Blaming children for their ignorance, II: who's responsible?

"Children should be responsible for their own learning." Familiar as I am with this education world truism, it was only after I saw it echoed in educatoral's comment to my recent post that I made the connection to our tendency to blame children for their ignorance.

Here's what educatoral writes:

I'm not sure I understand what you mean by saying that no one has ever even attempted to teach kids those things. I agree that we are in need of reform to help our students learn how to take charge of their own learning, but I don't think there is a lack of teaching. At least not a widespread lack of teaching. Maybe teaching is the problem because there is, IMO, lots of teaching going on yet very little learning by the students. And also 59% of students not achieving a basic level on a standardized test isn't proof that they don't understand the phases of the moon.

The problem is that the more responsibility we pass on to kids, the less responsibility we take; and the more time we spend trying to help our kids become responsible for their own learning, the less time we spend actually teaching them anything.

Furthermore, kids aren't little adults; they are novices who depend on direct, structured instruction in basic skills and fact-rich core knowledge before they're ready to start taking charge. Absent such direct instruction, there will, indeed, be "very little learning by the students." 59% of students not achieving a basic level on a standardized science test isn't proof that they don't understand the phases of the moon; it does, however, suggest that, on average, students are receiving a very low level of direct instruction of basic scientific knowledge.

Math problems of the week: Symmetry in Connected Math vs. Singapore Math

I. From the 8th grade Connected Mathematics "Kaleidoscopes, Hubcabs, and Mirrors" chapter, Investigations 2: Symmetry Transformations, end of unit Connections and Extension problems, pp. 38-39:

II. From the 4th grade Singapore Math Primary Mathematics 4B Workbook, "Congruent and Symmetric Figures" chapter, final exercises, pp. 100-101:

III. Extra Credit: Singapore Math moves on from symmetry after 4th grade; 8th grade Connected Math spends 40 pages on it. What sort of real-world problems and careers will Connected Math students be better prepared for as a result?

Blaming children for their ignorance

Every so often a front page article exclaims how ignorant today's children are about history, geography, and science. An astounding number think that Iraq is in Central America, for example, or have never heard of the Iron Curtain or what causes the phases of the Moon.

Implicit in the subsequent handwringing is the assumptiom that something is wrong with today's children. They're too obsessed with pop culture or digital media; they're incapable of paying attention in class; they lack intellectual curiosity. Whatever can we as a society do about this? The answer, these days, almost always goes something like this: we should try even harder to spur curiosity by trying even harder to make academics exciting in the same way that pop culture and digital media are.

Consider, for eample, an opinion piece in last week's Philadelphia Inquirer by Dennis Wint, president and CEO of the Franklin Institute Science Museum. In Wint's words:

[Benjamin] Franklin would no doubt be dismayed at how perversely ill-prepared our population is for an economy increasingly driven by science and technology... Only 40 percent of Pennsylvania's 11th-grade students scored as proficient in science on the most recent state tests. In Philadelphia, that number drops to 16 percent, meaning fewer than one in six students has the skills needed to compete in much of the modern economy.

But help is on the way:

My organization, the Franklin Institute, is striving to confront this problem. The challenge is to build excitement about science, improve science understanding in the city, and resolve the contradiction between our industries and our populace.

To these ends, the Franklin Institute, along with:

105 partners - including nearly all the city's colleges and universities, all its library branches, and many of its nonprofit science organizations - [are] banding together for the Philadelphia Science Festival, a two-week tribute to science starting today. Through April 28, there will be hundreds of events in the city aimed at connecting everyone, from preschoolers to professional scientists, with the science, technology, and engineering that make Philadelphia what it is.

Ah, science festivals.

And ah, making science relevant to daily life:

We're trying to overcome barriers by weaving festival activities into the fabric of city life. We're exploring the science behind some of the city's favorite things, such as Phillies games and our favorite foods. And most of the events will be free, selling very little besides an enthusiasm for the science that underpins our lives - and the region's future success.

Why doesn't it occur to anyone that the ignorance of today's students might be a result, not of unprecendented deficiencies in curiosity (and in exposure to the marvels of technology), but of unprecedented deficiencies in K12 instruction?

If only Mr. Wint would take a closer look at another parnership that his institution has engaged in: its parnership with the Philadelphia School District, the result of which is a high school known as the Science and Leadership academy. Here, for all the public accolades, for all the parents clamoring to get their kids in, and for all the emphasis on the thrills of hands-on science, 59% last year's 11th graders performed "below basic" on the very same state science exam whose atrocious city-wide results Wint cites in motivating the upcoming science festival.

Perhaps it's simply too difficult for people to believe that the reason why kids today can't locate Iraq or the former Iron Curtain or the relative positions of the sun, earth, and moon when the latter is full is that no one has ever even attempted to teach them these things.

Home schooling, week 8: The Sword of Damocles

I mentioned last week that one of the benefits of homeschooling goes to Mommy: she gets to learn, or relearn, stuff that she wishes she remembered from her earlier education--for example, the Sword of Damocles.

Why do I need reminding of Damocles' sword in particular? Isn't it one of our most frequent allusions to classical myths? Isn't it one of our preferred ways of dramatizing impending doom? In the words of idioms.thefreedictionary.com, "if a sword of Damocles hangs over someone, they are in a situation where something bad is likely to happen to them very soon."

But when, perhaps for the first time, I read this week's classical myth, I learned that what Damocles was experiencing was more than a sword hanging by a single horse hair over his head. He was also experiencing what it was like to be an all-powerful ruler. According to the myth, Damocles was placed in this precarious circumstance by the tyrant Dionysius, who had tired of this courtier of his carrying on about how wonderful it must be to enjoy such great luxury and power. Dionysius ordered Damocles to spend a day sitting on his throne, and it was there that Damocles looked up and saw the suspended sword. Shortly thereafter he begged permission to step down, having seen, as it were, Dionysius' point: that wonderful as it might seem to enjoy so much power, those that do also face constant threats from their many enemies.

Interpreted in this way, the Sword of Damocles might more appropriately symbolize the threats incurred by those in power, as opposed to an impending doom that might strike anyone. But perhaps it's harder to see in Damocles' sword the threats of parody, satire, muckracking, censuring, impeachment, bad poll results, and electoral defeat.

After all, how many of us ordinary folk can relate to what it's like seeing this particular kind of doom looming whenever we look up?

Programming--idealized education

J has just completed his latest Python program--one that lists all the prime factors of whatever number you input. He's really into the programming, and this has got me thinking about how ideally suited basic, interactive programming is to learning.

-It provides immediate feedback: as soon as you run your code you see whether it works, and if not, where the problems are.
-Learning is active: it's still up to you to figure out how to fix the problems.
-Standards are high: Computer programming is unforgiving--even of tiny errors. The program simply won't run if you make any mistakes.
-In particular, you must express things clearly and logically, without any syntax mistakes, missing steps, inconsistencies, or undefined terms.
-There's consistent, effective reinforcement: when you get it right, the gratification is immediate and intrinsic (your program works!)

Can't we make all learning this way--and stop saying it's bad to have high standards, unforgiving feedback, and the ever-present authority of an absolute truth that won't let you get away with anything?

J, in particular, is engrossed by this environment. Here's his prime factors program:

def div():
number = input('Enter the number: ')
division = 2
factor = 1
while division < number + 1:
if number/factor % division == 0:
print division
factor = factor * division
else:
division = division + 1
while 1==1:
div()

Math problems of the week: 2nd grade Investigations vs. Singapore Math

I. A 2nd grade Investigations homework sheet, assigned in mid-October:

II. The first assignment in the 2nd grade Singapore Math workbook (Primary Mathematics, 2B):

III. Extra Credit: Which is more challenging, Tens Go Fish, or Go Fish? What should Tomorrow's Number be?

Autism diaries XXV: Fate vs. Free Will

Why does he always ask his most interesting questions at 10:30 at night in the bathroom? Here I am, standing next to the toilet, ready to oversee his toothbrushing. He enters the room, walks over to the sink, takes his toothbrush, and then pauses, staring into the middle distance. Laying down his toothbrush he crouches down to the tile floor, turned away from me. Here we go. I close the toilet bowl and sit on the lid.

"Maybe, after I die, I will start a new life in a new universe." (Ever the skeptic, he's a big believer in Multiverse Theory). He turns his head back towards me.

"Maybe you've already died many times in many universes."

He turns away excitedly. "Maybe when I start a new life in another universe, my memory resets."

Actually, one of our most interesting conversations about the universe took place not in the upstairs bathroom, but in front of an exhibit at the New Haven Eli Whitney Museum last December: a complex, pinball machine-like structure of shoots, ramps, and drops, with various levers and pendula directing marbles one way or another depending on which direction they happen to be sloping or swinging in the moment.

"How many different ways can the marble go?" I asked him.

Lifting his finger he traced a dozen or so paths.

"Are the marbles' paths random?"

"No. They're not random." His answer was decisive.

"But do we know which way the marble will go when we drop it down the top shoot?"

"No." He paused. "It's random to us but it's not random."

"So it's ransom to us, but it's actually determined." I knew he knew the concept of determined; I seized on the chance to introduce its label.

He liked it. "It's determined."

"What about the weather? Is it random or determined?"

"It's determined."

"What about the universe?"

"Determined."

"But if it's determined, how can you have choices? How can you have free will?"

His solution to this age-old problem was instantaneous. "My brain is part of the universe."

I trotted out another one. "Are you the same as your brain?"

"Yes!"

Cut back to the upstairs bathroom, one spring evening a few days ago.

"What happens if you go past the edge of the universe?" he asks, putting down the toothpaste.

"Maybe by going past the edge of the universe you make it bigger." (I can play at this game, too).

"Maybe the universe is expanding in all four dimensions. The past is already there, but the future is not yet written." He puts down his toothbrush. "Maybe the universe is like a cone." And he demonstrates a cone expanding in multiple directions from a single point.

I shift my weight on the toilet seat, thinking of Minkowskian space time.

"Is the future determined?" I ask.

"Yes. All of the living things write the future together."

"What about nonliving things?"

"Nonliving things are determined by the big bang." he replies.

"And by living things."

"So the future hasn't been written. Your future is what you make it," he replies, switching gears from Hermann Minkowski to John Calvin by way of Back to the Future III. "I need to prove that I'm in a good universe by behaving myself. And looking carefully when I cross the street."

"Yes!"

Home schooling: week 7

In The Learning Gap, Stevenson and Stigler remark on much time is lost in American schools, (as compared with schools in East Asia) to transitions: time spent transitioning between classes; time spent transition from activity to activity within a class; time spent regaining the class's attention after it has been totally distracted by those lengthy transitions.

Now in my 7th week of home schooling H, I'm appreciating how easily home schoolers can go to the opposite extreme. No more laborious lining up and waiting to enter or exit rooms, buildings, and buses; no more waiting for everyone to wrap up an activity and locate all the materials they need for the next one; no more waiting until the class quiets down, or until someone finally answers the teacher's question, or until it's finally your turn for the teacher to help you out.

Instead, we can line up all the materials ahead of time, in order, on the long dining room table. Lunch is just one room away. The basement, or "gym" (roller skating and ping pong), is just below you. Mommy is never more than a couple of rooms away and can come running and your beck and call. For field trips, you just hop on your bike or catch the trolley a block away. That's not to say that we don't take breaks. But you have much more time for real breaks--and long breaks--when you're being so much more productive. For, besides minimal transitions, we try our best to have absolutely no busy work.

As Dierdre Mundy has observed in one of her comments on this blog:

If [schools] eliminated all the busy work, the school day would only be about an hour and a half long! And then people would have to PAY for babysitters!

Of course, as soon as you start home schooling you relinquish those baby sitting services, and may finding yourself not quite as productive in your other professional capacities as you were earlier.

Programming update: primes in Python

In my last post about programming I lamented the difficulty I was having downloading an interactive, basic programming package for my son. I got a lot of help from people posting in the comment thread, and decided to try out Python.  After downloading it (for free) from the Python website, I was able, with the help of a Youtube video, to see how to run it interactively on my Mac.

Since then, I discovered a great Youtube series that teaches the basics of Python in 44 short lessons (4-6 minutes each). J and I have spent the last few weeks watching these together, listening to Bucky, the Python tutor, as he typed out code in his Python shell window, and as we mimicked him in ours. 

(Bucky, by the way, has a huge number of teaching videos on his Youtube channel, TheNewBoston, including biology and geometry. He himself is a college drop-out who finds the Internet and Youtube a much more cost-effective environment for learning than college. Perhaps we'll find other ways to take inspiration from him down the road!)

J and I have now finished watching most of Bucky's videos and I've given him his first couple of programming assignments. First I had him write a simple program that would solicit an arbitrary  number and say whether it is odd or even. The next day I asked him to change his code to calculate instead whether the number is prime or composite. It took him about 20 minutes, and he needed a couple of vague guidelines from me and specific reminders from Bucky, but he did it on his own, down to his endearing garbling of "composite":

def prime():

    number = input("Tell me a number: ")

    num = 2

    while num < number+1:

        if number % num == 0:

            raw_input('Compositive')

            break 

        else:

            num=num+1

        if num==number:

            raw_input('prime')

            break

while 1==1:

    prime()

Interested parties can download Python, cut and paste this directly into a .py file, and check it out.  J's next assignment, meanwhile, will be a program that outputs all the prime factors of a given number.

Math problems of the week: 4th grade Trailblazers vs. Singapore Math

I. The final decimals problems in the 4th grade Math Trailblazers Discovery Assignment Book, "Using Decimals" chapter, (before two math games at the end of the chapter), pp. 153-154:

II. The final decimals problems in the 4th grade Singapore Math Primary Mathematics 4B Workbook, "Decimals" chapter, (before two decimal rounding exercises at the end of the chapter), pp. 32-33:

III. Extra Credit: a. What is your favorite version of base-ten shorthand? b. How long will it be before, following in Dan Meyer's footsteps, Traiblazers goes digital, Professor Peabody becomes an animated character, and his Hundredths Chart becomes an interactive game?

The conspirators that keep Reform Math in place

1. The education schools, of course. Nearly all of them have Progressive Education pedigrees, and the theory behind Reform Math, Constructivism, is the latest incarnation of educational progressivism.

2. Their student indoctrinees who become teachers, principals, curriculum consultants, curriculum developers, and grant readers for the deep-pocketed education division of the National Science Foundation.

3. The media, for whom classrooms of students in groups doing hands-on projects (and people who talk about what a great new idea this is), make for more attention-grabbing news than classrooms of students in rows doing pen and paper exercises.

3. Postmodernists and Critical Theorists, suspicious of the rigid truth and authority of traditional mathematics (and the idea that 2 + 2 necessarily equals 4), and seduced by Reform Math's open-ended problems, multiple strategies, meta-cognitive reflections, and resistance to single correct answers.

4. The many mathematicians who haven't looked closely at the curriculum but tend to like (and trust) what they hear about it. Here a whole separate paragraph is necessary:

More than others, mathematicians tend to remember traditional math as gratuitously tedious: perhaps for them the drills and algorithmic practice were especially tedious, and perhaps they weren't as dependent on others are on doing these things in order to obtain mastery, making drills seem pointless to boot. As teachers of college students, mathematicians are also constantly looking at the end of the pipeline, where what emerges are college freshman who increasingly lack conceptual understanding. Told by "education experts" that Reform Math emphasizes conceptual understanding over meaningless rote learning, they conclude that Reform Math is the remedy, rather than being part of the problem.

5. Those at the opposite end of the mathematical spectrum: mathphobes and their parents. People, that is, who don't value rigorous math and who themselves, and/or whose children, are not mathematically inclined and do "better" with Reform Math's version of mathematics.

6. Lay people who either know little (or care little) about mathematics, or don't have children in school, or don't examine their children's homework assignments and compare it to what they were doing in math at the same age--and who subscribe to current middle class cultural truisms.  Such people tend to love buzzwords like "hands-on", "conceptual understanding," "no one right answer," "multiple intelligences and learning styles," "child-centered," "taking ownership," and "making math relevant," as much as they flinch at "worksheets," "drill and kill," "mere calculation," "teacher-centered," "one right answer," and "dry abstraction."

7. Liberals of the knee-jerk variety who find anything traditional and authority-centered to be politically suspect; and/or who believe that traditional math instruction doesn't work for disadvantaged and/or nonwhite and/or non-Western children, and/or privileges privileged white children, thus widening the achievement gap .

On the other side? Nearly everyone who understands math deeply (at least through arithmetic, algebra, and geometry), cares about math, has taken a close look at the Reform Math curriculum, and has school-aged children. 

Unfortunately, however much more qualified members of this second group are to assess Reform Math, they're far outnumbered--and out-buzzed--by those populating the educationist / postmodernist / out-of-touch mathphilic / in-touch mathphobic / middle class populist / knee-jerk liberal fronts.

Home schooling: week 6

The basic routine continues, with a bike trip to the closest big library, following a course she plotted out on a local street map that she constructed beforehand. Prone to motion sickness, she much prefers field trips by bike over field trips by automotive vehicle, and we do those whenever possible. She also labeled and mapped the ancient world, locating once again the historical and mythical events she's been reading about.

Mom, meanwhile, is relearning what little she once knew about ancient history and then some. Indeed, while Mom is spending more time on daughter's education than ever before, she really appreciates how much more of it is quality time: (re)learning interesting stuff and rereading classic tales rather than bugging daughter about completing the latest Investigations worksheet and prompting her through the latest organizationally demanding, uninspiring (to us at least) project. Right now we're missing the Moon Journal... and are getting along much better as a result. 

The ideas that buzz: modern educators, clinicians, and writers

In this day and age, it's increasingly about buzz. The principals, headmasters, and institutional partners of our "best" schools (the ones that get front-page newspaper coverage, celebrity visits, and long waiting lists of eager applicants) are those most adept at public relations. The more buzz, the more applicants; the more applicants, the more cherry-picking of applicants; the more cherry-picked the admitted students, the higher the school's test scores and college admissions rates; the more impressive these statistics, the more buzz, and so the cycle continues, even if the school itself adds less academic value than many other schools that receive much less public attention.

Some of the most sought-after autism clinicians similarly buzz their way to success. The more potential clients you attract, the more you can bias towards those who look likely to undergo spectacular progress regardless of the actual quality of your clinical interventions.

And (as I know from personal experience) nearly all of today's writers must buzz their way to their book deals, where advances, advance publicity, and, ultimately book sales, are determined, not nearly as much as they should be by what you say and how you say it, but increasingly by who you are, who you know, and how many people therefore listen when you buzz out your sales pitch and talking points.

What about scientists? How much do personal connections and buzz determine who gets those big grants that are so essential to research (and tenure)? And what about artists and movie-makers?

Put another way, how many ideas--indeed, how many whole classes of ideas--will never get a public hearing, simply because they are specific to the sort of quiet introvert who doesn't know how, and/or doesn't want to bother, to out-buzz the ever rising din?

Problems of the week: 3rd grade Investigations vs. Singapore Math

Two ways to introduce fractions: I. A recently assigned 3rd grade Investigations homework sheet:

II. The first fractions problems in the 3rd grade Singapore Math workbook:

III. Extra Credit What sort of remediation activities should Investigations offer to 3rd grade students who aren't able to divide a heart in half and label the parts?

Between the basic elements and the fuzzy abstractions...

One of the biggest disconnects in education is the leap that so many K12 classes make between the low-level elements of a given subject and certain fuzzy heights of abstraction or fuzzy breadths of big picturism.

In math, it's either low-level "math facts" and terminology (7 + 8, 7 × 8, "liter," "ray," "kite," "box and whiskers," and "number sentence"), or "meta-cognitive" reflection and interdisciplinary/arts & crafts projects (explain why your answer is correct; reflect on what you still need to work on; invent a game using everything you know about math).

In social studies, it's either memorizing names, places, and terminology (who was William Penn; where is New England; what does "colony" mean) or broader themes (genocide; racism) or big projects (choose a country and write a travel brochure; invent a culture). 

In K12 writing classes, it's either individual words (spelling words, learning their definitions, or identifying their parts of speech), or paragraphs and beyond (the 5-paragraph essay, the personal reflection, the narrative, etc.).

In foreign language, there's a similar leap from word-level (vocabulary) to the level of conversational utterances (what's now called "communicative competence").

And, looking beyond the classroom and backwards into the pre-K years to therapies for autism, there's a parallel leap between the words and categories of Applied Behavioral Analysis and the naturalistic conversational pragmatics of DIR/Floor Time and Sally Rogers.

What lies between? What links the levels together and is all-too-often ignored by today's teachers and therapists? Structure. 

There's the mathematical structure of arithmetic and beyond, complete with the conceptual connections among addition, subtraction, multiplication and division; the standard algorithms of arithmetic; the base 10 number system; and the interrelationships between them all.  

There's the chronological, causal, and geographic structure of history (it's telling that while memorizing names and terminology is still popular, memorizing dates and sequences and global and relative locations is not): the matrix into which all the facts fall and become meaningful and memorable, and from which the broader themes emerge. 

There's sentence structure or syntax: the multiple ways to structure sentences and what to consider in picking the one that best delivers the message and best links up with and flows into the adjacent sentences. 

And there's the overall grammar of language: the multi-tiered structure that combines words together in the specific ways that make communication possible.

Why do so many educators (and autism experts) neglect these things? Is structure too dry and abstract; too hard to teach; presumed to be too hard to learn? Or, in our right-brain world, do people simply forget, or want to forget, that structure even exists?

So here's to making structure the centerpiece of instruction. After all, the route to mathematical understanding is understanding mathematical structure; the route to understanding history is acquiring an organized, fact-rich, core knowledge of history; the route to writing well is choosing among the myriad ways to structure sentences (for any given message, there are almost always more syntax-level options than there are options at the level of word choice); and the route to learning a new language (or mastering your first language) is understanding how the words fit together into grammatical structures.

Without structure, the basic elements are meaningless, unmemorable dross; the abstractions and big picture are a messy, uninteresting blur; and conceptual understanding--true conceptual understanding--however promisingly it sparkles in the distance, remains forever out of reach.

Home schooling: week 5

 This week's highlights include calculating area (as in this week's Singapore Math problems of the week), finishing Little Town on the Prairie and starting Prince Caspian, reading about Theseus and the Minotaur and the ancient Greeks, listening to Vivaldi's Four Seasons and Telemann viola and recorder concertos, watching Ocean World and Frozen Seas, and going to the Camden Aquarium with Daddy (while Mommy and older brother were off visiting colleges).

Yes, both of us parents have (somewhat) flexible schedules, and now I'm constantly reminded of how very lucky we are. I wonder how much higher home schooling rates would be if only more parents had the time and the scheduling flexibility.

Race to Remediation, II

I often hear people ask, "which is it -- are kids overworked or underprepared?" I think it's a false dichotomy. It is absolutely possible for kids to be both overworked and underprepared, and I think it's extremely common.  -FedUpMom

Beyond the ever more competitive college admissions process, there's a second reason for the unprecedented levels of stress experienced by today's high school students. This, too, is hinted at by Race to Nowhere, specifically when it addresses the pressures of preparing for the Advance Placement tests. But Race to Nowhere attributes this stress to the AP itself and leaves it at that, failing to address why AP tests might be so much more stress-provoking than they were a generation ago.

To answer this question, one shouldn't look forward towards the college admissions process, but backwards towards K8 education. Here, all those watered-down math and science classes and content-impoverished social studies classes disadvantage even our top students, such that by the time they reach high school it's hard--and extremely stressful--for them to make up for lost time, whether in math, biology, chemistry, or history.

Ironically, by blaming high schools and colleges rather than elementary schools and middle schools we may end up deciding to dumb down the high school curriculum and the AP tests, rather than redesigning our K8 classes so that they actually prepare students for high school level work, and those who are potentially capable of them for AP-level classes.

But in a society that touts slowing down, de-stressing, avoiding frustration, and boosting self-esteem, and that finds it so loathsome to target instruction towards those who are most academically capable, this is not likely to happen any time soon.