Coalition for Kid-Friendly Schools

I only wish this was Younger Daughter's school.

I liked this comment from the principal of PS 234, which is retaining Investigations Math:

The school's principal, Lisa Ripperger, emphasized that more important than any individual program is support for the teachers. PS 234 has a math and a literacy coach who work only with the teachers. "Nothing to me in my budget is more important than my two full-time content coaches," she said.

How did we get to the point that elementary-school teachers can't teach basic math without the services of a full-time specialist? Either the teachers are incompetent or the curriculum is baffling. Or, even more frightening, both.

When I started teaching Younger Daughter the times tables, she protested that she already knew them -- at least for 2, 3, 4, and 5 -- because she had been taught them at school. It turns out that what she knew is "skip counting" -- that is, "2, 4, 6, 8, ..." (Back in my day, when we weren't dying of the bubonic plague, we called this "counting by twos.") But if you asked Younger Daughter what 2 x 3 is, she had to think about it for a while, and the answer she came up with might or might not be correct. (She's getting better now, after a great deal of work on both of our parts.)

There's nothing wrong with skip counting, and it's a reasonable first step toward learning multiplication. This is typical of the new "fuzzy math" curricula (Younger Daughter's school uses "TERC Investigations") -- they include some reasonable first steps, but they don't follow through and actually teach the skills and facts you need to know.

The first unrelated-to-me kid that I tutored had a similar problem with adding fractions. I was impressed when she knew that 1/2 + 1/4 is 3/4. When I asked her how she knew this, she drew a little pie illustration. Again, this is a reasonable first step. But when I asked her what 2/50 + 1/100 was, she was completely stumped. That's because Trailblazers doesn't follow through and actually teach the algorithm for adding fractions.

Feh! The bad news is that the district of Upper Tax Bracket only adopted TERC Investigations a couple of years ago -- it'll take time for any kind of momentum to build against it. In the meantime, I'm teaching Younger Daughter math at home.

Since we're on break, I'm channeling my inner Tiger Mom and working hard with Younger Daughter. We're going through the "finished" Investigations workbooks that her second-grade teacher sent home, completing some of the untried pages and fixing mistakes.

So, I turn to an untried page and say, "Let's do this one". Then YD just looks at me expectantly. She's gotten so accustomed to having the teacher read the directions to her that she doesn't even try to read them herself. Me: "Go ahead and read the directions!" Several times YD has started reading the directions, and reverted back to her worst habits of word-guessing, reading "color" for "circle" and "equation" for "equals". I think it's a form of learned helplessness, and I think it's got to stop.

So I had Sainted Husband type up a list of all the vocabulary words that show up in the workbooks, and we'll start drilling them with YD as part of her daily reading practice. Not only is Investigations heavily language-based, which creates unnecessary roadblocks for a language-delayed child, but the language it uses is not remotely aligned with the reading curriculum. I'm sure YD isn't the only second-grader who has trouble reading words like "equation", or, God forbid, "trapezoid".

If I were purely homeschooling YD, I could choose what curricula to follow, and we could use it in a systematic way. But since I'm sending YD to public school and afterschooling her in an attempt to bring her up to grade level, I vacillate between using the best curricula I can find (phonics and Singapore Math) and preparing her to deal with her classroom environment, which pushes reading "strategies" and Investigations math. I just hope it all works for her.

Recently, Younger Daughter's teacher has sent home YD's workbooks from their math program, Investigations in Number, Data, and Space. Looking through these books, the first thing that strikes me is the (large) number of uncorrected errors. Does the teacher correct these workbooks at all? If not, what's the point?

Older Daughter told me that in her experience, this is one of the main differences between public and private school. She was amazed to find that in her private school, they go over the homework the next day, in class, with the goal that everyone should understand all the problems. Back in public school, homework might be graded, but there was no attempt to fix mistakes.

I don't get it. What good does it do Younger Daughter to write wrong answers, if she's never corrected? It's actually worse than not doing math at all -- she's confirming wrong ideas. On this page, she's made a consistent mistake, thinking that "doubling" is the same as "putting a 1 in front of". (Hence, "4 doubled is 14", "7 doubled is 17", "9 doubled is 19", and "8 doubled is 18".)

I can see why YD thinks that schoolwork is mostly a question of filling things out.

When I work on Singapore Math with YD, I check her answers immediately after she writes them, and if the answer is wrong, I erase it and we go back over the problem. Every page is filled out correctly by the time we're done. Isn't that how it's supposed to work?

While we're at it, I can't believe the amount of wasted paper in the Investigations workbooks. They use an entire page for one simple addition problem. This also results in worse handwriting -- YD's handwriting is neater in the Singapore Math workbook, which gives smaller spaces.

I want a dream lover
So I won't have to dream alone.
-- Bobby Darin, "Dream Lover"


TeacHer asked, in a recent comment:

I've been wondering about this recently: if you were to design the perfect school, how would it look? What about the perfect teacher?

Thanks for the question, TeacHer!

My dream school would combine the best of the progressive and traditional philosophies. From the best of the progressives, I would take an interest in the child as a complete human being, with physical and emotional needs as well as academic ones, and the goal of developing an independent thinker, with a continuing interest in learning. From the best of the traditionalists, I would take a true understanding and appreciation of content knowledge, including technical content like math and science, and a respect for linear, well-designed curricula.

So, with the progressives, I would throw out authoritarian classroom-management systems like PBIS and WBT, but with the traditionalists, I would throw out bad curricula like fuzzy math, non-phonics reading instruction, and meta-meta-meta "comprehension" questions that baffle and alienate small children.

My dream elementary school would assign no homework, or optional homework, and never restrict recess as a punishment, or for any reason. Teachers and administrators would work towards a genuine partnership with parents, not the current Jeeves-and-Wooster farce that passes for "partnership".

My dream teacher would be well-educated and genuinely interested in learning, as well as humane and caring (that's a surprisingly difficult combo to find!). She would be open to new ideas, and not ideologically wedded to certain techniques (and yes, I understand that a lot of important classroom decisions aren't under the teacher's control any more.)

And here's an impossible dream for you: just once, I would like to read a newsletter written by a teacher with no grammatical errors.

Readers, what would your dream school look like? How about your dream teacher?

The issue of "comprehension" is a boondoggle that educators use to make what they do look much more complicated than it actually is, and to justify bad curricula that don't teach comprehension or rote learning or anything at all.

For instance, confronted with a 6th-grader who can't add two fractions with large denominators (because she can't conveniently draw the pie chart), educators say "that's OK, the important thing is that she has deep conceptual understanding." (And how is the pie chart any deeper than the standard algorithm for adding fractions?)

Similarly, confronted with a 7-year-old who can't read because she thinks she should be able to guess everything from context, educators say, "that's OK, the important thing is that she WANTS to read, and she understands a great deal when you read out loud." (That's pretty much what Younger Daughter's first-grade teacher told us at Natural Friends!)

In both reading and math, educators (often, unfortunately, those who train the next generation of teachers) use the issue of "comprehension" to distract attention from the point that their methods don't work; then they promote false dichotomies in an effort to sound "progressive".

In math, the false dichotomy is between "rote learning" and "conceptual understanding"; in reading, the false dichotomy is between "word-calling" and "comprehension".

Now, it might happen that a child could have technical skills without deep comprehension. For instance, she might be able to perform long division without understanding why it works, or she might be able to read a word off a page without understanding its meaning or context ("Mom, what's a carriage return?")

But the opposite doesn't hold. You can't have deep understanding without technical skills. If a kid can't read a word off the page, or add two fractions, that doesn't magically prove that she has deep understanding instead.

Ideally, skills and comprehension should march together hand in hand. Kids should acquire skills and also understand how and why they work. This might be a gradual process; comprehension can deepen over time. Often, comprehension is the result of continued practice of technical skills (one more reason to teach the skills first.)

Part of an e-mail from Teacher Cranium, the Head of School at Natural Friends:

Capstone experiences are being planned for each grade. We had great success in the intermediate school (fifth and sixth grades) with this year's simulated mission to Mars. We anticipate deploying simulations as key aspects of the social studies curricula of seventh and eighth grades as well.

For example, preliminary conversations are under way pertaining to a study of medicine in which an Emergency Room simulation is the featured context within which students utilize what they have learned as they play the roles of doctors, patients, first responders, nurses, and hospital administrators. We have a contact at Local Hospital who has invited us to use the simulator there. Medicine may then be used as a lens through which to examine the history of ancient China.

I had high hopes for Teacher Cranium at this time last year. He was hired because of his rep for progressive education. I want to like progressive ed. I really do. I want my kids to have actual experiences besides schoolwork. I want them to grow as complete human beings. I want them to enjoy learning. These are all ideals that I share with progressive ed.

I have nothing against the mission to Mars project, or the mock economy that was created for the second grade. A visit to an emergency room simulator could be interesting for the kids, although how it relates to ancient China is a mystery to me.

But but but ... at the same time, there are basic skills that I want my kids to master. They need to be able to read fluently and type accurately (a goal we still have not reached with Older Daughter.) They need to know at least enough math that they will be able to handle their finances intelligently and make some sense of the statistics and economic theories they will encounter. I would love for them to have working knowledge of a second language, and perhaps be able to play an instrument or compete in a sport.

If the projects at Natural Friends were happening in addition to a solid curriculum that dependably taught kids their basic skills, it would be a wonderful school. (It still might not be the right place for Younger Daughter, but that's a different issue.) But in practice, the school uses lousy curricula like Reading Workshop and Trailblazers Math, because these have been sold as "progressive".

The problem with "progressive" curricula is that they teach appreciation instead of skills. There's nothing wrong with appreciation; courses in music and art appreciation can be interesting and valuable. But you can't staff an orchestra with graduates of music appreciation, and you wouldn't want to have your portrait painted by someone who had only looked at art, no matter how knowledgeable they might be. Orchestras must be staffed with people who can read music and play instruments, and portraits are painted by people who can draw the figure. These are skills that take years of study to acquire.

Similarly, there's nothing wrong with doing logic puzzles with kids. But it's not the same as teaching math skills. There's nothing wrong with using a pie chart to demonstrate why 1/2 + 1/4 = 3/4. But if you don't go on to teach the algorithm, you'll wind up with a kid who can only add fractions if the denominators are friendly enough to produce an easy pie chart.

My dream school would teach basic skills in the most effective and painless way possible for a few hours each day, and then do interesting projects and activities for the rest of the day. Where is that school, besides my fevered imagination?

I had to post this some time -- it's my favorite of the several youtube videos illustrating Tom Lehrer's "New Math". This one includes all the surrounding patter:


Actually, the "New Math" presented here is the way I was taught subtraction, and it isn't too bad. It's nothing compared to the "New New Math" ...

From Tom Lehrer's wikipedia entry:

Lehrer has said of his musical career, "If, after hearing my songs, just one human being is inspired to say something nasty to a friend, or perhaps to strike a loved one, it will all have been worth the while."

From a comment Chris wrote on his own blog:

This weekend I was at a party, and a bunch of parents were talking about their kids' experiences with math. The kids they were talking about were all fifth- or sixth-grade girls. Every one of those parents talked about how their kids had been in tears with frustration over their math homework. I've heard similar stories from other parents as well.

This seems crazy to me. What do we think is so all-important about fifth-graders knowing long division (or reducing fractions, etc.) that it's worth regularly making them so frustrated with the subject that they're reduced to tears? It doesn't seem crazy to wonder whether we're asking them to do stuff that they're just not ready for -- or at least that would be much easier a few years later.

Chris, I also had a fifth-grade girl in tears over her math homework. It's terrible. It sets the child up to hate school, hate math, and doubt her own abilities. It's one of the many experiences that has made me a campaigner against homework in elementary school.

But I can't agree with your second paragraph. You ask, "what do we think is so all-important about fifth graders knowing long division?"

You should know that Everyday Math, and other constructivist math curricula, don't teach long division. They teach "partial sums division", an extremely long-winded and error-prone substitute. Since they don't teach the standard multiplication algorithm either, the amount of work they propose to solve a simple division problem is mind-boggling. Here's a video showing their methods:

[フレーム]


Why is a child struggling with math? It could be that the child is simply too young for the concepts being taught. Or it could be that the child is using a lousy math curriculum that doesn't really prepare her for each next step in learning math, and presents a collection of time-consuming and inefficient strategies instead of teaching standard algorithms.

If your child is using Everyday Math, I assure you that the curriculum is itself a huge source of frustration. Is she also too young for the concepts being taught? Actually, I doubt it. If you tried teaching her fractions and long division yourself, you'd probably find she was perfectly capable of learning them.

All of us who send our kids to traditional schools run into the issues you describe. The problem is that it isn't really up to us to make decisions about what gets taught when. Your fifth-grader will soon be going to middle school, and soon enough she'll take Algebra. When she gets there, if she can't handle fractions, she will be in deep trouble.

This is largely a response to Chris' interesting post at A Blog About School about a local private school which is switching over to Singapore Math.

Chris professes to be a non-combatant in the Math Wars, although he's no fan of the Everyday Math his kids use. At the same time, he's concerned that his kids' school schedules an hour for math every day, but the kids barely have enough time to eat lunch, and they have art only once a week.

For me, there are two separate issues here. One is the time management practiced by schools, which is generally terrible. To the extent that schools even care about time management, their philosophy seems to be: "We're stuck with classrooms full of kids for 35 hours a week. We've got to do something with the kids so they won't riot and tear the place down. How can we possibly fill all that time?"

The impulse to fill the time results in dumb makework projects, some of which we parents get to see when they get sent home as homework (oh joy!)

Schools brag that their kids do an hour of math a day, as if that proves the school is serious about teaching math. But what exactly are the kids doing for an hour? If they're doing boring, pointless, time-eating measuring projects, more time ≠ more learning.

The second issue is that of curriculum. Chris is afraid that bringing in a serious academic curriculum like Singapore Math would mean using even more time in the classroom.

I would like to assure Chris that curriculum vs. time wouldn't have to work out the way that he fears. That is, a serious math curriculum like Singapore doesn't need to take more time than the schools are now spending on Everyday Math. If it was done well it would take LESS time. Why? Because it's clear and concise. Its goal is to teach real math skills and concepts in the most effective way possible.

I tutored a 6th-grader, using Singapore Math, for 7 hours before we left for our travels. My student covered about 2 years of math over that time, and she's solid with the basics. Granted, this is a very bright kid, and it was one-on-one tutoring, but it's some indication of how little time real learning requires under good conditions.

As good homeschoolers have proven over and over again, a coherent, serious curriculum can be taught in far less time than schools usually take up today. Then the rest of the day can be devoted to all the things we want our kids to have in their lives: recreation, sports, friends, and following their own interests.

What we usually see in school is the worst possible set of choices; that is, an incoherent, shallow curriculum implemented in the least effective way possible with the goal of using up a maximum of hours in the day.

I still remember the horror I felt at my first exposure to simultaneous linear equations. You know, this sort of thing:

2x + y = 7
3x - y = 8

I couldn't believe my ears when the teacher suggested we should just add the two equations together. How could this be? I thought it would violate the laws of God and man alike. It seemed completely arbitrary and inexcusable. It was a real "turn the giraffe upside down" moment for me.

Over time, I came to realize that it's OK to add the equations together because each equation represents two equal values. If 2x + y = 7, you can add the same value to both sides of the equation and the equals sign will still be true. In this case, the value we will add to both sides of the equation is contained by the second equation, 3x - y = 8. The equals sign means that 3x - y is the same value as 8, so we can 3x - y to one side of the first equation and 8 to the other side of the first equation, and the equals sign will still be true.

The power of the equals sign is a tricky concept. I recently showed my older daughter how to simplify one side of an equation, and she asked, "does this mean I have to do something to the other side?" I said no, because I hadn't changed the value of the expression that I simplified, so the equals sign still held true. I can tell she will need more work on this point.

This is where curricula like Trailblazers make a fundamental mistake. For some obscure reason, they explicitly discourage writing mathematical notation, in favor of either "mental math" or writing paragraphs explaining how you reached the solution. But it is essential that students practice writing the symbolic language of mathematics, which was developed over centuries with the exact purpose of expressing mathematical ideas in the most succinct, clear, and concise way possible.

Katharine Beals has an interesting blog post over at Out In Left Field. I wrote a long comment which was immediately eaten by Blogger, so I thought I'd write a post on my own blog.

Unlike Katharine, I consider myself both liberal and progressive, and I think progressive ed theory does have useful ideas. The implementation of progressive ed in traditional schools is usually horrendous, but I'm still open to the idea that progressive ed, done well, could be a beautiful thing. I care a lot about what school feels like for my kids, and I want an education that will help them develop as entire human beings. I want my kids to enjoy school and learning.

Although Katharine and I disagree in many ways, we agree on two points: homework should be eliminated in the early grades, and Reform Math is a disaster.

I don't think it's fair to include "lay people" among the conspirators who have promoted Reform Math. The fact is that lay people have zero influence over the schools, especially the public schools. Just ask Sara Bennett how much of a difference her book, and years of advocacy, have made to the homework problem. For that matter, ask the folks over at kitchen table math how much of a difference they've managed to make, after years of impassioned advocacy against constructivist math.

The previous discussion reminds me of a radio show that the Head of School at Natural Friends did last summer. As an example of the kind of deep problem that kids at Natural Friends might work on, he offered, "there are three people at a party. How many handshakes?"

I was completely baffled by this the first time I heard it. How the heck would I know how many handshakes? There are too many possibilities for a divergent thinker like myself.

There might be zero handshakes, because everyone in the room is germ-phobic.

There might be hundreds of handshakes, because it's a meeting of the Obsessive-Compulsive Handshakers Support Group.

If two of the three people are married to each other, they wouldn't need to shake hands, so there would be two handshakes (the husband and wife each shaking the third person's hand.)

If two of the three people are Orthodox Jewish men (not allowed to touch a woman other than their own wife), and the third is an unrelated woman, the only legal handshake would be between the two men.

Or it could be that each person shakes every other person's hand exactly once, in which case you have three handshakes.

That last possibility is actually the preferred one; the handshake question turns out to be a classic problem. For the problem to work as intended, it must be assumed (or better yet, stated) that each person shakes every other person's hand exactly once.

The problem is fairly sophisticated; as you add people to the party, you wind up taking the sum of an arithmetic series. I think it would go right over the head of a kid brought up on the thin gruel of Trailblazers Math.

Theirs not to make reply,
Theirs not to reason why,
Theirs but to do and die:
Into the valley of Death
Rode the six hundred.

(from The Charge of the Light Brigade, by Alfred, Lord Tennyson.)

"Ours not to reason why, just invert and multiply."

(origin unknown; describes the rule for dividing one fraction by another.)

The "just invert and multiply" rhyme is often quoted as a parody of bad traditionalist teaching, where kids just memorized algorithms, without understanding why they work or how to use them appropriately.

But I will confess that I've been meaning to teach "ours not to reason why, just invert and multiply" to the Trailblazers-befuddled 6th grader that I'm tutoring. At least it would help her remember the rule, and if she sees it enough times, we can approach real understanding.

While it may be true that just memorizing algorithms isn't enough, and that kids should ALSO understand how and why they work, you can't claim victory by just avoiding the standard algorithms.

Here's an interesting non-standard approach that I just learned about (from Those Frustrating Fractions):

My latest epistle to the Head of School at Natural Friends:

Teacher Cranium -- I recently had the following conversation with a "New New Math" educated kid:

Me: You know the shortcut for multiplying by 10?

Kid: Yeah, you just add a zero.

Me: OK, what's 53.5 x 10?

Kid: Um... 53.50?

Me (horrified): That's the same value!

Kid: Oh, right. Is it 530.5?

Kids need to understand that it's not just about "adding a zero", it's about shifting the place value. In an ideal world, you should be able to ask the kid, "why does 10 have this special property, but not, for instance, 8?" and eventually get the answer, "... because we're in base 10."

Sincerely, FedUpMom.

Many educators feel that if kids are actively doing something, that means they are engaged with learning; conversely, if kids are just sitting quietly, they are not engaged. I've heard this expressed both by those on the far right (e.g., Whole Brain Teaching) and those on the far left (e.g., constructivist math.) Whole Brain-ers think that the kids' constant gestures and talking means they're engaged; constructivists think that if kids are measuring and graphing, they're engaged.

Unfortunately, life is not that simple. It is possible to be mentally engaged while sitting quite still (e.g., while watching a movie), and it is also possible to be mentally absent while moving around (e.g., daydreaming while folding laundry.) You can make kids move around, but that doesn't necessarily mean that they're interested in what they're doing, or that they're learning anything in particular. A bad project is less engaging than a good lecture.

For I have known them all already, known them all:—
Have known the evenings, mornings, afternoons,
I have measured out my life with coffee spoons;
I know the voices dying with a dying fall
Beneath the music from a farther room.

(from The Love Song of J. Alfred Prufrock, by T. S. Eliot.)

We find that in doing measurement activities, children learn about number. It’s a two-way street. Our approach is not, “Well, we’ll teach the kids about number, and once they understand number, then we can teach them about measurement, because measurement is based on number.” We find it works the other way, too: by doing various measurement activities, which are very engaging for the students, they’re building their number ideas.

(from Math Trailblazers, quoting one of the developers.)

I think the program is pretty good with measurement. Kids like to measure things, and the program builds on that; it builds on their interests.

(from Math Trailblazers, quoting a 3d grade teacher.)

(From the comments to The Birds, the Bees and Constructivist Math.)

... for me the key issue is not whether a math program promotes the retention of mathematical facts or concepts, but rather whether or not it stimulates or enables further learning. I think constructivist math programs, by continually frustrating kids, and by denying them basic competence, make it difficult for students to know whether or not they like math or have any real interest in it.

... there are some constructivists who believe that the end—as well as the beginning—of math instruction must always be real world applications. I disagree with this, since to me math is a language, and any pleasure I once derived from it came from this aspect of it.

Years ago, parents could buy little picture books to read to their kids when the tykes asked "Where do babies come from?". Designed for thoroughly embarrassed parents (isn't that all of us?), the books went through the conceptual habits of most of the animal kingdom (insects, fish, birds ...) before arriving at humans. This way, blushing Dad had time to work up to the really difficult stuff, and if he was lucky, the kid might have fallen asleep!

My college biology teacher told us that some genius did a follow-up study. It was very simple: he went around to kids whose parents had dutifully read them the book, and asked the kids "where do babies come from?" He discovered that the kids, understandably, had gotten the different species all mixed up. A typical answer:
"Daddy holds the babies in his mouth until it's time to go to the hospital."

Constructivist math takes a similar approach, with similar consequences. When the kid asks "how can I multiply two big numbers together?", constructivist math behaves like the blushing Dad, loosening his shirt collar with one finger while replying: "Here's an ancient lattice method, and over here is a partial products method, and oh, look! let's measure our armspan!" while never getting around to the method that everyone actually uses.

Since the kids don't really understand any of the methods, they tend to combine them, using steps 1 and 2 of one method, followed by 4 and 5 of another method, and coming up with the wrong answer after a great deal of effort and frustration. I say, cut to the chase! Just teach them the standard algorithm.