Now’s a good time to Homeschool

If you’ve ever wanted to homeschool your kids, but been afraid of funny looks and disapproval from other people, now is the time. Not only will everyone nod along and say, “Oh, yes, I totally understand why you are doing that,” right now, but also, if it doesn’t work out, you can just send your kids back to school when things return to normal.

The basic supplies you need for homeschooling are very simple: paper, pens/pencils, and books. If you’re reading this in the first place, you probably already own a lot of books, but if not, try the library: many are doing some form of lending. (Or ask your relatives if any of them have some extra books they’d be willing to loan you–my grandmother sent us textbooks on algebra, geometry, and linear algebra.)

Different kids need different things at different ages, so obviously you have to adjust what you are doing to match your kids. A typical 5 year old will spend most of their time learning letters, numbers, simple words, and simple equations. A 15 year old will be studying for the SAT and APs. You can supply a beginning reader’s need for books with simple text like “The cat sat” by yourself (see those pencils and paper above), but obviously you’ll want a real textbook for AP Calculus.

Workbooks: If you’re worried about whether you’ll hit all of the material you’re supposed to cover, get a workbook. It doesn’t really matter which workbook you get–I’ve never met a workbook I didn’t like. Workbooks tend state which grade they’re for on the front and all cover similar material inside, though different brands go at different paces. An “all-in-one” will be thick and cover lots of topics, or if your kid needs to slow down and do a lot more math problems, get the Kumon books. (I have even used second-hand workbooks that I got for free from a neighbor by simply copying out the problems onto fresh paper.)

Online/computer-based programs: We’ve used a variety of computer-based learning programs, including videos on Youtube, Zoom classes, and of course “educational” aps. These vary hugely in quality. Personally, I wouldn’t want to get tied down in any sort of long-term commitment right when starting out because it limits my ability to try different things, but my kids have benefited tremendously from math videos on Youtube. (YMMV.) Just remember that there are only so many hours in the day, so if you’ve just invested in a bunch of workbooks, you might want to hold off on that online literacy program.

The most important thing is actually just sitting down and doing it. Most kids are not super eager to do schoolwork, at school or home, so there will probably be some reluctance. It can be frustrating when they flop around like dead fish or give answers like “a really big number” instead of actually doing the work. This is when you have to take a deep breath and remind them that they don’t get to play Minecraft again until they finish their work. I also reward mine with Nerds and let them earn long-term rewards like “a trip to the pool” (though, obviously, that’s on hold right now). The important thing is to just sit down and do some school work each day so that they and you get into the habit and stop protesting.

And not everything has to be on paper. Go outside and toss a ball back and forth while practicing multiplication tables. Practice spelling words while in the car. Add biology and history questions to the Trivial Pursuit box. It does take a little effort to set up, but once you’re rolling, you’re good.

Why do People believe wrong things, pt 2

Today’s post is a compare and contrast between articles. From Erin O’Donnell’s interview with Elizabeth Bartholet we have “The Risks of Homeschooling,” and from Michelle Malkin we have “What will it take to stop Google’s Kiddie Predators?

I picked these articles because they hail from opposite ends of the political spectrum (so we needn’t get caught up in blaming one particular side,) but both deal with potential harms to children. Children, of course, are very precious and people are naturally inclined to protect them, so the thought that someone out there is harming them is deeply motivating.

Alas, both of these articles are, if you know anything about the subject in question, absolutely terrible.

On Homeschooling:

Yet Elizabeth Bartholet, Wasserstein public interest professor of law and faculty director of the Law School’s Child Advocacy Program, sees risks for children—and society—in homeschooling, and recommends a presumptive ban on the practice. Homeschooling, she says, not only violates children’s right to a “meaningful education” and their right to be protected from potential child abuse, but may keep them from contributing positively to a democratic society. …

… Only about a dozen states have rules about the level of education needed by parents who homeschool, she adds. “That means, effectively, that people can homeschool who’ve never gone to school themselves, who don’t read or write themselves.”

And from Malkin:

Last spring, Google reported at an education conference that it had started making its cloud platform program accessible to K-12 school districts. Evergreen, Washington, public schools chief Derrick Brown (right) bragged about his district’s data-mining pilot program with Google. “We have tons of data in our school districts,” he is quoted outlining in Education Week,citing information gathered through “student information systems, instructional software programs, online surveys of children’s social-emotional well-being, and special-needs students’ individualized education plans.”

“All that data needs to go in a container,” Brown explained. And that container will be Google Cloud Platform. Now, imagine questionnaires and tests stored in the G-container measuring “social-emotional well-being” of children and their families according to politically correct ideology. Imagine being a parent who objects to mandatory vaccine laws or who holds “America first” views deemed “extremist” and “hateful” or who stores guns responsibly in your home—information that is not the business of a school district or Silicon Valley giant. Where’s the protection for such families? What’s the academic justification for gathering it?

Before we go on, I should probably go into a little depth on what, exactly, makes both of these articles terrible.

Batholet wants to ban homeschooling entirely. This is absurd on its face–no matter how many problems you think there are with homeschooling (like anything, there are of course some), there are also clearly times and places when homeschooling is the best possible option, like literally right now, because I’m writing this in the middle of the Covid pandemic. There are kids who homeschool because they were bullied in regular schools, or because they have chronic illnesses that make regular school days difficult, or because they just plain learn better at home, and all of these kids have an obvious right to carry on doing things that are good for them.

It is quite easy to propose legislation that allows children to homeschool while also protecting them against the kinds of abuses Batholet cites–there is no reason to hurt all of the other kids in the process.

Furthermore, since schools are controlled primarily at the state level, banning homeschooling across the nation would require a massive amount of legal coordination. The Federal government could threaten to withhold funds to states that allow homeschooling, but this would be a practical disaster with states like Texas and Montana. It’s a bit ridiculous for anyone with any knowledge of US law (let alone a law professor) to propose something this far from legal reality.

Batholet is concerned about the quality of education homeschooled kids receive, which is rather precious given that homeschoolers consistently out-perform public schooled kids on standardized tests, eg, Academic Achievements and Demographic Traits of Homeschoolers:

Is it possible for adults without specialized, university-level training in teaching to help their children learn what they need to learn? Numerous studies by dozens of researchers have been completed during the past 25 years that examine the academic achievement of the home-educated (see reviews, e.g., Ray, 2000, 2005; 2009b). Examples of these studies range from a multi-year study in Washington State (Wartes, 1991), to other state-specific studies, to three nationwide studies across the United States (Ray, 1990, 1997, 2000; Rudner 1999), to two nationwide studies in Canada (Ray, 1994; Van Pelt, 2003).

In most studies, the homeschooled have scored, on average, at the 65th to 80th percentile on standardized academic achievement tests, compared to the national school average of the 50th percentile (which is largely based on public schools). A few studies have found the home educated to be scoring about the same or a little better than public school students. …

Research shows that the large majority of home-educated students
consistently interact with children of various ages and parents outside their immediate family (see, e.g., Medlin, 2000; Ray, 1997, 2009b).

The second part of the socialization question asks whether home-educated children will experience healthy social, emotional, and psychological development. Numerous studies, employing various psychological constructs and measures, show the home-educated are developing at least as well, and often better than, those who attend institutional schools (Medlin, 2000; Ray, 2009b). No research to date contravenes this general conclusion. In a few studies, on some of the sub-measures within a study, the home educated have scored slightly lower (i.e., “worse” according to the conceptual paradigm the researcher was using) than those in institutional schools. …

A corollary of the socialization question deals with whether the home-educated child will eventually function well in the world of adulthood… Various studies have addressed this issue in multiple ways. It appears that the home educated are engaged, at least as much as are others, in activities that predict leadership in adulthood (Montgomery, 1989), doing well on their college/university SAT tests (Barber, 2001, personal communication) and ACT tests (ACT, 2005), matriculating in college at a rate that is comparable or a bit higher than for the general public (Ray, 2004; Van Pelt 2003), performing well in college (Gray, 1998; Galloway & Sutton, 1995; Jenkins, 1998; Jones & Gloeckner, 2004; Mexcur, 1993; Oliveira, Watson, & Sutton, 1994), satisfied that they were home educated (Knowles & Muchmore, 1995; Ray, 2004; Van Pelt, Neven, & Allison, 2009), involved in community service at least
as much as others (Ray, 2004; Van Pelt, Neven, & Allison, 2009), and more civically engaged than the general public (Ray, 2004; Van Pelt, Neven, & Allison, 2009). There is no research evidence that having been home educated is associated with negative behaviors or ineptitudes in adulthood.

This particular study found even higher academic success rates for homeschoolers, who consistently scored above the 80th percentile in all tested areas, even science and math. The authors also looked at parental education, which Batholet is so concerned about, and found that a whopping 0.5% of mothers who homeschool their children did not graduate from highschool.

The idea of banning the 99.5% of homeschooling families whose mothers were literate enough to graduate from highschool because of the 0.5% who didn’t is straight up absurd, which is why batholet used imaginary illiterate people instead of real statistics.

What about child abuse? I’d think that would be captured in the overall data on social/emotional well-being and eventual adulthood competency, but maybe people who abuse their kids make efforts not to let them take surveys about how happy they feel. Regardless, homeschooled kids hail from the demographics with extremely low overall abuse rates–the vast majority come from white, middle class households with two married parents, while the kids most likely to be abused come from Native American, Black, poor, single-parent or no-parent households (eg grandparents, foster parents). If you don’t already know this, you have no business talking about child abuse.

Again, if your goal is to help abused children, it is easy to think of much more effective legislation than just blanket targeting all homeschoolers.

Batholet’s final, and frankly most bizarre objection, is that homeschooled children will be unable to contribute to a democratic society. She seems to think there is a cabal of underground monarchists hidden deep in the American heartland, raising their children to heil King George III as the rightful monarch of our land and to agitate for unification with Canada.

Back to O’Donnell’s article about Batholet:

She views the absence of regulations ensuring that homeschooled children receive a meaningful education equivalent to that required in public schools as a threat to U.S. democracy. “From the beginning of compulsory education in this country, we have thought of the government as having some right to educate children so that they become active, productive participants in the larger society,” she says. This involves in part giving children the knowledge to eventually get jobs and support themselves. “But it’s also important that children grow up exposed to community values, social values, democratic values, ideas about nondiscrimination and tolerance of other people’s viewpoints,” she says, noting that European countries such as Germany ban homeschooling entirely and that countries such as France require home visits and annual tests.

Hoooo boy. There’s a lot here to unpack.

First, let’s go back to the beginning of compulsory education in the US, circa 1830. (The Founding Fathers thought compulsory education of so little importance to “democracy” that it took half a century to get going.) I have here in my child-rearing library Bernard Wishy’s The Child and The Republic: The Dawn of Modern American Child Nurture, published in 1968 but still a very good overview of precisely this era in American history.

Spend about half an hour with this book and you will discover first that the subject is quite dull, and second, that you do not care a whit what people in the early 1800s thought about education because their general ideas about child-rearing are so entirely alien to yours.

Many Americans in this era were Puritans who literally believed that babies were inherently evil and would not be good people until they realized the importance of Christianity and were “born again” in Christ. These folks took babies soiling their nappies as evidence of their satanic natures and believed you had to beat the devil out of them.

Although expressed differently by proliferating Protestant sects… by 1800 Calvinist views of the child and of a human destiny under God’s stern judgement had demonstrated remarkable staying power.

This heritage included Jonathan Edwards’ famous words that unrepentant children were “young vipers and infinitely more hateful than vipers.” Another view was that they were “not too little to die…not too little to go to hell.” …

Despite the prestige and weight we now give the more congenital “modern” ideas o the American Enlightenment, in the very hour of the triumph of American independence in the 1780’s there had begun a remarkable resurgence of Calvinist iews and religious conservatism… For the next half-ctury, orthodox ministers would also invoke the convenient spectre of Jacobinism to strenghten their demands for strict disciplien and early religious traiinign of the child. The future of the nation as well as the child’s soul were said to be in danger.

Remarkable parallel.

Continuing with Wishy:

It is perhaps risky to speculate about the hostility to children that the belief in infant damnation and strict training seems to express. … it is likely that the responsibilities and expense of many unwanted children created or intensified hostile feelings towards offspring. Whatever inspired them, the orthodox were reluctant to dampen the fires o Hell awaiting the child who had not started the arduous training needed for saving the soul…

Infants were “by nature sinners, and show us that… the wicked are estranged from the womb, they go astray as soon as they are born, speaking lies.” [Reverend Allan Hyde, Essay on the State of Infants, NY, 1830.] …

Among the more conservative writers on the child was the President of Amherst College, Dr. Herman Humphrey. His book Domestic Education (1840) was a cataloge of errors for the day and a guide for perplexed mothers and fathers. … he called for absolute rule by the father, accountable to “no earthly power.” Fathers should try to control the child diligently by the age of four months. …

Complete rejection of the belief in depravity or innate tendencies to wickedness did not appear generally in popular literature until just before the Civil War.

But what about the schools themselves?

… the degree of the workday teachers’ and ministers’ hostility to encouraging intellectual and critical independence in students should also not be underestimated. … Precociousness was unnatural, and “forced feeding” of ideas even worse for the child. …

Some of the most revealing of the “impressions” that might come from the schoolroom have been examined by Ruth Miller Elson in a study of American textbooks before 1865. [Footnote: … This study confirms the evidence presented here of the essential conservatism of the goals sought through new methods of nurture. The textbooks studied stressed: the rejection of Europe, the exaltation of the Anglo-Saxon and scorning of the immigrant, the moral failure implicit in poverty, the acceptance of one’s own station and duties as God’s will, the ignoring or attacking of reform movements, the rightness of class distinctions…]

I have quoted this at length just to emphasize the utter absurdity of Batholet’s claims. Anyone who knows anything at all about the subject knows this is all the exact opposite of what Batholet wants; she is only invoking it because she assumes you don’t know anything about the subject. 

Rather, Batholet is attempting a bait-and-switch, invoking sacred ideas like “democracy” when she actually means “modern progressive liberal values.” And it is totally true that the majority of homeschooling families don’t put much stock in modern progressive liberal values (though a reasonable minority of homeschoolers are liberal hippie types).  The bait and switch and faux-concern for abused children (who could be much more effectively protected via other measures) is necessary because Batholet knows that insisting on educating children about pro-LGBT matters against their parents’ will would never pass First Amendment religious scrutiny.

Now on to Malkin.

Malkin’s piece is a little more over-the-top in tone, but just as disconnected from reality. She starts off by calling Google “kiddie predators,” as though the execs at Google’s offices liked to go raping six year olds in their spare time.

The Silicon Valley behemoth has already admitted it illegally collected children’s personal information on YouTube without parental consent, mines students’ browsing habits and emails, and tracks kids’ locations, audio and search history through Google educational apps and logons that are required for millions of students to participate in public schools.

Is Malkin actually ignorant about the facts of this case, or is she misrepresenting it on purpose?

The recent Youtube decision did not involve YT/Google doing something that it knew was illegal. It involved the government deciding to enforce a particular law in a new way that it hadn’t been used before, which made something YT was doing retroactively illegal.

The law in question prevents websites from gathering data/information from children, but it used to apply only to websites like Facebook where you make accounts that require personal information like your name or age. These laws are why Facebook, Youtube, and similar websites do not allow people under the age of 13 to have accounts: it’s illegal.

What Youtube was doing, which was not illegal, was tracking the viewing patterns of all users. If you watch five videos about car repair, and then you search for a video about truck repair, Youtube notices and in the future is likely to recommend videos about truck repair to people who’ve watched videos about car repair. This is how Youtube playlists and recommendations are generated, not to mention recommended products on Amazon, people you might want to follow on Twitter, not to mention all of the ads. Mom and Pop stores, major corporations, and TV stations also collect similar data about their customers/users.

These algorithms are fundamentally useful. They let Amazon recommend the product you’re looking for, they let Google figure out what you’re trying to type when you misspell something, and they let Youtube figure out that ads for vibrators don’t belong on videos featuring muppets.

The court case which expanded the scope of the original law found that when Youtube collected data like “Users who watched Baby Shark videos tend also to watch Pikachu videos,” even though that data was not attached to a particular name, account, or user, since it was a child on the other end of the screen, the data came from a child and thus was illegal to collect. I would like to emphasize that TV stations do the exact same thing when they look at their ratings and determine that people who watch Dora the Explorer tend to also watch Go Diego Go, but this has not been declared illegal simply because it involves a TV screen instead of a computer screen.

This is a moronic decision, since Youtube has no way of telling who exactly is on the other side of the screen (maybe it’s me, because I think the Baby Shark and Pikachu songs are funny), and cannot effectively figure out who is watching the videos in order to specifically not collect their data. The result has been the mass-demonetization of videos aimed at children, as determined by a combination of YT’s algorithms and creators’ own admission. A variety of other restrictions also now affect these videos, preventing them from showing up in recommendations and disabling comments.

This is a disaster for anyone making content aimed at children, from toy reviewers to teachers, because not only are their videos harder to find, but they also can’t get paid for them. Like everyone else, content creators need to eat.

Worse, there is no clear definition of what is “intended for children,” because the law was not originally written to cover such cases, and the legal threat/burden for determining this is put on the creators, not YT. So if you are making Minecraft videos that you intended for other adults like yourself, but it turns out that 10 year old boys also like watching them, you can be in violation of the law and get prosecuted by the federal government, but if you mark your videos as “for kids” they will at best show up next to “Baby Sings ABCs” videos and you won’t make any money.

Anyway, all of this is what Michelle Malkin is reducing to “illegally collected children’s information on Youtube”. The rest of the article contains similar mischaracterizations or omissions of vital details. Take this:

Can you imagine a similar breach of minors’ photos and videos stored on students’ Google Drives or Chromebooks or smartphones or home computers used to log on to mandatory learning management systems integrated with Google, such as Canvas or Schoology or Blackboard? It’s easy if you try.

I can imagine unicorns. So what? We’re not here to imagine make-believe harms.

Notice how both articles invent hypotheticals or imagined harms. This would be reasonable if we were talking about the effects of proposed legislation or future inventions, but not in the case of already existing legislation and technologies. Since these things already exist, we can talk about their actual effects, not imagined ones.

Malkin’s article is worse in this regard (at least Batholet could cite the case of one homeschooling family that abused their kids, while Malkin could not cite a single case of harm to children due to Google/YT), but both are focused on imagined harm because the real life harms are so rare.

Why are both of these articles so far off-base?

Could the authors/Batholet be lying? I have no reason to think that Batholet is intentionally, consciously lying–she sounds too much like relatives I’ve had conversations with in real life who just spout off about homeschooling without knowing anything about it.

Malkin probably isn’t in it for the money, (being featured on VDare probably does not make you money,) but she could be intentionally misleading people because she sees Google/Youtube as her enemy.

I think both Batholet and Malkin are motivated by dislike of their enemies/outgroup. Malkin has written previously about YT censoring her, and Batholet clearly doesn’t like religious conservatives. Dislike of your enemy makes you more likely to believe absurd things about him (he must do terrible things, otherwise he wouldn’t be your enemy,) and attacking your enemy, even for imagined faults, raises your own social status within your own group. Meanwhile it is difficult for anyone within your group to question your claims because such questions look a lot like ‘trying to argue that the outgroup isn’t actually all that bad’, which leaves you vulnerable to attacks from other status-climbers.

The average in-group reader, then, only hears one dominant side being articulated by people they respect, and so if they do not have any independent knowledge on the subject (and none of us can know everything,) then they are more likely to believe the incorrect information.

So, TL:DR

People are more likely to believe wrong things when they

  1. Don’t know much about the subject at hand,
  2. The incorrect information comes from an authority within their in-group,
  3. It concern the out-group, or
  4. They’re repeating a euphemism without realizing it’s a euphemism.

(eg, Batholet’s claim that homeschooling is bad for democracy is really a euphemism for bad for her politics. If a euphemism gets repeated often enough, people start believing it literally, forgetting what it originally stood for.)

Homeschooling Corner: Summer Fun

Hello, everyone. I hope you have had a lovely summer. We ended up scaling back a bit on our regular schedule, doing about half as much formal “schoolwork” as usual and twice as much riding bikes and going to the playground.

Here are some of the books we found particularly useful/enjoyable this summer:

String, Straightedge, and Shadow: The Story of Geometry, by Julia E Diggins

This is my favorite book we read this summer.

I was looking for a book to introduce simple geometry and shape construction. Instead, I found this delightful history of geometry. It is appropriate for children who understand simple fractions, ratios, and the Pythagorean theorem, but it is not a mathematics textbook and only contains a few equations. (I’m still looking for an introduction to geometry, if anyone has any recommendations.)

This is a new edition of a book originally published in 1965, but its age isn’t really important because geometry hasn’t changed much in the intervening years.

The story begins with geometry in nature–the shapes of trees and flowers, spiderwebs and honeycombs–then develops a speculative account of how early stoneage humans might have become increasingly aware of and attuned to these shapes. Men saw the shapes of the sun and moon in the sky, and might have observed that an ox tied to a pole traced out a similar shape in the dirt.

Then Egyptian surveyors developed right triangles, used for measuring the corner of fields and pyramids. The Mesopotamians developed astronomy, and divided the circle into 360 degrees. Then came the Greeks–clever Thales, mystical Pythagoras, and practical Archimedes. And finally, at the end, Eratosthenes (who used geometry–literally, earth measuring–to measure the circumference of the Earth,) and a few paragraphs about Euclid.

Writing with Ease, by Susan Wise Bauer

There are many books and workbooks in this series, so you can pick the ones that best suit your child’s ability level. (The “look inside the book” feature is great for judging which level of textbook you want.)

I am sure these books are not everyone’s cup of tea. They may not be yours. But they were what we needed.

My eldest children are fairly different in writing needs, but I do not have time for separate curricula. One is a good speller, the other bad. One has acceptable handwriting, the other awful. One will write independently, the other hates writing and plays dead if I try to get them to write. These books have worked well for everyone. Spelling, handwriting, and general willingness to write have all improved.

Even if you aren’t homeschooling, this book might make a good supplement to your kids’ regular curriculum.

In science, we have been growing bacteria in petri dishes and looking at them under the microscope, with the help of Usborne Science and Experiments: The World of the Microscope (I think this is the same book, but cheaper.)

Petri dishes are cheap, agar is easy to make at home (it’s just like making jello,) and kids can learn things like “doorknobs are dirty” and “that’s why mom makes me wash my hands before dinner.”

Just be careful when handling large quantities of bacteria. Even if it’s normal household bacteria that you’re exposed to regularly, you’re not used to it in these quantities. The instructions recommend wearing gloves and safety goggles while handling bacteria and making slides out of them–and besides, kids like dressing up “like scientists” anyway.

The Super Source: Pattern Blocks and Geoboards

Our pattern blocks have been in the family for decades–passed down to me by my grandmother–but the geoboards are a new acquisition. I remember geoboards in elementary school–they sat behind the teacher’s desk and we never actually used them. I didn’t know what, exactly, geoboards were for, so I went ahead and got new workbooks for both them and the pattern blocks.

We are only a few lessons in, but so far I am very pleased with these. We have been talking about angles and measuring the degrees in different shapes with the pattern blocks–360 in a circle, 180 in a triangle, 720 in a hexagon, etc–which dovetails nicely with the geometry reading. The geoboards let us construct and examine a variety of different shapes, like right and equilateral triangles. The lesson plans are easy to use and the kids really enjoy them. Just watch out for rubber bands flying across the room.

Super Source makes workbooks for different grade levels, from K through 6th.

Learn to Program with Minecraft, by Craig Richardson

This book introduces Python, and is a nice step up from the Scratch workbooks. You may have to install a couple of programs, like Python and the API spigot, but the book walks you through this and it is not bad at all. There are then step-by-step instructions for making simple programs, along with bonus challenges to work out on your (or your kid’s) own.

The book covers strings, booleans, if statements, loops, etc, in kid-friendly ways. Best for people who already love Minecraft and can type.

Homeschooling Corner: A Mathematician’s Lament, by Paul Lockhart

Paul Lockhart’s A Mathematician’s Lament: How School Cheats us of our Most Fascinating and Imaginative Artform is a short but valuable book, easily finished in an afternoon.

Lockhart’s basic take is that most of us have math backwards. We approach (and thus teach) it as useful but not fun–something to be slogged through, memorized, and then avoided as much as possible. By contrast, Lockhart sees math as more fun than useful.

I do not mean that Lockhart denies the utility of balancing your checkbook or calculating how much power your electrical grid can handle, but most of the math actual mathematicians do isn’t practical. They do it because they enjoy it; they love making patterns with numbers and shapes. Just because paint has a very practical use in covering houses doesn’t mean we shouldn’t encourage kids to enjoy painting pictures; similarly, Lockhart wants kids to see mathematics as fun.

But wait, you say, what if this loosey-goosey, free-form, new math approach results in kids who spend a lot of time trying to re-derive pi from first principles but never really learning algebra? Lockhart would probably counter that most kids never truly master algebra anyway, so why make them hate it in the process? Should we only let kids who can paint like the Masters take art class?

If you and your kids already enjoy math, Lockhart may just reinforce what you already know, but if you’re struggling or math is a bore and a chore, Lockhart’s perspective may be just what you need to turn things around and make math fun.

For example: There are multiple ways to group the numbers during double-digit multiplication, all equally “correct”; the method you chose is generally influenced by things like your familiarity with double-digit multiplication and the difficulty of the problem. When I observed one of my kids making errors in multiplication because of incorrect regrouping, I showed them how to use a more expanded way of writing out the numbers to make the math clearer–promptly eliciting protests that I was “doing it wrong.” Inspired by Lockhart, I explained that “There is no one way to do math. Math is the art of figuring out answers, and there are many ways to get from here to there.” Learning how to use a particular approach—“Put the numbers here, here, and here and then add them”–is useful, but should not be elevated above using whatever approach best helps the child understand the numbers and calculate the correct answers.

The only difficulty with Lockhart’s approach is figuring out what to actually do when you sit down at the kitchen table with your kids, pencil and paper in hand. The book has a couple of sample lessons but isn’t a full k-12 curriculum. It’s easy to say, “I’m going to do a free-form curriculum that requires going to the library every day and uses every experience as a learning opportunity,” and rather harder to actually do it. With a set curriculum, you at least know, “Here’s what we’re going to do today.”

My own personal philosophy is that school time should be about 50% formal instruction and 50% open-ended exploration. Kids need someone to explain how the alphabet works and what these funny symbols on the math worksheet mean; they also need time to read fun books and play with numbers. They should memorize their times tables, but a good game can make times tables fun. In short, I think kids should have both a formal, straightforward curriculum or set of workbooks (I have not read enough math textbooks to recommend any particular ones,) and a set of math enrichment activities, like tangrams, pattern blocks, reading about Penrose the Mathematical Cat, or watching Numberphile on YouTube.

(Speaking of Penrose, I thought the chapter on binary went right over my kids’ heads, but yesterday they returned all of their answers in math class in binary, so I guess they picked up more than I gave them credit for.)

YouCubed.org is an interesting website I recently discovered. So far we’ve only done two of the activities, but they were cute and I suspect the website will make a useful addition to our lessons. If you’ve used it, I’d love to hear your thoughts on it.

That’s all for now. Happy learning!

What IS “Social Studies”?

Sometimes you can’t see the forest for the trees, and sometimes you look at your own discipline and can’t articulate what, exactly, the point of it is.

Yes, I know which topics social studies covers. History, civics, geography, world cultures, reading maps, traffic/pedestrian laws, etc. Socialstudies.org explains, “Within the school program, social studies provides coordinated, systematic study drawing upon such disciplines as anthropology, archaeology, economics, geography, history, law, philosophy, political science, psychology, religion, and sociology, as well as appropriate content from the humanities, mathematics…” etc. (I’m sure you did a lot of archaeology back in elementary school.)

But what is the point of lumping all of these things together? Why put psychology, geography, and law into the same book, and how on earth is that coordinated or systematic?

The points of some other school subjects are obvious. Reading and writing allow you to decode and encode information, a process that has massively expanded the human ability to learn and “remember” things by freeing us from the physical constraints of our personal memories. We can learn from men who lived a thousand years ago or a thousand miles away, and add our bit to the Great Conversation that stretches back to Homer and Moses.

Maths allow us to quantify and measure the world, from “How much do I owe the IRS this year?” to “Will this rocket land on the moon?” (It is also, like fiction, pleasurable for its own sake.) And science and engineering, of course, allow us to make and apply factual observations about the real world–everything from “Rocks accelerate toward the earth at a rate of 9.8m/s^2” to “This bridge is going to collapse.”

But what is social studies? The question bugged me for months, until Napoleon Chagnon–or more accurately, the Yanomamo–provided an answer.

Chagnon is a anthropologist who carefully documented Yanomamo homicide and birth rates, and found that the Yanomamo men who had killed the most people went on to father the most children–providing evidence for natural selection pressures making the Yanomamo more violent and homicidal over time, and busting the “primitive peoples are all lovely egalitarians with no crime or murder” myth.

In an interview I read recently, Chagnon was asked what the Yanomamo made of him, this random white guy who came to live in their village. Why was he there? Chagnon replied that they thought he had come:

“To learn how to be human.”

Sometimes we anthropologists lose the signal in the noise. We think our purpose is to document primitive tribes before they go extinct (and that is part of our purpose.) But the Yanomamo are correct: the real reason we come is to learn how to be human.

All of school has one purpose: to prepare the child for adulthood.

The point of social studies is prepare the child for full, adult membership in their society. You must learn the norms, morals, and laws of your society. The history and geography of your society. You learn not just “How a bill becomes a law” but why a bill becomes a law. If you are religious, your child will also learn about the history and moral teachings of their religion.

Most religions have some kind of ceremony that marks the beginning of religious adulthood. For example, many churches practice the rite of Confirmation, in which teens reaffirm their commitment to Christ and become full members of the congregation. Adult Baptism functions similarly in some denominations.

Judaism has the Bar (and Bat) Mitzvah, whose implications are quite clearly articulated. When a child turns 13 (or in some cases, 12,) they are now expected to be moral actors, responsible for their own behavior. They now make their own decisions about following Jewish law, religious duties, and morality.

But there’s an upside: the teen is also now able to part of a minyan, the 10-person group required for (certain) Jewish prayers, Torah legal study; can marry*; and can testify before a Rabbinic court.

*Local laws still apply.

In short, the ceremony marks the child’s entry into the world of adults and full membership in their society. (Note: obviously 13 yr olds are not treated identically to 33 yr olds; there are other ceremonies that mark the path to maturity.)

Whatever your personal beliefs, the point of Social Studies is to prepare your child for full membership in society.

A society is not merely an aggregation of people who happen to live near each other and observe the same traffic laws (though that is important.) It is a coherent group that believes in itself, has a common culture, language, history, and even literature (often going back thousands of years) about its heroes, philosophy, and values.

To be part of society is to be part of that Great Conversation I referenced above.

But what exactly society is–and who is included in it–is a hotly debated question. Is America the Land of the Free and Home of the Brave, or is it a deeply racist society built on slavery and genocide? As America’s citizens become more diverse, how do these newcomers fit into society? Should we expand the canon of Great Books to reflect our more diverse population? (If you’re not American, just substitute your own country.)

These debates can make finding good Social Studies resources tricky. Young students should not be lied to about their ancestors, but neither should they be subjected to a depressing litany of their ancestors’ sins. You cannot become a functional, contributing member of a society you’ve been taught to hate or be ashamed of.

Too often, I think, students are treated to a lop-sided curriculum in which their ancestors’ good deeds are held up as “universal” accomplishments while their sins are blamed on the group as a whole. The result is a notion that they “have no culture” or that their people have done nothing good for humanity and should be stricken from the Earth.

This is not how healthy societies socialize their children.

If you are using a pre-packaged curriculum, it should be reasonably easy to check whether the makers hold similar values as yourself. If you use a more free-form method (like I do,) it gets harder. For example, YouTube* is a great source for educational videos about all sorts of topics–math, grammar, exoplanets, etc.–so I tried looking up videos on American history. Some were good–and some were bad.

*Use sensible supervision

For example, here’s a video that looked good on the thumbnail, but turned out quite bad:

From the description:

In which John Green teaches you about the Wild, Wild, West, which as it turns out, wasn’t as wild as it seemed in the movies. When we think of the western expansion of the United States in the 19th century, we’re conditioned to imagine the loner. The self-reliant, unattached cowpoke roaming the prairie in search of wandering calves, or the half-addled prospector who has broken from reality thanks to the solitude of his single-minded quest for gold dust. While there may be a grain of truth to these classic Hollywood stereotypes, it isn’t a very big grain of truth. Many of the pioneers who settled the west were family groups. Many were immigrants. Many were major corporations. The big losers in the westward migration were Native Americans, who were killed or moved onto reservations. Not cool, American pioneers.

Let’s work through this line by line. What is the author’s first priority: teaching you something new about the West, or telling you that the things you believe are wrong?

Do you think it would be a good idea to start a math lesson by proclaiming, “Hey kids, I bet you get a lot of math problems wrong”? No. Don’t start a social studies lesson that way, either.

There is no good reason to spend valuable time bringing up incorrect ideas simply because a child might hold them; you should always try to impart correct information and dispel incorrect ideas if the child actually holds them. Otherwise the child is left not with a foundation of solid knowledge, but with what they thought they knew in tatters, with very little to replace it.

Second, is the Western movie genre really so prominent these days that we must combat the pernicious lies of John Wayne and the Lone Ranger? I don’t know about you, but I worry more about my kids picking up myths from Pokemon than from a genre whose popularity dropped off a cliff sometime back in the 80s.

“We are conditioned to think of the loner.” Conditioned. Yes, this man thinks that you have been trained like a dog to salivate at the ringing of a Western-themed bell, the word “loner” popping into your head. The inclusion of random psychology terms where they don’t belong is pseudo-intellectual garbage.

Updated values chart!

The idea of the “loner” cowboy and prospector, even in their mythologized form, is closer to the reality than the picture he draws. On the scale of nations, the US is actually one of the world’s most indivdualist, currently outranked only by Canada, The Netherlands, and Sweden.

Without individualism, you don’t get the notion of private property. In many non-Western societies, land, herds, and other wealth is held collectively by the family or clan, making it nearly impossible for one person (or nuclear family) to cash out his share, buy a wagon, and head West.

I have been reading Horace Kephart’s Our Southern Highlanders, an ethnography of rural Appalachia published in 1913. Here is a bit from the introduction:

The Southern highlands themselves are a mysterious realm. When I prepared, eight years ago, for my first sojourn in the Great Smoky Mountains, which form the master chain of the Appalachian system, I could find in no library a guide to that region. The most diligent research failed to discover so much as a magazine article, written within this generation, that described the land and its people. Nay, there was not even a novel or a story that showed intimate local knowledge. Had I been going to Teneriffe or Timbuctu, the libraries would have furnished information a-plenty; but about this housetop of eastern America they were strangely silent; it was terra incognita.

On the map I could see that the Southern Appalachians cover an area much larger than New England, and that they are nearer the center of our population than any other mountains that deserve the name. Why, then, so little known? …

The Alps and the Rockies, the Pyrennees and the Harz are more familiar to the American people, in print and picture, if not by actual visit, than are the Black, the Balsam, and the Great Smoky Mountains. …For, mark you, nine-tenths of the Appalachian population are a sequestered folk. The typical, the average mountain man prefers his native hills and his primitive ancient ways. …

The mountaineers of the South are marked apart from all other folks by dialect, by customs, by character, by self-conscious isolation. So true is this that they call all outsiders “furriners.” It matters not whether your descent be from Puritan or Cavalier, whether you come from Boston or Chicago, Savannah or New Orleans, in the mountains you are a “furriner.” A traveler, puzzled and scandalized at this, asked a native of the Cumberlands what he would call a “Dutchman or a Dago.” The fellow studied a bit and then replied: “Them’s the outlandish.” …

As a foretaste, in the three and a half miles crossing Little House and Big House mountains, one ascends 2,200 feet, descends 1,400, climbs again 1,600, and goes down 2,000 feet on the far side. Beyond lie steep and narrow ridges athwart the way, paralleling each other like waves at sea. Ten distinct mountain chains are scaled and descended in the next forty miles. …

The only roads follow the beds of tortuous and rock-strewn water courses, which may be nearly dry when you start out in the morning, but within an hour may be raging torrents. There are no bridges. One may ford a dozen times in a mile. A spring “tide” will stop all travel, even from neighbor to neighbor, for a day or two at a time. Buggies and carriages are unheard of. In many districts the only means of transportation is with saddlebags on horseback, or with a “tow sack” afoot. If the pedestrian tries a short-cut he will learn what the natives mean when they say: “Goin’ up, you can might’ nigh stand up straight and bite the ground; goin’ down, a man wants hobnails in the seat of his pants.” …

Such difficulties of intercommunication are enough to explain the isolation of the mountaineers. In the more remote regions this loneliness reaches a degree almost unbelievable. Miss Ellen Semple, in a fine monograph published in[Pg 23] the Geographical Journal, of London, in 1901, gave us some examples:

“These Kentucky mountaineers are not only cut off from the outside world, but they are separated from each other. Each is confined to his own locality, and finds his little world within a radius of a few miles from his cabin. There are many men in these mountains who have never seen a town, or even the poor village that constitutes their county-seat…. The women … are almost as rooted as the trees. We met one woman who, during the twelve years of her married life, had lived only ten miles across the mountain from her own home, but had never in this time been back home to visit her father and mother. Another back in Perry county told me she had never been farther from home than Hazard, the county-seat, which is only six miles distant. Another had never been to the post-office, four miles away; and another had never seen the ford of the Rockcastle River, only two miles from her home, and marked, moreover, by the country store of the district.”

When I first went into the Smokies, I stopped one night in a single-room log cabin, and soon had the good people absorbed in my tales of travel beyond the seas. Finally the housewife said to me, with pathetic resignation: “Bushnell’s the furdest ever I’ve been.” Bushnell, at that time, was a hamlet of thirty people, only seven miles from where we sat. When I lived alone on “the Little Fork of Sugar Fork of[Pg 24] Hazel Creek,” there were women in the neighborhood, young and old, who had never seen a railroad, and men who had never boarded a train, although the Murphy branch ran within sixteen miles of our post-office.

And that’s just Appalachia. What sorts of men and women do you think settled the Rockies or headed to the Yukon? Big, gregarious families that valued their connections to society at large?

Then there are the railroads. The video makes a big deal about the railroads being funded by the government, as proof that Americans weren’t “individuals” but part of some grand collectivist society.

Over in reality, societies with more collectivist values, like Pakistan, don’t undertake big national projects. In those societies, your loyalty is to your clan or kin group, and the operative level of social planning and policy is the clan. Big projects that benefit lots of people, not just particular kin networks, tend not to get funded because people do not see themselves as individuals acting within a larger nation that can do big projects that benefit individual people. Big infrastructure projects, especially in the 1800s, were almost entirely limited to societies with highly individualistic values.

Finally we have the genocide of the American Indians. Yes, some were definitely killed; the past is full of sins. But “You’re wrong, your self-image is wrong, and your ancestors were murderers,” is not a good way to introduce the topic.

It’s a pity the video was not good; the animation was well-done. It turns out that people have far more strident opinions about “Was Westward Expansion Just?” than “Is Pi Irrational?”

I also watched the first episode of Netflix’s new series, The Who Was? Show, based on the popular line of children’s biographies. It was an atrocity, and not just because of the fart jokes. The episode paired Benjamin Franklin and Mahatma Gandhi. Gandhi was depicted respectfully, and as the frequent victim of British racism. Franklin was depicted as a buffoon who hogged the spotlight and tried to steal or take credit for other people’s ideas.

It made me regret buying a biography of Marie Curie last week.

If your children are too young to read first-hand ethnographic accounts of Appalachia and the frontier, what do I recommend instead? Of course there are thousands of quality books out there, and more published every day, but here are a few:

A Child’s Introduction to The World

The Usborne Book of Living Long Ago: Everyday Life Through the Ages

What Your [X] Grader Needs to Know So far I like these, but I have not read them all the way through.

DK: When on Earth?

More important than individual resources, though, is the attitude you bring to the subject.

 

Before we finish, I’d like to note that “America” isn’t actually the society I feel the closest connection to. After all, there are a lot of people here whom I don’t like. The government has a habit of sending loyal citizens to die in stupid wars and denying their medical treatment when they return, and I don’t even know if the country will still exist in meaningful form in 30 years. I think of my society as more “Civilization,” or specifically, “People engaged in the advancement of knowledge.”

Homeschooling Corner: Science (geology and geography)

 

I have yet to find any “science kits” that actually teach science–most are just science-themed toys. There’s nothing wrong with that, but don’t expect your kid to re-derive the principles of chemistry via a baking soda volcano.

Smaller kids aren’t ready for the kind of thinking required for actual scientific research, but they can still learn plenty of science the mundane way: by reading. So here are some of our favorite science books/activities:

We did geology over the winter, centered around Rocks, Rivers, and the Changing Earth. It’s a lovely book (reading level about second grade?) with instructions for many simple experiments (eg, put rocks, sand, water in a glass jar and carefully shake/swirl to observe the effects of different water speeds on riverbanks) and handily complements any nature walks, rock collecting trip, or expeditions to the seashore.

WARNING: This book was published before plate tectonics became widely accepted and so has a confused chapter or two on how mountains form. SKIP THIS CHAPTER.

We also tried making polished stones in a rock tumbler (verdict: not worth the cost.)

After geology, we transitioned to geography with A Child’s Introduction to the World: Geography, Cultures and People–from the Grand Canyon to the Great Wall of China. I admit that geography sounds more like social studies than science, but it flows so perfectly from our understanding of geology that I have to mention it here.

I like to read this with a globe and children’s atlas at hand, so I can easily demonstrate things like latitude and longitude, distances, and different map projections.

With spring’s arrival we also began a study of plants and insects.

If you’ve never started your own plants from seed, any common crop seeds sold at the store–beans, peas, corn, squash, and most flowers–will sprout quickly and easily. If you want to keep your plants indoors, I recommend you get a bag of dirt at the garden center. This dirt is supposed to be “clean”; the dirt found outside in your yard is full of bugs that you probably weren’t intending on studying in your living room.

Speaking of bugs, we bought the “raise your own ladybugs” and butterflies kits, but I don’t recommend these as real caterpillars are nowhere near as cute and interesting as the very hungry one in the story. I think you’re better off just collecting ladybugs in the wild and reading about them at home.

The Way Things Work (also by this author: How Machines Work: Zoo Break) This is a big, beautiful book aimed at older kids, maybe about 10+. Younger kids can enjoy it if you read it with them.

Super Science: Matter Matters is a fabulous pop-up/lift-the-flap book about chemistry. We were very lucky to receive this as a birthday gift. (Birthday hint: the homeschooling families in your life would always like more books.) The book is a little fragile, so not appropriate for younger children who might pull too hard on the tabs, but great for everyone else.

Magic Schoolbus anything. There are probably several hundred books in this series by now. Who Was Albert Einstein? We finished our math biographies, so on to science bios. Basher Science: Astronomy  This is cute, and there are a bunch in the series. I’m looking forward to the rest. Professor Astro Cat‘s Atomic Adventure (also, Space!)

Homeschooling Corner: Math ideas and manipulatives for younger grades

Archimedes

When you love a subject and your kids love it, too, it’s easy to teach. When you’re really not sure how to approach the subject or your kids hate it, it gets a lot trickier. (See: spelling.)

So I thought I’d make a list of some of our favorite math related materials–but please remember, all you really need for teaching math is a paper and pencil. (Or less–Archimedes did math with a stick and some sand!)

Countables

Little ones who are just learning to count and add benefit from having something concrete they can hold, touch, and move around when thinking about concepts like “two more” or “two less.”

You can count almost anything–pebbles, shells, acorns, pennies, Monopoly money, fingers–but having a box of dedicated, fun, colorful countables on hand is useful. My favorites:

Abacus. The abacus has the lovely advantage that all of its counters are on rods and so don’t get scattered around the room, stepped on and lost. I made my own abacus (inspired by commenter Dave‘s abacus) out of a shoe box, plastic beads, pipecleaners, and tape. You can count, add, subtract, multiply, divide, etc., on an abacus, but for your purposes you’ll just need to learn addition and subtraction.

Different abaci have different numbers and arrangements of beads. If your kids are still learning to count/mastering addition and subtraction up to ten (standard kindergarten goals,) I’d use an abacus with 9 beads per string. (Just like writing numbers, after you get to nine on the “ones” string, you raise up one bead on the “10” string.)

We adults tend to take place value for granted (“it’s obvious that we use the decimal system!”) but switching from column to column can be confusing for young kids. There’s no intuitive reason why 11 doesn’t = 2. The abacus helps increase awareness of place value (typically taught in first grade) because you simply run out of beads after 9 and have to switch to the next row.

Once kids have the basic idea, you can switch to a more advanced abacus like the Soroban. The top bead on the Soroban is worth 5, so students count 1-2-3-4, then click the 5 bead and clear the unit beads, then add unit beads to the five to count 6-7-8-9, then click one bead in the tens column and clear all of the beads in the unit and five column. My apologies if it sounds complicated; it really isn’t, it’s just a little tricky to put into words.

You can get abacus workbooks; I have not used any so I cannot review them but they look fun. Rather, I just use the abacus as a complement to the other math problems we are already doing. (I have read Mr. Green’s How to Use a Chinese Abacus, which was the only book my library had on the subject. It is a very good introduction aimed at adults.)

Counting Penguins

There is nothing magical about penguins; I just happen to like them. The set has 100 penguins in ten sets (distinguished by color) plus ten “ice bars” that hold ten penguins each. (Besides addition and subtraction,) I find these useful for introducing and visualizing multiplication , eg, 3 rows of 5 penguins = 3×5.

Counting Cubes

For bigger numbers, we have a bag of 1,000 interlocking cubes. Kids will want to just plain build with them, like Legos, which is fine–a fun treat after hard work. You can easily use these to represent 1s, 10s, and 100s (it takes a while to assemble a full 1,000 cube,) and to represent operations like 3x3x3, helping bridge both place value and multiplication. Legos work for this, too, though you’ll probably want to sort out ones that are all the same size and shape.

 

Pattern Blocks

(I think I’ve been incorrectly calling these tangrams, though the principles are similar.)

These pattern blocks are a family heirloom, sent to me by my grandmother upon the birth of my first child. I played with them when I was a child; my siblings played with them; now my children play with them. Someday I will pass them on to my grandchildren… but you can also get them on Amazon. (We use these with a book of pattern block activities that hails from the 80s; I am sure there are many good books of a similar nature published within the past couple of decades.

Apparently there are workbooks with pattern block activities aimed all the way up to 8th grade, but I have not read them and cannot comment on them.

Cuisenaire rods

We didn’t use cuisenaire rods when I was young, but I think I would have liked them. Similar to the tangrams pattern blocks, there are lots of interesting workbooks, games, and other activities you can do with these.

Building toys

Open-ended building toys (Legos, Tinker Toys, blocks, magnetic tiles) come in almost endless forms and can be used to build all sorts of geometric shapes.

Fractions

Fraction blocks and fraction circles are both handy.

Games

Almost any kids’ board game can be transformed into a math game by adding cards with math problems to be solved before completing a turn or using math dice. Your local games shop can help you find dice with numbers higher than six, or you can just tape paper onto an existing cube to make a custom die of your liking (like an + and – die). There are also tons of fun logic games; I pull these out whenever kids start getting restless.

Books

There are so many great math books, from Sir Cumference to Penrose, that I can’t hope to list them all. I encourage you to check out your library’s selection. Here are a few of my favorites:

The Adventures of Penrose the Mathematical Cat (plus sequels) makes a very pleasant enrichment portion of our daily maths. Each day we read one of Penrose’s stories (on subjects like Fibonacci numbers, primes, operations, etc) and do a short, related math activity.

Penrose is probably most appropriate for kids in mid to late elementary, not little ones just learning to count and add. (Note: the first story in the book was about binary, which flew over my kids’ heads.) Sir Cumference is more appropriate for younger learners.

Mathematicians are People, Too: biographies of great mathematicians. I’m not keen on the title, but my kids liked the chapter on Archimedes.

Balance Benders These workbooks come in different levels, from beginner to expert. Each puzzle presents students with a drawing of a balance with shapes on either side, and asks them to figure out, from a choice of answers, which statements about the shapes are true, eg “One circle equals two squares” after viewing a balance with two circles and four squares. (We also do logic puzzles and picture sudoku.)

 

Textbooks

I am not recommending any textbooks because I don’t have any idea which is the best. We don’t use a pre-packaged curriculum, because they tend to be expensive–instead I’ve just picked up a whole bunch of different math texts at the second hand shop and been gifted some lovely hand-me-downs from relatives. At this point I might have too many math books… I use 3 or 4 interchangably, depending on exactly which concepts we’re covering and whether I think the kids need more practice or not. I recently lucked into a volume of the “What your X Grader Needs to Know” series, and it gives a very nice overview of grade-level math expectations (among other things.)

Incidentally, the local public school math expectations appear to be:

Kindergarten: Reliably add and subtract the numbers 0-10; add small numbers to numbers between 10 and 20; be able to write all of the numbers from 0-20; count to 100.

1st grade: Place value; add and subtract one and two digit numbers with no regrouping.

2nd grade: Add and subtract multiple two an three-digit numbers.

I think they only explain regrouping in third grade.

In my experience, kids can do a lot more than that. These aren’t the standards I use in my classroom. But if you’re struggling to get your kindergartener to concentrate on their math worksheets, just remember: professional teachers don’t actually expect all that much at these ages. (And my kids don’t like doing a bunch of worksheet problems, either.)

Don’t sweat it. Do a few problems every day, if you can. Try teaching the same material from different angles, if necessary. Don’t be afraid to pull out pencil and paper and just make up a few problems and work through them together. Make patterns. Play games. Relax and have fun, because math at these ages really is beautiful.

Homeschooling Corner: The Well-Trained Mind, by Susan Bauer and Jessie Wise

Today we’re reviewing Susan Wise Bauer and Jessie Wise’s The Well-Trained Mind: A guide to Classical Education at Home. (H/T to commentator Jefferson for the recommendation.)

The Well Trained Mind is not the sort of book that lends itself to quoting, so I won’t. It is, however, an extremely practical guide to homeschooling, with specific advice for each year, from pre-K through highschool, including information on how to write highschool transcripts, grades, and prepare your kids for the academic paperwork portion of applying to college. It is a kind of homeschooling reference book. (There are multiple editions online; I purchased the one in the photo because it was cheaper than the newer ones, but you might want the most recently updated one.)

By now I’ve probably read about a dozen books on homeschooling/education, everything from Montessori to Waldorf, Summerhill to Unschooling, math and science curriculum guides for preschoolers, and now The Well-Trained Mind.

The data on homeschooling is pretty good: homeschoolers turn out, on average, about as smart as their conventionally schooled peers. (I forget the exact numbers.) They tend to be better than average at reading and writing, and a bit worse than average at math and science. Unschooled kids (who receive very little formal instruction in anything,) tend to turn out about a year behind their peers, which isn’t too bad considering all of the effort that goes into conventional schooling, but I still can’t recommend it.

The Well-Trained Mind is an excellent staring point for any parent trying to get their feet under themselves and figure out the daunting task of “OMG How do I do this?” It lays out a subject-by-subject plan for every year of schooling, down to how many minutes per day to spend on each part of the curriculum.

If that sounds too detailed, remember that this is just a guide and you can use it as an inspirational jumping-off-point for your own ideas. It’s like arranging all of the colors of paint in a nice neat circle before you paint your own masterpiece.

If you need a curriculum–either because your state requires it, or it requires you to cover certain topics, or you would just feel better with a curriculum to guide you before you leap in unsupervised, this is a very good guide. If you already have your curriculum and you feel secure and confident in what you’re doing, you might find the information in this book superfluous.

Bauer and Wise lay out what’s known as the Trivium: grammar, logic, and rhetoric.

Elementary school is the “grammar” stage. At this age, students are learning (mostly memorizing) the mechanical rules they need for education, like letter sounds and times tables. At the logic stage, children begin applying what they know and trying to figure out why things happen. Rhetoric is for the highschoolers, and since I don’t have any highschoolers I didn’t read that part of the book.

The curriculum for the younger grades is straightforward and easy to use: 10 minutes a day of alphabet/phonics for the preschoolers, increasing over the years to include spelling, grammar, reading, and math. The authors particularly encourage reading history (they have a specific order) and children’s versions of classic novels/myths.

Their approach to writing is interesting: in the lower grades, at least, children do very little generative writing (that is, coming up with and writing down their own ideas,) and focus more on copy work–trying to accurately and neatly write down a few sentences their parents give them, and otherwise expressing themselves out loud.

This stands in stark contrast to how writing is taught in the local schools, where even kindergarteners are expected to start writing little stories or at least sentences of their own devising.

This works great for some kids. My kids hate it. I think the combination of tasks–hold the pencil properly, now form the letters, arrange them into a word, spell the word properly, oh, and come up with an original idea and a specific sentence to write about the idea was just overwhelming.

So Bauer’s approach, which breaks the mechanics and creative work into two different parts, is a welcome alternative that may work better for my family.

Bauer and Wise are strong advocates of phonics instruction (which I agree with) and make an interesting point about emphasizing what they call parts-to-whole instruction and avoiding whole-to-parts. In the example they give, imagine giving a child a tray of insects (presumably fake or preserved,) and showing them five different kind of insect legs. The child learns the five kinds, and can then sort the insects by variety.

Now imagine handing the child the same tray of insects and simply asking them to take a good look at the bugs, figure out what’s the same or different between them, and then sort them. Well, children certainly can sort objects into piles, but will they learn much in the process? Let the children know what you want from them, teach them what you want them to learn, and then let them use their knowledge. Don’t expect them to work it all out on their own from scratch with a big pile of bugs.

I’ve noticed that a lot of children’s “educational” TV shows try to demonstrate the second approach. The characters have some sort of problem and the try to think about different ways to solve it. This is fine for TV, but in real life, kids are pretty bad at this. They struggle to generate solutions that they haven’t heard of before–after all, they’re only kids, and they only know so much. This doesn’t mean kids can’t have great ideas or figure stuff out, it just means they have sensible limits.

This is the same idea that underlies their approach to phonics–not that it’s wrong to memorize a few words (sew does not rhyme with chew, after all,) but that kids benefit from explicit instruction in how letters work so they can use that knowledge to sound out new words they’ve never seen before.

Whole language vs. phonics instruction isn’t quite the controversy it used to be, but there’s something similar unfolding in math, as far as I can see. Back in public school, they didn’t teach the kid the “algorithm” for addition and subtraction until third grade. My eldest was expected to add and subtract multiple two-digit numbers in their HEAD based on an “understanding of numbers” instead of being taught to write down the numbers and add them.

Understanding numbers is great, but I recommend also teaching your kids to write them down and add/subtract them.
AND FOR GOODNESS’S SAKES, WRITE EQUATIONS VERTICALLY. Always try to model best practice.

Many kids acquire number sense through practice. Seeing that 9+5=14 whether they are in the equations 9+5 or 5+9, 45+49 or 91+52, helps children develop number sense. Give children the tools and then let them use them. Don’t make the children try to re-invent addition or force them to use something less efficient (and don’t teach them something you’ll just have to un-teach them later.)

The authors recommend teaching kids Latin. I don’t recommend Latin unless you are really passionate about Latin.  IMO, you’re better off teaching your kids something you already speak or something they can use to get a job someday, but that’s a pretty personal decision.

 

Here’s how our own schedule currently looks:

After all of the holiday excitement and disruption, I feel like we’re finally settling back into a good routine. What exactly we do varies by day, but here’s a general outline:

2 Logic puzzles (I’m not totally satisfied with our puzzle book, so I can’t recommend a specific one, but logic puzzles come in a variety of difficulty levels)

2 Tangram puzzles (I like to play some music while the kids are working)

1 or 2 stories from Mathematicians are People, Too: Stories from the Lives of Great Mathematicians (Warning: Pythagoras was killed by an angry mob, Archimedes was killed by an invading soldier, and Hypatia was also killed by an angry mob. But Thales and Napier’s chapters do not have descriptions of their horrible deaths.) This is our current “history” book, because I try to structure our history around specific themes, like technology or math.

Math: multiplication tables and/or fractions

A game of some sort, like Mastermind, Fraction Formula, or Chess. (No-Stress Chess is  good teaching set.)

Science and/or social studies reading (the subjects often overlap.) I happened across a lovely stack of science, math, and social studies texts at the local used book shop the other day. When I got home, I realized they’re from India. Well, math is math, no matter where you’re from, and the social studies books are making for an interesting unit on India. In science we’ve just started a unit on Earth science (wind, water, stones, and dirt) for which I am well-prepared with a supply of rocks. (Come spring we’ll be growing plants, butterflies, and ladybugs.)

Free reading: my kids like books about Minecraft or sharks. Your kids like what they like.

Grammar/spelling/copywork: not our favorite subjects, but I’m trying to gradually increase the amount we do. Mad Libs with spelling words are at least fun.

I never manage to do as much as I want to do.

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.