29%. This means the downward shift is only 17%, much less than the 60% I previously stated. I clearly wrote down the wrong numbers while studying the polls, and I should have gone back and double-checked it. Dumb. My mistake. Thank you so much for this clarification! It’s a huge difference.

It also points out an interesting idea, one that reverses my view in the original article. I had suggested that trust in public schools went from 72% of the population down to 12%, when in fact for over forty years less than 30% of the U.S. population has held high trust in public schools. The number is now down to 12%, as stated. So the real story is the surprising (at least to me) long-term trend of holding such little trust in our schools.

There is also a significant storyline in the high numbers who now have Very Little or No trust in public schools. In fact, in 1973 only 11% of Americans polled held Very Little or No trust in our public schools, while today 31% have Very Little or No trust in them. ~OD

The Public School Implosion

(A Staggering Shift!)

by Oliver DeMille

I’ve been studying a lot of polls lately, because I’m interested in really understanding the American people, the electorate, and the trends that are currently determining our national future. Not that polls are perfect, by any means. But they do give us important insight into what people are thinking right now.

As I’ve researched, I keep finding interesting little trends in the data. And, at times, I run across some shockingly big realities that will clearly have a major impact on our society. For example, we’ve seen a major shift in the way most Americans think about leading societal institutions.

Just consider what Gallup Polls show about the following changes between 1975 and 2014 in our trust/distrust of major institutions:

Public Schools 29 12
Congress 14 4
The Presidency 23 14
The Supreme Court 20 12
The Health Care/
Medical System
44 17
Church/Organized Religion 43 25

*Source: gallup.com/poll/1597/confidence-institutions.aspx, 2014

The Stand Out

While the general trend in all these categories is a serious loss of public trust in important institutions, one really stands out: Public Schools. As the following chart shows:

FROM 1975 TO 2014
Congress -10
The Presidency -9
Supreme Court -8
Health Care/Medical System -27
Church/Organized Religion -18
Public Schools -17

*Source: ibid.

This is very telling. We are not only raising a generation of young people whose native language is “Digital” (for many of them, English is literally a second language—as evidenced by youth who stand or sit next to each other in the same room and carry on lengthy conversations by text messages rather than talking aloud), but also a generation whose core language decidedly isn’t Trust.

The Old and New

This is a change from the 1970s, 80s, and 90s schools and neighborhoods where most of today’s parents were raised. While the native Boomer and Generation X language was often skeptical of non-friends, we grew up in an environment where a core trust in our communities of friends, family, and adult supporters still dominated society.

This is no longer the case, at least not to the same extent. The native dialect our children are growing up in now spans the scale from mistrust to distrust to cynicism. This is fueled by any regular contact with the Internet or social media, where a thick skin is a required dialect and disregarding a majority of what you read is just part of a young person’s accent.

The Relevant Conversation

In all this, the biggest loser is childhood, a protected place of safety and acceptance where a young person can grow, find himself/herself, and take the time to explore his/her possible place and role in the world. Technology has significantly shortened this time of natural innocence for nearly all young people.

Wise parents are aware of this, and deal with it head on. Specifically: Talking directly to your children and youth about when and what to trust, and not trust, is certainly as important as language arts, math, science, or history. Such conversations and lessons are often even more relevant and immediate than academics.

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Q. What do you think is the most common problem of homeschoolers? TJEd-Q&A

A. First and foremost, even among “dyed in the wool” homeschoolers, there is widespread neglect of the Core Phase. I believe this is because of our tendency to identify so strongly with our label of “home-schoolers” that our family culture can easily become defined by academic achievement.

Core-Ready-Nest-eggs-meme I remember when I had three teeny little ones under three (and knowing that I wanted to homeschool) how anxious I was to “get on with it!”

I had learned to read before I even remember trying; I had an older sister who loved to play “school”, and by the time I was four I was an independent reader. So I just assumed that my bright and precocious little kids would also find it easy, and I considered that the measure of my success for a time. I was impatient and self-conscious and worried that I would fail.

Thankfully, our first child was one who would not be rushed. I hadn’t realized until the writing of this article how critical that was for the culture of our family and the application of the principles that we promote.

Stumbling into Core Phase

Because Little Oliver was more like his father (who did not read fluently and well until he was almost 12 years old), I felt that it would be best for our family not to emphasize reading as a skill by which they should measure their worth, intelligence, knowledge or ability to succeed in new endeavors.

I purposely steered our “school” time toward things that fortified the children as individuals and established our family culture, waiting for the cues that Oliver was ready (both developmentally and emotionally) to master reading.

The happy result was that we discovered for ourselves—and quite by accident—the purpose of the Core Phase.

Because we have tried to feed the spirit and the intellect on content rather than skills mastery, because we have modeled a love of learning and provided a rich environment, and because we have waited until they are anxious to apply themselves to the task, the children not only have that fearlessness that I referred to, but they have the innate sense that their education is their own responsibility.

And as it happens, the skills are quite easily mastered with a more mature, motivated and confident student, who cares about his own education!

My husband and I are examples, mentors, guides, facilitators, instructors, but they cannot expect us to educate them. They intuitively know that it is their job to supply the desire and the effort necessary in order for them to achieve their personal, spiritual and educational goals.

In a word, we will do all in our power to inspire and facilitate – but at the end of the day, they will have to educate themselves.

School at Home?

Cocoon-Core-meme I have witnessed many well-intentioned mothers and (particularly) fathers – ourselves not excluded – who pressure their children into structured time and activities that model public school settings and timetable.

They cite the need for self-discipline and excellence as the reason for their strivings.

I would suggest that self-discipline and excellence are internal values, and are not developed in an environment of compulsion. I also believe that it is difficult to teach these values without a physical medium that allows the student to see the workings of choice and consequence.

By this I mean that learning excellence is easier and teaching self-discipline is more effective when the child sees the natural consequences of his or her choices, as in:

“If I say that I weeded my rows of the garden, when I really didn’t, everyone will know it isn’t true, and I’ll have to do it later anyway and it will be more difficult if I put it off.”

Caring for animals and gardens provide a routine, repetition, and reward that the child’s mind can grasp. These are our methods of choice, but I know of another family that I look up to that has used the father’s dental practice as their medium. The oldest child is a certified dental assistant who, at fifteen, is working on her college degree with distance learning, having paid for the entire under-graduate program in advance with her own earnings (she is successfully in Scholar Phase).

The children go early each morning with their parents to do the janitorial and other preparatory work before the office opens for the day. It isn’t too difficult for a medium-sized young person to understand that they can’t cut corners when sterilizing dental equipment without serious repercussions.

Core-Nest-Guardian-meme They learn to take pride in their cleaning when the professional appearance of the office directly affects the family’s well-being, reputation and prosperity. And as employees of the business, if their performance is sub-standard they are subject to being reassigned or fired.

In the examples I have given (and there are probably as many ways to teach these principles as there are parents reading this post) consequences are nearly immediate and the necessity of consistency and exactness become obvious as they experience the consequences of their choices.

In this way the child learns self-discipline and excellence in a very personal and internal way.

Then when he is older and is having a hard time mastering some math skill or wants to develop an article to submit to a magazine, no one needs preach to him what self-discipline or high standards of excellence will get him. He learned those lessons getting dirt under his fingernails when he was only seven.

Equal and Opposite Problem: Neglect of Scholar Phase

While neglect of the Core Phase is a great problem, there is—as you would expect—an equal and opposite problem: those who do discover and capitalize on the Core Phase can tend to take it and use it for their whole philosophy, as if that’s all there is.

Core Phase parents  It is the foundation; but virtue isn’t the single, solitary attribute we’re to acquire. We need to proceed onward and incorporate others.

From the very first, the role of the parent is to model, inspire, and facilitate scholarship; that’s the parent’s job. It’s not the parent’s job to educate the children, but rather to model self-education.

With appropriate care for the right environment, relationships, resources and opportunities, the healthy child will naturally move from Core to Love of Learning and then on to the Scholar Phase. In fact, they will often want to follow you into Scholar Phase before they’re totally ready.

They’ll go back and forth; they will model scholar behavior for a few hours—then give it up for six months. Many of the factors that govern these transitions are rooted in biology, and not just environment, so nature is actually working in your favor on this point!

Know the principles of success and then trust the process. Every day, every year has its purpose, and getting ahead of the schedule is not an advantage; in fact, it may entail doing some backtracking to really set things right.

Two Steps Forward, Four Steps Back

We tend to press kids when they’re just tiny. Everyone around them seems frantic about their learning. They live in a state of tension. We give them tasks just ahead of their developmental stage and force them to reach for things that are uncomfortable. Educational Philosophy-1000px

We rob them of their sense of mastery over what they do know and personal power over what they can do.

They can tend to feel stupid, disrespected and impotent. By the time they should be moving into the Love of Learning they either don’t have the will to try anymore, or they’re so adept at playing the pleasing game that it can hardly be called an educational process.

Most children in today’s schools will have received a significant portion of their homework assignments by the time they are twelve. Then in their teens they’re told, “These are the best years of your life. Go to assemblies. Play sports.”

It’s 100% backwards.

It is our hope to get people to take the pressure off when the children are young and get them to put the pressure on when they are older.

The Leadership-model Scholar Phase is as rigorous as the Core Phase is carefree—and the process of applying the principles runs counter-intuitive to the Conveyor-belt model at both ends of the spectrum.

Just getting started with homeschool and/or TJEd? Click here for Rachel’s 6-Point Plan for New and Re-starting Homeschoolers >>

For more on the Phases of Learning, click here >>


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