what understanding without procedural knowledge looks like

Extremely useful comment left by palisdesk:


on the 5th grade students she assessed:

I assessed a whole [5th grade] cohort in math (only one was a special education student, and he was no worse than the rest), with similar results.

They scored well in understanding "concepts." Whoop-de-doo. But none could reliably do computation with regrouping, do mental computation of any sort, measure accurately, use a number line, name fractions, or do any operations with fractions or decimals. Surprisingly they could not even count money correctly!! They could not figure out elapsed time, nor read non-digital clocks.

What good is all this great "conceptual understanding" if you can't count coins under $3.00, measure the length of a board, find the perimeter of a triangle or determine whether to add or subtract to compare two numbers? The one thing most were good at was reading graphs -- pictographs, bar graphs and simple tables.

Some of these students were quite bright and had good reasoning ability but what they ALL lacked was knowledge of number facts, facility with algorithms, precise vocabulary (perpendicular, acute angle, numerator, range), an organized approach (if guessing didn't work they were stuck), in short MASTERY at any level. Like [instructivist's] students, all have had nothing but fuzzy blah-blah since entering school. Few to none can afford Kumon and most don't have computers at home or access to them, so even that kind of practice is not available to them.

A recent study of teacher competence in our district found that most teachers in 5-8 grade mathematics did not themselves show mastery of the subject at that level. I think we may have come full circle. The system is now being run by people who are its products, and many are quasi-literate and numerate, however bright and caring they may be. Also, the lack of any kind of intellectual rigor or scientific and statistical training in their preparation has left them vulnerable to every fad that comes down the pipeline.

conceptual understanding w/o procedural knowledge:

The best way to illuminate my point would be to contrast my findings with what might have occurred in "the old days." Time was -- the 50's? 60's? when you might often find students who could proficiently, or at least adequately, perform basic operations -- including, in many cases, operations with fractions and decimals -- but would have been at a loss to explain what they were doing, or why they were (for instance) regrouping in subtraction, or inverting fractions to divide them. It was not considered necessary for students to have a "deep" understanding of the number system per se. Most of us (I remember this myself) "got it" in the process of learning the algorithms and how to apply them, and did (eventually) understand why you had to regroup, what you were doing when inverting fractions (I would have wanted to show how it works, even now it would be hard to explain succinctly in words, but it's easy enough to demonstrate).

The children I was assessing -- with a detailed, widely-used norm-referenced diagnostic math test and also with a locally developed "performance assessment" -- showed the opposite pattern. They understood about place value (haven't played with Base 10 blocks for years for nothing), knew that multiplication is repeated addition, that fractions can name parts of an object, or members of a group, and so on. They could show you (with the ever-present manipulatives), or draw a diagram and explain. They could tell you why you have to rename the ones as tens, why you have to keep the decimal points lined up, what the value of various coins etc. is, what the "big hand" and the "little hand" on a clock indicate, and so forth.

What they could NOT do was reliably apply a procedure to come up with an answer. Given a problem like 24X86, they knew this means you make 24 groups of 86 (or 86 groups of 24), but would get lost trying to build them with blocks or count out the tally marks. If they tried to use the algorithm, typically they got directionality, order of steps, etc. all mixed up, and they didn't know the number facts. The brighter ones would figure out the answer had to be something around 2000, but many did not even get that far. When counting coins, they lacked a strategy such as, counting the quarters first, then the dimes, then the nickels, etc. They randomly counted each one separately and continually lost count. They didn't know how to "count up" to find a difference (or an interval between numbers or clock times).

This is so helpful. It makes sense to me that a student could have some degree of conceptual understanding without procedural knowledge, and yet when I try to think of how that would work I come up with a blank. It's clear to me, for instance, that my "conceptual understanding" of unfamiliar subjects -- economics, say -- is thin at best. God is in the details.



hyperspecificity for conceptual knowledge -- ?

One thing I think I see happening with palisdesk's 5th graders is "hyperspecificity" for conceptual understanding. I'm used to seeing hyperspecificity for concrete knowledge. I hadn't really thought about hyperspecificity for concepts such as the meaning of multiplication. It makes sense, though. I'm pretty sure it happens to me all the time, teaching myself algebra 2. I'll have a basic conceptual understanding of a concept -- logarithms, say -- that doesn't immediately transfer to a problem type I haven't done before. I'll try to come up with an example to post.

As usual, I'm hamstrung by a lack of terminology. Our sturdy workhorse words -- procedural, conceptual -- are failing to give me the distinctions I need within the category of "conceptual understanding."

These 5th graders have for arithmetic what I have for logarithms: some kind of start-up understanding of the concept that won't take them very far when confronted with an actual logarithm problem in the flesh.



thank you palisdesk, pissed-off teacher, instructivist, redkudu, dy/dan, nyc educator, exo, smartest tractor (I'm sure I'm leaving others off ....)

For parents and the broader public schools are a black box. Mike Schmoker says that's by design; the official term for management in schools is "loose-coupling," which means, I gather, that the goal of management is to protect the core functions of the organization from outside scrutiny. (more later...much, much later)

Teachers who share their experiences with outsiders are functioning as the education reporters our country needs but does not have.


Robert Slavin on transfer of knowledge
hyperspecificity posts
loose coupling & instrutional leadership

tales from the front, part 2

from pissed off teacher --

A zillion years ago when my son was in first grade and computers were still a novelty, he decided to write his spelling words on the computer. The little twerp was using copy and paste to write them the required ten times. When I made him stop, he told me "but my teacher said it was okay". As I said, computers were new and she did not know how he was using it.

Kids have always cheated. We just have to be smarter than them to stop them in their tracks.

The middle school's Civil War Museum exhibit last spring put the kids' papers on display. Ed looked at every paper & saw a huge amount of internet text. Same thing the year before at the Jason Project exhibit. Many papers included downloaded text. A couple of papers were the same paper.

Of course most people didn't notice because they were looking at the crafts projects, not the papers.

Crafts projects are to a middle school what misdirection is to a magician.

Possibly.

tales from the front

from Cheryl T in Singapore:

I once had a 9th grade student who turned in an essay on Greek mythology that was totally plagiarized. When confronted with the computer screen shots of the essay's genesis, he denied it up one side and down the other.

Finally, he broke down, blurting out, "But I didn't even write the essay -- my MOM did!" I spoke that night with the mom, who freely admitted ghost-writing her son's essay. She claimed not to know that cut-and-pasting huge swaths of someone else's writing was wrong. Where to begin?!?

(This happened at a GREAT public high school north of Chicago...)

My favorite cheating story happened at Iowa, where I was teaching the freshman rhetoric course. One of my students plagiarized her entire essay, word for word, from the textbook. She denied having done so and then, when I opened up the textbook and did a side-by-side comparison, said, "I remembered."

Of course, now that I have two autistic kids, it strikes me that she could have remembered....

cut and paste

from a comment left by NYC Educator:

I'm amazed at the number of kids who simply copy things off the net, with the labels still there, and expect me not to notice it was written by some professional hack writer instead of an ESL student.

True!

They all do this! Not just the ESL students, everyone.

Ed was talking to a French journalist this week who told him kids in France do the same thing. They think writing means downloading from the internet. The less sophisticated kids cut and paste things whole; the more sophisticated kids cut and paste individual sentences, piecing them together as they go along.

It's as if the basic unit of composition is no longer words but sentences, and you look up the sentences you need on the internet not in the dictionary.

National Survey of Algebra Teachers

How have we missed this?

Research Question #2: To the degree that the teachers believe students need to be better prepared, what are the major shortcomings?

The teachers were asked to rate the importance of a “solid foundation” in the each the 15 skill/knowledge areas asked about with respect to their target class students’ background preparation. Since the same background skills and knowledge for which the teachers rated student background as inadequate were also rated as important, the following areas emerge as the major shortcomings: rational numbers, word problems, and study habits.

Final Report on the National Survey of Algebra Teachers for the National Math Panel (pdf file)
National Mathematics Advisory Panel

They're not too keen on parents:

Research Question #12: Do they find more parents helpful in encouraging students in their mathematics studies, or do too many parents make excuses for their children’s lack of accomplishment?

Questionnaire item II.1i asked teachers to rate the extent to which they see “too little parent/family support” as a problem in their school. The responses indicate that about 28% of the algebra teachers feel family participation is a serious problem and another 32% believe lack of family participation is a moderate problem (Figure 13).

It's a bit difficult to cess out what this means exactly. The question itself seems off-base; the handful of direct quotations from teachers have nothing to do with parents "encouraging" their kids versus "making excuses" when their kids do badly:

The written-in “verbatim” responses most often mentioned included handling different skill levels in a single classroom, motivation issues, and student study skills. Some notable responses were:

Walking into a class of 30 students in which 1/3 of them don't have the prerequisite skills necessary to be in the class. Many of whom don't know their basic arithmetic facts and know they aren't going to be successful from day one no matter how hard they try.

Students come to me without a basic understanding of math. I am constantly re-teaching concepts that should have been mastered in the earlier grades.

Parents not letting me do my job as I see fit. (Autonomy in the classroom.)

Getting students and parents to believe that education is important. Students don't do their homework...you call the parents...they say that the student will start doing the work (and coming to tutorials). The students still don't do the h.w. -and still don't come to tutorials.

Engaging students who have come to believe that they are stupid because they are struggling with my state's cognitively inappropriate standards.

Report's conclusions:

The Algebra I teachers generally reported that students were not adequately prepared for their courses. The teachers rated as especially problematic students’ preparation in rational numbers, solving word problems, and basic study skills. A lack of student motivation was by far the most commonly-cited biggest challenge reported by the teachers. The problems the teachers identified with the pre-Algebra I mathematics curriculum and instruction and with the lack of parental support for mathematics were likely to be contributing factors to the lack of adequate student preparation and motivation.

[snip]

In light of the generally favorable views the teachers report with respect to curriculum and instruction, the issue of unmotivated students implicitly is something the teachers view as more of an “algebra-student problem” than an “algebra-teacher problem”. The generally-negative views expressed by the teachers of parental support for mathematics reinforce that attribution. Taken together with the generally negative ratings of background preparation, the lack of student motivation suggests that careful attention to pre-algebra curriculum and instruction in the elementary grades is needed, both to remedy the specific skill deficiencies as well as to identify ways in which negative attitudes toward mathematics are developed.

Our schools need a paradigm shift. If you've got an "algebra-student problem" then you also have an "algebra-teacher problem" by definition and you need to take action. Institute supervised homework study halls, formal reteaching of foundational skills, whatever.

Motivation as the Magic Key to All Learning is overrated in any case, I think. How motivated were Siegfried Engelmann's students in Project Follow-through? How motivated are the KIPP kids?

My own 8th grade child is not exactly gripped by a coursing desire to learn algebra. However, he is learning algebra, and he's learning it pretty well. That has to do with the teacher.

And, yes, it has to do with "parental support for mathematics," which in our case means that I do every homework assignment so I can check C's work and have him re-do the problems he missed.

You can't leave algebra up to student motivation.

Mathcounts Help Needed

Okay, my math kid has been working on his practice sheets for the upcoming Mathcounts competition next year. He seems to be doing great with the practice problems, but the warm-ups sometimes seem harder.

I'd love to help, but as many of you know, I am the resident Math Phobe of KTM. With the husband out of town, you are my only hope to helping him with this one particular problem. I have a feeling it is something really obvious.

Here it is:

"The sum of two numbers is 32, and the product of these two numbers is 48. What is the sum of the reciprocals of the two numbers? Express your answer as a common fraction."

I have the answer sheet, but no explanation on the best way to approach this.

Any and all help would be appreciated. Speak slowly, though....although the kid will probably understand what you're saying.

SusanS

2 teachers out of 50

This is exactly what I'm seeing:

Of a staff of more than 50, only one other teacher and I have more than 10 years experience, and I'm the only one with much expertise in instructional issues. There is definitely a generation gap in knowledge and skills, no fault of the newer folks. Most had no preparation at all in curriculum, behavior management, instructional design, teaching skills etc. Lots of philosophy instead. I don't dare contemplate what things will look like in another 10-15 years.

My district is hemorrhaging experienced teachers.

In their place we hire novices. More than half of our new hires have never taught; the rest have fewer than 5 years' experience. The administration's stated intention, with all new hires, is to grant tenure. A great deal of time and energy are devoted to mentoring and supporting new teachers who are struggling.

My district has, in the past, refused even to interview experienced math teachers. One person denied an interview was qualified to teach math and physics. He had glowing recommendations. Another experienced NY teacher was told that if he taught here he would have to take a pay cut to the salary of a 5th year teacher. He has retired from the public schools and is now teaching in a private school.

I wonder whether this qualifies as a form of age discrimination? Someone asked the Board about the average age of new hires; the answer was, "We're not allowed to ask age." Wouldn't a policy of interviewing only novices be a problem in terms of age discrimination?

I suppose not. We do interview and hire career changers.


10-year rule

I should add that we've had some terrific young teachers. It's not the case that a young teacher can't be good. She can. (Mostly, these days, it's "she.")

It is the case that he or she isn't as good today as he or she is going to be.


The Why Chromosome
Practice Makes Perfect (the 10-year rule)

palisadesk on guerilla instructivism

This WAS an interesting article. However, there must be tremendous variability -- ours is considered an excellent plan, but I did the math and if I retired now I would have to live on 46% of my current income (doable if I moved to a trailer park or seniors' home -- but I'm not attracted to the former nor eligible for the latter). Even at max pension is 60% of previous income. The coup de grace is that one has to purchase one's own medical and dental plan, and there are no comparable ones available from any providers at any price. This isn't so much a consideration for actual seniors but it is if you're in your 50's. Correspondents from other large districts in the east and Midwest have similar stories.

Fighting the system is something that does definitely lose its appeal over time. Guerrilla instructivism is energy-draining. Can't agree more about the frustration of being confronted with one obstacle after another every time you want to actually teach or help a kid. However I do still get an iconoclastic rush out of defying authority and successfully teaching basic skills: the pedagogical equivalent to manning the lifeboats. One consolation is that if I get REALLY p.o.'d I only have to give 10 days' notice. I could get a pleasant job in a bookstore or something to stay afloat. Of a staff of more than 50, only one other teacher and I have more than 10 years experience, and I'm the only one with much expertise in instructional issues. There is definitely a generation gap in knowledge and skills, no fault of the newer folks. Most had no preparation at all in curriculum, behavior management, instructional design, teaching skills etc. Lots of philosophy instead. I don't dare contemplate what things will look like in another 10-15 years.

pissed-off teacher on why we are losing experienced teachers

That article hits it on the nose--if I retired today I would be bringing home more money than I am working full time.

I don't work for the money, or for the few extra dollars I will make by staying longer, I am working because I really love what I am doing. Most of us 55 year olds are staying for that same reason. We are leaving, not to get more money but to get away from a system that is abusing us and abusing children. Kids are being forced to learn things they don't understand, and will never understand or need. Classrooms are over crowded. There are no meaningful tutoring programs and the system keeps piling on more and more tests. Older teachers are being harrassed. The schools only want the young ones who are earning a much lower salary and will jump as high as any admin tells them too.

We are just tired of the BS. WE are tired of being fought every time we want to do something to help a kid. We might as well take the money and enjoy our lives.

farewell to the baby boomers

fresh horses

It is a profoundly erroneous truism, repeated by all copy-books and by eminent people making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle—they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.

A.N. Whitehead, An introduction to mathematics, 1911 New York: Holt, p. 41

He makes this observation while discussing mathematical symbolism:

One very important property for symbolism to possess is that it should be concise, so as to be visible at one glance of the eye and to be rapidly written.

Two Million Minutes

Two Million Minutes

THE DOCUMENTARY
Regardless of nationality, as soon as a student completes the 8th grade, the clock starts ticking. From that very moment the child has approximately

…Two Million Minutes until high school graduation…

Two Million Minutes to build their intellectual foundation…Two Million Minutes to prepare for college and ultimately career…Two Million Minutes to go from a teenager to an adult.

How a student spends their Two Million Minutes - in class, at home studying, playing sports, working, sleeping, socializing or just goofing off -- will effect their economic prospects for the rest of their lives.

How do most American high school students spend this time? What about students in the rest of the world? How do family, friends and society influence a student's choices for time allocation? What implications do their choices have on their future and on a country's economic future?

school for horses

Working on the horse chapter has been unnerving.

Arguably the number one animal welfare problem where horses are concerned is poor teaching. Horses are in the same predicament as U.S. children; many trainers use ineffective techniques while ignoring the techniques that actually work. Not surprisingly, the techniques that work for horses are the same techniques that work for children. Direct instruction based in learning theory.

For horses, success in school is a matter of life and death, as a horse who can't be ridden will likely be euthanized. One study in France found close to 2/3 of all domestic horses being euthanized for reasons other than ill health. (source: Equine Behaviour by Paul McGreevy A terrific book.) "Reasons other than ill health" means one of two things or both:

• horse can't be ridden
  
• horse has behavior problems
  

These outcomes are, in most cases, training failures although they are blamed on the horse. The parallel to children, who can also fail in two ways (failure to learn; failure to behave) is haunting.

brain melt

My brain is officially fried.

Dogs, cats, horses.....and on to cows:

It is now well established that domestic animals construct responses to their environment that depend on experience and on integration of several features of the environment, including social partners.

source:
Ontogeny of social awareness in domestic herbivores
I. Veissier a,), A. Boissy a, R. Nowak b, P. Orgeur b,
P. Poindron
Applied Animal Behaviour Science 57 1998.233–245

Why I Don't Assign Homework

Liz Ditz left a link to Dy/Dan's blog.

I love this guy!


the homework problem

Here's what I love about Dy/Dan's post on not assigning homework.

First and foremost, not only has he thought out his position, he's researched it for a Master's thesis. The research is icing on the cake; the fact that he is so closely scrutinizing and adapting his "practice"^* in response to his students' achievement is what makes me long to have a kid in his class.

Ed and I have been talking about the homework issue lately, mostly because C's social studies teacher told Ed he has students who never do their homework. We were both surprised to hear this though we shouldn't have been.^** Kids not doing homework is a chronic issue for teachers everywhere.

Here's a Phi Delta Kappan article on the subject:

I tried to figure out why promising students in my own geometry classes persistently failed. Every year students entered my classes not fully prepared for the large body of new concepts, vocabulary, skills, and logical principles that are central to a college-prep geometry course. With rare exceptions, the deficiencies were surmountable, provided that these students accepted the need to study and work on sample problems outside of class. But, despite a claimed orientation toward college, many of them failed geometry, in large part because of "homework resistance" that seemed rooted in early elementary school and shaped by adolescent identity pressures.

Occasional missed geometry assignments weren't a big deal in my classes. After all, an unknowable but surely substantial portion of completed homework involved copying from classmates. An additional portion consisted of "homework simulations" with correct answers to odd-numbered problems (which have answers in the back of the book) embellished with jottings that gave the appearance of work. So, like most of my colleagues, I gave credit for homework but based most of a student's grade on tests, quizzes, and in-class projects. Class time was an intense geometry experience for all but the most tuned-out. But since test questions looked remarkably similar to those covered in homework, students who didn't do the homework had trouble passing tests or participating fully in class.

At year's end, out of 90 geometry students in three sections, 38 had completed less than 60% of the assignments. Of these 38, two quite talented students managed to earn a semester grade of C, another three earned D's, and the remaining 33 all earned F's. In contrast, all but a handful of the students who had completed 80% or more of the assignments passed with grades of C or better.

The puzzle. Why would so many students willingly waste a year sitting through geometry class and earn zero credits toward graduation? All had managed to pass algebra, and many even had good attendance in my class. Most had the requisite mathematical ability and would have passed had they spent 40 to 50 minutes daily outside of class on the homework. Free tutoring and homework help were available at lunch and after school, but no one showed up more than once or twice; most never came at all. What were they thinking? Countless frustrating conversations convinced me that most students in this situation can't tell you the teal reasons for their behavior, because they themselves don't know. They offer a charming variety of excuses, evasions, defensive maneuvers, mea culpas, and doleful expressions, many well practiced from prior confrontations with parents or counselors. Almost all say that to succeed they would need to start doing all their homework. They further insist that they want to be successful. So what's going on that students can't explain to us - or to themselves?

Homework Inoculation and the Limits of Research
Bruce Jackson
Phi Delta Kappan Sep 2007 Vol. 87, Iss. 1 pg. 55

Jackson's idea is that the practice of having kids do largely pointless homework assignments in K-5 in order to build "good homework habits" leads instead to homework refusal when kids reach middle school age and begin to assert themselves. Homework inoculation.

So....the cure for h.s. kids not doing homework is to get rid of homework K-5.

I'm sure that will work.

This is the kind of thing that makes me want to send this fellow a link to Karen Pryor's web site. Pryor makes short shrift of such motive mongering. She doesn't care to learn why a dog is behaving badly; she doesn't want to hear his history:

Karen helped me learn to read Ben's canine signals accurately, unhindered by my own emotion....She was the one, who during one of Ben's fits in class, came over, gently put her hand on my arm and calmly said, "Emma, it is only behavior."

"Only behavior?" I gasped. Could it be so simple? This "behavior" had caused me so much grief in my life, both personally and professionally. It had become a source of tension in my marriage and almost caused me to lose several friendships....I had allowed Ben's aggression to balloon into a problem that took over our lives. I found hope that night in class, with Karen's calm words: "It's only behavior." After all, through positive reinforcement, behavior--any behavior--can be changed.

Click to Calm Healing the Aggressive Dog
by Emma Parsons

Animal behaviorists make a useful distinction between ethology and psychology.

You do need to know ethology (how does this species act & think?)

You don't need to know much about psychology (how does this particular animal act and think, and why?)

When it comes to students not doing their homework, all you really need to know is that procrastination is a core human behavior that is not going to be conquered any time soon and certainly not by high school students. Asking students what they are thinking when they fail to spend 50 minutes a night doing geometry homework is absurd. They're not thinking about geometry one way or the other. That's the point.

This teacher needs to forget about what students are thinking and ask the school to send a behavior analyst to his class to change the incentives. A mere amateur like myself can spot some major de-motivators in his data.

If he can't round up a professional, he should read a book on behavior analysis and figure it out himself. ^***

The "homework situation" appears to be an unholy mess. Setting aside the question of homework quality, I would like to see schools adopt policies of supervised homework like the one in place at La Salle High School. If a student is not getting homework done at home, I would assign him to a supervised homework study hall where he would get it done because a responsible adult would see to it. And I would make this a positive experience, not negative.

If I had my druthers, our schools would drop-kick the many state-mandated character-ed implementations over the stadium wall and replace them with school-wide positive behavior plans devised by the Bob and Lynn Koegels of this world.

Or else just hire a whole lot of teachers like Dy/Dan.


^* hate that word, but it's correct in this context
^** I have no business being surprised by any failure to complete assigned work...
^*** I'm starting with Karen Pryor's Don't Shoot the Dog, which I will be using for my kids and for me.

US Students Do Worse in Science and Math

This just in.

U.S. students are lagging behind their peers in other countries in science and math, test results out Tuesday show.
The test, the Program for International Student Assessment, was given to 15-year-olds in 30 industrialized countries last year. It focused on science but also included a math portion.
The 30 countries, including the United States, make up the Organization for Economic Cooperation and Development, which runs the international test.

U.S. students ranked 24th in math.

I hate projects

My fifth grader came home recently with a “Global Warming” handout that included these proclamations:

Do your share, show you care. . . .
If you don’t do your part:
- everyone will die
- the Earth will burn
- there will not be any community in the world

It turned out this was prepared by a fellow student as part of her project on the topic of global warming. All students have been assigned similar projects, and the theme seems to be environmental causes. I think we all know the drill. Take a huge topic. Assign an elementary student to research the Internet. Make a poster along with dioramas, poems, songs or puzzles. Present to class. Yuck!!

Having watched my kids progress through the public school system being assigned numerous time-wasting projects that teach very little practical academic content or skills, I have developed an abhorrence for most of these. Additionally, I’ve observed the alarmist, unscientific message about global warming that seems to pervade much of the curriculum.

However, this particular example sent me over the edge a bit.

(Of course, I don’t fault the child or even the teacher in this case. In fact, my observation is that this student is unusually bright and probably completed this project without much parental help. Good for her!)

farewell to the baby boomers

pension plans and the 55-year old retiree

it's going to get worse before it gets better

from the May 2007 issue of Phi Delta Kappan, international world headquarters of constructivist fuzzery (subscription required):

THE MATH classroom is, and probably always will be, a center of controversy. Teachers, mathematicians, and researchers may never come to agreement on exactly how their beloved subject is to be represented in school. That said, aren't we all making some obvious mistakes? I contend that there are some practices, common to nearly all math classrooms, that we can all agree simply must be done away with. Here are my four prime candidates.

1. Forty problems a night. Most of my mathematician friends and I are only able to solve about two problems a year - if we're lucky! Tell a mathematician you've solved even five problems in a single day, and the first thing she will think is, "They must not have been very interesting problems." Outside of mathematics, does anyone you know ever get 40 things done in a day? [ed.: Everyone I know gets 40 things done in a day.]

2. The third-person czars of math problems. A strange, anonymous set of people are constantly referred to in math classrooms. We frequently hear teachers and students ask such questions as "What do you think they mean in problem number 4?"...Who are these people?...If we decide, as we often do, that our classrooms are going to be guided by the mathematics of the past, then let's at least talk about real people - not mythical ones. [ed.: Perhaps math textbooks could include a photograph of Skip Fennell.]

3. Teachers give problems; students give answers. If only mathematics were that easy! A mathematician would arrive at her desk to find that her problems were all there, waiting for her in a list. The reality is that the largest challenge in mathematics is finding a good problem to solve or theorem to prove - a single conjecture that is both interesting and approachable...[Y]ou would be hard pressed to find a classroom where the students regularly face the challenge of finding a good problem.

4. Suppose a student still "doesn't get it" by the end of a math class, and the teacher decides not to set him straight for the time being. Many people would label such a decision as "immoral," fearing that it would endanger the student's academic future. Because of the high stakes we attach to learning math in school, we seem to lose our perspective on these matters. Do we really think that mathematical learning is that simple and straightforward? Might a student have a richer mathematical experience if he is allowed to fumble around with a misconception for a few days than if he is steered promptly to the "truth"? [answer: Having now watched my own child fumble around with a misconception concerning the distributive property for the last 2 1/2 years, I would prefer America's math teachers stick to the business of clearing up misconceptions not fostering them. Alternatively, if fumbling around is to be the goal, let's knock off giving students grades of C, D, and F on tests due to fumbled answers, shall we?]

We must deemphasize answers and correctness as the only worthy goals in mathematics. Sure, "right answers" are an important part of math, but they aren't always the bottom line. Instead of always asking, "What's the right answer?" we should also wonder, "What's the right question?" and "What's the most interesting way to the answer?" Mathematics is about bold, adventuresome ideas, and the history of the subject is therefore fraught with mistakes, contusion, and invalid convictions. Let's make the classroom a bit more like the discipline and allow our students to revel in the "wrong" while they pursue the "right." [ed.: Reveling in the wrong is incompatible with being graded on a curve. You'd think a person majoring in math education would know this.]

source:
Four Practices That Math Classrooms Could Do Without
Nick Fiori
Phi Delta Kappan May 2007 Vol. 88, Issue 9, p. 695
author bio: NICK FIORI is a doctoral candidate in mathematics education at Stanford University, Stanford, Calif.

Here is our situation, demographically speaking. Ed schools stopped teaching the methods of direct instruction in the second half of the 1980s. Teachers who earned Masters degrees in education in 1980 are now in their mid-50s which is retirement age in my district (and, I gather elsewhere, too). They are leaving the profession in droves.

Nearly all certified teachers under the age of, say, 45 have been taught constructivism and constructivism alone. And while Robert Slavin claims that a new back-to-basics movement is brewing inside ed schools, I'm skeptical. (If others have seen a shift, let me know.) The fact that a doctoral candidate in Stanford's school of education would assume that "we can all agree" on these four propositions tells me that as yet there has been no challenge to the orthodoxy.

This means that ed schools are still producing constructivist teachers who will teach for 25 years before retirement benefits kick in. Many if not most of these new teachers will not be mentored and overseen by baby-boom era teachers trained in direct instruction as earlier cohorts of constructivist-trained teachers were.

They will be mentored and overseen by 40-year old constructivists.

Suncast Powerblade

best snow shovel on the planet

You can use it as a hand snowplough. Amazing!

My latest rant

Chi-square in high school?

What we are up against

Math isn't what it used to be

This isn't an article it's an advertisement for Everyday Mathematics. There isn't even a single mention in the article of the possibility that some parents, teachers, and schools might not like it.

Some selected quotes:

The curriculum is designed to integrate strategies such as algebra, probability, geometry and statistics into the lessons for students as young as kindergarten and first grade. Also through the lessons, students are taught several different techniques to solve problems, while traditionally, students were only taught one way.
...
Fremgen said another benefit is that most of the math ideas spiral through the curriculum throughout the year, so if students don't understand a method or concept the first time, it will come around several other times for them to try again.
...
The program's success also may be because of the curriculum's real-life applications that allow students to use what they learn in everyday experiences, Fremgen said.

This reporter didn't even need to get out of bed to write this article. All she had to do was have the textbook creators fax in the article to her editor.

"Teachers Swamp a Parley on Preschool"

from the Sun:

At least 10 Upper East Side nursery schools are closing their doors today to make time for a conference on an Italian teaching philosophy that is challenging American methods.

Nearly 900 people will crowd the 92nd Street Y to learn about Reggio Emilia — named after the small Italian town, population 140,000, where the approach was developed and that is known for its fine wines and parmigianas — and hundreds more are scheduled to tune in to the 92nd Street Y's first major Internet broadcast of a conference.

Unlike many foreign countries, Italy does not outscore America on standardized tests (its children score about the same), but its approach to teaching 4- and 5-year-olds has captivated educators across this country. They say the philosophy elicits more from the young children than ever seemed possible.

Reggio eschews traditional lesson plans and instead encourages 4- and 5-year-olds to develop their own projects.

About 500 Americans visit Reggio schools in Italy every year to marvel at these projects, and a traveling exhibit of the projects has been making its way across the country. The U.S. liaison to the nonprofit Reggio Children group that organizes the exhibit, Lella Gandini, said interest appears to have grown "immensely" in the past several years, especially in New York.

The director of All Souls School on the Upper East Side, Jean Mandelbaum, one of the school directors who allowed children to skip a day so staff could attend the conference, said that when she first visited Reggio she was astonished to see the quality of work produced by the schools' method. "It looks like they're geniuses, but they're not geniuses. These Italian kids who are wonderful are no more wonderful than our American kids," she said.

By giving children more time to do longer projects and allowing them to dictate their own curriculum, the Reggio method brings out the best in them, she said. At her school, she said, children have created a life-size penguin; several robots, and a model of the 79th Street cross-town bus — all through their own ingenuity. Through the process, teachers make sure to pass on certain skills. They also push students to revisit projects, making them months-long endeavors rather than the fancy of just a few hours.

"The idea is not to just splash something off and bring it home to mommy. Rather, most of the work is considered work in progress," she said.

etc.

Oh yes. Yet another "challenge" to American teaching methods. Nobody here in America has ever heard of the project method.

It's hopeless.

We're all going to have to band together and start charter schools to teach the liberal arts disciplines via direct instruction. We'll hire Siegfried Engelmann and the precision teaching folks to oversee.

We'll also recruit a disciplinary specialist or two to see to it we're teaching the actual disicplines as they exist in the real world, not the fantasy interdisciplinary world of the American ed school.

When it comes to the liberal arts disciplines, the "real world" is the world of the professors and researchers who produce the knowledge our schools are supposed to teach.


the liberal arts disciplines:

• mathematics
  

• English
  

• science

• philosophy
  

• history
  

• foreign languages
  

• music
  

• art

Ed says many colleges include the social sciences as a liberal arts discipline.

Ed speaking:

Each discipline has a corresponding set of skills that emerge from the discipline. In mathematics you have quantitative reasoning; in science you have the scientific method; in history you have historical analysis. Some form of competency in writing is usually attached to English.

Ed thinks it's important to have the disciplines "first" and the skills second, because it's too easy to get into "interdisciplinary mush" when it's the other way around. If your requirement is "social scientific reasoning" as opposed to history, then a student can take a smorgasbord of courses in anthropology, sociology, etc, without taking a history course, thus missing a fundamental discipline in the liberal arts canon.

Ed again:

There's no question there are social scientists who would disagree with this, but it's not for nothing that public and private schools both require history not social science. That's true because most people see history as a fundamental liberal arts discipline. Most people also make the rightful assumption that every citizen needs to know something about the history of his own country to exercise his citizenship rights effectively. The social studies movement agreed with this premise, but got rid of the study of history and kept the study of citizenship.

Rubric Burn

My wife and I just got back from our 15 minute parent-teacher meeting. We might have seemed rude, but we couldn't chitchat. We dived right into our biggest concern - making sure that our son gets the rubric before working on the assignment, knowing the exact due date, and getting the results and grade back in a timely fashion so that we can go over them with our son. These things haven't been happening. Many assignments don't have rubrics. Our son can take some of the blame, but there needs to be a process that is designed to make it easy for us parents. They expect involved parents, but they have to give us the tools.

The big issue was about rubrics for individual assignments and for overall grades. Our rubrics go from 1 - 5. I don't think anyone gets a 1 and kids only get 5s if, well, I don't know why and his teacher couldn't really explain when or why. I told her that 5s seem to something like an A+. She said it was more than that. The kids have to show how their assignment is somehow related or integrated with other subjects in an abstract way. Of course, the school doesn't teach them about this or show them how to do this. Some rubrics do tell the students what they have to do to get a 5, but there is always the proviso that there has to be something more. What that more is, they never say. I told the teacher that kids want to get 5s but they aren't taught how. She really didn't have much to say other than (in so many words) "That's the point".

A 3 indicates that the student is meeting state expectations. I told her that I have seen the state expectations and tests and consider a 3 to be a 'C' grade. She seemed surprised to hear me say that. I'm not sure why. A 2 grade indicated (in a very broad sense) that there is a problem that needs to be fixed. A 2 is a 'D' grade.

That leaves the 4 grade to cover the range of 'B' to 'A'. Some teachers have suggested that rubrics are just another form of grading like A, B, C, and D. They aren't. They are non-linear and very poorly defined. Kids struggle to get 5s because they think that it's an 'A'. My son can't always explain why he gets a 3, 4, or 5 on an assignment or test. Grades are supposed to give students some sort of feedback to help them with future assignments. This is not happening.

Even math tests are translated into rubric grades of 1 - 5. My son hasn't had enough graded assignments for me to plot rubric grade against percent correct on his tests. I'm betting that the relationship is nonlinear. The math teacher doesn't allow the test to go home. It has to go into their portfolio and stay at school. Don't they think these things through? I'd like to give them a rubric.

New Elementary Algebra

I think I'm going to take tonight off and spend my time raiding the Comments for new posts.

from Myrtle:

I've only recently discovered this feature on Google. For example, I've been using this book for supplemental word problems in Algebra:

New Elementary Algebra (1879)

Word problems start on page 139 and go on and on and on.

and:

Fifty Famous Stories Retold for free in Google Books


I've spent my share of time pouring over Google Books these past few weeks. Sometimes they decide I've abused my privileges & they cut me off.


a farmer and his sheep

A farmer has in his pasture 63 head of cattle, consisting of cows, calves and sheep. There are twice as many calves as cows, and twice as many sheep as calves; how many has he of each sort?

Ans. 9 cows; 18 calves; 36 sheep.
New Elementary Algebra
p. 139

logarithms shmogarithms

When I get my life back, I am going to conquer logarithms.

Thanks to Myrtle (lots of cool stuff at Myrtle's blog - I need to get out more), I have two sources outside my Saxon/Dolciani/Foerster stash here:

• How should logarithms be taught?
  

• The Big L

nominally high performing, part 2 ...

Mindless Math Mutterings posts the passage from Richard Elmore that has given me a formal term for the kind of affluent school district William Sanders calls slide and glide:

nominally high performing

One of the huge fallacies of performance-based accountability systems is the misconception that nominally low-performing schools don't know what they are doing and that nominally high-performing schools have something to teach them.

[snip]

Most high-performing schools in our highly segregated society have gotten there not by knowing a great deal about instructional practice or improvement but by getting and holding on to students in high socioeconomic groups. The practice in most nominally high-performing schools is emphatically not about improvement but about maintenance of a certain level of confidence with the surrounding community. When I speak about improvement with people in these schools, they often look at me as if it had nothing to do with them. Most of the knowledge about improvement is in the schools where improvement is occurring, and most of those schools are, by definition, schools with a history of low performance.

A Plea for Strong Practice
Richard Elmore

The funny thing is that inside a high-performing district everyone "knows" the schools are high-performing because of the families. The families know it; the school knows it. It's an open secret.

But while people know this, they don't ask what value the school is adding to what the students brought with them to school. Instead the schools is assumed to be high-performing because the students are high-performing (and student performance is never seen in comparison to private or international schools).

Can't remember whether I've mentioned our middle school principal's Back-to-School-Night skit performed in the fall of 2006 a few short weeks after he'd taken his position here.

It was a skit inspired by No Child Left Behind.

"I don't like No Child Left Behind," he said. "But it does have one good idea, which is evaluating the quality of your school. It's a good idea to evaluate the quality of your school. So I'm going to tell you the 4 characteristics that determine the quality of a school."

Off to the side were standing 4 middle school girls holding poster boards flat against their legs.

"The first characteristic in evaluating the quality of your school," the principal said, "is the school."

Girl number 1 turned her poster over revealing characteristic number 1: School.

"But if you're putting it all on the school," the principal continued, "that's too much."

In retrospect, that was the moment I should have started sending away for applications to Catholic schools. That I didn't see this at the time can probably be attributed to the fact that I was curious to discover what other characteristic one could use to evaluate the quality of one's school besides the quality of the school.

"The second characteristic you can use to evaluate the quality of your school," the principal said, "is the quality of the students."

The second girl from the left turned her poster board over.

Students

"The third characteristic is quality of the parents."

Poster board: Parents

"The fourth characteristic is quality of the community."

Community

"You have a quality community," the principal said. "I've been driving around your town admiring all the nice lawns with the beautiful grass. In my old school, one day I was walking a student home and there were some boys standing in the street and one of them said, 'Principal, do you want to buy some drugs?'"

And there we left it. Proof positive that we have a high-quality middle school because we have high-quality students, high-quality parents, and a high-quality community.

All of which it is possible to determine by the quality of our lawns.

Climbing Mt. Parnassus

I had never heard of this book until Myrtle left this comment:

Tracy Lee Simmons "Climbing Parnassus" is even more divergent. It traces the history of classical education throughout the centuries and chronologically speaking should be read before Diane Ravitch's "A Century of Failed School Reforms" which picks up about in 1900 where Simmons leaves off.

The difference between Simmons and Wise Bauer is that Simmons gives you the "whys" of classical education and Wise-Bauer gives the "hows." I would summarize her hows as being for non-expert parents. Her area of expertise is writing and English, not physics and math and while her recommendations in those areas certainly won't send anyone into an educational death spiral, they also aren't nearly as clever and insightful as what she has to say about English, composition, history, and foreign language.


and here is an excerpt from Well-Trained Mind: left by Concerned Parent:

The Parrot Years:

Houses rest on foundations. Journalists gather all the facts before writing their stories; scientists accumulate data before forming theories; violinists and dancers and defensive tackles rely on muscle memory, stored in their bodies by hours of drill.

A classical education requires a student to collect, memorize, and categorize information. Although this process continues through all twelve grades, the first four grades are the most intensive for fact collecting.

This isn't a fashionable approach to early education. Much classroom time and energy has been spent in an effort to give children every possible opportunity to express what's inside them. There's nothing wrong with self-expression but when self-expression pushes the accumulation of knowledge offstage, something's out of balance.

Young children are described as sponges because they soak up knowledge. But there's another side to the metaphor. Squeeze a dry sponge, and nothing comes out. First the sponge has to be filled.

[snip]

So the key to the first stage of the trivium is content, content, content. In history, science, literature, and, to a lesser extent, art and music, the child should be accumulating masses of information: stories of people and wars; names of rivers, cities, mountains, and oceans; scientific names, properties of matter, classifications; plots, characters, and descriptions. The young writer should be memorizing the nuts and bolts of language-- parts of speech, parts of a sentence, vocabulary roots. The young mathematician should be preparing for higher math by mastering the basic math facts."


If you haven't noticed yet, Amazon has a dandy new rotating-books carousel feature that lets you scroll through all the other related books people who purchased the book you're looking at purchased. What a fantastic research shortcut. If I know a book is good -- or, more importantly, that it's considered good by the experts whose work I'm writing about^* --- I can instantly learn what other books are in its category.

I found Animals in Translation in the carousel for The Psychology of Learning and Behavior by Barry Schwartz, which is causing me to contemplate purchasing it just to find out what the connection is specifically.

Back to Mt. Parnassus; the carousel there has one book I own and like very much: The Laurel Wreath and Harp: Poetry and Dictation for the Classical Curriculum.

Another 3 I'm interested in:

• Composition in the Classical Tradition
  

• Fifty Famous Stories Retold
  

• Increasing Academic Achievement with the Trivium of Classical Education

^* make that trying to write about

School performance info - your predictions?

I wanted to share information on an interesting experiment going on in Sumner County, Tennessee, and solicit predictions.

One of my clients, an organization called the Education Consumers Foundation, has been doing a lot of work with value-added data in Tennessee. (For those unfamiliar with value-added, it basically allows you to isolate and measure schools' contribution to student learning, regardless of the socioeconomic, etc. characteristics of their students.) Tennessee has the most advanced value-added system in the country and has been collecting data since the early 90s, so there's a rich pool of good data available from the state here.

While Tennessee offers great information on the performance of its elementary and middle schools, we've found that almost no one is aware of this data or understands what it means. So we've launched a pilot initiative to see what happens once parents and other community members are given this information.

Last Monday, we sent a package of information to every household in Sumner County - 55,300 pieces in all - containing an introductory letter and a brochure with school-by-school information on their value-added performance rankings, TCAP proficiency rates, and free/reduced lunch rates (a proxy for poverty). I've posted these materials in PDF format: you can download the letter here and the brochure here.

IMHO, I think this is powerful stuff, but we're just at the very beginning stage of the pilot. I'd like to think it's going to make a huge impact, but it's entirely possible that it will be ignored.

I'd love to hear thoughts on this initiative from other KTM folks, and your predictions for what will happen in Sumner County. Will the community at large ignore this? Is it likely to create a significant conversation in the community? Will people push their local schools to improve?

Essentially - is this the path to real school improvement, or is this mailing going to fall on deaf ears?

If anyone's interested, I'll share updates as we go along - as I mentioned, the mailing just dropped last week, so it will take a while for this to all play out.

(For clear and complete disclosure purposes, I'll repeat that ECF is a client, but I don't feel any conflict of interest in posting about this initiative - they're a nonprofit group and have nothing to gain from this. If there are any issues, I'll trust in Catherine to remove this post.)

brute memorization

Terrific post from Instructivist on the subject of memory and memorization.

This is something I've struggled with: how to distinguish "brute memorization" (my term for it) from "natural memorization" or, in instructivist's phrase, "thoughtful memorization."

Constructivist philosophy defines the word "memorization" as most folks do: the student sits down with a set of flash cards and commits material to memory.

I assume (don't know) that the flash card approach is essential in some realms: foreign language courses, law school, med school.....yes?

But "brute memorization," generally speaking, probably isn't the best way to go about acquiring knowledge, and is not the method a knowledge-focused curriculum like Saxon Math employs.

Unfortunately, we don't have a term for the kind of memorization Saxon Math induces.

Saxon Math produces memorization via spaced repetition, which is, I believe, the way everyday life produces memorization.

Here is my sense of the way in which natural memorization works:

• content to be committed to memory is broken into the smallest meaningful units
  

• the smallness of the units allows each unit to be held in working memory (or consciousness) in its entirety
  

• using working memory, the student distributes his practice of these small units over time (distributed practice or spaced repetition)
  

• in time the units being practiced naturally enter long-term memory
  

This seems to be the way most material enters long-term memory in the day to day. One repeatedly encounters and/or practices an idea or skill until one simply "has it."

Example.

I'm going to guess that quite a few ktm readers and commenters now possess a usable or at least semi-usable definition of the term working memory.

Did you acquire this by sitting down with a flash card and rotememorizing it?

No.

You acquired a usable knowledge of working memory by repeatedly encountering the term in posts and comments until you remembered it.

This process is natural, and it is inevitable. Memory is a core function of the brain; people who don't remember things have brain disorders. Bad ones.

Constructivist antipathy to memory and remembering is quite perverse -- it is unnatural, as a matter of fact -- but it is consistent with constructivist antipathy to knowledge.

The brain naturally acquires knowledge. Yes, I know the brain does not naturally acquire knowledge of algebra absent a good textbook and teacher ( ! )

However, if you have a good textbook and/or teacher it is entirely natural to acquire knowledge of algebra whether you give a damn about algebra or not. As a matter of fact, it's entirely natural to acquire some knowledge of algebra even with a mediocre textbook and a so-so teacher. Repeated practice causes us to remember what we've practiced, period.

If you don't want students acquiring knowledge, you're going to have to oppose memory and memorization.

.....................................

As to direct memorization and its place in formal education or in any training program, my sense is that it is often the fastest route to remembering. From time to time Saxon will tell the student, "Memorize this." His meaning is always: You're going to need this, you're going to use this, just go ahead and memorize it.

Direct memorization is a shortcut.

I think.

.....................................

hmmm...

Direct memorization probably isn't a bad term for the kind of simple, straightforward, put-it-on-a-flashcard-and-practice-it memorization constructivists call "rote."

Anchoragegifted’s Weblog

Anchoragegifted’s Weblog

Last night I ran across the Anchorage School Districts Gifted Blog. It's a great idea for communication, but I hope to see it updated a bit more.

I posted a comment asking for more information, so hopefully I can spur some debate.

Update: sorry, I had meant to post this to my site, but selected the wrong blog. And yes I know I haven't been very active... blame it on the move to Alaska.

homeschooling is good

Now, keeping in mind that I’m a second grade teacher and that MY American History teacher taught in the EXACT same manner as above and I don’t remember a THING about American History, here’s a proposed list of assignments that I would have liked to have seen on the board.

* Who lived in pre-colonial America? Choose one people to read up on, create an artifact relevant to these people and be prepared for show-and-tell.

a teacher's reaction to a high school history class in which assigned textbook chapters had been written on the board

I've come to the conclusion that today's educators are anti-book. [update: this is way too sweeping and cranky. Cranky is bad. So is sweeping. Obviously, "today's educators" do not speak as one. And, as Dr. Stipes points out, it would no doubt be equally correct to assert that today's students are anti-book. So I take it back. I may have to stick with the claim that "today's educators administrators" are pro-SMART Board, however. Because I'm cranky.]

Pro-technology, anti-book.

Take my district (please!) The high school and middle school share a brand-new, two-story, Barnes-and-Noble-esque library that has very few books. The library has so few books, I'm told, that this year the school removed shelves to make the absence of books less glaring.

Parents at the 4-5 school are raising money to buy books for the library there.

High school kids come home and tell their parents the reason they're not reading more books in Honors English is that there aren't enough books to go around. (Teacher says it's not so, but if teacher is correct, why aren't the kids reading more books?)

And we've all heard tell of textbook shortages. Some of us have experienced textbook shortages firsthand (Spanish books that couldn't come home with kids because there weren't enough to go around in the case I know of.)

Occasionally people send emails concerning the book situation to the school board. The school board responds saying the book shortage has been addressed and we have all the books we're supposed to have.

Technically that may be true, though I have heard two stories of textbooks not showing up until, in one case, 2 months into the year; not until mid-year in the other. The students made-do with packets until the real books showed up.

Why would that be?

If we have all the books we're supposed to have, shouldn't we also have them when we're supposed to have them?

So we seem to be experiencing a degree of mystery where books are concerned.

There is no mystery when it comes to technology. We have vast heaping quantities of technology; we have rooms bursting at the seams with technology. We have computer labs (where middle school students can access at least one X-rated web site, I'm told); we have music labs; we have SMART Boards up the ying yang.

How many SMART Boards is that you ask?

Forty five.

The district's goal for last school year was the purchase and installation of 45 new SMART Boards and we met that goal.

No word on number of books purchased or read.

more fun with WAC

re: If WAC sweeps the country as I fear it may, we'll have our public schools producing kids who hate writing as much as they hate math, Concerned Parent has this to report:

I have anecdotal evidence for that, and then some. The scenario you describe was happening to A. She was developing acute writing phobia by fourth grade. This extremely verbal, well read, talkative child would have almost nothing to say when presented with a writing assignment or prompt. She would virtually shut down. Her confidence was almost completely eroded. Having a clear road map has been life altering. She's actually relishing her writing assignments and no longer goes around saying "I'm a terrible writer." This is where we were not too long ago. What's most amazing is how quickly things have turned around.

[snip]

Last year in fourth grade there were mostly shoebox type "writing" projects dispersed through the year. There was one big writing project about a U.S. state that was to be done completely at school which ended up a total disaster. The rest were really psuedo-writing with it becoming more of a presentation that didn't really require structured writing (she dressed up and acted out the characters of Sacagawea and Elizabeth Blackwell.)

It got more serious around testing time in the spring when everything was in preparation for the CMTs. It got to the point that this child, who reads and comprehends at about a twelth grade level, was having breakdowns over short answer response questions at the fourth grade level. This shouldn't have happened, but it did.

There were no traditional book reports and I rarely saw drafts going through any type of editing process. There just didn't appear to be a method for teaching writing going on at all. She was overwhelmed and really began to hate anything having to do with writing.

I agree that remediation with the right methods can make a world of difference in a short amount of time, particularly if the child is a good reader. Having a process puts it all together and it just sort of "clicks".

This jibes with Vicky's and Susan's experience.

I'm going to have to go into the writing remediation biz: go into it or invent it. Either one.



the process

David Klein's AP/IB grades changed by Fordham

This is distressing news.

Based on my own n of 1, I'm sure David's original grades were correct. C's camp counselor last summer, who is attending Rensselaer Polytechnic, told me the IB math sequence he'd taken in high school was a joke. He didn't learn much calculus, but he did write a "research" paper. Looked some stuff up and slapped it together.

I wish to heck I knew what I did with my notes on the conversation. He gave me a rundown of the many topics IB didn't mention while students were busy slapping together low-quality papers.

If I run across them, I'll post.

A few years ago I checked out the IB web site. The lower grades IB curriculum was entirely constructivist, which made me think the upper-grades curriculum couldn't be far behind.

.............................

It was a lot of fun having C. in camp with a math-brain counselor. The counselor would tell him things like, "I don't like to read and write papers. I just like to do math." This was an utterly novel concept to C, who quoted it to me verbatim on a number of occasions.

Barry's letter to the NY Sun

Will get the Sun story on Texas rejecting Everyday Math (subscription required, I presume) posted at some point (horse chapter takes precedence). The Sun carried the story as front-page, banner-headline news. The word "fuzzy" appeared in the subhead.

In the meantime, here is Barry's letter to the Sun:

I am very happy to see that the New York Sun ran a front-page story about Texas' challenge of Everyday Math [Front Page, "Texas Challenges City on Math," November 20, 2007].

To my knowledge, the New York Sun is one of the few papers in the country that has covered this development. Given that Everyday Math commands a 20% market share of textbooks for K–6, Texas' decision is an important one.

The Everyday Math program does not cover math well and certainly does not pursue mastery of the material as other programs do such as Saxon, or Singapore's math program.

By placing this story on the front page, the New York Sun has done a great service and perhaps the story will be viewed as a long overdue wake up call to the educational damage such dangerously lacking programs have caused to our children.

BARRY GARELICK
National Advisor
NYC HOLD
McLean, Va.

This letter is a hoot:

Kudos for covering the important story of the Texas Board of Education rejecting Everyday Math, Grade 3 for its schools [Front Page, "Texas Challenges City on Math," November 20, 2007].

I have lived through Everyday Math with three children who are now in high school and beyond.

In my community, students flock in huge numbers to Kumon Math or other tutoring services because of the deficiencies in Everyday Math. Everyday Math and other Reform Math or Standards Based Math curricula have done a woeful job of preparing students with a sound math education.

Students who are taught by these curricula are typically calculator-dependent, and unable to perform basic math functions because they are deemphasized.

Greater emphasis must be placed on making math fun and expecting the students to discover how to solve math problems on their own. This topic needs more exposure across the country if we are to produce well-educated students capable of competing in our global world. Thanks for drawing attention to it.

MARGUERITE BLISS
St. Louis, Mo.

Gee.

Students don't get to discover stuff in Everyday Math and it isn't fun.

Who knew?

I'm a big fan of the Sun.

Today's banner headline:

Talks are set on ending battle of Iraq
Quiet Announcement Signals Start of U.S., Iraq Parley

And so the Battle of Iraq is to be brought to an end, in T.S. Eliot's phrase, "not with a bang but a whimper."

With the eyes of the world focused on the Middle East peace talks in Annapolis, Md., President Bush's war tsar, Lieutenant General Douglas Lute, quietly announced that the American and Iraqi governments will start talks early next year to bring about an end to the allied occupation by the close of Mr. Bush's presidency.

Meanwhile, over at the Times, we've got:

Seeking a Mideast Path, Bush Offers a Nudge and After a Rough Start, Spitzer Rethinks His Ways.

This reminds me of another Times episode years ago when we were living in L.A. We subscribed to both Timeses: the NY Times & the LA Times.

The annual AIDS conference was on and both papers were covering the proceedings on the front page.

Early on, possibly on the first day of coverage, the LA Times reported that there had been a breakthrough in AIDS treatment. My memory (not fact-checked) is that one of the presenters had reported on 6 HIV positive patients he'd treated, not one of whom had progressed to AIDS.^* They were reporting a miracle. To this day, I remember sitting at the table, pouring over this story, wondering if it could possibly be true.

What did the NY Times have to say about the 6 patients?

Nothing.

The TIMES had a story on insurance discrimination against people with AIDS or some such.

I was horrified. How could the LA Times be reporting the first effective treatment for AIDS (and back then it was AIDS) and the NY Times have nothing? That had to mean the LA Times was wrong, I thought.

Next day, same thing. The LA Times had a second story on the new treatment for AIDS; the NY Times had another dreary prejudice-against-gays or AIDS-in-Africa boilerplate feature, the kind of AIDS story they'd been running for years and could write in their sleep.

By then I was getting nervous for the LA Times. I was thinking they had to have gotten the story wrong and were going to be Humiliated on the World Stage. (I had only a foggy notion of how newspaper journalism worked.)

I wish I could remember now how long it took the New York Times to pick up on the treatment story. I think they finally figured it out on Day 4. Meanwhile I was getting up every morning and grabbing both papers to see which world we were living in.

Were we living in a new world, the world in which AIDS would become HIV?

Or were we still living in the old world, the world of the epidemic?

The answer was that we were living in the new world and the New York Times had missed it.


^* I'm pretty sure the presenter was David Ho.

Kendall/Hunt values your feedback!

They must have seen me coming.

it is important that Trailblazers is not put down

Scarsdale to try new elementary math programs
by Carrie Gilpin

In an effort to "see what's out there,” Scarsdale is trying out four math programs in 30 K-5 classrooms this year, according to assistant superintendent Paul Folkemer, and will settle on one of them, or remain with the existing program, Trailblazers, by spring. A few teachers at Scarsdale Middle School will also participate in the pilot math program.

"We have been very happy with Trailblazers and it has served us well for 10 years, but change is healthy and we want to see what is out there," said Math Committee chairman Nancy Pavia.

“The process is energizing, and puts the subject area on the front burner," said Folkemer. "It is good for us, and at the end, we could come out of this staying where we are with Trailblazers."

Implementing any new program next fall would also be "a budget issue," said Folkemer. "We don't want to get ahead of ourselves, but we won't be able to make any decision until a draft of the budget is completed. We will go in under the assumption that we have the funds to move forward by fall."

Each of the 30 volunteer teachers will test two of the four programs, substituting units of Trailblazers for similar units of one of the test programs. The district is awaiting materials and will begin the first of the pilot program trials at the end of this month, said Pavia.

Pavia said the timing of the pilot is excellent since Trailblazers' second edition is out and needs to be purchased by the district. or a different program purchased.

"This has been very thoughtfully done," she said, stressing there is broad representation of teachers within all five elementary schools and in all six levels from K-5.

A few teachers in middle school will also participate in the pilot. "Increasingly, we have been trying to invite them into conversations with us about elementary school math," said Folkemer.

Some teachers involved in the pilot program announced it to parents at the elementary schools' open houses. Folkemer said he is scheduled to give a report on the pilot program, as well as other district initiatives, to the Scarsdale Board of Education on Tuesday, Oct. 9, during the board's regular business meeting at 8 p.m. The board will meet that night at Edgewood School.

Pavia said parents would see different materials coming home in their child's backpack during the year, and that nothing would be sent home for homework that hasn't already been covered in class.

Will pilot program math students be confused? "I don't think so at all," Pavia said. "The methodology is slightly different but that shouldn't make it confusing. If parents have questions, of course they should address them with the teacher," said Pavia, stressing that naturally it will not be "perfect."

Both Pavia and Folkemer said it would not be possible to test out a new math program without actually teaching it to students.

Pavia said teachers have been discussing a change in program for several years. They considered many possible programs and came up with the following four: Everyday Mathematics, a program from the University of Chicago; Think Math!; Scott Foresman"s Investigations; and Singapore Math. The programs all have slightly different approaches and the National Council of Teachers of Math has endorsed the first three.

“Singapore Math is the one that is slightly out of the box. It is very rigorous and is written by the Ministry of Education there. It is structured slightly differently and has many positive aspects,” said Pavia.

Folkemer said that many teachers “really like” Trailblazers, a program felt by many parents to be heavily language-based.

“Any program we use must have a balance of a strong skill base with conceptual and problem-solving elements,” said Folkemer.

“Language is all around us, and mathematics requires language. But to calculate accurately is critical. Algorithms and fact work is just as important,” Pavia said.

Trailblazers functions on a "spiral” method, where a unit of say, fractions, is touched upon, then students move to another topic, and then com around to fractions again.

“Math by its nature is a spiral, but Trailblazers is a very tight spiral. The programs we are looking at are not quite as structured. Whatever program we use, we will modify it to match it with our own curriculum,” said Pavia.

Folkemer said a presidential commission on math teaching led the NCTM to come up with a list of “Curriculum Focal Points”—important math topics for each grade level, pre-K through grade 8. Focal points are areas of emphasis that serve as organizing structures for curriculum design and instruction at and across grade levels.

“When we Trailblazers years ago, we adopted it as our curriculum,” said Folkemer. “Now, we have written our own math curriculum and any program we use will be modified to fit within our curriculum.

So why does the district need to purchase any program if it has written its own curriculum?

Pavia said it would not be a good idea to teach math without a purchased program. “Teachers are generalists. I’ve always had a program, which is critical for consistency among the schools. It is a foundation upon which we will build and teach our own curriculum,” she said.

“I think it is important that Trailblazers is not ‘put down,’” said Pavia “Change is forward movement and we are looking and learning if there is a better way to teach math,” said Pavia.

Scarsdale Inquirer 10-5-2007

Kerrigan & test prep

Speaking of test prep, Kerrigan is superb test prep for the essay portion of a standardized test. Amazing.

C. wrote two practice test essays yesterday using the X-1-2-3 set-up for both. The first was pretty bad, but he improved dramatically on the second.

Bonus points: X-1-2-3 results in mini-essays that can be easily typed up and edited by the parent/teacher, like so:





C's version is on the left; our lightly edited version is on the right. Ed says it helps tremendously to see your work edited and I think he's right.

I wonder whether a teacher would find it faster and easier to edit student's mini-essays rather than comment on them? (Teachers could copy-edit/revise just one paragraph or one aspect of the essay, etc.....)


C's X-1-2-3 sentences

X People who rescue animals from bad conditions are heroes.
1. They give animals a second chance at a good life.
2. They punish people who are cruel to animals.
3. They provide people with a new pet to love.

X Video games do not cause children to act out violently.
1. Video games do not cause school shootings.
2. Video games let children act out their emotions on screen and not in real life.
3. Video games limit the violence you can do to yourself by allowing you to simulate risky activities instead of acting them out.

truc

Some of you will remember back when we coached C., then age 10 I think, to answer all open-ended math questions with the words:

I used a strategy of guess and check and then I looked for a pattern.

Yesterday we were frantically trying to teach C. how to write in time for him to take the ISEE test next Saturday, and we came up with two sure-fire trucs:

• The final paragraph should being with the word "Finally."
  

• The concluding sentence or paragraph should begin with the words "For all of these reasons."

It works.

Singapore Math approved for use in CA

wow

This is news.

model method

I came across what may be a terrific web site for non-math majors trying to teach the Singapore Math curriculum the other day:

Teach Kids Math Using the Model Method

I could have used this site when I first started working through Challenging Word Problems Book 3 lo these many years ago. My knowledge of arithmetic was so fragmented at the time that I didn't immediately perceive the various "genres" of bar models. Each problem I solved seemed almost to call for a whole brand-new, never-before-seen bar model. (Not quite, but close enough.)

I needed a map of the world.

One of the blinding revelations that came to me via bar models was the reason for the word "difference" as in the expression: "Find the difference." It had simply never occurred to me that subtraction was two things (scroll down - may need to hit refresh a couple of times):

• how much is left when you take away "X"?
• what is the difference between two numbers?

The great thing about the "Teach Kids Math" site is that it lists "Comparison" on a separate button on the sidebar. You can take one look at that page and realize: nobody ever mentioned "comparison" back when I was in school.

I'm not so crazy about the way they draw the comparison model, though. In all of the Singapore books I've seen, they've drawn the comparison model the way I did (though the bars aren't "stacked" the way I stacked them...don't know why I did that.)

I'll probably have C. take a look at the site.