Homeschooling Corner: Erdos, Fibonacci, and some Really Big Numbers

One of the nice things about homeschooling is that it is very forgiving of scheduling difficulties and emergencies. Everyone exhausted after a move or sickness? It’s fine to sleep in for a couple of days. Exercises can be moved around, schedules sped up or slowed down as needed.

This week we finished some great books (note: I always try to borrow books from the library before considering buying them. Most of these are fun, but not books you’d want to read over and over):

The Boy who Loved Math: The Improbable Life of Paul Erdos, by Deborah Heligman, was a surprise hit. I’ve read a bunch of children’s biographies and been consistently disappointed; the kids loved this one. Improbable, I know.

I suppose the moral of the story is that kids are likely to enjoy a biography if they identify with the subject. The story starts with Erdos as a rambunctious little boy who likes math but ends up homeschooled because he can’t stand regular school. My kids identified with this pretty strongly.

The illustrations are nice and each page contains some kind of hidden math, like a list of primes.

Professor Astro Cat’s Frontiers of Space, by Dominic Walliman. This is a lovely book appropriate for kids about 6-11, depending on attention span and reading level. We’ve been reading a few pages a week and recently reached the end.

Minecraft Math with Steve, by Steve Math. This book contains 30 Minecraft-themed math problems (with three sub-problems each, for 90 total.) They’re fairly simple multiplication, subtraction, division, and multiplication problems, probably appropriate for kids about second grade or third grade. A couple of sample problems:

Steve wants to collect 20+20 blocks of sand. how much is that total?

Steve ends up with 42 blocks of sand in his inventory. He decides that is too much so drops out 12 blocks. How many blocks remain?

A bed requires 3 wood plank and 3 wools. If Steve has 12 wood planks and 12 wools, how many beds can he build?

This is not a serious math book and I doubt it’s “Common Core Compliant” or whatever, but it’s cute and if your kids like Minecraft, they might enjoy it.

We are partway into Why Pi? by Johnny Ball. It’s an illustrated look at the history of mathematics with a ton of interesting material. Did you know the ancient Greeks used math to calculate the size of the Earth and distance between the Earth and the moon? And why are there 360 degrees in a circle? This one I’m probably going to buy.

Really Big Numbers, by Richard Evan Schwartz. Previous books on “big numbers” contained, unfortunately, not enough big numbers, maxing out around a million. A million might have seemed really good to kids of my generation, but to today’s children, reared on Numberphile videos about Googols and Graham’s number, a million is positively paltry. Really Big Numbers delivers with some really big numbers.

Let’s Estimate: A book about Estimating and Rounding Numbers, by David A. Adler. A cute, brightly illustrated introduction. I grabbed notebooks and pens and made up sample problems to help the kids explore and reinforce the concepts as we went.

How Big is Big? How Far is Far? by Jen Metcalf. This is like a coffee table book for 6 yr olds. The illustrations are very striking and it is full of fascinating information. The book focuses both on relative and absolute measurement. For example,  5’9″ person is tall compared to a cat, but short compared to a giraffe. The cat is large compared to a fly, and the giraffe is small compared to a T-rex. My kids were especially fascinated by the idea that clouds are actually extremely heavy.

Blockhead: The Life of Fibonacci, by Joseph D’Agnes. If your kids like Fibonacci numbers (or they enjoyed the biography of Erdos,) they might enjoy this book. It also takes a look at the culture of Medieval Pisa and the adoption of Arabic numerals (clunkily referred to in the text as “Hindu-Arabic numerals,” a phrase I am certain Fibonacci never used.) Fibonacci numbers are indeed found all over in nature, so if you have any sunflowers or pine cones on hand that you can use to demonstrate Fibonacci spirals, they’d be a great addition to the lesson. Otherwise, you can practice drawing boxes with spirals in them or Pascal’s triangles. (This book has more kid-friendly math in it than Erdos’s)

Pythagoras and the Ratios, by Julie Ellis. Pythagoras and his cousins need to cut their panpipes and weight the strings on their lyres in certain ratios to make them produce pleasant sounds. It’s a fun little lesson about ratios, and if you can combine it with actual pipes the kids can cut or recorders they could measure, glasses with different amounts of water in them or even strings with rock hanging from them, that would probably be even better.

Older than Dirt: A Wild but True History of Earth, by Don Brown. I was disappointed with this book. It is primarily an overview of Earth’s history before the dinosaurs, which was interesting, but the emphasis on mass extinctions and volcanoes (eg, Pompeii) dampened the mood. I ended up leaving out the last few pages (“Book’s over. Bedtime!”) to avoid the part about the sun swallowing up the earth and all life dying at the end of our planet’s existence, which is fine for older readers but not for my kids.

Hope you received some great games and books last month!


Homeschooling Corner: Math Philosophy

Music is a hidden arithmetic exercise of the soul, which does not know that it is counting.–Gottfried Leibniz

Fibonacci Spiral

You may have noticed that I talk a lot more about math than reading or writing. This is not because I dislike the language arts, but because they are, once learned, not very complicated. A child must learn to decode symbols, associate them with sounds, and then write them–tricky in the beginning, but most children should have the basics down by the age of 6 or 7. For the next several years, the child’s most important task is simply practice. If a child has a book they love to read, then they are already most of the way there and will probably only need some regular instruction on spelling and punctuation.

Math, by contrast, is always advancing. For every new operation or technique a child masters, there is another waiting to be learned.

I don’t hold with the idea that mathematical concepts must be taught in a particular order or at particular ages–I introduced negative numbers back in preschool, they’ve learned about simple logarithms in elementary, and they seem none the worse for the unusual order.

Count on Math gives the logic behind Particular Order:

Developmental sequence is fundamental to children’s ability to build conceptual understanding. … The chapters in this book present math in a developmental sequence that provides children a natural transition from one concept to the next, preventing gaps in their understanding. …

When children are allowed to explore many objects, they begin to recognize similarities and differences of objects. When children can determine similarities and differences, they can classify objects. When children can classify objects, they can see similarities and difference well enough to recognize patterns. When children can recognize, copy, extend and create patterns, they can arrange sets in a one-to-one relationship. …

This developmental sequence provides a conceptual framework that serves as a springboard to developing higher level math skills.

This logic is complete bollocks. (Count on Math is otherwise a fine book if you’re looking for activities to do with small children.)

Humans are good at learning. It’s what we do. Any child raised in a normal environment (and if you’re reading this, I assume you care about your children and aren’t neglecting them) has plenty of objects around every day that they can interact with, observe, sort, classify, etc. You don’t have to dedicate a week to teaching your kid how to tell “similar” and “different” in objects before you dedicate a week to “classifying.” Hand them some toys or acorns or rocks or random stuff lying around the house and they can do that themselves.

Can you imagine an adult who, because their parent or preschool skipped straight from”determining similarities and differences” to “making patterns,” was left bereft and innumerate, unable to understand fractions? If the human mind were really so fragile, the vast majority of people would know nothing and our entire civilization would not exist.

More important than any particular order is introducing mathematical concepts in a friendly, enjoyable way, when the child is ready to understand them.

For example, I tried to teach binary notation this week, but that went completely over the kids’ heads. They just thought I was making a pattern with numbers. So I stopped and switched to a lesson about Fibonacci numbers and Pascal’s triangle.

Then we went back to practicing addition and subtraction with regrouping, because that’s tricky. It’s boring, it’s not fun, and it’s not intuitive until you’ve really got base-ten down solid (base 10, despite what you may think, is not “obvious” or intuitive. Not all languages even use base 10. The Maya used base 20; the Babylonians used base 60. There are Aborigines who used base 5 or even 3; in Nigeria you’ll find base 12.) Learning is always a balance between the fun stuff (look what you can do with exponents!) and the boring stuff (let’s practice our times tables.) The boring stuff lets you do the fun stuff, but they’re both ultimately necessary.


What else we’ve been up to:

Fractions, Decimals, and Percents, by David A. Adler. A brightly-colored, well-written introduction to parts of numbers and how fractions, decimals and percents are really just different ways of saying the same thing.

It’s a short book–28 pages with not much text per page–and intended for young children, probably in the 8 to 10 yrs old range.

I picked up Code Your Own Games: 20 Games to Create with Scratch just because I wanted to see what there was outside the DK Workbooks (which have been good so far, no complaints there.) So far it seems pretty similar, but the layout is more compact. Beginners might feel less intimidated by DK’s larger layouts with more white space, but this seems good for a kid who is past that stage. It has more projects than the shorter DK Workbooks but they’re still pretty simple.

I also happened across a Singapore Math Workbook, which seems fine. Sample problem:

Emily and Jasmine had the same number of stamps. After Emily gave Jasmine 42 stamps, Jasmine had twice as many stamps as Emily. How many did Jasmine have at the end?

At a movie, 1/4 of the people in the theater were men, 5/8 were women, and the rest were children. If there were 100 more women than children, what was the total number of people in the theater?

Our recorders arrived, so now we can play music.

Finished reading The Secret Garden, planted seeds, collected and identified rocks. Nature walk: collected fall leaves and pressed flowers. Caught bugs and observed squirrels for Ranger Rick nature workbook. Read about space and worked with cuisenaire rods. Etc.


Homeschooling Corner: Flying Kites

We had a lovely, windy day, so we grabbed the kites, invited the neighbors, and headed out to the park.

Homeschooling does put additional responsibility on the parents to help their kids socialize. That doesn’t mean homeschooled kids are necessarily at a disadvantage viz their typically-schooled peers when it comes to comes to socializing (I went to regular school and still managed to be terribly socialized;) it’s just one more thing homeschooling parents have to keep in mind. So I am glad that we’ve had the good luck recently to make several friends in the neighborhood.

I’ve been looking for good, educational YouTube channels. Now I haven’t watched every video on these channels and I make no guarantees, but they seem good so far:

Welch Labs:

Welch Labs also has a website with a free downloadable workbook that accompanies their videos about imaginary numbers. It’s a good workbook and I’m working through it now.

TedEd, eg:

VSauce, eg:

Numberphile, eg:

The King of Random, eg:

We finished DK’s Coding in Scratch Projects Workbook and started Coding in Scratch: Games Workbook, which is slightly more advanced (longer projects.)

The Usborne Times Tables Activity Book is a rare find: a book that actually makes multiplication vaguely fun. Luckily there’s no one, set age when kids need to learn their multiplication tables–so multiple kids can practice their tables together.

In math we’ve also been working with number lines, concept like infinity (countable and uncountable,) infinitesimals, division, square roots, imaginary numbers, multi-digit addition and subtraction, graphing points and lines on the coordinate plane, and simple functions like Y=X^2. (Any kid who has learned addition, subtraction, multiplication and division can plot simple functions.)

We started work with the cuisenaire rods, which I hope to continue–I can’t find our set on Amazon, but these are similar. We’re also using Alexander Warren’s book You can Count on it: A Mentor’s Arithmetic Patterns for Elementary Students for cusienaire activites.

If you’re looking for board game to play with elementary-aged kids, Bejeweled Blitz is actually pretty good. Two players compete to place tiles on the board to match 3 (or more) gems, in a row or up and down. (A clever play can thus complete two rows at once.) We play with slightly modified rules. (Note: this game is actually pretty hard for people who struggle with rotating objects in their heads.)

Picture Sudoku is fun for little kids (and probably comes in whatever cartoon characters you like,) while KenKen and magic squares and the like are good for older kids (I always loved logic puzzles when I was a kid, so I’d like to get a book of those.)

I’ve found a website called Memrise which seems good for learning foreign languages if you don’t have access to a tutor or know somene who speaks the language you want to learn. They probably have an app for phones or tablets, so kids could practice their foreign langauge on-the-go. (Likewise, I should stow our spelling book in the car and use car rides as a chance to quiz them.)

And of course we’re still reading Professor Astro Cat/working in the workbook, which involves plenty of writing.

For Social Studies we’ve been reading about fall holidays.

Hope you all have a lovely October! What are some of your favorite educational videos?


Homeschooling Corner: Introducing Mr. Poop & Custom Dice

I happened to have a poop-shaped pinata sitting around (Why? Look, sometimes these things just happen) of the pull-the-flap-on-the-bottom variety rather than the smash-it-with-a-bat kind, so I decided to add a little fun to our day by filling Mr. Poop with school-related ideas written on strips of paper. Give Mr. Poop a shake and a scrap of paper flutters out–today’s idea was to design your own game, which the kids are working on now.

I’ve decided to incorporate the Cub Scout handbooks–which have lots of useful information about subjects like first aid, water safety, civics, history, etc.–into our rotation. (The Cub Scouts have a different handbook for 1st, 2nd, 3rd, and 4th graders.) Today we learned about knots–mostly square knots–complemented with The Camper’s Knot Tying Game. Knots are practical for anyone, but also good practice for kids with fine motor difficulties.

Over in Professor Astro Cat, we’re collecting space dust, keeping a moon journal (the eclipse was well-timed for this) and made impact craters in the sandbox. The book recommends spreading out newspaper indoors and using flour or cocoa powder, but sand, outside, is much easier to clean up. (Walmart sells beautiful colored sand for like $4 a bag. I sprinkled some green on top of the regular brown sandbox sand to simulate Earth’s surface.)

Custom Dice

There are lots of interesting dice–math dice, fraction dice, letter dice, place value dice, etc. Customized dice are easy to make: just take a cube (you probably have a building block or letter cube or some Legos lying around,) cover it with paper, and write whatever you want on the faces. (Note it is probably best to write on the paper before applying tape, as many pens won’t write properly on tape.) I have a custom die with +,-, <, and division signs on it that I use along with custom “numbers larger than six” dice for math games. (“Looks like you rolled 5,000,000,000 divided by 7,000!”) (For smaller kids, you may want to stick to + and -.)

I’m still trying to work out good ways to teach history. I’ve got some rudimentary ideas, but I’ll save them for later.

Homeschooling Corner: What is Educational?

Many years ago, I worked at a toy store. (It was a lot of fun–I like feeling helpful.) One day I was helping a grandmother pick out a gift for her young granddaughter, a  6-month old whom she proudly informed me was really at the developmental level of a 9-month old. She asked me to recommend something “educational” for the child.

Being, (I confess) not very good at this, I responded in confusion that pretty much everything is educational for a baby. Babies are learning all the time.

One of my co-workers helpfully jumped in and found her a stuffed dog that’s supposed to help babies learn to read.

Many years and a great deal of IQ and education research later, I stand by my original position: “educational” toys for babies probably aren’t. It would be great if we could find some magical technique–say, playing Classical music to your fetus–that could reliably make people into geniuses, but so far we haven’t actually found any.

Does that mean you shouldn’t play Classical music to your fetus? Of course not. There’s no evidence that Classical music hurts babies. It’s just highly likely that being the kind of person who would play Classical music to your fetus is a bigger factor in how your kids turn out than the actual music. But if you hate Classical, don’t sweat it.

If you’ve been hanging around the HBD-osphere for a while, you probably already know that adult IQ appears to be about 50% genetic and 50% random chance. That doesn’t mean you shouldn’t try to teach your kids things (you should definitely teach your kids things.) It just means that it’s more important to be good and kind to your kids than to buy them any particular toy or splurge on baby genius classes.


The youngest child has been really into rocks and crystals lately; at this age, they’re still fascinated by freezing cups of water to make ice. A little food coloring (rainbow ice!) fresh mint leaves, flowers, whatever you want to add makes the ice extra interesting; add salt for a lesson about icebergs and the ocean. I don’t know if this is really educational, but it’s fun.

The rest of our time has been focused primarily on regular old rote material–times tables, multi-digit addition and subtraction, handwriting, typing, spelling, etc. Luckily these skills are pretty flexible and so can be taught to multiple kids at different levels. Competitive multiplication games (try to call out the answer first!) work well in our household.

We also learned about If-Then statements in code and the Apollo 11 moon landing, which resulted in them coding a short animation about the moon launch.

I do hope that once I feel a little more secure about their basic skills, we can move outside for some active learning/PE/map-making type activities.

Homeschooling Corner

Welcome! Highly unscientific polling has revealed an interest in a regular or semi-regular feature focused on homeschooling.

Note that I am NOT some homeschooling guru with years of experience. We are just beginning, so I want some other people to discuss things with. I don’t have a curriculum picked out nor a coherent “philosophy,” but I am SO EXCITED about all of the things I have to teach I couldn’t even list them all.

I was thinking of starting with just a focus on what has been successful this week–which books/websites/projects we liked–and perhaps what was unsuccessful. I invite all of you to come and share your thoughts, ideas, questions, philosophies, recommendations, etc. Parents whose kids are attending regular schools but want to talk about learning materials are also welcome.

One request: Please no knee-jerk bashing of public schools or teachers. (I just find this really annoying.) Thoughtful, well-reasoned critique of mainstream schooling are fine, but let’s try to focus on the homeschooling.

This week’s successes:

DK Workbooks: Coding with Scratch (workbook) has been an amazing success.

Like many parents, I thought it’d be useful to learn some basic coding, but have no idea where to start. I once read HTML for dummies, but I don’t know my CSS from Perl, much less what’s best for kids.

After a bit of searching, I decided to try the the DK Coding with Scratch series. (This particular workbook is aimed at kids 6-9 yrs old, but there are others in the series.)

Scratch is a free, simple, child-friendly coding program available online at You don’t need the workbook to use Scratch, (it’s just a helpful supplement.) There are also lots of helpful Youtube videos for the enterprising young coder.

Note: my kids really want to code because they want to make their own video games.

In general, I have found that toys and games that claim they will teach your kids to code actually won’t. (Eg, Robot Turtles.) Some of these games are a ton of fun anyway, I just wouldn’t expect to become a great coder that way.

Professor Astro Cat’s Frontiers of Space is as good as it looks. Target market is 8-11 years old. There’s a lot of information per page, so we’re reading and discussing a few pages each day.

There are two other books in the series, Professor Astro Cat’s Intergalactic Activity Book, which I’m hoping will make a good companion to this one, and Astro Cat’s Atomic Adventure, which looks like it fills the desperately needed “quantum physics for kids” niche.)

I’m still trying to figure out how to do hands-on science activities without spending a bundle. Most of the “little labs” type science kits look fun, but don’t pack a lot of educational bang for your buck. For example, today we built a compass (it cost $10 at the toy store, not the $205 someone is trying charge on Amazon.) This was fun and I really like the little model, but it also took about 5 minutes to snap the pieces together and we can’t actually carry it around to use it like a real compass.

Plus, most of these labs are basically single-use items. I like toys with a sciency-theme, but they’re too expensive to run the whole science curriculum off of.

Oh, sure, I hand them a page of math problems and they start squawking at me like chickens. But bedtime rolls around and they’re like, “Where’s our Bedtime Math? Can’t we do one more page? One more problem? Please?”

There are only three math problems every other page (though this does add up to over 100 problems,) the presentation is fun, and the kids like the book better than going to sleep.

The book offers easy, medium, and hard problems in each section, so it works for kids between the ages of about 4 and 10.

There’s an inherent tension in education between emphasizing subjects that kids are already good at and working on the ones they’re bad at. The former gives kids a chance to excel, build confidence, and of course actually get good at something, while the latter is often an annoying pain in the butt but nevertheless necessary.


Since we’ve just started and are still getting in the swing of things, I’m trying to focus primarily on the things they’re good at and enjoy and have just a little daily focus on the things they’re weak at.

I’d like to find a good typing tutor (I’ll probably be trying several out soon) because watching the kids hunt-and-peck at the keyboard makes my hair stand on end. I’d also like to find a good way to hold up workbooks next to the computer to make using the DK books easier.

That’s about it, so I’ll open the floor to you guys.

Some thoughts for homeschooling parents

You can’t build up immunity to a disease by never experiencing it.

I hear a lot of people around these parts vowing to homeschool their kids because of this that or the other public schools are doing–usually something related to modern liberal politics. They’re afraid of their kids learning about gay marriage, or social justice, or something similar, so they decide that the solution is just to keep the kids at home where they can learn without the agenda.

Now, to be clear, I have nothing against homeschooling–all of the evidence and studies I’ve seen on the subject indicate that it is a perfectly fine way to educate a kid, so long as the parents are mentally healthy, not-abusive, etc. If you happen to live in an area where there aren’t a lot of other people around, then you might want to consider conventional schools just because your neighborhood makes it difficult to associate with other humans, but otherwise, I see homeschooling as just another method of educating a kid. If your goal is merely to provide your kid with the best education possible, this post is not for you.

However, if your goal in homeschooling is to prevent your kid from learning about broad social trends, political ideologies, or ideas you don’t like, anecdotal evidence suggests you will fail.

Your kid will grow up, they will leave the house, and then they will learn about all of the stuff everyone else believes. If everyone out there believes X, and your kid is even remotely neurologically normal, then your kid will learn about X and start believing it.

Remember, the vast majority of normal people pick up their ideas and beliefs from the other people around them. This is not a bug. This is a very important ability. Other people are treasure troves of useful information about how to stay alive and not die. Imitating others is how you learned to talk, which things are good to eat, and how to behave in new situations. If you’re standing near a road with your friend, and they suddenly jump back, it’s in your interest to jump back, too.

Inability to properly imitate others is extremely problematic and one of the basic symptoms of autism.

So, like I said, if your kids are remotely normal, they will pick up the values of the dominant culture upon exposure. And then they will decide that you were a looney nutcase.

I’m going to talk about the personal experiences of 5 people I know who were homeschooled by conservative Christians. I’m not cherry-picking; they are all the homeschooled people I know.

One went to Bible college, got pregnant, dropped out, and got married. This person still professes Christian faith, but believes far more in materialism.

The second dropped out of college, became a die-hard SJW, and changed genders. I doubt they are still Christian, and they regard their parents’ faith as a cult.

Third completed college, but has become a die-hard SJW. Has a very dim view of conservative Christianity. No children.

Fourth became an atheist liberal who believes in gay marriage and abortion.

Fifth became a die-hard SJW who hates conservative Christianity, thinks their parents were culty, and makes pornography.

If you want an in-depth look at how this happens, I recommend the webcomic Dumbing of Age.

What happened?

In all of these cases, the parents homeschooled to keep their kids isolated from certain ideas, ideologies, or behaviors. The kids graduated with very little experience of the world. They did not have a thorough understanding of how the world works, the philosophies out there, and why, exactly, their parents disagreed.

As a result, when exposed to the meme-viruses of the world, they get infected. They have no defenses.

In my experience, the vast majority of conservatives cannot articulate a coherent explanation for their beliefs, and do not attempt to explain their underlying reasoning to their kids. Many of them, I suspect, simply believe as they do because of habit, convenience, or because everyone else in their area does. Liberalism, by contrast, has put a lot of effort into making arguments against conservative beliefs.

For example, let’s take gay marriage. Common conservative arguments against gay marriage are “Ew! Gay people are gross!” “God says homosexuality is a sin,” and “The purpose of marriage is to make children.”

Liberals have all sorts of counter-arguments, like, “Ellen DeGeneres isn’t icky,” “Separation of Church and State,” and “But we let infertile people get married.”

In short, if it is really important to you that your kid think gay marriage is a bad idea, you’d better have a better, more coherent argument than that. Same for everything else in your memeplex/ideology/worldview–up to and including the existence of god. You might think your proof for the existence of god is pretty solid, but most of the people your kids will be associating with will probably think rather little of your proofs.

If you can’t explain your ideology and rigorously support it, showing your kids that your explanations of how the world works is better than the dominant ones, then you’d be better off just letting your kid go to public school and then doing your best to defend any objections to the curriculum when they come up. Your kids might think you’re kind of weird (just as I thought my parents were kind of weird in the early 90s for defending the use of aerosols/CFCs and not being concerned about the hole in the ozone layer), but they won’t hate you or think you’re a loon.