kitchen table math, the sequel: 2/17/08 - 2/24/08

## Saturday, February 23, 2008

### why worksheets may be better than flash cards

I've mentioned a few times that I had no luck using flash cards to teach C. his math facts. Paper flash cards didn't work; online flash cards didn't work. We futzed around with those things for what seemed like eons.

What worked - and worked fast - were the Saxon Fast Facts worksheets.

Maybe this explains it:

Mr. Karpicke's studies suggest that if you want to implant facts in long-term memory, it's best to receive feedback on a quiz after a short delay of 5 to 20 minutes. But flashcards (at least as they are ordinarily used) give feedback immediately.

In an experiment presented last month at the annual meeting of the Association for Psychological Science, Nate Kornell, a postdoctoral fellow in psychology at the University of California at Los Angeles, and Robert A. Bjork, a professor of psychology there, asked people to study 20 word pairs on flashcards during a one-hour period.

Half the participants reviewed the full cycle of 20 cards eight times. The other half broke up the pile into small stacks, studying five cards at a time, reviewing them eight times, then moving on to the next small stack.

Early in the experiment, the people using the small stacks felt pretty good about their progress. They predicted (on average) that on the final exam, they would remember 68 percent of the words. The people studying the full stack, by contrast, predicted that they would remember only 53 percent.

But on the final exam administered at the end of the hour, their performance was actually the opposite. The people who repeatedly studied the full cycle of cards had an average exam score of 80 percent, while the "small stack" participants scored only 54 percent.

Now, you might say that's just because the "small stack" participants had forgotten the words that they studied in their first batches, early in the hour. But even on the words they studied in their last batch, the small-stack participants scored just 68 percent, so their performance still trailed that of the full-stack group.

This is just the latest piece of evidence, Mr. Kornell says, that cramming doesn't work. When you study an unfamiliar fact again and again in immediate succession, he says, it feels much better embedded in your memory than it actually is. It's much better to create an interval between the times you study an item. (The people cycling through the full stack of cards studied each card every seven minutes or so, which is a decent interval.)
Why Cramming Doesn't Work

The Saxon Fast Facts worksheets are designed to be done in 5 minutes or less.

C. used to do his sheet in 3 or 4 minutes (it would be 5 or a bit more the first couple of times, but he always progressed quickly).

So: time delay of a few minutes.

Those sheets worked like magic with another boy who was classified SPED. (High-end SPED: the kind of kid who wouldn't be SPED if schools practiced direct instruction and precision teaching.) His progress from one week to the next was almost bizarre. First time I gave him one of the sheets to do he took 10 minutes at least. Second time - one week later - he was down to maybe 7 minutes.

Third and last time: he came in under five with no mistakes.

You can buy the Saxon Fast Facts books as stand-alones, but you have to buy the solution manual, too, I think.

## Friday, February 22, 2008

### How To Study, from A Pro

From the British Psychological Society's blog, BPS Research Digest:

Although as students we have all spent countless hours studying, we receive little guidance in how to study effectively. There are no shortcuts to effective studying, but in general, being actively involved in learning makes studying effective. Some specific points are obvious: pay attention in class, do the reading, don’t procrastinate, while others should be obvious but aren’t: study in a quiet place without distractions, don’t send text messages during class, ask questions if you are confused.

Here are three unintuitive but very effective ways of studying based on findings from psychological research:

Also check out Professor Kornell's webpage for more provocative information.

### androgogy

I just thought I'd throw that out there.

(scroll down)

### The Teacher by Jocob Abbott, 1844

The Teacher by Jacob Abbott, 1844

Thanks to Google, gems like this are being preserved.

There are three kinds of human knowledge which stand strikingly distinct from all the rest. They lie at the foundation. They constitute the roots of the tree. In other words, they are the means, by which all other knowledge is acquired. I need not say, that I mean, Reading, Writing, and Calculation.

Teachers do not perhaps always consider, how entirely and essentially distinct these three are from all the rest. They are arts; the acquisition of them is not to be considered as knowledge, so much as the means, by which knowledge may be obtained. A child, who is studying Geography, or History, or Natural Science, is learning
facts,--gaining information ; on the other hand, the one who is learning to write, or to read, or to calculate, may be adding little or nothing to his stock of knowledge. He is acquiring skill, which, at some future time, he may make the means of increasing his knowledge, to any extent.

This distinction ought to be kept constantly in view, and the teacher should feel that these three fundamental branches stand by themselves, and stand first in importance. I do not mean to undervalue the others, but only to insist upon the superior value and importance of these. Teaching a pupil to read, before he enters upon the active business of life, is like giving a new settler an axe, as he goes to seek his new home in the forest. Teaching him a lesson in history, is, on the other hand, only cutting down a tree or two for him. (p. 64)

…and social studies is a worm-eaten leaf that had not yet appeared on the tree.

For some of his thoughts about math, I recommend reading pages 90 – 95. He manages to explain longitude at the first grade level! (And while he claims that his steps were too short and could be lengthened, I confess that I thought they were just about right for me, and I’ve done extensive work with polar math in the past.)

## Wednesday, February 20, 2008

### Core Knowledge, Saint Paul style

At least two Saint Paul public elementary schools (not counting any charter schools) claim to be Core Knowledge schools. One of them, Randolph Heights elementary states on its website here:

"Randolph Heights has been teaching the Core Knowledge curriculum since 1999, and was recognized as an official Core Knowledge school in December 2006. "

Well, that's nice. What does it actually mean? The CK site is clear that it does not dictate methods or materials use; Core Knowledge is about what students should learn, not how they should learn it.

What's the typical use of CK at Randolph Heights look like? Here's the 5th grade web page excerpt:

Everyday Math will help your child learn many new concepts such as Number Theory, Estimation, Geometry, Division, Fractions, Decimals, Percents, Exponents, Negative Numbers, Coordinates, Area, Algebra, and Probability.

We will using the Reader’s and Writer’s Workshop models for our Literacy Block. Your child will be involved with Guided Reading Groups, Book Groups, and reading independently. We will be learning reading strategies such as making connections, visualizing, making predictions, questioning, inferring, and summarizing through mini-lessons, authentic literature, and personal responses to their own reading.

Your child will be gathering seed ideas and developing ideas in a writer’s notebook. From these ideas, we will be writing and publishing Personal Narratives, Procedural Writing, Informational Writing, Writing Conventions, and Response to Literature. We will use Mentor texts to study author’s craft. Vocabulary will be developed with Word Wall and Spelling activities, and students will be practicing their handwriting skills with the Handwriting Without Tears curriculum."

Where does CK fit into this? The sixth grade web site makes it more clear:

OUR DAY
8:55 am -9:30am Homeroom & Morning Meeting
9:30 am- 11:10 am Readers’ & Writers’ Workshop
11:10 am- 12:00 pm Art, Phy-Ed or Science
12:05 pm - 12:35 pm Lunch
12:35 pm-1:45 pm Everyday Math
1:45 pm-2:05 pm Recess
2:05 pm-3:05 pm Core Knowledge Curriculum
3:05 pm-3:35 pm Social Studies

### Changing our Assumptions

In the earlier post , I commented that I consider people awfully good at being rational given their initial conditions--it's that their initial conditions can be so far from accurate that they have issues.

Catherine said in the comments in response
"I generally think that the nutty things people do usually make perfect sense from their perspective...Nevertheless, people do -- and then carry on doing -- a lot of things that bring them grief. Then they carry on being surprised that they are experiencing grief."
This habit of ours to repeat things that bring us grief, is a good example of bad priors. "My friend won't be late THIS time, she knows I can't afford to miss this plane flight" comes from unreasonable initial conditions: the prior probability that a friend will arrive on time is based on wishful thinking, or other friends, or what should be, but not adjusted to the evidence.

Why is it SO HARD for us to change our prior probabilities, even in the face of lots of overwhelming data? I don't know enough neuroscience to answer this question, but it's clear that by the time we're late adolescents or adults, our prior probabilities for our experiences in the world are pretty darn fixed.

We've got priors for the littlest details in our world. We've got priors for the next word in the sentence to be a verb, and priors for the next note in a song. This is why the sight-reading method and whole language methods can be so destructive: the students' brains are busy creating priors for "this word starting with "s" is going to be "sleep" ", rather than actually READING the word and finding out it's "silent".

Changing our priors is really what that "slowly pushing the wall" analogy is about. For kids, whether it's their behavior around chores or their learning to read, we're better off trying to be darn sure that the priors we're forming in their minds are true, rather than finding out later that they've become prejudiced against the symbols in front of them.

### dumbfounded

Today I learned several things about the Saint Paul, MN public school district that made me dismayed, but one that had me dumbfounded. I shouldn't have been surprised, but still, what I learned was so clearly an admission that what's best for students has NO PRIORITY in the district's calculus that I couldn't believe they admit it.

As background, let me state that every school in the SP district is run "independently" in terms of philosophy, including every neighborhood elementary school. Some are Core Knowledge schools. Some are Achievement Plus schools. Some are Montessori. At least one claims to be a Differentiated Learning school. This, combined SP's rules allowing parents to apply to any school in the district through neighborhood reassignment or the nearly 3 dozen various magnets sounds like there must be a school that's perfect for you somewhere, right?

So what did I learn?

School start and end times for all Saint Paul public schools are set by the SPPS's Department of Transportation.

That's right, their DoT determines when each school starts and ends based on their logistical plan for bus routes and available buses.

To be clear, let me elaborate: the DoT does not determine a uniform start time for the schools in the district. Each Saint Paul school may start at a *different* time, and start times are not guaranteed from year to year.

I heard this marginally defended today, as well. The argument was that this time issue allowed parents to choose the school "most convenient to their schedule."

Not to malign the complex issues that arise with multiple kids and juggling of careers, but to exercise school choice in order to make your commute more convenient seems the ultimate admission that you don't value academic excellence, or perhaps more likely, that even though you had all of the above choices, you know it *doesn't matter which school you attend*. But more the point, that's what the school district is telling the students, too, isn't it?

### Bride of Wildenstein

Rich divorcee Jocelyn Wildenstein spent a rumoured £2million on cosmetic surgery to keep her husband, but succeeded only in ruining the good looks she was born with.
These photos are not for the faint of heart.

You've been warned.

The kicker:

The first time Wildenstein saw his newly-sculpted wife, he was said to have screamed in horror, unable to recognise her.

The horror.

### The Everyday Math Survival Guide

From what I've seen so far, Everyday Math (EM) has few redeeming qualities as a primary source of elementary math instruction. I have heard that it works well as a supplemental source of instruction. I suppose the idea is 1. to use EM as a source of somewhat atypical practice problems and 2. that students will get more out of EM's conceptual oriented pedagogy if they have a firm prior understanding of the underlying procedures.

I remain somewhat dubious of the efficacy of both of these rationales. From my experience with the first and second grade EM materials, a large percentage of EM's practice problems are simplistic, dopey (that's a technical term), or both. Usually both. And, the amount of practice problems is woefully inadequate even for students who don't require as much practice (i.e., the students who typically excelled under the traditional curriculum). Moreover, EM's "conceptual understanding" is wildly overrated. Conceptual understanding does not begin and end with pattern matching as the authors of EM seem to think. A much better supplemental curriculum for teaching conceptual understanding is Singapore Math, but I digress.

Nonetheless, the best way to get through EM without befuddlement and tears is to treat EM as a supplemental curriculum. This implies that some other curriculum needs to be used as the primary curriculum. It also implies that the primary curriculum needs to stay ahead of the rather steep spiral employed in EM. This won't be easy because teaching to mastery takes longer that teaching to exposure which is how EM accomplishes its brisk pace and steep spiral.

Step One: Identify the Enemy. Beginning no later than kindergarten, you need to identify the math curriculum used in your school. If it is EM or some other fuzzy curriculum you need to select, secure and begin using a primary math curriculum in order to not only get a jump on first grade but to also take advantage of the light homework load of kindergarten and (hopefully) first grade.

Step Two: Select Your Weapon. I'm going to cut right to the chase here and tell you that my weapon of choice is Connecting Math Concepts (CMC). Other popular choices are Saxon and Singapore Math, but I picked CMC primarily because I thought it would minimize the amount of work I'd have to do. So far it has and I don't expect that to change. There are other reasons to select CMC:

1. It is fully scripted. This is key because while I fancy myself as an expert of elementary math, I am smart enough to know I am no expert in teaching elementary math. And, quite frankly, I don't want to become one. All I know is that when I try to teach a concept using my own words, I get a blank stare at least 50% of the time. When I use the script, I've never gotten a blank stare in over 200 lessons. You can't argue with that kind of success and I don't plan to.
2. The scripts are short. The teacher-led parts of each lesson take about 15 minutes to get through. The rest of the lesson involves the student working problems he's just learned or working distributed practice problems. I spend this part of the lesson in the teacher lounge, i.e., on my couch. I only emerge at the end to do a work check and to say "good job." Now, that's what I call teaching.
3. Zero prep time. My prep time consists of opening up the teacher's manual and doing some pre-reading as the student works some problems. I suppose if I was presenting to a class of lower-performers, I'd want to home my performance. But one non-low-performing student can tolerate an unpolished performance.
4. The scripts use simple language. Simple language is good because since you're going to be pre-teaching a student who is on the younger side of the expected student level.
5. Ample distributed practice. Distributed practice is built into the curriculum. This means you don't have to make-up your own practice sets. This means less work for you.
6. More is more. The curriculum is designed so that lower-performers can succeed. This means that your average or high performer will succeed as well. The only trick is to know when to cut back on practice problems, when to skip lessons, and when to convert teacher-led sections to independent work (this is a classroom curriculum in which some students will likely be absent, so teacher-led portions are repeated for absent students. My student, by definition, is never absent.) The general rule is that it is easier to cut than it is to supplement.
7. Relatively cheap. You can pick up used materials for about \$100 from EBay. Textbooks and workbooks are easy to come by. Teacher presentation books not so much. The presentation books are the script. There is supplemental materials, but you can generally skip those unless the student needs extra practice, which is unlikely.
8. Aligns well with EM. Almost everything taught in EM has been covered in CMC, at least so far. Concepts that have not been covered are generally concepts that most consider outside or tangential to traditional elementary math anyway, so relying on EM to teach these concepts is largely inconsequential. These are inert concepts anyway, nothing builds on them and they are not important to future learning, so not learning them to mastery now isn't critical.
9. CMC is aligned with Math Mastery. Math mastery is a dvd/online review course for elementary math. It was designed to remediate struggling students, but that doesn't mean you can't use it for review or for teaching some topics for the first time. The lesson presentation is very similar to CMC, except that it's multimedia. Kids like that kind of stuff. Go check out a sample lesson. My son wanted me to teach him multi-digit division. That's a topic that doesn't get covered until CMC level D where it is spread out over the course of the year. he didn't want to wait that long, so I just put in the division mastery dvd and he was introduced to division problems. He needs a lot more practice before I'll claim that he's learned it. But it's a good start.

Step Three: Calibrate your weapon. I've done the hard work for you here. No later than midway through kindergarten begin level B and strive to finish one level every 12 months. That's about three lessons a week at most. Remember weekends are your friend. So is summer vacation. And winter/spring breaks. Just don't go too long between lessons since the student is likely to partially forget newly taught topics if they've lain dormant too long. Why cause more work for yourself? Plus, one of the reasons why you're not relying on EM as the primary curriculum is to avoid this deficiency in the first place.

At this point you may be asking: what happened to level A? You can skip level A if you've taught your child how to count to twenty and how to recognize and write numbers, i.e., the knowledge that most middle-class families send their children to school with. plus, for some reason level A is difficult to find second hand. Also, level B reviews much of level A for the first few lessons anyway.

Step Four: Fire. Right now my son is in second grade and we are just finishing up level C of CMC and we have really slacked off this year since he has quite the busy social calendar this year and the amount of homework he's getting has increased. Nonetheless, we are way ahead of the EM curve by quite a bit. He can typically complete his EM homework in about 5 minutes with minimal parental involvement or explanation. I never have to re-explain an EM lesson to him because he already understands the underlying concept. And, he scores well on his tests. In short, I don't have to worry about what he's learning in EM or whether EM is adequately preparing him for higher level math.

The only problems we have are primarily related to bookkeeping. He is fluent with his math facts and can do quite a bit of arithmetic mentally. As a result, he doesn't like to show his work for work he can do mentally, especially when "show his work" means drawing a 7 x 8 array of dots or any of the other superfluous crutches EM relies on to excuse itself from teaching to mastery.

This is not exactly a bad problem to have.

I would have preferred that his school teach him properly in the first place for the same reason that I don't like having to re-bake bread I've bought from a bakery (especailly an expensive bakery).

So if you find yourself in the same situation, this is one proactive way to survive Everyday Math. And, it surely is less painful than going the reactive route which I do not recommend. Motivation is a difficult thing to win back once you've lost it.

### concerned teacher on how to teach organization

concerned teacher left this comment re: teaching organization:

And while we are teaching students how to organize any kind of notebook, it is important to "check", often at first, to see that students are following the proper organizational procedures.
Don't expect a disorganized student to learn it quickly or to even know if he is not doing it properly.

It will come easier for some, who are just "natural organizers", but we must not fail to help those for whom it is not easy.

I read that it takes doing something 30-35 times for it to become a habit. And it must be done properly every time for that habit to be formed.

Teaching students how to organize is like laying down tracks to guide them through the year. But tracks are no good if the student doesn't stay on them. And for some students, if they get off, they won't know where or how they got off or how to get back on.

from The Learning Gap:

The Asian teacher faces a very different set of demands from those faced in the American classroom. Dealing with thirty-eight to fifty children, with no tracking or separation according to their level of ability, imposes a strong need on the teacher to create order and structure. This is accomplished in several ways.

First, teachers make an explicit effort during the early months of elementary school to teach children techniques and skills that will allow them to function effectively in a group. Children learn how to move from one activity to another, how to arrange the contents of their desks so that they can find things easily, how to pay attention, how to follow directions, and how to speak loudly and clearly so that they can be understood. By equipping children with these skills, Asian teachers are able to handle large classes in a smooth and unflustered manner. Children's easy transitions from one activity to another and their readiness to carry out classroom routines occur not because Asian children are docile or passive, but because they have been taught efficient and useful ways of handling themselves in the classroom. Asian teachers are willing to take the time to teach these skills because, among other reasons, they know they will reap the benefits for more than a single year. The same group of children will remain with the teacher for two year, or sometimes even three or more.
p. 62

C. has had a number of teachers throughout middle school who directly instructed the kids on how to organize and manage their materials. This year's Spanish teacher is so precise she will tell the, "Put this paper here; put that paper there; throw that paper out." He's doing fantastically well in Spanish for the first time in 3 years, and I don't think that's an accident.

Thinking about it now, I bet if I went back through C's middle school years I would find that he's tended to do best in classes in which teachers directly taught and monitored organization.

His social studies teacher this year, who is in charge of teaching and overseeing the research paper all the 8th graders write, has it down to a science. He gives the kids a daily assignment to complete for the paper, and he checks at close intervals to find out whether the assignments have been done.

C. has been coming home every night saying cheerfully, "I have to do my social studies research" and then hustling off to the basement to work.

I think this is an invaluable lesson in the critical skill of getting long projects done day by day instead of, for example, waiting until the deadline is 8 weeks away and then pulling 2 months of all nighters.

Not that I know anyone who would do such a thing.

## Tuesday, February 19, 2008

### rational utility maximisers of the world unite!

a comment left by Tracy:

I regularly participate in a website devoted to the discussion of Jane Austen books, and it is surprising how often someone posts saying they don't understand why one of her characters made some decision that was not rational. A surprising number of people apparently expect everyone to act like the economists' stereotype of a rational utility maximiser and are confused when they don't.

And of course, if you think everyone is a perfectly rational utility maximiser, when you encounter someone doing something bad, the likely explanation is that they fully intended it, and therefore are bad people.

It's a hard process to raise some awareness in a person that they themselves are probably flawed as well.

This is a chronic source of amazement around here.

I mean, here I sit, not doing what I'm supposed to be doing (writing Wildlife Chapter), not managing my time well (or at all), not maximizing these my Peak Years of Productivity.....and, meanwhile, over in the parallel universe that is a public middle school, kids are receiving grades of F on their notebooks for poor organization.

I don't get it!

There are so many disorganized adults abroad in the land that "Professional Organizer" is a job.

Does it seem reasonable to anyone outside a public middle school that a sixth grade child:

a) can competently organize his math notebook
b) will promptly learn to organize his math notebook just as soon as he receives a grade of F for not organizing his math notebook?

It does not.

### the project method

I have a new bad web habit, thanks to Susan S.

So I was sitting here glued to my monitor, gaping at Spoiled Pageant Queen when the Project Method popped up.

Watch to the middle.

You'll plotz.

I promise.

### Total Lunar Eclipse - Ringside Seating Available

Don't miss the total lunar eclipse on Wednesday evening. Observers anywhere in the Western Hemisphere are promised quite a gorgeous display. If you miss it, you'll have to wait quite a long time for the next one -- 2010!

In the Americas, the eclipse happens during convenient evening hours on Wednesday, the 20th, when people are up and about. In the time zones of Europe and West Africa, the eclipse happens during the early-morning hours of Thursday, the 21st.

Earth’s shadow will totally engulf the Moon from 10:00 to 10:52 p.m. Eastern Standard Time, or 7:00 to 7:52 p.m. Pacific Standard Time [ ]. The partial phases of the eclipse last for about an hour and a quarter before and after totality.

Find out more about the total lunar eclipse at Sky and Telescope here and here.

February 20th's Eclipse of the Moon
All of the Americas will have ringside seats . . . weather permitting.
by Alan M. MacRobert

Sky and Telescope March 2008

### Parents Rise Up Against A New Approach to Math

Today you should be grateful--grateful your don't live in Prince William County, Virginia.

Greg Barlow, an Air Force officer in the defense secretary's office at the Pentagon, was helping his 8-year-old son, Christian, one recent night with a vexing problem: What is 674 plus 249?

The Prince William County third-grader did not stack the numbers and carry digits from one column to the next, the way generations have learned. Applying lessons from his school's new math textbook, "Investigations in Number, Data, and Space," Christian tried breaking the problem into easier-to-digest numbers.

But after several seconds, he got stumped. He drew lines connecting digits, and his computation amounted to an upside-down pyramid with numbers at the bottom. His father, in a teacherly tone, nudged him toward the old-fashioned method. "How would you do that another way?" Barlow asked.

What a horror show.

Here's a picture of Greg.

Anyone recognize that expression of exasperation?

This'll make him feel better.

"I don't know what happened in Prince William. Have the parents visited the classrooms? This has to be a decision made by everyone that's affected by it," said Cathie Dillender, a senior Pearson executive who handles math issues. "We have a lot of happy customers out there. We're all educators, too, and we certainly wouldn't publish a program that would not work with the kids."

Sure you wouldn't.

As for Greg Barlow in Prince William, the former fighter pilot with college degrees in aeronautics and astronautics, he finds himself in a new role: home-school dad. He has spent about \$100 at Sam's Club and Costco on math textbooks.

Poor bastard.

The engineers and scientists are always the canaries in the coalmine.

## Monday, February 18, 2008

Some interesting exceprts from Geraldine E. Rodger's "The Case for the Prosecution, in the Trial of Silent Reading Comprehension Tests, Charged with the Destruction of America's Schools."

Geraldine Rodgers is an amazing lady, much of what I know about phonics and reading, I learned from her. I'll let her quotes speak for themselves (plus, I've been sick, so anything I write myself is likely to be off a bit.)

“All those silent reading comprehension tests are a massive fraud. Back before 1911, when Binet of France originated the FIRST real intelligence tests, he used oral reading comprehension to test native intelligence, which is itself un-teachable. Binet’s reading comprehension paragraphs are STILL used to test intelligence. So reading comprehension scores are really IQ scores!” (p.1)

“The point remains: the phonic-trained reader is FREE when he is reading. Whether he pays attention or not depends on his training – AND on his mood, just as it does at home when his mother tells him to close the front door when he goes out. He may or may not leave it swinging. But the sight-word trained child can only read BY paying attention – divided attention, it is true. He will score lower than the best phonics children but higher than the phonics child who is not interested. This, I am convinced, is the reason school systems still buy sight-word basal readers. They may yield more consistent “reading comprehension” scores. A large sales job needs to be done to convince administrators that “reading comprehension” does NOT test reading but only intelligence plus attention, once the children know the high-frequency words.” (p. 206)

You can read a portion of Chapter 1 online at Amazon, it is the excerpt when you "search inside". In these pages, she talks about the deaf-mute origins of sight word teaching, syllables, Locke, Basedow, and how “Two currents of educational thought flowed from his teachings. One supported TRUE progressive education, and its respect for human will with its corollary, personal responsibility. The other supported the philosophy which eventually resulted in materialistic psychology and its denial of the existence of the human will. The two wires crossed in Columbia Teachers College in the early 20th Century. That short circuit has almost destroyed American Education.”

### how do character educators see children?

I sat in my kitchen, stunned by what I had just heard on the evening news: A young girl in a neighboring city had been sexually molested by other children under the age of 10. News reports about children and teens violently hurting one another, committing crimes, and sometimes taking lives made me wonder about what might have influenced them to act as they had. I began to consider the impact that I have on the moral development of the lst graders in my classroom. Could I do more to influence how they treated others?

I have always taught my students such concepts as honesty and respect, but usually in response to something negative that has already happened. I wanted to foster their desire to developpositive character traits before I had to deal with negative behavior. Although I believe that families provide the foundation for character development, I also agree with Thomas Lickona that "schools cannot be ethical bystanders at a time when our society is in deep moral trouble" (1991, p. 5). More than 90 percent of respondents to a 1993 poll agreed that schools should be involved in teaching such values as courage, caring, acceptance, and honesty (Elam, Lowell, & Gallup, 1993). Although I knew that my efforts could not cure all the ills of the world, I decided to try to make a difference in my little corner. My two challenges were to find time for character education and to create a program that worked.

source:
How Character Education Helps Students Grow
by Gloria Rambow Singh
Volume 59, Number 2

I'm just going to go ahead and call this moral panic.

I don't like moral panic.

### l squared on "collect and correct"

I teach college, so I feel a little as though I shouldn't have to collect homework...but, of course, I do. If you don't collect it, they don't do it. Collecting the homework may be the single most effective thing I do to improve student learning. I don't check all the problems, just 2-4 representative ones, but it still makes a big difference.

### Overlap of Consciousness and the trouble with spot checks

One of the underlying assumptions in the "it's the student's fault" paradigm of education is that students are simply un, non, or irrational thinkers. They can not be trusted to proceed rationally from premises to conclusions. They cannot be trusted to behave predictably. They are taught perfectly reasonable methods for solving something, and yet they do something completely unexpected instead.

But this is false. Students, even poor students, are not un or non or irrational thinkers. They drawn perfectly reasonable, rational, and valid conclusion to problems. They managed to do so and get the wrong answer because their premises are wrong, and they draw perfectly reasonable conclusions given their initial premises. If you had their premises, you'd end up in the same place.

As a grad student, what I found so compelling about teaching was figuring out where students were going astray. I thought of it as a puzzle: to understand "Why in the world does the student think THAT?!?!!?"

Solving the problem meant creating of "an overlap of consciousness". That sounds silly, but fundamentally, you cannot understand what your student does or doesn't understand unless you are so well inside their head that you can see from their perspective.

You have to pay enough attention to them to understand what premises they actually hold, not the ones you think they hold.

Correcting an error by fixing the end point wasn't enough because unless I got to the root of the problem, I'd never fix the error that led them down the wrong path. Correcting their error required an overlap of consciousness, a willingness to let go of my own assumptions and listen to what they were saying about how to solve a problem. I had to let go of my own knowledge, and be where they were.

Here's an example: telling someone who tried to solve "what is 4% of 150" and gotten the wrong answer after they did 150 / .04 that "you take a percentage of something by multiplying, not dividing" will elicit "okay". IT WILL NOT STICK. Why? because they had SOME REASON for doing it that way--somewhere, somehow, someone told them something that made them think that made sense. If you just tell them "no, do it this way", that bad reason will still be in their heads, and when they next get confused or lost or frightened, they will default to the path in their neurons that they've already made: The Wrong One.

What needs correction is understanding why they made that mistake, and what premise they are following. And you need to get to the root of that before anything else will really come together.

(Why might someone divide by 4%? Because they are trying to take a part of a whole, right? And when you take 32 into 8 parts, you divide 32 by 8. Isn't this 4% just a part of a whole?)

As a lecturer, you're responsible for fixing these mistakes and doing everything possible to not create these mistakes in the first place. That's the real puzzle of teaching: how to bullet proof your lesson against misleading your own students. Because by and large, it's the teacher's fault. We don't pick good examples, or good counter examples. We don't realize what other assumptions we're working with. We get sloppy. We don't try to model the mind of someone who knows much less than we do about what we're presenting. But if we are going to improve, we are going to have to create an overlap of consciousness.

Herein lies the problem with spot checks of homework. From one perspective, homework is to provide the student enough practice to learn mastery of a subject. But from another perspective, it's the teacher's only possible opportunity to create an overlap of consciousness with the student.

In college, it's possible (though still not likely) to query students well enough to understand where they went wrong, where you, the teacher or the book, misled them. In 5th, 7th, or even high school, it's practically impossible to get at this by querying, because the students will simply shut down. Unless you ask in the most gentle and subtle way possible, they will hear you asking "Why did you do that? why did you think that?" and hear CRITICISM. And that will be the end of you knowing what they think.

So the only way to create the overlap of consciousness if by a thorough investigation of their work, and a very problem-solving model in our minds. Why would a student make that mistake? What assumptions in their mind could have led them there? Is that consistent with other assumptions they are making, even on correct problems? How could what I said/left unsaid/assumed led to this?

You must do their homework with them, in your own mind. You must go through their homework from their perspective, and you won't do that in a 10 second spot check.

A spot check only allows you to see the mistakes---to see that correction is necessary. It doesn't provide fertile enough ground for you to figure out why they made those mistakes, or where they were misled. Reteaching isn't enough, either, because in all likelihood, you'll reteach them the same error, albeit unknowingly, or you'll just add layers of confusion onto the underlying error. Unless you can get to the point where you know why they made the mistake, where you can say "no, THIS IS NOT TRUE, I MISLED YOU" you really aren't fixing their problems.

Teachers must get creative to create an overlap of consciousness with their student. They must stop assuming they know what their students think, let alone why their students think the way they do. From there, they can build lessons that treat the source of confusion.

### bring back self esteem

I've mentioned a couple of times that I regret the fact that "character education" has replaced "self-esteem" as the psychosocial focus of public schools.

Of course, I have to assume that in practice any given school's definition of "high self esteem" may have been "self esteem on our terms," which in turn probably meant low self esteem, not high. But I still prefer self-esteem to character as a school's guiding principle.

Character education, in my experience, has been quite punitive. It almost has to be given its premise, which is that the character students have developed at home needs improvement -- and that the character of school personnel doesn't.

This is where the Bible has it right.

I'm not crazy about the notion of children as inherently more flawed than grownups to tell the truth. Very young children possesss all kinds of sweet, altruistic impulses along with the usual obnoxious impulses. Rightly or wrongly, I tend to see kids as innately good in a fundamental sense.

I'd like my kids to attend a school in which administrators, teachers, and support staff feel the same.

middle school and depression

Which brings me to middle school.

The difference between a middle school and a junior high, we have repeatedly been told, is that middle school "educates the whole child."

What does that mean?

It means, first of all, that academics often take a back seat to "character" education activities. Middle school kids here are required to attend a character ed assembly each and every month; to my knowledge the school has never, not once in 2 1/2 years, staged an assembly devoted to an academic or intellectual topic. Ed, reading Martin J. Wiener's English Culture and the Decline of the Industrial Spirit 1850-1980 last summer, wondered whether character education is always be opposed to academics. I think it may be.

Beyond this, I am coming to feel that character education, as implemented by so many of our public schools, is incompatible with the creation of a positive school environment. You don't hear Karen Pryor talking about "bad" horses and "bad" dogs -- quite the opposite. Pryor's view of dog aggression is: "It's just a behavior!"

Middle school kids would be far better off if middle school behaviors like not knowing how to keep track of 6 or 7 different courses at the same time were not viewed not as a sign of poor character.

Disorganization is just a behavior is a far more humane way to understand a spacy 11-year old. Giving a 6th grader an "F" on his notebook for disorganization strikes me as bad for the 6th grader.

Little did I know that middle schools crop up in research on the development of depression in adolescence as a contributing factor:

source:
The Development of Depression in Children and Adolescents
Dante Cicchetti and Sheree L. Toth
February 1998
American Psychologist

Vol. 53, No. 2, 221-241

Blechman, E.A., McEnroe, M.J., Carella, E.T., & Audette, D.P. (1986). Childhood competence and depression. Journal of Abnormal Psychology, 95, 223-227.

Eccles, J. S., Lord, S., & Roeser, R.W. (1996). Round holes, square pegs, rocky roads, and sore feet: A discussion of stage-environment
fit theory applied to families and school. In D. Cicchetti & S. L. Toth (Eds.), Rochester Symposium on Developmental Psychopathology: Volume 7. Adolescence: Opportunities and challenges (pp. 47-92). Rochester, NY: University of Rochester Press.

Higgins, E. T., & Parsons, J. E. (1983). Social cognition and the social life of the child: Stages as subculture. In E. T. Higgins, D. W. Ruble, & W, W. Hartup (Eds.), Social cognition and social behavior: Developmental issues (pp. 15-62). New York: Cambridge University Press.

National Research Council. (1993). Losing generations: Adolescents
in high-risk settings. Washington, DC: National Academy Press.

Rosenberg, M., Schooler, C., & Schoenbach, C. (1989). Self-esteem and adolescent problems: Modeling reciprocal effects. American Sociological Review, 54, 1004-1018.

I have more than once seen the "transition" to middle school cited as a source of profound stress in the lives of young adolescents. Typically researchers and authors seem simply to assume that "transition" from one school to another per se is the source of difficulty.

I am coming to think that the middle school model in and of itself, its core assumptions, is bad for children -- bad, or at least not good. When you assume that other people's children universally require substantial character education, how reinforcing can you be?

### Here’s one reason I support school choice

In a story about NCLB, a parent is critical of her children’s school:

"Over the years, Victoria Woisin has noticed a change in the types of projects her children are assigned in school.

And it's not necessarily to her liking.

"The emphasis is more on writing correctly, without as much creativity," said Woisin, a stay-at-home mother of three girls in the White Plains schools. "It just took the fun out of it."

Hmm . . . . When the schools hear parents say things like this, I guess I shouldn’t blame them for doing things like using personal journals as the predominant method of teaching writing in elementary schools. This same parent would probably consider a poster project, instead of an old-fashioned book report, to be a suitable creative outlet for her child. With a poster project a fifth grader can then show her creativity with drawing, coloring, cutting and pasting images from the book. Forget about learning to write a well-crafted expository essay. That just takes the "fun out of it".

## Sunday, February 17, 2008

Susan S sent this --

woo hoo!

### sample essay from Six-Way Paragraphs

Glance through the table of contents of a grammar school or high school mathematics textbook an you are likely to encounter the term rational number. While you are familiar with whole numbers, fractions, decimals, and percents, you may well wonder what a rational number is and how you passed through your school mathematics classes without encountering one.

In fact, you did learn definitions, computation, and applications for rational numbers, although they may not have been identified as such in your class. A rational number is any number that can be expressed as a ratio of two whole numbers, and so 4/5 (the ratio of 4 to 5), 2/3 (ratio of 2 to 3), and in fact all fractions are members of the set of rational numbers. Also included are all terminating decimals such as 0.25 (equal to 1/4 or 1 to 4) and repeating decimals like 0.333 ... (equal to 1/3 or 1 to 3). Percents are rational numbers, too, as any percent has an implied denominator of 100; for example, 35 percent equals the ratio 35 to 100, or 335 out of 100 parts. Even ordinary, everyday whole numbers are members of the set of rational numbers, since a whole number such as 4 can be written as 4/1 or the ratio 4 to 1. So your math classes have involved work with all these types of rational numbers as you learned to compute, estimate, and solve problems with them.

This brief description of the major subsets of the rational numbers may give you the impression that all numbers are rational, but that is not the case. For example, the square root of the number 9 is 3, a rational number. But the square roots of numbers such as 5 and 10 do not equal whole numbers and cannot be expressed as ratios. So the square roots of numbers that are not exactly divisible are not rational numbers.

source:
Six-Way Paragraphs in the Content Areas Advanced Level
Based on the work of Walter Pauk
p 124

I don't know how to teach reading comprehension, or whether the Six-Way books work. But I like them very much.

A side note: I bought this one because I was going to use it to give C. "precis-writing" assignments. The idea was for C. to read a Six-Way passage and then cut the word length by 100 words a pass.

That turned out to be impossible. The passages are so tightly written that neither of us could figure out what to cut.

(Not sure about that last sentence.... "not exactly divisible" - is that a correct way to describe a repeating decimal?)

The fun thing about all the Six-Way books is that the passages are chock-full of factoids.

I like factoids.

Here's the one on stunt people C. and I tried to cut.