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IndySchooler Notes

Copyright © 2024 by Ari Armstrong
This material originally was published between August 5, 2020, and January 1, 2022, at IndySchooler, and ported here on May 26, 2024. See also the tag-indyschooler and tag-education tags on my archives page.

Tang Math Card Games

January 1, 2022

My family has been enjoying Tang Math card games. I purchased two sets, "Home Kit Jr." for K–2 and "Home Kit Sr." for grades 3–5. (You can also buy the decks singly, but I think that's a bad deal.) These are great as math exercises; they are less fun but okay as games.

The basic idea of Kakooma is to look at a grid of five or nine numbers and find two numbers than sum (or multiply) to a third. Numtanga shows numbers or values written in different ways; the idea is to find matching numbers on two different cards.

My favorite game is Expresso. A card shows four numbers. You role a die. Then, using two to four of the numbers (or three or four of the numbers with the harder cards), you figure out a way to add, subtract, multiply, or divide to reach the value on the die. This can get quite challenging.

What we did is just go around in a circle with everyone taking a turn solving an Expresso puzzle. You can also make this competitive my seeing who can find a successful solution first, but generally that would favor the person fastest at finding such patters, so I don't think that would be much fun.

Here's another way to make the game harder and more competitive: Take turns, but each player tries to find as many solutions for each card and die roll as possible. Then, the player with the most successful solutions wins the card. In cases of a tie, the person whose turn it is (or who is next in line) wins the tie.

Bryan Caplan's Ambitious Homeschooling

September 19, 2021

Economist Bryan Caplan runs the most ambitious homeschooling program I've heard of. Importantly, his two older sons, now in college, always were interested in academics and were serious students. Caplan provided an environment in which they thrived.

Caplan's sons took numerous Advanced Placement tests starting in 7th Grade, learned Spanish thoroughly, aced the SAT, attended several college classes, and successfully placed a peer-reviewed history paper while still in high school.

Neither Caplan nor his sons were impressed by the local public schools (or, rather, they were strongly negatively impressed): "The academic material was too easy and moved far too slowly. The non-academic material was humiliatingly infantile. . . . With the noble exception of their calculus teacher, my sons' high school teachers just showed videos and treated teens like babies."

Caplan's sons did very well with college admissions and scholarships. Yet, surprisingly (to me), "they were waitlisted by Harvard and Columbia, and rejected by all the lesser Ivies."

For those interested in homeschooling and in education generally, Caplan's review, and his previous remarks on the subject, are well worth perusing.

Lenticular Printing

September 19, 2021

You know those bumpy images that appear to move or change colors as you tilt them? What are those, and how are they made? When my son asked me that I had only a rough idea. So we looked up a couple of videos to explain the production process for this lenticular printing. Wikipedia has a page too.

Golden's Mines Museum of Earth Science

September 3, 2021

The Colorado School of Mines in Golden, Colorado, has a great two-level museum of earth science, free to enter. Mainly it's a collection of exotic and interesting minerals, with some fossils, mining equipment, and other items thrown in.

Younger kids probably won't be too interested in looking at minerals for long stretches of time. However, the museum has a fun scavenger hunt set up where children can locate toy donkeys hidden in the displays. And downstairs children can walk through a fun "mine shaft" and complete a mineral puzzle. I think most kids would find the museum fun for at perhaps an hour or two. Older kids and adults with an interest in minerals may want to stay much longer.

Golden is a lovely town to walk around, with a creek and many pleasant statues along the streets and walkways. And various restaurants are within a twenty-minute walk of the museum. So the museum could become part of a fuller field trip.

Core Knowledge Releases New Language Arts Materials

September 3, 2021

Core Knowledge Language Arts On August 24, 2021, Core Knowledge released new language arts materials for sixth grade. Although most of the material relies on additional books, included in the set is a reader on ancient Rome and another on social justice. The works are in draft form; I don't know when the final versions might be released.

I'll note as an aside that, in my view, the reading by Ida Tarbell on Standard Oil (in the work on social justice) is basically wrong. For a corrective, see Alex Epstein's history.

Gustafson's Introduction to Montessori

August 7, 2021

Mike Gustafson, who founded the Massachusetts Montessori Atlas Academy, sat down with Jon Hersey to discuss his school and its approach.

The Montessori approach, says Gustafson, recognizes two key principles. First, "children . . . are forming themselves. They are doing the work. No one else can do it for them," although adults can "help them with it," of course. Second, an appropriate environment matters "to help them grow and develop to reach their full potential."

Gustafson says that Maria Montessori looked for materials "not only to attract [children's] attention, but to direct it toward some purposeful end."

I'm very sympathetic with this general approach. I have wondered if the Montessori approach can sometimes be too rigid and formalistic. For example, this morning my six-year-old built a Lego kit with my wife. Isn't that as developmentally helpful as the standard Montessori materials? How flexible and adaptive is the Montessori approach?

Gustafson addresses this question indirectly by discussing his son's fascination with cars; he is learning the names and even the speeds of different cars.

Hersey suggests that many people have the opposite concern, that Montessori does not provide enough structure. That hasn't been my concern, as I've been more drawn to self-directed learning. Gustafson says the structure within Montessori helps a child develop agency. "The external structure in a Montessori environment matches the internal needs of a child," he says. On the other hand, he says, certain sorts of "structure," such as requiring children to do work that is too easy or hard for them, or that they're not interested in, are unhelpful.

I've hit only a few highlights of the discussion here; the entire exchange is well worth a listen.

Core Knowledge Releases U.S. History Texts

July 28, 2021

Core Knowledge has released a two-volume U.S. history aimed at students grades 7 and 8. Although I have not yet had a chance to review the materials, I'm optimistic that the set will fit in nicely with my homeschool materials. Like many other Core Knowledge books, this set is available for free pdf download. See also my post on Core Knowledge books for grades 1 through 8.

Endlings Explores Family Themes

July 28, 2021

It's a rare film or television show that appeals both to young children and to adults. Endlings (Hulu) is one such show. It's excellent.

Set in the near-future, the show tells the story of a man who cares for four foster children, each with a unique set of problems. This is the thread with rich themes of building family and dealing with loss that will keep adults as well as children interested. The second-layer story involves a space alien who travels around the galaxy picking up the last surviving members of species heading to extinction. In this future, elephants are in big trouble. The humans and the alien join forces to save exotic animals (mostly escaped aliens) and to thwart the meddling of a woman with darker motives.

The production is high quality, and the acting is consistently good—especially that of Neil Crone, who portrays the foster father. I genuinely enjoyed the entire series (two seasons), and I felt good letting my six-year-old absorb its thoughtful and positive messages.

Chris Edwards on Education Reform

July 28, 2021

In a recent podcast episode with Michael Shermer, Chris Edwards, a teacher and author, points out that online resources can take the place of many in-class presentations. He's obviously right about that, but he's not too specific (at least here) about what future role he sees for classrooms and teachers. My sense is that teachers should use classroom time for things obviously done better in groups, such as certain sorts of science projects. I think that classroom math instruction often is useless but that one-on-one tutoring always will be helpful, especially for students falling behind or with special needs. I suppose that certain sorts of math lessons are especially amenable to a group setting. (Interestingly, at this moment, my six-year-old is watching newly released Generation Genius videos on K–2 math, which are quite good.)

Edwards also points to the obvious truth that measuring educational results by time that students spend in seats is absurd. What matters is mastery. My own sense is that students waste an enormous amount of time in classrooms. I think that, especially in younger grades, students should spend limited time in deep concentration learning the traditional subjects and spend the rest of the day playing and working on their own projects. That's basically the approach I take in homeschooling.

I found Edwards's remarks thought-provoking; it's a long discussion, but some people will be interested in the entire exchange.

Brook, Gorlin, and Girn on Parenting

July 11, 2021

Yaron Brook recently hosted psychologist Gena Gorlin and education attorney Rebecca Girn to discuss parenting from an Objectivist perspective.

They discussed the extraordinary value of witnessing a little person grow up and develop.

They also discussed how parenting can go wrong. Girn described how some parents treat their children as subordinate to their lives in some way, as by expecting a child to carry on the family business or to pursue the values the parent missed or neglected.

The three confronted the challenges of parenting. Girn said, "I think you have to want it [parenting] in the fullness of what it actually is, and it's not always pretty or romantic."

All three waited a period of years after getting married to have children and discussed the advantages of doing so.

Parenting can be a springboard to self-development. Girn said parenting "pushes you tremendously as a person; you really live up to your children and try to be your best self because of your children."

Gorlin added, "When it becomes the kind of hardship that you've embraced because you've done some of that thinking and simulating ahead, and have realized, yeah, this is a worthy challenge, then all of the complexity and all of the struggle becomes inspiration, it becomes fodder for growth."

People who find themselves thrown into parenting also can succeed, Gorlin explained, "depending on, at that moment in time, how do they think about it and embrace it, and do they lean in, and does it really blossom into a great love and major life project for them."

Another benefit of parenthood is reconnecting with the world through a child's eyes. Brook said, "Children actually help you start noticing things about the world that you take for granted."

Girl aptly described the major goal of parenting: "The simple thing is, you want your child to grow up. You want your child to be independent. You want him to be the person that he wants to be, that he feels fulfilled in life. . . . What I'm trying to do as a parent is give [children] everything that they need to be able to make good choices that are authentic, independent choices, and to set them up for success."

Girn also offered a great insight on "virtue education" for young children: "The issue for me with my children is I want them to have values. . . . I want them to have things that they love and care about. . . . I want them to connect with something and be purposeful about it, and kind of lose themselves in it. And I think the seeds of virtue are all kind of wrapped up in that." She said overt "morality training" at a young age "can go down a really bad path of basically indoctrination." Morals, then, should be taught mostly implicitly and through modeling at a young age.

An especially great segment (starting at 1:41:53) addresses "authoritarian" parenting versus the fostering of self-discipline.

Previously, Brook interviewed Matt Bateman (Gorlin's husband) on education. Elsewhere, Bateman and Ray Girn (Rebecca's husband) talk about education and agency.

All three people approach parenting and their careers from the perspective of Objectivism, Ayn Rand's philosophy. Yet one need not have knowledge of those ideas or general agreement with them to appreciate the speakers' insights, which apply broadly. The entire discussion is well worth watching for potential and current parents.

Horwitz on Economics

June 28, 2021

In my view, Austrian economics is a great place for students to start because it focuses on the logic of economic activity rather than on mathematical modeling or statistical analysis. And most of what goes by the name "Austrian economics" just is economics and is compatible with mainstream economics.

Steven Horwitz has written a short (and free!) book on the subject that would be appropriate for advanced high school students (as well as for adults). And Horwitz recorded seven short lectures to accompany the book.

There are some peculiarities that people should be aware of. Austrian economists tend to be free market advocates and less supportive even than other economists of government interventions in the economy. The school of economic thought tends to be associated with libertarian politics. Horwitz's book is published by the libertarian Cato Institute. If you're into that sort of thing, you might especially enjoy Horwitz's book; if not, you might be especially keen to balance Horwitz's presentation with material from other schools of thought.

Last year I had the opportunity to host Horwitz on my podcast to discuss his book on Hayek and the family. That was a lot of fun. Yesterday (June 27), I was saddened to learn, Horwitz had succumbed to cancer. So I've been thinking about him and was reminded of his introductory materials on Austrian economics.

When I was a high-school student, I learned introductory economics from two main sources: Milton Friedman's Free to Choose and Henry Hazlitt's Economics in One Lesson, both libertarian classics. Unfortunately, I don't know of a comparable introductory text from a more-mainstream perspective (although I suppose there is one).

If you're looking for something more mainstream, Khan Academy has quite a lot of material on economics. And Marginal Revolution University, produced by Tyler Cowen and Alex Tabarrok of George Mason University, has loads of videos and other materials. Although Cowen and Tabarrok definitely are libertarian-leaning, their approach to economics is solidly mainstream (and they have out a well-regarded college textbook too). Especially for students who prefer video presentations and want to learn about economics, I'd start with MRU.

Steve Spangler's Science Effect

April 28, 2021

I love Steve Spangler's science shows. More importantly, my five-year-old loves them. Recently I had a chance to talk with Spangler about his work, his views on science education, and his professional response to the pandemic. (My child joined for a few minutes!)

See also Spangler's DIY Sci show (broadcast or streaming) as well as the Spangler Effect, and Sick Science on YouTube.

Shafik on Socialization

April 17, 2021

Michael Shermer hosted a fascinating discussion with economist Minouche Shafik, mostly about welfare policy but partly about parenting and education. (I won't address the political issues here.)

Starting at the 50:44 minute mark, Shafik discusses education and parenting. She first points out that the "old education model" in which people are educated from around the age of six to their early twenties doesn't apply very well to the modern world, in which people tend to work more years and tend to need additional education and training later in life.

A bit later she says that kids "benefit enormously from having their fathers around at a young age."

Shermer asks Shafik (around minute 56) about the balance between active parenting and parents (especially women) working. Shafik says the question brings her into "very controversial terrain." Yet her read of the research is that "parents really matter in the first year." But "after the first year" to eighteen months, "it's really good for children to play with other children, to engage with other adults."

Shafik continues, "The studies show that children who are in daycare after the first year-and-a-half perform better in terms of educational outcomes and social and emotional behavior than children who are at home." She points to Germany, where (she says) the government subsidized people staying home longer with their children and educational outcomes fell.

I haven't read the studies in question, but offhand I worry about correlation-causation issues. Generally, I'd expect that married parents who put their children in daycare to be educated, career-oriented go-getters. So their kids probably do well regardless. But, where kids have challenging or not so great home lives, I'd expect the shift to organized childcare to often be better for the child. Anyway, I expect it's probably simplistic to conclude that sending a child to daycare at eighteen months necessarily is better for the child (not that Shafik concludes that). I expect that individual circumstances matter enormously.

The obvious issue for homeschoolers is that sending children to daycare or to formal school hardly is the only way to expose kids to other children and to other adults. Generally, "homeschoolers" do many activities outside the home with other families. And of course kids can interact with many adults other than classroom teachers. There's an enormous difference between literally sticking a kid at home with little outside social interaction and "homeschooling" in the sense of actively engaging with the broader world and the people in it.

In households with a single working parent or with two parents who work outside the home, homeschooling often isn't practical. Most homeschooling parents I've met work flexible hours from home, work part-time, or work in the household (without a paycheck). Homeschooling becomes easier for many families if one or both parents can work (for a paycheck) from home, which is becoming more common.

Sum Swamp with a Twist

November 8, 2020

Sum Swamp is a great game for young children just learning to add and subtract. There's just one problem: Because, as written, the outcome depends completely on luck, the game isn't very fun. But there's a simple way to modify the directions to add an element of strategy and make it a vastly better game.

The basic setup is that you move your game piece through the board based on the dice you roll combined with some space-specific operations. On each turn you roll two number dice plus an operations dice (addition or subtraction).

The strategy variant is simple: After a player rolls the three dice, the player may re-roll (once) any or all of the dice. Usually a player can improve his roll considerably by doing this, but occasionally a player may have to live with a worse outcome. This also speeds up the game. I'd limit the re-roll only to a primary roll. For example, if a player lands on a space marked "even" or "odd," a player has to roll an even or odd number (respectively) to leave the space; I wouldn't allow a re-roll in those special cases.

You could play the game with (up to) four young children with adult oversight. My wife and I play the game with our five-year-old, and we have him calculate the rolls for all of us. It's really good practice for adding and subtracting numbers up to six, and, with the rule variant, it's fun to play.

The Heinemann Science Series

November 6, 2020

I really love the Heinemann "InfoSearch" science series; unfortunately, the books are no longer in print. You might be able to pick up some of them used, though, as through Amazon or eBay.

Each book is 32 pages and filled with solid information, simple experiments, and historical context. The pages are laid out nicely in full color.

If I find another in-print series I like as well I'll write about it; for now I feel fortunate that I was able to collect ten books from this series. My five-year-old loves them.

Reading Life on Earth

November 2, 2020

David Attenborough's 1979 Life on Earth takes readers on an amazing journey through the history of life and its varieties today. The book (of which many used copies are available) contains many remarkable full-color photos of living creatures, making it accessible even to younger children.

After flipping through all of the photos with my five-year-old son, who has a budding interesting in biology, and reading a few random sections, we decided to read the entire book slowly, a page or two per day. The book is a little over 300 pages, so we'll be done within six months to a year. Of course older children can read it on their own.

The text is beautifully written, although it's laid out in fairly dense and small type. I have a hard time reading it aloud for long periods of time. But handing a page or two at a time works great for my eyes as well as for the kid's attention span. I recommend the book (regardless of whether one agrees with Attenborough's politics, which he discusses elsewhere).

Free Gutenberg Ebooks for Young Readers

November 1, 2020

Project Gutenberg makes available, at no cost to users, an extraordinary number of out-of-copyright books in various ebook formats. Here I round up links to famous works suitable for young (and older) readers.

Those looking for a longer list of books than what I offer here can see Open Culture's list of 800 free ebooks. See also Open Culture's list of Harvard Classics, the volumes of which are available through Internet Archive and Project Gutenberg. And see Project Gutenberg's Bookshelves (collections of related books) and Bookshelves for Children.

Fiction

Pride and Prejudice, and other works, Jane Austen.

The Wonderful Wizard of Oz, and other works, Frank Baum.

A Little Princess, Frances Hodgson Burnett.

Don Quixote, Cervantes.

A Christmas Carol, and other works, Charles Dickens.

Great Expectations, and other works, Charles Dickens.

The Brothers Karamazov, and other works, Fyodor Dostoyevsky.

Crime and Punishment, and other works, Fyodor Dostoyevsky.

The Count of Monte Cristo, Alexandre Dumas.

The Man in the Iron Mask, Alexandre Dumas.

The Three Muskateers, Alexandre Dumas.

The Iliad and Odyssey, Homer.

The Hunchback of Notre Dame, Victor Hugo.

Les Misérables, Victor Hugo.

Ninety-Three, Victor Hugo.

A Doll's House, Henrik Ibsen.

An Enemy of the People, Henrik Ibsen, translated by R. Farquharson Sharp.

The Call of the Wild, Jack London.

White Fang, Jack London.

Boule de Suif, Guy de Maupassant. This work also contains many other short stories by the author.

Anne of Green Gables, L. M. Montgomery.

The Scarlet Pimpernel, Baroness Orczy.

Pollyanna, Eleanor H. Porter.

Chantecler, Edmond Rostand, translated by Gertrude Hall.

Cyrano de Bergerac, Edmond Rostand, translated by Gladys Thomas and Mary F. Guillemard.

The Romancers, Edmond Rostand, translated by Barrett H. Clark.

A Midsummer Night's Dream and the complete works of Shakespeare.

Romeo and Juliet and the complete works of Shakespeare.

Frankenstein, Mary Wollstonecraft Shelley.

Antigone, Sophocles, translated by Francis Storr. This set also includes Sophocles's two other famous "Theban" plays.

Dracula, Bram Stoker.

The Adventures of Huckleberry Finn, Mark Twain.

The Adventures of Tom Sawyer, Mark Twain.

A Connecticut Yankee in King Arthur's Court, Mark Twain.

The Prince and the Pauper, Mark Twain.

The Importance of Being Earnest, Oscar Wilde.

The Picture of Dorian Gray, Oscar Wilde.

Nonfiction

Note: I'm including certain fictitious works in this category, such as The Republic and The Aeneid, because people typically read them for insights into history.

On the Origin of Species, and other works, Charles Darwin.

My Bondage and My Freedom, Frederick Douglass.

Narrative of the Life of Frederick Douglass.

The Souls of Black Folk, W. E. B. Du Bois.

Autobiography of Benjamin Franklin

Republic, and other works, Plato.

The Wealth of Nations, Adam Smith.

The Aeneid, Virgil.

The Boyhood Adventure of Stone Fox

October 31, 2020

Ten-year-old Willie has a heap of problems. His grandfather and caregiver, distraught over the likelihood of losing his Wyoming potato farm, is bedridden. Willie's doctor friend urges Willie to leave his grandfather to the care of others and abandon the farm. The local banker sees selling the farm as Willie's only way out.

But Willie is not ready to give up hope. Can he work the farm himself? And can he raise the funds necessary to save the farm? That is the adventure that John Reynolds Gardiner takes us on in his 1980 short novel Stone Fox.

One day at the store Willie sees a flyer for a sled race. The entry fee is substantial, the prize money impressive. Willie and his dog Searchlight run their sled expertly and know the local terrain well. But can a young boy and his maturing dog really compete in a race with the best sled runners around, including the formidable Native American Stone Fox? That is the heart of Gardiner's story.

This is a great adventure story for children (and adults). It is not very realistic on several levels, starting with the grandfather's psychology. So it is best taken as allegorical, with a spoonful of suspended disbelief.

Willie embodies independence, determination, grit, and heroism. Searchlight is the hardest working and most loyal companion a boy could hope for. And Stone Fox proves a daunting opponent.

A warning: the ending is intense. When I read the story aloud I stopped mid-sentence and had to pause before continuing.

I learned about this book from Van Damme Academy's reading list, and I heartily endorse it.

Fall Leaf Colorings

October 25, 2020

My wife did a very simple and fun leaf coloring project with our son. Gather up some Fall leaves, put them between paper, and use the side of a crayon to capture the outline and texture of each leaf. The colorings make great seasonal cards.

Fun Halloween Stories

October 23, 2020

It's nearly Halloween! My five-year-old loves hearing spooky stories—just not too spooky. I thought I'd share some of our favorites.

For the youngest readers, Here Comes Halloween is not scary at all; it's about dressing up in costumes.

Two of my five-year-old's favorites are Five Little Pumpkins and Five Black Cats. The stories are fun to chant in rhyme. "The second one said, 'There are witches in the air!'"

Goodnight Goon is a funny spoof of Goodnight Moon. "Goodnight claws and goodnight jaws. . ."

Although it's only superficially about Halloween, Room on the Broom is a standout. Julia Donaldson is a gifted author of children's books, and Axel Scheffler adds colorful and fun illustrations. The story begins, "The witch had a cat and a hat that was black, and long ginger hair in a braid down her back." The story is about making friends and coming to your friends' aid. The short film at Amazon based on the story also is excellent.

When I was a child I loved listening to the Disney recording of Haunted Mansion. Featuring the voice of Ron Howard, the story follows a couple who enter a spooky mansion during a rain storm only to find themselves on a ghostly tour. It's a little scary, but the ghosts expressly don't hurt people. Listening to the story with my child brought back many of my own childhood holiday memories.

A Simple Dice Game for Adding and Subtracting

October 4, 2020

The dice game Yatzee is great for older children to work on sums. But what about younger children? Yahtze is just too complicated for those just starting out with math. I toyed with the idea of modifying Yahtzee for younger children but came up blank. But then I hit upon a simple two-dice game that my five-year-old has enjoyed.

Here is the simplest version of the game. A player roles a single die to determine the action and then rolls two dice to determine the score for the turn. The first role sets the scoring rule as follows, as applied to the subsequent roll of two dice:

1. Add the numbers (the top numbers in all cases).
2. Subtract the numbers.
3. 0 points.
4. Multiply the numbers (simpler variant: Double the larger number showing).
5. Double the sum of the numbers.
6. Lose 5 points.

Then you add the score from your turn to your total score. That's basically it. Players take turns and either play until one player surpasses a certain total score within a round of turns (say, 100) or until every player takes the same number of turns (say, 10).

Obviously the simple version of the game is pure luck. To add a bit of strategy, adapt the rules as follows. On the first role, the player can either accept the outcome or re-role (once). On the role of two dice, the player can either accept the outcome or re-role one die (once).

For kids a little more advanced, I do enjoy Yahtzee as a family game. Such games are a fun way to give kids a bit more basic math practice.

Skepticism about Learning Styles

October 2, 2020

How much should we tailor a child's instruction to the child's preferred learning "style"? I was surprised when someone I know from the field of education, Kevin Currie-Knight, suggested that learning styles aren't too meaningful. Currie-Knight suggested a couple of starter articles: "Learning Styles as a Myth" from Yale's Poorvu Center and "The Myth of 'Learning Styles'" by Olga Khazan. (See also my podcasts with Currie-Knight.)

The Poorvu article begins, "Learning Styles refer to the idea that students learn best when course content is pitched to match students' self-reported media preferences. Endless potential frameworks for categorizing learning styles exist, but the most popular one divides students into three types: visual, auditory, and kinesthetic learners. . . . Yet the overwhelming consensus among scholars is that no scientific evidence backs this 'matching' hypothesis of learning styles. . . . While all learners can develop subjective preferences for studying or digesting material, studies deny that students learn better through a self-reported learning style."

The article does not deny that there are such things as learning styles. Instead, it suggests, "Students benefit when instruction provides various ways to enter into learning. . . . Instructors can incorporate active learning, group work, and inclusive teaching strategies to invite students to engage their full faculties and experience peer learning. . . . Research shows . . . that students learn more deeply from words and visuals than from words alone."

Khazan goes through some of history and research surrounding learning styles. She summarizes, "A lot of evidence suggests that people aren't really one certain kind of learner or another." Moreover, according to one study she cites, "continually accommodating [an] auditory learning style" may actually do a disservice to some students by not sufficiently "strengthening their visual word skills."

I appreciate psychologist Daniel Willingham's advice (as Khazan quotes): "It's much better to think of everyone having a toolbox of ways to think, and think to yourself, which tool is best?"

How does all this square with my personal experiences? I guess I took it for granted that different students have different learning styles, but it doesn't especially surprise me that "the literature" seems not to support tailoring instruction to a learning style.

I continue to think it is obvious that it really matters that parents and teachers take into account a student's particular needs. For example, some students enjoy (or at least tolerate) sitting for hours with a book or workbook, whereas other students find that difficult or distressing. Some children need more physical activity than others. Some children need more time to socialize than others. At a broader level, then, different students have different educational needs.

I do very much like an integrative approach. Especially younger children need to manipulate things with their hands, which is why I like things such as counting blocks and beads. I think all of us benefit from a combination of written text (once we can read), conversation, and visual displays when learning most new things. Especially when children engage with STEAM fields, hands-on activities, such as recreating simple science experiments, are essential. Although I've always been a bit skeptical of some of what passes for "kinesthetic learning," I see a role for drama and role-playing and the like. Especially younger children learn an extraordinary amount simply through creative play. And of course physical exercise is valuable in its own right.

Generally, I think attentive parents and teachers remain aware of what works and what doesn't work for a given child and continually adjust their approach accordingly.

How to Nurture Young Readers

September 28, 2020

Reading books opens a world of knowledge, inspiration, and moral guideposts. But learning to read is hard, and reading seldom offers the immediate and continual dopamine rewards that various sorts of screen time promise. What can parents do to help their children develop the cognitive skills to read as well as a love of reading?

Lindsay Journo and Cornelia Lockitch offer an excellent introduction to the topic in their newly released talk (actually recorded last year), "Nurturing the Reader in Every Child."

Journo and Lockitch note that reading complex works of both fiction and nonfiction proves enormously rewarding to individuals, and widespread reading contributes to a flourishing culture. Yet many people read less and less as they spend ever more time hooked to their electronic devices. Although screen time can be valuable, Journo and Lockitch note, it can also displace reading.

What can parents do to help nurture the cognitive skills and interests their children need to become strong readers? "Set the right conditions from the very beginning," Journo and Lockitch suggest.

They offer three main pieces of advice: Make books available to children, make reading a focus of time spent together, and create a language-rich environment. Not only should parents make sure that children see them reading books on their own, parents should actively read with their children from an early age.

On a personal note, my wife has been reading to our child in the evenings since we brought him home from the hospital. That has been a really nice time for them to connect, learn, and share some exciting and thought-provoking stories. We read throughout the day too, of course.

I really like Journo and Lockitch's advice to tell young children simple stories about everyday events, such as going on an elevator ride and walking into a crowded and chilly room.

Journo and Lockitch see three main impediments to children becoming strong and motivated readers (aside from possible physiological issues): the allure of screens and especially the high but superficial rewards of social media and video games, "ill-considered rewards" for readers that distract from an authentic love of reading, and a failure to recognize a child's skill level and interests. On this last point, parents should not try to push a child to read a book that is too hard for the child, too thematically advanced, or simply uninteresting to the child.

Journo and Lockitch also offer some specific advice for helping young children learn the skills of reading. Unlike speaking, reading does not come naturally and effortlessly to children, they note. One bit of advice I like is to first introduce children to the sounds, rather than the names, of letters. (My wife and I did both, and in retrospect I see how the focus on the sounds was more valuable.)

Here are three activities that Journo and Lockitch recommend. Do "I spy" games for objects starting with certain letter sounds ("I spy something that starts with 'mmm'"). Ask (for example), "How many sounds to do you hear in 'sand'?" Ask, "What word is formed by the sounds p-e-t?"

Journo and Lockitch close with a strong defense of the phonics approach to reading and a spirited critique of the so-called "whole language" approach. Although I have long been convinced of the soundness of the approach that they here review, they convinced me that I need to step up phonics work with my own five-year-old.

To illustrate the issue at hand, consider how many ways there are to spell out the long "ay" sound. As one list of English phonemes shows, each of these twelve words contains the same long "ay" sound: "bay, maid, weigh, straight, pay, foyer, filet, eight, gauge, mate, break, they." (See also a pdf sheet with phenomes.) Helping a child become consciously aware of the many different ways to spell out the same basic sound is enormously helpful, crucial even.

On a personal note, I remember learning to read with basic phonics instruction from my mom. Once I got some of the basics, I pushed on without complex formal phonics work (but with implicit phonics awareness) and became a voracious reader. But obviously many kids do need some extra help with this, and all kids can benefit from a developed approach.

For older children struggling with reading, Journo and Lockitch say that more intensive intervention may be necessary. They like the Orton-Gillingham approach.

Journo and Lockitch offer a great reading list (via DropBox) for adults (about teaching kids to read) and for children.

Here I have offered but a brief and incomplete overview of this wonderful and enlightening talk by Journo and Lockitch. I heartily recommend the complete talk, including the question period, for parents of emerging readers.

Magformers Promote Spacial Reasoning

September 26, 2020

My kid loves Magformers, plastic shapes with magnets embedded. He plays with them as toys; I appreciate them because they promote spacial reasoning. You can build squares into cubes, triangles into pyramids, and combined shapes into many complex 3D figures.

They are a bit expensive. I got lucky and bought multiple sets from a family off of CraigsList. One of the sets we got has specialized shapes for building dinosaurs. My son enjoys building the dinosaurs but I don't consider those packs essential. (Magformers offers many other sorts of packs that can get quite expensive.) If I were going to buy sets new, I'd go with a basic starter pack plus perhaps a gear pack.

Update May 26, 2024: My child also likes Picasso Tiles.

Perler Beads Offer an Inexpensive Way to Visualize Large Numbers

September 26, 2020

As adults, digit placement is second nature: ones, tens, hundreds, thousands, etc. It's easy to forget that the way we now use numbers was an important cultural invention. And it's easy to forget how hard it was to learn digits as a child. One of my biggest surprises as a homeschooling dad of a kindergarten-age child has been seeing what a conceptual leap it is to grasp digit placement. It helps enormously for kids to see visually what we're talking about.

Of course it's easy to make groupings of ten coins or whatever. I've used wooden cube blocks to illustrate two-digit numbers. But doing ten stacks of ten, and then ten stacks of a hundred, can be a challenge. That's where Perler beads and pegboards come in. You can get a large set for around thirty bucks and then iron together sets of ten and a hundred. (Or you can save some effort and spend over a hundred bucks on Montessori "golden beads" if you prefer. There's also a lower-cost foam option. You can also do art projects with the Perler beads if you're so inclined.

Update, June 28, 2021: Although I do like the Perler beads for visualizing big numbers, practically speaking, I turned to the foam blocks for routine instruction. To my mind these are a must-have item for beginning math students. The beads are a little too small for counting; the blocks are just right. It occurred to me that you could also just buy a jumbo pack of wood blocks and glue them together into rows of ten and squares of a hundred. But the foam blocks come cheap and ready-made.

You can also make some great counting and adding kits out of Perler beads.

A Pocket LED Microscope Is an Amazing Learning Tool

September 25, 2020

The Carson LED pocket microscope is, for the money (less than $14), the single-best science tool I've purchased. After using a clunky old microscope with a mirror, the new microscope is a dream. I popped in a AA battery to power the light and immediately got great results. It "only" offers 120x magnification, but for kid use it's perfect. Plus it's cheap enough that I won't worry about it getting broken, so it will be great for backyard and camping use.

Just using a standard iPhone I took some pretty-good photos of a leaf, a feather, and a pen mark on paper.

Brain Quest Workbooks Make Great Supplements

September 25, 2020

If you're looking for ridiculously cheap supplementary materials for your home preK–6 curriculum, check out the Brain Quest workbooks. Honestly I don't know how they sell these lengthy (some over 300 pages), full-color (and printed in the U.S.) workbooks so cheaply—obviously mass printings help. And my five-year-old enjoys working in them. If you use these at all, for the money, you can't possibly go wrong.

These workbooks cover the basics in reading, writing, arithmetic, science, and social studies. They also have games and fun activities. My son currently is working in the kindergarten book, and he enjoys solving the mazes and tracing the letters. Although I hardly consider these a complete curriculum, they are a great and economical supplement.

I just bought the entire set at once so my kid can go through them at his own pace. You might consider buying them year-by-year, so if your child stops enjoying them you can stop buying them. Obviously parents can start with the workbook most suited to the abilities of their child (Amazon's look-inside feature is probably helpful for deciding this). I'm pretty confident my child will go through the entire set, hopefully at an accelerated pace.

The entire set of 15 workbooks consists of 8 standard workbooks (preK–6) plus 7 "Summer" transition books (which are shorter). So one possibility is to buy only the regular-year books.

Fun with Magnets and Electricity

September 24, 2020

Magnetism and electricity are strange and amazing forces. How can one object act on another object at a distance without any apparent intermediary contact? If I blow a piece of paper, I act on the paper via the breeze I create. But magnets do surprising and nonintuitive things. Although young children are not ready for the full theoretical basis of electromagnetism (I'm not even ready for the full basis), with some basic supplies they can explore how magnets and electricity operate in the world.

This is one of these projects that just costs some money. You can't print off magnets, find them in the back yard (usually), or cut them out of paper or other cheap supplies. Perhaps you can borrow supplies from a school, friend, or coop. Here I offer some Amazon links for people interested in buying supplies.

A word of warning: The items discussed here contain small parts and should not be used with children who put things into their mouths. Also, I use the supplies with my five-year-old, below the "official" age, and provide adult supervision. I'm not recommending that; use these things at your own risk!

The cheapest magnets useful for young kids are magnetic letters and numbers, which do duel-duty for spelling.

A "magnet stick" is useful to explore polarity (magnets can both attract and repel). Although I don't have this particular kit it appears to me to be a good one.

Unfortunately my favorite kit is no longer readily available (it's the "Electricity & Magnetic Combination Kit" by Popular Playthings.) But there's a kit very much like the one I have (although more expensive), the Thames & Kosmos Electricity & Magnetism Science Kit. What I really like about kits such as these is that you can power an electromagnet and hence illustrate the connection between electricity and magnetism. Also, these kits are really good for illustrating serial versus parallel connections.

My kit has a hand-crank generator; the Thames kit does not. A generator is great for showing that mechanical energy can be converted into electrical energy. You can buy a hand-crank generator independently. Just be sure, if you use this with other kits, not to crank too fast or you might burn out components.

My second-favorite kit is the beginner Snap Circuits. What I like about this set is it's well-made and it illustrates some basic electronics. My son loves the fan, which pops off and flies on its own (although that's not especially educational). What I don't like about the set is that various plastic boxes that contain complex electronics are not see-through, so in effect these are mysterious "black boxes." Still, it's a great set especially for the money.

Franny K. Stein's Warning to Overstressed Families

September 23, 2020

What happens when children and their parents overstress themselves with activities? Grandparents gave us a book that my child loved and that, once my wife explained the story (she'd read the book to our child), I had to read too. The book is from the Franny K. Stein series (which I'd never heard of); the title in question is The Fran with Four Brains. It's about one stressed out little girl.

It's a silly book but one with an important message. Sometimes Franny just likes to relax and do "regular-kid things." "But her mom wanted Franny to have the opportunity to be the best she could be, and try new things, and learn about stuff they might not be teaching in school. Franny's mom had told her that it was important to do her best and always strive for excellence." So Franny's mom enrolls her in bagpipe lessons, soccer, and a cooking class.

When Franny finds herself exhausted and overworked, she creates three robots to spread the work around. The adults don't even notice they're robots. But these robots, in their quest for misplaced "excellence," create problems of their own. Read the book to see how Franny gets herself out of this mess.

Finally Franny and her mom have a heart-to-heart in which the mom admits all the activities are wearing both of them out. She says, "I think maybe we don't have to be excellent at everything. I think we need to pick a couple of things, and we should try to pick the things you really and truly enjoy. And maybe, sometimes, we could just do nothing."

Finally they realize that this "nothing"—spending quiet time together—can be "a kind of excellence that was totally worth striving for."

A Spontaneous Lesson on Dimensions

September 23, 2020

I was working with my five-year-old in Dimensions math, and we came across an exercise that asks the students to circle all of the circles shown. Some of the shapes represent cylinders; one represents a football. Obviously the top and bottom of a cylinder are circles. But what about a football? This led to an interesting discussion about dimensions.

I asked my son to imagine a football and then imagine that the point was toward his face. What would he see? A circle! So the cross-section of the football is a circle, so he circled the football. (I added in a little note with the relevant qualifier.)

Then we had some even deeper discussions on the topic. Is the ceiling 2-dimensional or 3-dimensional? It's flat—mostly. But we have a popcorn ceiling, so it's obvious the ceiling is not perfectly flat. What about paper? At that point we actually got out the microscope to look at paper magnified. I pulled up some good imagery of paper shown under really good microscopes. Obviously paper is not truly 2-dimensional.

There was a funny moment where I explained (as best I could) that nothing in real life actually is 2-dimensional; everything is 3-dimensional. A 2-dimensional plane is a mental abstraction in which we imagine away height. My son was (momentarily) crestfallen that 2-dimensional things don't actually exist (beyond our abstractions). But, for practical purposes, we can take certain things as flat, as they're flat enough to assume flatness for the task at hand. (More technically, I'd say the concept of "flat" does not imply a lack of small-scale 3-dimensionality).

Then we also talked about the difference between a 2-dimensional shape as printed on a flat piece of paper versus the 3-dimensional object that such a drawing (sometimes) represents. To drive home this point I held up a real cylinder so we could see how its shapes appear from our momentary perspective. As printed, the "cylinders" on the paper are drawn using ovals, not circles. But those ovals represent circles of a cylinder.

This was pretty heavy-duty stuff for a five-year-old. He seemed to basically follow the discussion—although I'm sure we'll have to come back to those difficult ideas many times before they fully "stick."

Here is the broader pedagogical point: I never assume that the most important lesson is the one most obviously at hand. My kid knows what a circle is; we were just quickly pushing through the book at hand as review. But dimensionality—now that's interesting!

Dads Homeschool Too

September 20, 2020

Most parents who take lead on homeschooling their children are moms. That's fine, but sometimes the dads are overlooked. Although I've never met another dad who takes lead on homeschooling, as I do, I know such dads are out there.

Many homeschooling groups on social media are dominated by women, so much so that the presumption sometimes seems to be that only women participate. I regularly run across messages addressed to "Mamas" and invitations to events for "moms." I'm not complaining. But I would like to gently encourage homeschooling moms to remember that some of us are homeschooling dads—and to encourage the dads to actively participate.

I think people also should bear in mind that some homeschooling families have two moms, two dads, or a single parent. And, in some homeschooling families, Grandma or Grandpa or some other family member takes lead.

I do think it's common for one spouse or the other to take lead with homeschooling, even though, in two-adult households, normally both parents play a vital role. When I claim to take "lead" on homeschooling, I mean only that I play the larger role during "normal work hours." Since my wife started working mostly from home during the pandemic, she has been able to take some short breaks during the day to interact with our child, and of course she helps enormously on weekends and during evenings. It is a genuine partnership. Still, I do the research on learning materials, I handle much of the instruction, and, usually, I'm the one who takes our kid to homeschool events.

I don't see any inherent problem with couples giving top priority to the career of the more-successful partner, so long as both people embrace the situation and neither person feels overworked or undervalued. My wife has been very successful in her career, so our decisions have tended to prioritize her career. We've agreed that I'd maintain a more-flexible schedule (and make less money) and take lead on homeschooling. I'm able to pursue a meaningful career within this arrangement, plus I have a very deep interest in education, so for me the situation works out great. My wife is happy, our child is happy, and I'm happy. So why not?

If two parents are able to perfectly balance their careers and their work at home, more power to them. That's quite common when both people work full-time jobs. But, in large families and in homeschooling families, I think it's more common, although hardly universal, for greater division of labor between spouses. I don't think every family needs to look the same. I think every family needs to find that path that works for them and that "we" need to celebrate this diversity of approaches.

Of course residual gender bias in our culture means that some men feel guilty or emasculated if they play a larger-than-usual role in homemaking or homeschooling. And I think even some women continue to see "husband as breadwinner" as "normal." I think it's important for people to consciously recognize that such gender bias, whatever its source, is a load of nonsense. Women can be as successful in their careers as men, and men can be as successful with homeschooling as women.

Homeschooling comes in many flavors. We can appreciate them all.

Watching Class Dismissed

September 18, 2020

The 2015 documentary, Class Dismissed, covers the basics of homeschooling in theory and practice. My wife and I recently watched and enjoyed the film, and I would recommend it especially to people first thinking about homeschooling, new to it, or struggling with it.

The film follows one main family as the "grumpy and overworked" kids withdraw from school and the family seeks to homeschool. They struggle with it, and we watch how they change tactics over time. The film spends less time, but important time, with several other homeschooling families.

The film has a villain and a hero of history (and its selections are sensible). The former is Horace Mann, who brought the regimented Prussian system of education to the United States in the 1800s. Today, that style of education has metastasized into the "test factories" which are modern schools. Thankfully, in the 1970s, John Holt started a new movement for self-directed learning, which blossomed into the homeschooling movement. Although most states once banned homeschooling, all now allow it (with varying degrees of regulation).

The difference in basic philosophy is stark. Mann-style education sees children as receptacles to receive the knowledge and skills chosen by experts and imparted to children by an expert teacher. Holt-style education sees children as naturally curious people with complex and highly individual interests who crave and need substantial autonomy. As is obvious given that my family homeschools, I'm basically aligned with Holt.

The film shows examples of various sorts of homeschooling, although it leans into unschooling. Unschooling basically means that a child charts a unique path and decides what to do during the course of the day. I've never liked the term "unschooling," and the film suggests to me a reason why. Supposedly Holt borrowed the term from 7Up's advertising campaign claiming that its product was the "uncola." Of course that ad was complete nonsense; 7Up was and remains a cola, with almost identical ingredients to every other soda (mostly carbonated water and sugar). Whether or not the Holt story is true, it strikes me that "unschooling" has a similar problem—even the most diehard "unschooler" allows for traditional instruction. I prefer the term "self-directed learning," which allows for instruction and even for a standard schoolroom setup, if the child wants that.

One of the advocates of unschooling in the film struck me as overly preachy; the message seemed to be that if you're not homeschooling her way you're doing it wrong. To me that's contrary to the entire purpose and vibe of homeschooling. Let a thousand flowers bloom—or ten million.

The film also shows both a family that uses a rigorous classical curriculum and a private "school" for self-directed learning. So I appreciate that the film shows different approaches.

I take seriously the warning of some people interviewed in the film against "authoritarian" homeschooling. Someone mentions that around half of people who try homeschooling drop out within the first year. The film suggests, and I think this is probably right, that the reason most people fail (who do) is that the parents basically try to recreate standard school in the home rather than give self-directed learning a chance.

I am in a different position than many homeschooling families. I do think that regular school seriously messes up some children and pounds their natural love of learning out of them. My child is only five and has never attended regular school. So some people have transition problems that my family just hasn't had to deal with. The film discusses the idea of "deschooling" upon leaving school—giving children a chance to decompress and rediscover their own interests before getting serious about any alternative education program. (Professor Kevin Currie-Knight also discusses this in my podcast episode with him.)

Hopefully the film will give hope to struggling homeschooling families with its portrayal of children successfully making their own decisions. I love this line from one of children interviewed: "It's fun to learn without having to learn."

A Day in the Life of an Independent Learner

September 18, 2020

The more I witness independent learning in action, the more I am convinced that children can successfully chart their own paths. Yesterday I wrote an essay, "Fostering Kids' Autonomy Works," on this topic. This is a follow-up to describe my son's self-directed adventure yesterday.

My wife, who had the day off, again took lead on homeschooling. (So this was not a typical day; usually both of us parents are busier with our own projects.) She started the day by asking our child what he wanted to do during the course of the day. He initially laid out three projects on a chair: a magnet kit, a card-matching game, and a dinosaur 3D wood model kit. Then he added a Lego T-Rex kit and a printed 3D figure set that a friend had given us.

Then it was time for breakfast, and my wife asked our son if he wanted to help make it. He said yes, and together they made pancakes out of a recipe book that a relative had given our son as a gift. (Our child is interested in cooking, so we try to foster that.) To help make the pancakes, my son had to work with measurements and simple math.

Then, all of his own accord, my son played the card-matching game with my wife for half an hour. This is a good memory exercise. Then our son colored a print-out for a 12-sided shape, and my wife helped him cut it out and glue it into the 3D shape. That took around an hour. He spent another hour working with a magnet kit. Then he spent a solid 2.5 hours building the Lego T-Rex. That is extraordinary concentration. (I wrote more about Lego kits elsewhere.)

Then our child obviously was getting tired, so we agreed that he could watch TV. He chose something about mechanized "dinosaurs." Then, as a family, we watched the original Pete's Dragon and discussed aspects of it. Our son closed out the day watching some science videos and then reading with Mom. (He never did get to the wood kit.) Obviously self-directed learning does not mean learning in a vacuum. We've collected lots of materials for possible projects for our son to do based on his interests. We sometimes suggest projects he might be interested in and also help him with his projects. As I've written, self-directed learning is compatible with, and I'd even say dependent on, interactive parenting.

In short, this was an extraordinarily productive day in terms of my son's education. He was basically in charge of crafting his day at every step, and he thoroughly enjoyed his day. Self-directed learning works!

In Praise of Lego Kits

September 18, 2020

Lego kits help kids develop spacial reasoning, learn to patiently follow detailed directions, and grasp some basics about mechanics. They provide a great opportunity for parents and their children especially at younger ages to work on a project together. And kids end up with fun toys.

Various themed lego kits (dinosaurs, space exploration) also present an easy segue to lessons about science.

Although some of the kits recommend ages 7–12, my son started working with them (with adult supervision) at age four. Just be sure kids have gotten over putting small objects in their mouths! Use at your own risk.

A couple of my son's favorite kits involve dinosaurs and spaceships (paid links). One thing I really like about the T-Rex kit is that it has some interesting hinges and ball joints to allow movement.

Films for Kids

September 18, 2020

Here I briefly review a few films that my family has enjoyed and that I think are great for kids.

Coco, 2017: Coco is a strange but wonderful film that draws on traditions surrounding the Day of the Dead. The mythic background is that, after people die, they enjoy an afterlife so long as people living still remember them. Our hero is a young boy who, wanting to explore his love of music, visits this land of the dead in search of an ancestor who was a great musician. But things are not as they seem, and the boy must race against time to put right past wrongs. The film explores the value of family and the importance of doing what you love. The animation is amazing; my five-year-old was enthralled.

Mary Poppins, 1964: This is one of the absolute all-time great musicals and children's films. Although I also enjoyed the sequel, to my mind nothing can match the magic of the original film, led by the amazing Julie Andrews and Dick Van Dyke. The story is a simple one of a father learning to relax a bit and enjoy time with his children. The songs and performances are excellent, and animation blends perfectly with the live action.

Pete's Dragon, 1977: I rewatched this film with my five-year-old and had forgotten how violent it is! It shows threats of child torture and enslavement, child abuse (a teacher beats a child in class), and public drunkenness. It also has some wonderful songs and a great story about friendship and family. The basic story is that Pete, having run away from a brutal family that had enslaved him, finds a new home with a kind woman who runs a lighthouse. Oh, and Pete has befriended a dragon that can turn invisible. When a snake-oil salesman comes to town, he sets his sights on capturing the dragon. We paused the film a few times to discuss child abuse, drunkenness, and snake-oil products.

Parasitism in Nature

September 16, 2020

If you're looking for a creepy science lesson, check out parasitism in nature.

There's a type of fungus that takes over an ant and causes the ant to crawl up a branch and latch on, where the fungus grows and spreads. Different types of fungus can attack different animals.

Wikipedia has an entry. The Atlantic and National Geographic also have articles.

National Geographic has a short video about this. BBC has another video.

Deep Look has a good video about a fungus that attacks a fruit fly.

But ants don't always get a raw deal from fungus. Some types of ants farm fungus for food (Deep Look again).

There's also a parasitic worm that takes over a snail and causes the snail to turn into a colorful and easy-to-grab treat for birds. Then the worm reproduces inside the bird. See Wikipedia or Wired for articles, or see National Geographic for a video.

National Geographic also has a video about a type of wasp that invades a caterpillar.

MoMooMath offers various examples of parasitism.

StoneAgeMan has a video about mutualism, commensalism, and parasitism.

Tactile Triangle Fun

September 16, 2020

My five-year-old had fun playing with foam sheet triangles I cut out—and we even introduced Pythagoras's theorem for right triangles.

I was inspired by some sample materials offered by Math Expressions). One thing this source recommends is to discuss the difference between "turning" a triangle piece and "flipping" the piece.

I made up some right triangles with sides of lengths 3, 4, and 5 inches, and I figured I might as well work this up into a lesson about Pythagoras. Before I did this, we measured the sides of different triangles to see that the longest side is not always a round inch (when the other sides are round inches). So the 3-4-5 triangle is a special sort of triangle.

By cutting out and marking squares with sides 3, 4, and 5 inches, we could see that the square of the shortest side, plus the square of the middle side, is equal to the square of the longest side. I did not try to write down the formal equation or to demonstrate the universality of the theorem. This is just an illustration of the theorem for a particular triangle. But at this stage I thought that was the perfect level of complexity.

We also peaked at some basic facts about Pythagoras and looked up on Google maps where he lived.

You could use card stock for your triangles. For this, though, I really like the feel of foam sheets. The foam pieces stick to each other just enough to be helpful.

Tips for Keeping Your Kids Safe on Social Media

September 14, 2020

Although I think the documentary The Social Dilemma is overly alarmist (as I've written elsewhere), it raises legitimate concerns about children's use of social media. In one dramatized scene of the film, a girl posts a photo of herself to social media and someone makes fun of her "big ears," leading to her crying in the bathroom. Social media use can lead to (or at least exacerbate) bullying, addiction, self-image problems, self-harm, and conspiracy mongering. What can parents do?

The psychologist Jonathan Haidt (who appears in the film) recommends three main steps for parents: Forbid all devices at least 30 minutes before bedtime, forbid social media until high school, and limit total daily device use.

In the film, Haidt suggests talking with kids about their daily use. Haidt notes that, when asked, most kids will give a pretty reasonable answer for how much time they should be spending on their devices in a day—perhaps a couple of hours at most. The problem is that kids, like all of us, can lose track of time and end up totally surprised by how long we actually spend on social media. This is why talking about and enforcing daily limits can be a good idea.

In a Twitter thread (and related talk), Haidt offers some statistics to support his recommendations. He points to "the sudden and sharp rise of depression and self-harm among U.S. teens, especially girls, after 2011." This is obviously concerning (even though longer-term trends show a decline in teen suicides in the years following the late 1980s prior to the more-recent rise).

My kid is only five years old, so I haven't had to deal with the pre-teen and teen social angst yet. I have had to deal with general screen time issues, however, and this has led to some discussions and policies surrounding content and access.

My general plan is to set some firm limits supported by real data and to explain in detail the reasons for our household policies. I have already had many discussions with my child about why a developing body and brain need physical activity and real social interaction. I try always to come back to the principle, "My job is to help you develop into a successful, thriving adult, and so that's why . . ."

The only sort of social media in which my child engages at this point is YouTube, on which I set tight limits. On his tablet device, I approve only certain (educational) YouTube channels. When we watch YouTube together on the "big screen," I routinely explain to my child the nature of advertising. "Why are they showing you this?" I ask. He already understands at a basic level that people spend money on advertising to try to get other people to buy stuff or behave differently.

My hope is that, by the time my child finds himself in the pre-teen social stew, we will have had enough conversations about advertising, social pressure, bullying, addictive behaviors, predatory behaviors, brain development, and (simplified) evolutionary biology that we'll be able to slowly and safely expand his use of the internet, until the point when finally (in high school) he'll be ready for Facebook and the like. I'm trying to build the foundation for healthy online behaviors now. We'll see how well this all works out—so far I'm hopeful.

September 23, 2020, update: For a much more positive view of kids using technology, including social media, listen to Jordan Shapiro's remarks. Shapiro argues that it's probably a good idea to introduce such technology to children when they're younger but that adults should monitor use.

Incidentally, you can also use foam sheets to make up your own fraction wheels.

Tabletop Dinosaur Dig

September 13, 2020

Grandma brought the five-year-old some plaster blocks with little toys inside. Surprisingly, my kid loved digging out the toys. (This would drive me crazy.)

Of course you could get some plaster and molds and make your own kits. Once our initial supply ran out, we just ended up buying a 12-pack of blocks from Amazon (paid link). I like this particular product because the "bones" are also decent-quality plastic toys.

My kid spent around four hours (!) over two days digging out one set of "bones." I regard that as cheap entertainment—and a nice break for parents. And you can integrate the project with some actual science education about dinosaurs and paleontology.

Here we're watching actual scientists digging out actual dinosaur bones at the Denver Museum of Nature and Science.

One-Off Science Videos

September 10, 2020

Elsewhere I've discussed some science video programs that my child and I really like. Here I want to list some fun one-off science videos we've found.

Bats and White Nose Syndrome: This article and TedEd video discusses a fungus that attacks bats in North America. The video is more general.

How a Piston Works: The piston in a gasoline engine is a wonderful example of the conversion of chemical energy to motion. Good videos on this include those from Toyota of Orlando, Automotive Basics, and Yasha Verma.

The History of Steel: Jason Crawford gives an hour talk on the subject.

A Five-Minute History of Concrete: Jason Crawford gives a great five-minute history of concrete (embedded in a longer video; I'm included the appropriate time stamp for the start point).

How to Make Charcoal: This is a really fun video by Primitive Technology, via Jason Crawford.

Great Science Video Series

August 31, 2020

Like many parents, I have struggled with how much screen time to allow my child. What I've settled on is tightly limiting "junk" TV and videos but allowing moderate amounts of quality videos. At this point I do not merely tolerate screen time; I actively welcome it as an important contribution to my child's education. Here I want to briefly review several high-quality science series that my five-year-old absolutely loves.

Mystery Doug

Mystery Doug is a series of over a hundred science videos produced by Doug Peltz and the team at Mystery Science. The videos are available at no charge through YouTube and Mystery Science's web site. When viewed through the web site, which (I think) requires free registration, the core videos accompany supplementary materials.

My child loves these short videos, and so do I. The set-up is that Doug introduces some mystery of nature—"Where does salt come from?", "Why are flamingos pink?"—then explains the context of the question and gently guides viewers to the answers. What I especially like about Doug's approach is that he doesn't just tell students the answers; instead, he encourages students to draw on what they already know and on new information to anticipate the answers. So the videos are not just about knowing what scientists know but thinking how scientists think.

One video that I especially liked and learned a lot from is Doug's explanation of why Pluto is not a planet.

My family also has a household subscription to Mystery Science, which takes the same basic approach, and which we also really love. Some of that material is available at no cost. As of this writing, the cost for a year's homeschool membership is $49, which I regard as absurdly cheap. It's a great deal.

A disclosure here: I personally know one of the people involved with starting Mystery Science. I get no financial benefit from praising its programs.

Here is a fun anecdote: After watching Doug's video on airplane flight, I wrote in to the company to complain that the information didn't comport with what I believed. Turns out I was wrong, and Doug was right. I thought the curved-wing airfoil is more important to lift than it actually is. The curvature does have some effect (which I won't try to describe here), but simply the angle of the wing plays a huge role. So Doug's video is not comprehensive but it's correct as far as it goes. Anyway, this is one video out of scores.

Thanks to Doug and his staff, my child has developed important insights into the workings of the natural world and the methods to learn more about it.

It's Okay to Be Smart

Joe Hanson's It's Okay to Be Smart, a YouTube series of over 300 videos (and counting) produced by PBS, is another of my child's favorites. Sometimes Hanson meanders into current events—for example, he has several videos about COVID-19—and I'm okay with that.

Although I've personally watched only a few of these videos, I am consistently impressed with them. These are aimed at a more mature audience than are Mystery Doug videos, but that hasn't bothered my five-year-old at all.

Deep Look

Deep Look, another PBS series available through YouTube, is not squarely aimed at children, but it's fine for kids. It tends to focus on the strange and the gross, such as face mites. It also introduces viewers to some essential concepts of biology, such as sexual selection. For example, one video describes how male earwigs do battle with their pincers. The cinematography is excellent, and the videos offer some really vivid and memorable lessons.

Generation Genius

Generation Genius costs $95 for a year of home use, which I think is well worth the price. These videos, which tend to run 10–20 minutes, seek to offer a more-organized presentation of science. Interestingly, although the videos are categorized by three age groups (K–2, 3–5, and 6–8), my five-year-old just watches all of them at will. I figure if he doesn't get everything in the more-advanced videos he can return to that material later.

The main presenter, Jeff Vinokur, has a doctorate in biochemistry, so he's definitely qualified. He's a dynamic presenter—a bit cheesy for my tastes, but I'm not the target audience.

The second day we had this program, my kid threw a minor fit when we insisted he turn it off for dinner. I figure if you have to literally tear a child away from learning about science, the program is a good one.

Wild Kratts

Wild Kratts is part science, part superhero entertainment. It's hard to describe how much my child loves this show. I once had to capture a poisonous spider in the house and traipse it down to the open space so that it could live "free and in the wild"—one of the Kratt brothers' iconic expressions.

The set-up is that the Kratt brothers discuss animals and the natural world, then their cartoon alter-egos get "creature powers" to do battle with various villains.

From the show my child has learned, for instance, how various creatures form a food web, a really important discovery.

A few full episodes of the show are available at no charge on the web site. Amazon offers a few seasons through Prime. All of the seasons are available through Amazon through a PBS Kids upgrade, which costs a few extra dollars per month.

By the way, PBS Kids also offers Daniel Tiger and Dinosaur Train, two more of my child's favorites (although he's largely outgrown Daniel Tiger at this point). If kids are into dinosaurs, Dinosaur Train offers lot of interesting facts in the context of fun stories.

* * *

I'm sure there are other great science shows out there that we haven't tried yet. I haven't watched any Xploration DIY Sci shows (also available through Amazon Prime) but it's on my list (see update). I haven't watched any of Khan Academy's science videos yet.

Update: Readers also recommend Smarter Every Day and Mark Rober. Netflix picked up Emily Calandrelli's Emily's Wonder Lab. Stat has an interview (text) with Calandrelli.

Update (September 6): I finally watched a couple episodes of Steve Spangler's Xploration Station DIY Sci, available on Amazon or through Spangler's web site. These videos are really amazing. Spangler combines real science education with fun experiments and stunts. For example, to illustrate air pressure, he makes a steel drum implode. A fun detail: Spangler lives in Denver, close to me!

I don't see videos as a substitute for hands-on science, of course. We also do simple science experiments at home, we have a microscope and such, and we get a lot out of the local nature museum. But for good, dynamic introductions to the natural world and the scientific way of thinking, the video series we've found are fantastic.

Battleship Teaches Strategy, Sportsmanship, and Basic Coordinates

August 22, 2020

Battleship is the best game I know of to introduce basic coordinate geometry. And it's a lot of fun. If for some reason you've never played it: Each of two players places ships in a "sea" of labeled rows and columns. Then players take turns guessing where the other player's ships are. Players are required to say whether a guess is a "hit" or a "miss" and whether a "hit" results in a sunk ship.

There's some strategy involved; you have to be careful not to inadvertently let slip a detail that could help your opponent. (My five-year-old is terrible at this.)

And of course the game can be good for learning sportsmanship. A significant amount of luck is involved, so hopefully kids learn to be gracious if their opponent gets lucky and wins.

My five-year-old is not quite ready to play on his own, but he enjoys playing teams with an adult.

Visualize Digits and Multiplication with Wood Cubes

August 18, 2020

Raising a child helps you remember just how hard it was to learn certain things. Most kids pick up counting to ten without much problem (after they learn to talk). But grasping double-digit numbers (and beyond) is a greater conceptual challenge. Now you have to be able to count groups of ten (and then groups of a hundred, and so on) and represent them with digit placement. Later on, multiplication (and then exponents) build on a child's earlier conceptual knowledge.

I've found that a pack of wooden cubes can help illustrate the relevant concepts nicely. When a child can see, for example, two sets of ten blocks, plus three extra blocks, the child can more-readily grasp the number 23. One issue I've seen is confusion about the number 23 versus the addition of 2 and 3; the difference is very easy to show with blocks. Of course the blocks are also really good for practicing simple addition and subtraction.

Although my five-year-old is not ready to tackle multiplication formally, we have started to work on it informally by setting up grids of blocks. He can see, visually, that two by two is four, three by three is nine, and so on.

The blocks are also excellent for illustrating exponents.

I recommend getting a pack of at least a hundred blocks. They're also fun just to build structures. I consider these a key part of a math teacher's toolbox.

DragonBox Apps Make Math Fun

August 17, 2020

I absolutely love DragonBox math game apps. They make math concepts intuitive and fun. My brother used them for his kids and sang their praises, so I got them too. Here I review the four apps aimed at children ages 4 to 9: Numbers, Big Numbers, Algebra 5+, and Magnus' Kingdom of Chess. The company also has apps for advanced algebra and for geometry; I'll buy those down the road when my child is ready for them.

In Numbers, children play with "Nooms," which are monster-like creatures that can be combined and broken apart in units. So if you add a one-unit Noom to a three-unit Noom, of course you get a four-unit Noom. For the Puzzles children have to create the correct sized Nooms to fit together into a pattern. Games involving "Ladders" and a "Sandbox" introduce double-digit numbers. And in a Run action game children collect coins.

Big Numbers is a world-development game. You pick apples, and you can "spend" these apples on things like new apple trees and diamonds. So the game involves adding and subtracting items into the double digits. It's a fun game in that you achieve progressive goals.

Algebra 5+ is a really clever introduction to balancing equations. The game begins with symbols (such as monsters) and ends with traditional-looking algebraic equations. The game introduces good habits: For example, if you add something to one side of the equation, you have to add it to the other side before you can move on. If both kids and parents get stuck, they can find DragonBox's "walkthrough" videos. This "game" is hard enough that some younger children probably will have trouble with it. My sense is that kids will enjoy it when they're ready for it. Of the four apps, it's the least game-like and the most like traditional math. It's fun because each equation is a sort of puzzle.

Finally, Magnus' Kingdom of Chess is an adventure game wherein the player moves through the world as a chess piece moves. You begin as a king and so can move one space in any direction. The game includes simple chess sequences. For example, if as a king you approach enemy pawns, you have to attack them from straight on or from the side. If you move into a square diagonally in front of a pawn it will attack you. In the game you collect coins, find keys and unlock doors, find hidden passageways, and so on.

I think a lot of people have the attitude that, if it ain't dry and boring and presented by an adult as a monologue, it ain't education. I think that's a destructive presumption. The DragonBox apps demonstrate that children can learn math in an intuitive and playful way.

Update May 26, 2024: When I first used these apps, they were available to buy for individual downloads. Now they are available by subscription. Now that my child is eight he no longer uses these.

Fraction Wheels Foster Intuitive Learning

August 16, 2020

My five-year-old is not ready to add mixed fractions. But, by using a fraction wheel, he is already beginning to grasp, intuitively, how fractions work.

Just today, I got out the fraction wheel pieces, and he said he wanted to "build them" himself. He put a half-piece together with a third-piece, then tried to complete the circle. He tried a fourth-piece—too big. Then an eighth-piece—too small. He could see right away, once he tried it, that a sixth-piece added to a third-piece equals a half. He didn't need to know how to formally convert one-third to two-sixths for this, but he could see visually that one-third equals two-sixths. He also immediately saw that three sixth-pieces are a half and six of them are a whole.

Obviously I'm not going to try to teach him formal fraction conversions until he has a better handle on the four basic operations (addition, subtraction, multiplication, and division). But I think this early work with the fraction wheel set will put him in good shape to grasp adding and subtracting complex fractions later on.

I know there are some really well-crafted fraction wheels with little handles on the pieces; the disadvantage of these is that you can't stack pieces on top of each other.

My wife and I created a simple fraction wheel set that you're free to download. For best results, print these out using different colors of paper and then glue them to card stock or cardboard, or just print them out on cardstock if your printer can handle that. Or you can just buy a set.

Core Knowledge Free Materials for Grades 1 to 8

August 11, 2020

Update May 26, 2024: This section and the next two have been substantially changed from their original versions.

Core Knowledge offers an enormous amount of educational materials for preschool through eighth grade.

The "Ancillary Materials" and "Domain" segments offer lengthy teachers' guides along with "flip books" and "image cards." The idea is for the teacher to read or explain material as children look at their own printed images. This is a rather clunky system for homeschool use.

The "skills" sections offer some student readers that you might be interested in. Although these readers mesh tightly with Core Knowledge's approach to reading, I didn't find some of the stories very compelling. But I do quite like Fables, The Green Ferm Zoo, and Kate's Book.

The "skills" sections also provide student workbooks. I'm not sure yet if I'll use these in the future (my child is just now kindergarten age). Although I really like the kindergarten workbooks, the first-grade workbooks seem a little basic and boring to me. But I'll see.

Finally we get into the informative readers (or "student books"), including Mesopotamia and Exploring Light and Sound. These I like a lot (overall).

Also, if you like, you can buy or borrow E. D. Hirsch's What your First Grader Needs to Know (the series go through sixth grade).

For Grade 2, I'm again skipping past the "Ancillary" and "Domain" materials. I'm also skipping the workbooks at this point. I'm pretty skeptical of their value. They contain, for example, multiple-choice questions about essays, which I think are stupid. (But if you want to try them be my guest.)

I wasn't too impressed with most of the language arts readers for this year, but Bedtime Tales and The War of 1812 Reader look interesting.

Readers for History & Geography and Science include Ancient India and Properties of Matter.

This is interesting: Core Knowledge offers "Core Classics Teacher Guides" filled with discussion and questions about various great works of literature: A Midsummer Night's Dream, Don Quixote, Narrative of the Life of Frederick Douglass, Gulliver's Travels, and more. This is for grades 4–8.

Fourth grade readers include The Middle Ages and Energy Transfer and Transformation. Fifth grade readers include Early American Civilizations and Astronomy. Sixth grade readers include World Deserts and The Making of America.

Core Knowledge Free Kindergarten Materials

August 10, 2020

I'm a big fan of Core Knowledge's dozens of student readers, free as pdf downloads. But the materials are harder to use (at least for homeschoolers) at the preschool and kindergarten levels.

Each unit of History & Geography and Science includes a lengthy teacher's guide as well as "student book," which I find particularly useful. A given unit might also include other materials that I regard as less useful.

The "Assessment and Remediation" guides contain some great worksheets and read-aloud materials as well as a lot of instruction for teachers. The "Big Book" focuses on reading. The "Skills" books contain worksheets that you might want to print out—these are really good. The "readers" should work great with a Kindle or comparable device (or printed out).

A dozen units are called "domains" (I'm not sure why). I find this material difficult to use in a homeschool environment because it is split between very-long teachers' guides and sets of "image cards" and "flip books" that students are supposed to look at as a teacher discusses them.

A good way to get (much of) the relevant Core Knowledge materials in these areas is to buy or borrow E. D. Hirsch's What Your Kindergartner Needs to Know.

Core Knowledge Free Preschool Activities

August 9, 2020

You may be aware of Core Knowledge, the educational program started by E. D. Hirsch Jr. Various charter schools, for example, base their programs on Core Knowledge (not to be confused with Common Core). And you may be aware that Core Knowledge offers an enormous amount of K-8 learning materials online at no cost to the user.

Last year I started downloading the student readers in pdf form. Volumes cover history (such as Ancient Greece and Rome), science, and literature. These are amazing resources especially for homeschooling families on a budget. I have an old Kindle reader (the kind with the button keyboard) dedicated to such educational books.

What I didn't realize until recently is that the preschool level offer a lot of great material presented as "activity pages" rather than as "readers." These offer content for parents to read with their children as well as simple activities.

If you're looking for more content along these lines for preschoolers (and willing to buy or borrow a book), my five-year-old has really enjoyed my wife reading with him Hirsch's What Your Preschooler Needs to Know.

The Place for Bob Books

August 7, 2020

Great literature Bob Books are not. But that's not their purpose. Their purpose is to hold children's hands during their first journeys into reading. And for that they're great.

These very-short books turn simple words into simple sentences with just enough story and humor to hold a child's interest for the few minutes it takes to read one of them.

I picked up Sets 1–3, plus a kindergarten set, used via eBay. For months they sat on a shelf. Several times I tried but failed to interest my four-year-old in them. I think their usefulness is all about timing.

My child, now five, has learned the alphabet and can recognize and write lower and upper case letters. Most of the time he associates the correct sound with a letter, although he still sometimes mixes up the similar-looking letters d, b, and g. He is just now gaining the ability to string together the sounds of letters into words. I am reminded of how hard this can be in English (as opposed to, say, Spanish), what with all the different possible letter sounds—we pronounce (for example) "one" the same as "won." Bizarre.

I tried again to interest my child in a Bob Book—and this time he was receptive. In two days he's read the first four books. I figure we'll aim to read two or three per day until we finish. Then if he wants to start over, great; if he wants to be done, also great. I consider the Bob Books as a transition to him reading for himself his first "real books." Once the Bob Books have served that purpose I'll pass them along to the next child.

So, to summarize my advice: Get a a few Bob Books (or something comparable) when your child is learning the alphabet and the letter sounds. Check in with your child every week or so to see if the books seem interesting. When and if they do, go for it. But don't overdo it; I've found that reading through a single book in one sitting is actually fairly taxing for the child, though it takes but a few minutes. When the books no longer hold the child's interests, move on to something more substantive.

Learning about Human Progress

August 5, 2020

I'm a big fan of Jason Crawford's work for The Roots of Progress. Crawford's main theme is that people have improved their lot dramatically through science, technology, and the underlying causes of those developments. So why not make more of an effort to teach children about human progress? In a July 27 Interintellect discussion that Crawford hosts, several educators weigh in on the topic.

I agree with Lisa VanDamme, founder of VanDamme Academy and one of the presenters, that the project of teaching children about human progress quickly can run into problems. First, she notes, "progress" is not a primary field unto itself, at least in terms of K-12 education, although aspects of it properly integrate with history and science (which are both major fields of study). Second, the proper aim of education is to enable children to ably pursue their own values and live their own lives, not to convince children to embrace certain conclusions (such as "progress is good"). That said, as VanDamme also notes, well-educated children typically will turn out to be the sort of people who do appreciate human progress (among many other things).

Kyle Steele (one of VanDamme's associates) adds a great point: Properly, children have lots of room to explore their interests outside of their core education. For example (as several speakers discuss), a child keenly interested in music might want to limit time spent learning core subjects and maximize time spent practicing a musical instrument. Similarly, a student keenly interested in science, technology, or entrepreneurship might want to spend disproportionate time in those areas. So, for example, Crawford organized Progress Studies for Aspiring Young Scholars. This fits perfectly well as an extension or special-interest program with the sort of core education that VanDamme has in mind.

The entire discussion is fascinating. (Those interested in learning more about Crawford's project also can check out my podcast discussion with him.)

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