Lift Up Your Hearts!

It often pays to find the story behind the headline—or the social media post.

The Facebook blurb from our local library was annoying. Here's how it began:

1000 BOOKS BEFORE KINDERGARTEN: A round of applause for A----, who has read another 1,000 books before kindergarten—for the third time! On her way to becoming a young, brilliant scholar, Seminole County Public Libraries is proud to be part of A----’s journey as she grows her vocabulary, boosts her critical thinking, and enhances her cognitive development. 

I was annoyed, but looked further and discovered that our library has a program to encourage parents to read aloud to their preschool children. It's a little sad that adults need stickers as an incentive to read to their children, but we've all been there with some good habit we're trying to acquire. So it looks like a good thing.

What bothered me about the Facebook post was the implication that the achievement belonged to the child, and that she had actually read 3000 books. I've known a few kids who taught themselves to read before formal schooling, but that's not what is meant here. Maybe I'm being pedantic, but I don't think so: As valuable as being read to is, it is not the same as actually reading the words on the page.

I have a similar problem with adults who claim to have read a book when actually what they've done is listen to someone else read it to them. Don't get me wrong; I enjoy audio books and find them invaluable for absorbing content while doing repetitive work, exercising, and driving. But that's a different experience from reading, even for adults, and especially for a child who hasn't yet developed the skill of decoding print.

And I'm not sure it's a good idea to let a child believe he has done something worthy of great praise when the effort was on the part of his parents. Sort of like getting an A on a homework assignment done 95% by your dad. Or getting a Pulitzer Prize for something written by ChatGPT.

Curious about the quantity of books, I looked up my own reading tally. I have been keeping track of the books I read since 2010 (making note of the few that were audiobooks). I consider myself an avid reader, but it took me until mid-2024 to reach the 1000-book mark. So I commend all the parents who achieved that in reading to their preschool children.

Then again, from what I can tell, my just-turned-two granddaughter is probably nearing the 750 mark with Sandra Boynton's Barnyard Dance, including many repetitions of turning the pages herself and telling the story as she remembers it, complete with stomps and claps.

And no, I don't include books read to grandchildren in my own reading list, even though I don't limit myself to adult-level reading.

It is usual to speak in a playfully apologetic tone about one's adult enjoyment of what are called "children’s books." I think the convention a silly one. No book is really worth reading at the age of ten which is not equally (and often far more) worth reading at the age of fifty—except, of course, books of information. The only imaginative works we ought to grow out of are those which it would have been better not to have read at all. — C. S. Lewis, On Stories

When was the last time you were threatened by a gang of thugs wielding spiralizers? Apparently that is a danger in the United Kingdom. Either that, or the chefs' union is lobbying hard to keep teens from trying to break into their business. Or possibly Bob the Tomato and Larry the Cucumber have more power than I thought.

This story, posted by a woman in the UK, popped up on Facebook, and I quickly copied the text. I regret not catching the image, too, as that would have shown how small, unpowered, and insignificant the device in question is. But you'll get the idea.

I know many things are going nuts in the UK, though I don't know anyone personally who can vouch for them. But the following story, if it is true—and at least it has the ring of truth and not clickbait—shows that at least in one area they are even crazier than America, which is saying a lot.

What I want to know is… When did the world go completely mad? Did I miss it?

Let me explain…

Yesterday, I was shopping in a well-known store with a red and white logo With my 10-year-old son.

Among the impulse purchases were a red nose day Tshirt for my son, a gift for the teacher and this lovely spiralizer/vegetable grater for me.

My helpful son unloaded the items onto the checkout desk while I removed my purse from my handbag, at which point the young lady on the desk said “I’m sorry, I can’t sell you that.”

She proceeded to explain that as the spiralizer was not to be sold to anyone under 18 and my son was the one who placed it on the counter, it was deemed that the vegetable cutting device was for him.

Bewildered, I said ”but it’s a spiralizer, and quite obviously it’s for me.”

She refused the sale.

I asked if I could purchase it separately.

She refused the sale.

I asked if I could speak to the manager and they could make allowances for such an obvious fault with the rules.

The manager refused the sale.

I told the manager it would probably be a good idea to put some sort of signage up to let customers know that minors should not be unloading shopping to help their parents.

She obviously misunderstood as she pointed out the signage on the packaging that clearly says “Do not sell to under 18s”.

I left the store confused and a little perturbed and resigned myself to a lifetime of chunky vegetables in my recipes.

You can however all rest safe in the knowledge you will never be faced with a vegetable shredding 10-year-old wearing a Feathers McGraw T-shirt roaming the streets of Cumbria… all thanks to the vigilant staff of the West Cumbrian store.

You can't sell a spiralizer to a 17-year-old in the UK?

I'm assuming a much-more-potentially-dangerous kitchen knife would meet with similar restrictions. At what age are people allowed to cook on that side of the Atlantic? How about to wash dishes, which would undoubtedly include knives.

I don't remember when I started helping in the kitchen, nor when our own children did, but I know that most of our grandchildren started learning how to use kitchen knives at the age of two (well supervised, of course), and by four were reliable helpers in cutting up vegetables for a salad. I know that's early, even for America, but if David Farragut could command a ship as a pre-teen (there is some difference of opinion as to whether he was 11 or 12), surely it is a bit excessive to restrict the use of sharp objects to those 18 and older.

This excerpt from Village Diary by Miss Read (Dora Jessie Saint) captures both my frustration with the disservice our educational system does to bright children, and my nostalgia for conversations that can be both contentious and contented.  The speaker is a schoolmistress in a small, rural English village. The book was published in 1957, and the author was herself a teacher.

[We had] a most agreeable and stimulating argument about children's reading. Mr. Arnold ... maintained that children are not ready to read before the age of six, or even seven; and that all sorts of nervous tensions and eyestrain can be set up by too much emphasis on early reading.

I maintain that each child should go at its own rate, and that the modern tendency is to go at the rate of the slowest member of a reading group, and that this is wrong. There are, to my mind, far more bright children being bored and very frustrated because they are not getting on fast enough with their reading, than there are slow ones who are being harmed by too-rapid progress. I have known several children—I was one myself—who could read enough simply-written stories to amuse themselves at the age of four and a half to five. We were not forced, but it was just one of those things we could do easily, and the advantages were enormous.

In the first place we could amuse ourselves, and reading also gave us a quiet and relaxed time for recovering from the violent activity which is the usual five-year-old's way of passing the time. ... Secondly, the amount of general knowledge we unconsciously imbibed, stood us in good stead in later years. ... Even more important, the early poems and rhymes, read and learnt so easily at this stage, have been a constant and abiding joy. ...Thirdly, the wealth of literature written and presented expressly for the four to six age-group—the Beatrix Potter books are the first that spring to mind—can be used, loved and treasured to such an extent that is not possible to a late reader.

The battle raged with great zest. ... Mr. Arnold twinkled, and said I was a renegade, but that he must admit that he had seen no cases of nervous disorders in my school. And after school [we] enjoyed a cup of tea in my garden, among the apple blossom, with the greatest goodwill, each knowing that he would never convert the other, but content to let it be so.

That's the bill for my first semester of college, in 1970. In 2024 dollars, that would be just under $16,000. (Inflation calculators differ, but not by much.)

Let's not look at the total bill, but annual tuition, which is easier to compare.

• Annual tuition at the University of Rochester in 1970: $2600 
• Approximate equivalent in 2024 dollars: $21,020
• Current annual tuition at the U of R: $65,870

Why is the inflation-adjusted cost of a college education at my alma mater more than three times what it was when I was there?

• Is the education three times better than it was then? (Highly doubtful.)
• Are the professors being paid three times as much? (Not the ones I know.)
• Are the graduates earning three times the salaries? (A quick investigation indicates the entry-level salaries for a position similar to my first job in 1974 are, adjusted for inflation, very similar to mine back then. But that's far from the whole story. I was in a tech field—computing, the early days—where one could easily expect a salary that justified the cost of college. How many of today's graduates can say the same? Today, far more students are "attending college," but studying what they should have learned in high school, and graduating with degrees that give them little hope of commensurate employment.)
• After four years of college, are today's graduates that much more mature, responsible, capable, well-read, well-rounded, generally competent, and prepared for adulthood—employment, marriage, parenthood, and contributing to society? Are they happier and more well-adjusted than we were? (A small minority are very impressive. But for far too many, college has been a tragic waste of both precious time and an obscene amount of money.)

If the parents in each generation always or often knew what really goes on at their sons’ schools, the history of education would be very different. — C. S. Lewis, Surprised by Joy, 70 years ago

Eventually parents are going to wake up to what a poor job colleges are doing. — a math professor friend, 25 years ago

When is this bubble going to burst? — me, now.

Whatever you think about Facebook, there's no doubt it can be unintentionally amusing

I mostly find its "Reels" feature to be annoying, and have more than once looked without success for a way to turn it off completely. The short videos it shows are mostly reposted from Tik Tok, which I don't otherwise see. Sometimes they are interesting, sometimes they are genuinely informative and helpful, but all too often I find them infused with a negative view of life, even when they are undeniably—even addictively—entertaining.

Sometimes, however, something unexpected shows up and catches my eye.

If you don't have access to Facebook, you may not be able to watch the video, unfortunately. I spent too much time trying to find a version I could embed here, without success. I hope that link will take you to something you can see, but if not, it doesn't matter.

My readers know that one of our granddaughters plays on her high school girls' soccer team, and that the team has been wonderfully encouraging and supportive of her family during her sister's leukemia journey.

Here's another way they showed their character.

What caught my eye (more accurately, ear) in this video, and made me listen all the way through, was that it's not often when I hear mention of their tiny New Hampshire high school in nationwide media. I think this is the only time I have, actually. So it made me jump.

The short version of the story is that some of the team members did not want to play against a certain other team on their schedule, which included a boy in their lineup. First, in principle, because theirs is a girls' league, not a mixed one, and also because they found the boy physically threatening. The team's coach handled the situation extremely well: those girls who objected to playing that game were excused without any penalty, and the team played the game without any fuss. Somehow it made the news anyway, but I'm proud of the way they handled the situation calmly and fairly.

Our granddaughter? She played the game, with the support of her parents, even though they all thought it unfair for a boy to be on the opposing team. Why? I can't speak for them, but here are a few reasons that came up in our discussion:

• After all she's been through, Faith wanted to support her team, and to play soccer.
• It wasn't the other team's fault that they had a boy on the team—it was a state ruling that forced them to do so.
• Boys and girls often play successfully on the same soccer team—although that's usually at the younger levels, before males gain a significant physical advantage over females.
• They've played against other teams with girls she found more physically threatening than this boy.

The game was played successfully and without incident. I honestly don't remember which team won. In a way, they both did. Don't misunderstand me: The teams should never have been placed in this position, and the state rule that made it happen needs to be fixed.

But bad things happen in this life, and when they are met with quiet grace, that deserves to be celebrated.

Thanks to the very valuable eReaderIQ, I learned that C. S. Lewis's The Screwtape Letters is currently on sale at Amazon for $0.00. You can't beat that price for excellent content, and it also includes Screwtape Proposes a Toast.

This was a good year for books; not a record, but a very respectable 77 books, 6.42 per month. The fiction/non-fiction ratio was almost exactly the same as last year. No doubt about it: fiction is a lot easier to read when you are at risk of being interrupted. I've been working on RFK Jr.'s The Wuhan Cover-Up for many weeks. It's fascinating, frightening, and frustrating; having read The Real Anthony Fauci two years ago, I'm certain it will also be enlightening, important, and highly accurate. But like that book, it's also so packed with references and documentation that it takes focus to be able to do it justice. The book that is capturing my attention at the moment, Brandon Sanderson's Warbreaker, is not light reading—nearly 600 pages of a complex story filled with unpronouncable names—but there's no denying it's more fun to read.

The stats:

• Total books: 77
• Fiction: 63 (82%)
• Non-fiction: 13 (17%)
• Other: 1 (1%)
• Months with most books: April (10)
• Month with fewest books: July (2)
• Authors read most frequently: Four stood out: Mark Schweizer (15), Jenny Phillips (10), Brandon Sanderson (9), and Robert Heinlein (8). The next highest was three, a position held by several authors.

Here's the list, sorted by title; links are to reviews. The different colors in the titles only reflect whether or not you've followed a hyperlink. The ratings (★) and warnings (☢) are on a scale from 1 to 5, with 1 being the lowest/mildest. Warnings, like the ratings, are highly subjective and reflect context, perceived intended audience, and my own biases. They may be for sexual content, language, violence, worldview, or anything else that I find objectionable. Nor are they completely consistent. For example, Brandon Sanderson's books could easily rate a content warning in all of the above categories, yet they are mostly not inappropriate to the context and could be considered quite mild—for a modern book. Your mileage may vary.

I love books. I've loved books for longer than I can remember, since my parents read to me long before I could read for myself—as naturally as a bird-parent drops food into its hatchlings' mouths.

The transition from non-reader to reader was not without its stumbles. Even at my advanced age, I still remember Charlotte's Web with both pleasure and pain. My parents had been reading the book out loud to the family. As the oldest child, the one who could now read on my own, I grew impatient with the one-chapter-at-bedtime pace, and the next day picked up the book and continued the story on my own.

Maybe that's not always a bad thing, but it meant that I was alone when I encountered Charlotte's death. If there was some of the deadly sin of Avarice in my action, it carried its own punishment with it. Ah, well—rites of passage are not meant to be easy.

The transition from non-reader to reader is one of the most significant milestones in modern life, one we don't share with our more primitive ancestors. As recently as 1900, more than 10% of the American population was illiterate. Somewhere between 1969 and 1979, that dropped to below 1%. This, of course, takes no account of how well people read, nor the more disturbing trend of can read but don't. But that's not the question that emerged recently, prompting me to write.

(Yes, this is a new post, not one pulled from my storehouse. It was supposed to be a quick and easy post to make. I should have known better.)

The question is whether or not there are other decisive milestones on the literacy journey, once one has mastered reading Of course there are significant steps in the progress of that mastery, a big one being the transition from being able to decipher words to the technique having become so automatic that it is accomplished with no conscious thought at all to the process, only the content. For example, I can read French well enough to enjoy some books, but it's nowhere near an automatic process.

(I think that there's a point still further, when conscious thought creeps back in, but I never made it through Mortimer Adler's How to Read a Book, much less apply his techniques, so I can't say from personal experience.)

What I'm wondering is how significant to the reader has the advent of e-books been. It's not of the order of the act of reading itself, but the Kindle has certainly changed our lives and reading habits. I'm definitely bimodal when it comes to books: There's nothing like the pleasure of reading a physical book, but e-books have distinct advantages as well, such as being able to carry a vast library in a handheld device, and to search the text, and make notes, and highlights, and to copy excerpts via cut-and-paste rather than laborious typing. On the other hand, e-books don't really belong to us; we may like to think so, but they can be taken away from us at any point. So I will read with the physical books, and I will read with the e-books also.

After that long introduction, here's the incident that gave me pause: After reading six Kindle books in a row, I began another in physical form. (Brandon Sanderson's Warbreaker, if you're curious.) I was reading along, and when it came time to turn the page, I unthinkingly swiped my finger across the lower right-hand corner of the book. That's the way I turn the page with my Kindle

Guess what? It didn't work with the physical book, and I was momentarily taken aback. Even more interesting, I still find myself repeating the motion on occasion, and I'm 143 pages into the book.

The human mind can be peculiar, sometimes.

Citoyen de la Galaxie by Robert A. Heinlein (original publication 1957, this French edition 2011)

Back in August, I quoted a passage from Robert Heinlein's Citizen of the Galaxy. Inspired by this, and a good deal available for the Kindle version, I decided to reread it—in French.

It was a surprisingly delightful experience.

I had three years of mediocre French classes in high school, and have been working very casually, though consistently, with DuoLingo since I was a beta tester for them back in 2012. I have many frustrations with DuoLingo, but this week I discovered that it has actually given me a lot of French vocabulary and a pretty good feel for grammatical structures. I really enjoyed reading Citoyen de la Galaxie.

Naturally I didn't read it as quickly as the English version, but I surprised myself. My goal had been to work my way through ten pages per day. Instead, I was so caught up in the story that I finished it in just about a week.

It must be admitted that I was not a stranger to the story, which helped enormously. I first read Citizen of the Galaxy when I was in elementary school, and I've reread it several times since. How many times I have no idea, but I know that I last read it in 2017—before that, I don't know, except that it was earlier than 2010, when I began keeping track of the books I read. As I read the French, I was astonished to find the words of the English version coming back to me. Between that, the DuoLingo vocabulary, and occasional help from the Kindle French-English dictionary available at a touch, the reading was easy enough to keep me going.

I would not at all expect the same ease with an unfamiliar book. But the experience was exciting, especially since I would often find myself actually thinking in French for a few minutes after a session of reading.

Author S. D. Smith explains that his children's books are good but not safe—and why that's important. Authors like Smith prepare the ground for children to grow into the heroes we will desperately need.

One of my favorite Substack people (Heather Heying, Natural Selections) wrote this in her article entitled, "It’s an Upside Down World, and You’re Living In It."

I used to be a Democrat. Two of the things that I did that felt democraty include:

I bought as much of my food as possible at farmer’s markets, and got to know the farmers who grew my food. I bought organic, and avoided GMOs. When given a choice, I bought food that was grown closer to how it had been before humans got involved—cows that had spent their lives grazing outside, coffee grown in the shade on farms with canopy trees, tomatoes and strawberries picked at perfect ripeness, transported as little as possible, eaten fresh and raw.

And I refused pharmaceuticals except when absolutely necessary—the notable exception being vaccines, which I barely questioned until Covid raised my awareness. Over the counter drugs were no better. The rule of thumb in our house was: the longer it’s been on the market, the more likely it is to be safe. Aspirin seemed like a pretty safe bet, as did some antibiotics, in moderation. Everything else? Buyer beware.

I still do these things. My behavior was always informed by an evolutionary understanding of the world, a fundamental preference for solutions that have stood the test of time (e.g. beef over lab-grown meat), and wanting as little corporate product and involvement in my life as possible. Such behavior just doesn’t seem democraty anymore. It seems like the opposite.

In response, I wrote the following.

For decades, I have been saying that the Republicans need to reinvent themselves as the party of human-scale life. Seeing Trump and Kennedy together call to Make America Healthy Again gives me more hope in that direction than I've had in a long time.

Your beautiful, healthy approach to living felt Democrat-y to you, but in my life it has always been embraced by a mixture of folks, from hippies to conservative Christians, who shared a love of what we saw rejected by mainstream society: children and family life; non-medicalized childbirth and homebirth; the critical importance of breastfeeding; independent and home education; the belief that children can be far more competent and responsible than we give them credit for; small businesses; small farms and natural foods; the superior flavor and health benefits of raw milk and juice, pasture-raised animals, and organically-grown fruits and vegetables; homesteading and preserving/restoring the land; reclaiming heritage breeds and seeds; and a deep concern for the environment that was called conservation before it was taken over and ruined by the environmentalist movement. 

If the Republican Party will truly embrace and fight for these values, I will in turn be thrilled to have finally become a Republican after 56 years a Democrat. The beginning of the end of my complacency with the Democratic Party was discovering the party's intense opposition to homeschooling—despite the fact that so many of the home education pioneers were radical liberals in their day.

Home education may have been the beginning of my disaffection, but the disconnect between the Democratic Party and the values I thought were their priorities became more and more obvious, accelerating at a most alarming rate, to the point where I agree with Dr. Heying again:

The democrats are claiming that they’re on the side of the little people. The only proper response to such claims is this: No. No you are not. Stop lying. And: No.

Republicans, this is your chance. Don't blow it by infighting, nor by sabotage from within. Reach out to the Independents and disaffected Democrats—like Dr. Heying, and RFK Jr., and Sasha Stone...and me—who are reaching out to you, willing—eager—to put aside our differences long enough to do the really hard work of seeking and saving that which is rapidly being lost.

David Freiheit, who is still "my favorite Canadian lawyer," despite now living in Florida and no longer practicing law, interviewed Sam Sorbo, a woman who had not been on my radar at all, about homeschooling. I said that Sam was not on my radar, but as he introduced her and mentioned her husband, his name rang a bell for me. I had no idea why. I can hear my family laughing at me, because, while my brain can easily cough up trivia like the second lines of famous poems, there seems to be a black hole in my memory when it comes to people associated with popular music and movies. They will be proud of me, however, because it didn't take me (okay, me and Google) long to solve the mystery: Kevin Sorbo was one of the stars (and better actors) of The Firing Squad, the movie that we watched just a couple of weeks ago.

Puzzle solved, I could settle down and enjoy the interview, which I share here. The content starts at 4:47 and goes on nearly to the very end, making it over an hour long. The school stuff starts about 22:00; what comes before is the story of how she got to that point, which I also found interesting. As an old-time homeschooler—20th century, with grandchildren homeschooling in the 21st)—I love hearing today's homeschooling journeys, how things differ, how they are the same, what we've learned, what we've forgotten. Above all, I like to hear the enthusiasm of converts and potential converts. Do this, not because the alternative is so bad (although it often is), but because this is so good!

When our daughter and her family moved to a small town in New Hampshire, the disadvantages were obvious to me. Over time, I've learned to see the advantages as well. Two segments of the following America's Untold Stories video make me all the happier they live where they do, and I want to tell my grandchildren: Hang on to your hometown! But also, be aware of what's happening elsewhere, so you can recognize the beginning stages when they come to you.

Back when our children were still in elementary school, I attended a conference at which a speaker regaled us with horror stories of what was going on in public schools. I'm afraid I didn't take her too seriously, because—like so many people who are passionate about an issue—she came on too strong, and painted a picture far too bleak to resonate with my own experiences. I was very much involved in our local public schools, and had not seen the abuses she was describing. The thing is, she was right. She was ahead of her time, and her stridency put people off—not unlike the Biblical prophets. But all she warned against came to pass, and orders of magnitude worse.

One reason I like America's Untold Stories is that Eric Hunley and Mark Groubert pull no punches without being strident, and more often than not have personal experiences to back up their concerns. Caveat: I haven't listened to the entire show, which is over two hours long at normal speed, so I don't know what else they talk about. The first segment I'm concerned with here, about the "Homeless Hilton" being built in Los Angeles, runs between the 17-minute mark to minute 26; from there until minute 48 deals with the New York City school system.

[Quoting Manhattan school board member Maud Maron] Parents, and the children of immigrants who came from former Communist countries—Eastern Europeans and the Chinese—were saying, "Maud, we know what this is, and this isn't good."

It's easy to think, "Well, that's Los Angeles and New York; it has nothing to do with my town, my city, my schools." To that I can only say, weep for those cities, pray for those cities—and be awake and aware of how your own home might be at risk of starting along the same paths.

The advantages of homeschooling certainly aren't new to me, but I still love to read about people's happy experiences. You can read all of this one for free, though as I recall you may have to give them an e-mail address. (Oh, how I love having our own domain, and being able to create "throw-away" e-mail addresses as desired; it's the e-mail equivalent of using generated credit cards, which I also love.)

This is the story of Nadine Lauffer, now 18 years old, who began her schooling in the Netherlands. Knowing no English when her family moved to Florida, she had to repeat kindergarten, but as with all children who are exposed to new languages that young, that was no problem for her, and she continued in public school until fourth grade. At that point, frustrated by the lack of individual attention in the crowded public school, and impressed by the personalities of the homeschooled children they met at church, her family embarked on their own home education adventure.

“The teenagers,” she said, “were very different from the normal teenagers that I'd met coming from the public school system. They were more attentive, they knew how to talk to adults, and they were joyful.”

Nadine continued to homeschool through high school, going through a difficult period where she struggled with what she might be missing by not being in public school. Until, that is, she investigated and decided that she was actually lucky to have missed out on much of the high school experience. In addition, she began to take responsibility for her own education, which is, after all, the primary goal of homeschooling.

[After hearing a talk by Andrew Pudewa, founder of the Institute for Excellence in Writing], Ms. Lauffer was encouraged to go through her high school experience in a way that fit her and to focus on her love of learning rather than trying to mimic what was going on in public schools.

Nadine's account isn't much different from the experience of millions of other homeschoolers, but in a world gone crazy, we need happy stories, and the reminder that there's still a good number of people in the world who are not insane (even in public schools, though it can be harder there).

An article in today's Orlando Sentinel boasts this headline: Florida students make ‘substantial gains’ on state tests, new results show. I'm not going to say much about this happy headline, except to note that the joy includes the fact that only 22% of third graders failed to read at grade level, down from 27% last year. Other statistics are similarly dismal. This in a state that U.S. News & World Report ranked #1 in education.

But it's not the schools I'm taking issue with at the moment. It's the newspaper, which with the article ran this photo of middle school students learning math. (Photo credit Willie J. Allen Jr/Orlando Sentinel) (click to enlarge).

As near as I can figure out, the problem is to find the distance between two points on a Cartesian plane, (-3, -3) and (-3, -4). What's written is not the way I would have approached the problem, but—assuming scalar distance, since no direction was specified—the answer is, indeed, 1. I'm also assuming that some of the work was done in the student's head, and these are just notes taken along the way.

Nonetheless, instead of a room full of (possibly) eager math students, what stands out to me—in an article bragging about improvement in math scores—is the equation,

3 - 4 = 1