Place Value Part 2: Base Ten for Young Students

One of the most fundamental mathematical concepts, yet one of the most poorly understood, is place value. The typical primary school lesson presents only a superficial, nominal understanding of place value. Students learn merely to correctly name the place-value columns, or identify the digit in a given column, but they often do not understand the significance of the column names.


In Part 1, The Chocolate Factory, I introduced a middle school activity for rebuilding often weak base ten foundational concepts. The activity extends understanding to place value in other bases. In Part 2, I will introduce activities suitable for much younger children. Young children can construct the meaning of base ten place value through many activities and games.

There is some evidence from Jean Piaget's work as illustrated in the video, that base ten is conceptually out of reach for very young children. If there is demand, I will present some activities that help young children explore “Two Land” and “Three Land.” Years ago I field tested a unit called “The Land of Hand” which of course would be “Five Land” in the terminology of the video.




Today I am going to concentrate on base ten, or “Ten Land.”
1. Morning Circle
Many kindergarten and first grade teachers have a regular morning circle time when they gather the children and go through a structured routine of talking about the calendar, the season, birthdays and other topics using a set of visual materials that are permanently on display. The two main math components are the calendar and the base ten pocket chart. The periodicity of the calendar lends itself to a number of activities for building number sense. The base ten pocket chart is decribed below.

The teacher prepares a display of three horizontal pockets with transparent envelopes on the front of each pocket. On the side is a cup full of Popsicle sticks and a stack of cards numbered with the digits from 0 to 9. Pocket charts can also be purchased from various vendors. Every morning the teacher takes one Popsicle stick and places it in the far right pocket (as you face the display). Each day the teacher replaces the card in the envelope to reflect the number of sticks in the pocket.

On the tenth day, the teacher places the tenth stick in the pocket and then makes a show of pointing out there are ten sticks. The teacher then bundles up the ten sticks with a rubber band and places the bundle in the middle pocket. The pocket envelopes should now show (empty, 1, 0) representing 1 bundle of ten sticks and 0 single sticks. The teacher goes through the Popsicle stick routine every day.

On the hundredth day, a celebration day in many schools, the teacher gathers the 10 bundles, ties them together with a piece of yarn and places the whole bundle in the far left pocket and changes the display to show (1,0,0) representing 1 packet of 10 bundles, 0 bundles of 10 sticks, and 0 single sticks. The teacher continues the routine until the last day of school at which point the display should show something like (1, 8, 5).



2. Trading Activities and Games

Playing games is a natural way for children to acquire all sorts of different aspects of number sense. Years ago I checked a book out of the library that was chock full of wonderful tutoring games. The book has long since gone out of print but no matter. I found the author, Peggy Kaye's website. Here is my version of a game she calls "Fifty Wins."

The teacher creates two boards on heavy card stock, one for each player. Each player also has a die. I recommend using extra large die if you can find them. Each player also has a collection of 50+ beans, pennies, or other counters. My own modification involves using the board at first, then doing away with the board and playing with pennies and dimes.




Each child casts their die in turn, and draws the number of counters that matches the number of dots on their die, placing one counter in each of the small squares of which there are nine. Upon accumulating the tenth counter, they transfer ten counters to one of the five big squares. The first person to get fifty counters wins. Children learn there can never be more than nine in the one's place, and that the ten's place is precisely groups of ten. If three big squares are filled and none of the little squares, they can see very clearly 3 (groups of ten) 0 or 30.

A modification I have made is to use poker chips for counters. I change the design of the board so that the nine little squares become a long rectangle outlined in one color (say blue) and the big squares are outlined in another color (say red). Then as the child accumulates 10 blue chips, the child exchanges the 10 blue chips for one red chip and places it in one of the red squares. The poker chip modification leads quite naturally in the penny-dime modification I mentioned earlier. I have also used the same poker chips with the same color signification for "The Chocolate Factory" activity, blue for leftovers, red for boxes, white for cases.

Another modification of mine which may be considered a weakening of the game is the use of a die to generate numbers. The original game uses a spinner where some of the fields say “Win 10.” At the beginning the child will dutifully count out ten beans and place them one by one in the small squares, only to have to transfer the entire group of ten to a big square. Very soon the child counts out the ten beans and straightway places them in a big square. The opportunity to realize a group of ten in one turn is lost when die are used, but I suppose you could use a set of two dice. I like the die because the child does not have to read words or numerals. With die, the child has only to match, by one-to-one correspondence, the beans to the die spots. There is no need to reference numerals at all, so the game stays squarely focused on number and avoids number/numeral conflation.


“Make Fifty” is just one example of what is known as a “trading activity.” Cuisenaire rods also work well for trading activities. Every ten cubes makes one rod. Any base-ten block set goes one step further where every ten rods makes one flat, and every ten flats makes one cube. Many base ten block worksheets can be adapted to active lessons.

All manipulatives have limitations and some researchers are concerned about the limitations of base ten blocks. Nevertheless, with a good mix of activities, the teacher can address the differing learning styles of each student.

Stuff to Avoid
Worksheets
Generally speaking, worksheets should be avoided. Nevertheless, I like to design special worksheets as data recording instruments for math labs utilizing base-ten blocks and Cuisenaire rods. Students can learn a lot of math without writing numerals. In fact, a foundation of math reasoning skills without reliance on numerals helps children acquire the concept of the difference between numbers and culturally-determined symbols for numbers such as Arabic numerals. Schools “accidentally on purpose” teach children to confuse number and symbol. Cuisenaire has a few such worksheets along this idea, but I have some problems with the worksheet design. Maybe I'll collect my math lab worksheets into some kind of cohesive with comprehensive directions for using them with children and make them available.

Computer-Based Materials

Too many of the computer-based materials, animated mathematics and virtual manipulatives, though so appealing to adults, often have a magical quality to young children. Regrouping happens before their very eyes but they do not understand the mathematical concept and mechanism. They do not get from the computer what I call the psychology of numbers, or how numbers behave. It is just a lot of cool special effects without specific mathematical concept acquisition benefit.

Calculators

Despite the National Council of Teachers of Mathematics (NCTM) claims to the contrary, calculator studies with the youngest students show no advantage in the development of children's number sense. In 2002, I conducted a major survey of research, research critiques, case studies, and editorials. I periodically asked NCTM to provide me a list of what they characterized as supporting research, but they never did. I found no basis for NCTM's assertion that research backed their recommendation for calculator use in the earliest grades. I found that calculator usage need not hinder the development of math reasoning skills, but it may in fact do so. Teachers report that children become overly dependent on the calculator and have difficulty learning to evaluate the reasonableness of their answers. They trust the calculator more than themselves.

Links

The following is a list of links of base ten lessons. They are presented as is. Many exemplify what I believe are the main weaknesses of most base ten teaching.
Lesson plans reviewed by teachers:
Crayola Tally Sticks:
Applet: but better off using concrete manipulatives.
An Unreviewed Collection of various resources:
A favorite resource for getting teaching ideas:
Vendor:

Lesson Plan: The Chocolate Factory or Place Value in Algebraic Thinking

Because students typically have fuzzy notions of place value, they may be able to correctly name the place-value columns, but they often do not understand the significance of the names. For example, they cannot give a mathematical explanation of why regrouping works. One reason may be that they rarely receive mathematical explanations.

The explanations may certainly be chock full of numbers yet without having the least connection to the way the numbers work. A good example is the standard method for finding 10% of a number: just move the decimal place one digit to the left. The method is nothing but a trick, and our children learn to mistake performance of tricks for understanding of math.

Students need help in constructing mathematical explanations. In an activity I call “The Chocolate Factory,” students pack chocolates in boxes, then in cases, while keeping a tally. At the end of the activity, students will be able to trade and regroup in order to add or subtract.

I usually use beans instead of chocolate because it is less messy and less tempting. I explain that the students are working for Hershey Chocolate Company packing chocolates as chocolate pieces roll down the conveyor belt a la a famous “I Love Lucy” episode. The number of chocolates in each group is simulated by drawing a card from a shuffled deck with no picture cards. A specially made set of number cards with spots but no numerals would be better. Students pack the pieces into boxes of ten pieces each, then pack the boxes into cases of ten boxes each, keeping a running tally in a table on the blackboard.

Draw	Cases	Boxes	Leftovers
1			/////
2			////////
Result		/	///
3			//////
Result		/	/////////
4			//
Result		//	/
	etc. until, say,
Result	/////	//////	///

Each pair of students shares a set-up: 100 beans, a container capable of holding ten beans to represent boxes, and a larger container to hold ten “boxes.” The teacher explains that the rule of the game is that a “box” can only hold ten beans. Once a box is filled, they begin filling another box, and so on until they have ten boxes. Ten boxes are then packed into a case.

The teacher shuffles the cards and holds the deck face down. The teacher uses any suitable method to select a student to pick a card. The student takes a card from the deck (a five-spot in the example) and shows it to the class. Each pair counts out five beans and puts them in a “box.” The teacher records the five as tally marks in the “leftovers” column. Another student picks a card (an eight spot). The students count out eight beans and the teacher records the tally in the “leftover” column The students use the beans to fill a box, pointing out that they have one full box and three leftovers. The teacher records the result with one tally mark in the “box” column, and three tally marks in the “leftover” column.

It is important to give students experience with “Cases, Boxes and Leftovers” before renaming these columns “100’s, 10’s and 1’s.” Another advantage to using the column names, “cases, boxes, leftovers” is that the activity can be recycled later for teaching any base. I have found it is more helpful to rename the “ones” place “leftovers”. Then it is easy to explain that there are leftovers when the amount is insufficient to fill a box. Thus, there will never be 10 leftovers, because 10 will fill a box, thereby adding 1 to the tally in the “Boxes” column. Converting the final tally in the table to numerals yields 563. Students readily understand that as they accumulate 10 boxes, they transfer those boxes as 1 case and put a tally mark in the “Case” column. It is often at this very point the light bulbs go on, and students see the why carrying works for the first time.

Then we repeat the activity, but the cards now simulate consumed chocolate (yum). From the deck, a student draws, say, an eight-spot to stand for eating eight pieces. Students will naturally want to open a box to accomplish this. As they take a box, they erase a tally mark and dump the 10 chocolates (beans) with the leftovers, and record ten more tally marks for a total of 13 tally marks in the leftover column. They continue subtracting in this way. This activity is very similar to most trading activities, but seems to be more effective at building the concept of place value because we avoid giving the columns numerical names at the outset.

With older students we simultaneously keep a record of this computation in the standard algorithm. Again, students often understand regrouping for the first time. We expand and repeat the activity with other groupings which I have carefully planned in advance. I tell students that they have done such a good job that now they work for a more expensive chocolate company, perhaps Ghirardelli, where chocolates are packed in boxes of 5 pieces, and cases of 5 boxes. I give the students 158 chocolates, knowing full well they will again end up with 5 cases, 6 boxes, and 3 leftovers, the same tally as for the Hershey exercise.

In the ensuing class discussion, we talk about why the first 563 (10 to a box) has more chocolate pieces than the second 563 (5 to a box). Students discover that neatly lining up their addition and subtraction columns is not merely for neatness sake, but because the columns have real meaning. Students find they can work just as readily in other bases as long as they remember the basis (pun intended) of the groupings. (It is also valuable to finish the base five regouping so that there is one crate of 5 cases, one case of 5 boxes, one box of 5 pieces, and 3 leftovers, or 1113 in base five, and why "563 base five" is technically illegal).

If working in base ten, I prefer to name the columns from right to left “leftovers, 10, 100, 1000,” etc. As the Chocolate Factory activity illustrates, the “ones” are “ones” only because there are not enough of them to make a “ten”. They are the ungrouped leftovers, whether in base ten or any other base. In fact, students get very comfortable with working in a variety of bases and discover that for any base (b), the column names will be (from right to left) “(leftovers), (b), (b x b), (b x b x b), and so on. For example, they would name the base 7 columns “(leftovers), (7), (7 x 7), (7 x 7 x 7), and so on.

I like using the parenthesis early on so students become familiar with the idea of parenthesis holding a number just as cupped hands hold an apple, and that a number can have different appearances, and all are still equivalent. In practice, I often go beyond leftovers, boxes, and cases, and extend the activity to crates, trucks and warehouses. Just like the the song from School House Rock says, “Don't you worry 'bout the big numbers, they're just bigger, that's all.”

Later the columns can be renamed with exponents, 10^2, 10^1, 10^0 or 7^2, 7^1, 7^0. Then it is a small step to b^2, b^1, b^0 (where b stands for "base"), then x^2, x^1, x^0. Students often practice writing in expanded notation without ever grasping real significance of what they are doing. In algebra, many polynomial expressions are really bases in disguise. For example, the base 10 tally and the base 7 tally were both 563. Algebraically, both would be expressed as 5x^2 + 6x + 3, where x is the base. The algebraic expression is nothing more than expanded notation. If x is 10, then the expanded notation is (5 x 10^2) + (6 x 10) + (3 x 1). If x = 7, then the expanded notation is (5 x 7^2) + (6 x 7) + (3 x 1). Rewriting numbers as polynomial expressions often makes calculations in different bases much easier, and The Chocolate Factory activity enhances such algebraic understanding.

There is a vendor, Digi-Block, who sells a manipulative that would be ideal for the base 10 chocolate factory. The set has pieces, boxes and cases. Each box holds exactly 10 pieces, and each case holds exactly 10 boxes. The big advantage is that students are prevented from overpacking or underpacking. I have usually had to rely on materials I have scrounged: beans, little cough syrup cups for boxes, and little containers to hold 10 cough syrup cups. If you are looking for basic base ten blocks, Nasco probably has the most complete assortment anywhere.

Whole-System Reform

Yeah, that's what we need for education in America—whole system reform. But it sounds daunting and overwhelming. Is whole system reform even possible? Opposing ideologies argue themselves into stalemate, and the upshot is nothing changes. Teachers ride the roller coaster of one educational fad after another. A few schools here and there may garner media attention for their success in raising the academic of achievement of their students, but their results seem immune to wholesale transfer. A great strategy with proven results in one school fails dismally in another.

Actually, America has experienced a form of whole-system change. “Reform” is the wrong word. The change has been gradual and insidious, taking decades to get where we are today. Decades ago, a strong liberal arts education was the objective of any student dreaming of a bright future and social mobility. Now the university is a job-training center, and some people think "liberal arts" is a political term.

Wasn't whole-system reform the goal of No Child Left Behind? Is whole-system reform even a reasonable goal?

Ontario, Canada thinks it is. In fact, they say they have accomplished whole-system reform.

We have done (whole-system reform) in Ontario, Canada, where we have had the opportunity since 2003 to implement new policies and practices across the system-all 4,000 elementary schools, 900 secondary schools, and the 72 districts that serve 2 million students. Following five years of stagnation and low morale, from 1998 to 2003, the impact of the new strategies has been dramatic: Higher-order literacy and numeracy have increased by 10 percentage points across the system; the high school graduation rate has risen 9 percentage points, from 68 percent to 77 percent; the morale of teachers and principals has improved; and the public's confidence in the system is up.

For the Canadians in Ontario, whole-system reform does not mean taking on every single issue. It means diligently accomplishing a set of “core policies and strategies.”

Whole-system reform is possible, but it must be tackled directly. There are no single-factor solutions. By implementing a core of fundamental components, system leaders can get results in fairly short order, and build on those results for sustainable futures.

Ontario worked on six “fundamental components.”

1.The entire teaching profession.
2.A small number of ambitious priorities-literacy, numeracy, and high school graduation.
3.The two-way street between instruction and assessment.
4.Distributive coordinated leadership at all levels of the system.
5.Focused, mostly nonpunitive, comprehensive, relentless intervention strategy.
6.Use money to drive reform only in the service of the previous five fundamentals.

Those six fundamentals seem pretty comprehensive and the report lacks specific details. What exactly did everyone do to accomplish the fundamentals?

The only way to get whole-system reform is by motivating and mobilizing the vast majority of people in the system.

There we are, the crux of the problem—motivating and mobilizing the vast majority of people in the system. Did the leaders simply order mobilization by fiat or did they motivate individual buy-in?

One major piece is the student success program. Instead of restricting curriculum as we have so often done here in the US, Ontario believes expanding the curriculum is the way to go. Ontario students can choose a specialist major in a number of fields.

Specialist High Skills Majors are now available in:
Agriculture
Arts and Culture
Aviation/Aerospace
Business
Community Safety and Emergency Services
Construction
Energy
The Environment
Forestry
Health and Wellness
Hospitality and Tourism
Horticulture and Landscaping
Information and Communications Technology
Manufacturing
Mining
Transportation

Students can choose a work coop situation. Back in the day, my own high school in California offered work coops. Maybe it's time to bring them back.

Our students are plugged in anyway. What about offering high school students online courses? Ontario offers fifty of them.

How about this idea? Dual credits.

Students participate in apprenticeship training and postsecondary courses, earning dual credits that count towards both their high school diploma and their postsecondary diploma, degree or apprenticeship certification.

Clearly, Ontario's main strategy for motivating success is to give students a rich variety of choices. Meanwhile, many American schools have been eliminating choices and electives. American universities have been following suit, so that students must strictly follow a curricular flow chart if they expect to graduate, and the number of available electives has been reduced as more and more classes become required in order to ensure, as one example, exposure to multicultural information. Breadth is no longer built into a liberal arts education. With the emphasis on meeting the market demand for job training in the university, liberal arts may be a dying concept.

An Alternate Theory of Human Evolution?

Elaine Morgan hypothesizes that humans evolved from a water primate and laments the lack of interest and research within the scientific community.

She questions the prevailing Savannah theory because of the intriguing questions it does not answer:

1.Why are humans the only Savannah animal to walk upright?
2.Why are humans the only Savannah animal with a layer of “blubber” directly under the skin?
3.Why are humans the only “naked” Savannah animal?
4.Why are human babies born with so much fat, compared to other mammalian babies?
5.Could capacity for speech be related to the ability to control air flow similar to the control exhibited by diving birds and other water animals?

And many more questions.

She is not the only one skeptical of the Savannah theory. Many “real” scientists have developed doubts.

The Savannah theory suggests that our hominid ancestors evolved on the dry plains of Africa, and the theory still has many supporters.

In a separate BBC documentary, Mrs. Morgan graciously advises young scientists to avoid imperiling their careers over her hypothesis. If sound, she says, the theory will eventually prevail. If unsound, her theory deserves to be discarded.

Did humanity arise out of water? It has to be considered.

Cellphones the New Calculators?

Dear ---,

As I understand your research proposal, it sounds like you are collecting an anthology of ways to use the IPhone as an instructional instrument.

The current cell-phone-as-tool-of-instruction discussion reminds me very much of similar discussions when calculators became ubiquitous.  Oh, lookie, lookie, we can play games and we can make upside-down words. First graders will learn place value and regrouping as they do +1 over and over watching the changes in display. We will even be able to teach chaos theory in the fourth grade.  The National Council of Teachers of Mathematics went so far as to recommend calculator use with first graders as part of their standards, but later qualified the recommendation with the words "under the guidance of a skilled math teacher."

I have compiled an extensive review of the literature on calculator use with our youngest students. The most generous conclusion is that at best calculators do no harm.  "At best" is not good enough.  The games, clever tricks and so on have not lived up to the claims. 

I am concerned we are repeating the same mistake with cellphones.  It seems you have already decided cellphones have educational potential.  Researchers are not supposed to pre-decide.  If you are assuming that cellphones will be of positive use in the classroom, then you might be laboring under an unexamined assumption.  Unexamined assumptions are often fatal flaws in research. Even professional researchers are not immune.   Another unexamined assumption I often encounter regarding cellphones is the idea that since the kids have them anyway, we might as well figure how to make use of them. However, some schools require the students to check their cell phones at the door. Or some parents exercise their parental right to deny cellphones to their children. Schools even now experience difficulty when they assume that each and every child has independent internet access at home.

It seems to me that your research topic is a worthy one, but that perhaps you should focus on designing a research study that may contribute the necessary knowledge preliminary to collecting ideas such as the one about ELL students animating their vocabulary words.

As a college professor, I do not worry too much about students having cell phones except that I expect them to be turned off in class.  If they are surreptitiously texting or playing games in their laps, and miss stuff that might show up, oh I don't know, on the midterm, that is their responsibility and they must face their own consequences.  After all, they are adults. But I worry about our responsibility to minor students.

I just finished teaching in a summer program for 4-8 grades.  They all had cell phones.  The program director had told them to turn off their cell phones during "class" but most ignored his request.  After all this wasn't school they reasoned, sometimes out loud.  They were constantly texting and playing games in their laps, and then complained that they did not get very much out of the summer program.  Parents were not happy either and thought we teachers should have disciplined their children more strictly.  Some teachers actually did discipline children, but those children often dropped the "class" of the "mean" teacher the very next day, and transferred to another "class."  Some classes escaped this problem entirely.  I mean, it is pretty hard to text and do woodworking, karate, or swimming at the same time. :-)

Good luck with your thesis.

The Ugly Flip Side of Meritocracy

(paraphrased) If you believe in meritocracy, then those with the potential and work hard will reach the top, and those who deserve to be at the bottom will be at the bottom. Failure within a goal of meritocracy is much more crushing...When we think about failure, what we fear is not so much loss of money. It is fear of the judgment and ridicule of others

Alain de Botton of the School of Life was talking about success and failure, but take his premise further, and he seems to be suggesting that an education system based on what he calls the beautiful, but crazy idea of meritocracy fundamentally damages society.

It used to be that a poor person was seen as unfortunate, today a poor person is called a loser... Meritocracy is a crazy idea. The idea does not take into account the effect of all sorts of random uncontrollable events. St. Augustine said, “It is a sin to judge any man by his post,” or into today's language, it is a sin to judge someone by their business card... It would be insane to call Hamlet a loser, though he has lost.

What kind of burden are we putting on our children if we indoctrinate them to the idea that each and every one them can “reach the top?” The motivation may be pure, but what of unintended consequences? For one thing, there simply are not enough slots at the top, and for another, it is a myth that we have total control of our own outcomes.

These days there are two kinds of self-help books. The first kind tells you you can do anything, the second kind tells you how to deal with low self-esteem. That tells you something.

Our schools have the exact same dichotomy. Teachers are always on the one hand promising success to every student, as expressed in the title of a literacy program, Success for All. On the other hand, and running on a parallel track are admonitions to prevent failure because of self-esteem. Many people have observed a lack of congruence between self-esteem and genuine achievement. The students might not be very good at whatever, but they sure feel great about themselves.

It is bad enough not getting what you want. It is worse to call what other people want you to want what you want and not get that.

Okay, let's try that sentence again. If you do not decide your own goals, but let other people, that is, society determine your goals, and then adopt those outwardly imposed goals as your own and fail, that failure is worse than failing at goals you independently assign yourself. How many of us have actually examined our so-called goals and dreams under the magnifying glass of self-knowledge? Do we even know what we want, or have we so internalized externally imposed dreams that we can no longer tell the difference?

No one wants to pigeon-hole children early on. Every parent wants their child to have access to every opportunity. Labeling is dangerous precisely because once the label has been affixed, it may very well become indelible. Do we work to create a system of true equal opportunity and let the chips fall as they may? The American ideal is to educate each child to their potential, but honestly, are we actually striving for the ideal? Or do we consider the Japanese view of meritocracy, to deliver the same education to each child, and let the child make of it what they will?

The Foolishness of Educational Ethnocentrism

Anytime the Japanese education system, and the advisability of adopting some of its features, comes up, most certainly voices will arise in dissent. Americans have heard somewhere that Japanese students are so driven they commit suicide in droves, that their education emphasizes rote and regurgitation, and a whole host of other negative attributes. Thusly reassured that the American system is not so bad by comparison, everyone goes back to sleep, confident that the proclaiming of some supposed negatives eliminates all positive features of the Japanese system from further consideration. What a foolish response!

Once upon a time, not so long ago, the Japanese were at the top of their game in their corner of the world. Or so they thought. The Tokugawa Shogunate came into power around 1600 bringing peace and stability to what had been a land ravaged by competing warlords. Socially, class distinctions were rigidly drawn and fiercely maintained. The Shogun made the laws; punishments were severe. The Shogun, the daimyo (literally “great names”) and their samurai retainers topped the vertical social scale, followed by farmers, then craftsmen, and at the bottom, merchants, those despised handlers of “filthy lucre.” Japan experienced an economic boom, enriching especially the merchant class to the dismay of the ruling class.

Most of what Westerners admire culturally came out of this period also known as the Edo period.

The Edo period is nowadays seen as the high-water mark pf Japanese cultural tradition... Beasley, W.G. (1999). The Japanese Experience: A Short History of Japan. pg. 171

That poet laureate of haiku, Basho, wrote during the Edo period. A new kind of drama, kabuki, was first performed in Kyoto. Hokusai produced his famous woodblock print, The Great Wave Off Kanagawa.



Nevertheless, after a couple hundred years, Japanese society was becoming acutely stressed by the increasing disparity of wealth and especially the redistribution of wealth from the samurai class to the merchants. Contradictions and inconsistencies plagued the carefully constructed system. Throughout the Edo period the Japanese had limited interaction with other foreigners, first the Portuguese, and then the Dutch. Then one fine day in July 1853, the people beheld Commodore Perry and his Black Ships coming over the horizon. He was not well received. No matter, he would return the following year. And so he did with twice as many ships. He meant to open Japan to the West and he succeeded by threat of his greater military power. Ten years later, the threat was made real when in 1864, a coalition of four countries launched a fleet of seventeen ships which bombarded the coast at Shimonoseki to open the straits for trade.

The Japanese realized they had lost the ability to compete and set out to rectify the situation. The Japanese sent students to the West to study just about everything with a view to acquiring whatever made sense for them to adopt and adapt to their own culture and society. Before Commodore Perry, the Japanese had held an unswerving confidence in their own superiority. Perhaps if they had been strong enough militarily to repel the foreigners, they might never have questioned their superiority. They realized they had lost the ability to compete. In order to compete militarily, they realized they needed to educate their people. They understood they had to (as the President said), “outeducate in order to outcompete.” Much of their present educational system was first adapted first from the Prussians and modified by influences from America.

America is in a similar situation today. There is an unshakable confidence in our own superiority in spite of contradictory evidence. But many Americans do not seem to feel the urgency of the situation. The main arena of competition today is not military but economic. What will it take, the economic equivalent of Commodore Perry's Black Ships? In order to outcompete economically, we have to outeducate our children. Strangely, calls to learn from others, such as the Japanese, are met with resistance and rationalizations.

It reminds me of an incident a few years ago when a group of Japanese Christians decided that California was a pretty wicked place in need of missionaries. The response from the Californians they visited was anger and derision. “We sent missionaries to you. How dare you think of sending missionaries to us?” Now it is not necessary to go off on a rabbit trail about Christianity and missionaries. The point here is the attitude displayed. It is educational ethnocentrism to think that it is impossible the Japanese should have anything to teach us. If we are not careful, we may wake up one day and find we have been outcompeted. Game over.

Most of what is written in American media about Japanese schools is mistaken. Very few writers have the long-term experience and fluency in Japanese to make sense of their observations. Japanese children are not rote-and-regurgitate robots.

At primary school, there are many opportunities for children to take the initiative to study on their own or in small groups, but the entire class almost always comes together again after a while to discuss findings and conclusions. Indeed, Japanese primary classrooms are very impressive for their emphasis on inquiry and exploration.

What helps to underpin the combination of energetic inquiry and discussion is the unremitting effort to develop a classroom community. All children take turns in leading the class, and all participate in a great variety of small groups for organizing everything from chores (including cleaning) to fun and games. This is often very effective in developing a sense of mutual consideration and respect.

In Japan, all education is essentially moral and Japanese education seeks to foster integrated wholeness in every child.

At secondary school, most children join after-school clubs, mainly run by teachers, which offer sporting or cultural activities, usually almost every day of the week. Sports clubs in particular play an important role in instilling an ethos of effort and self-discipline, as well as enabling children to develop non-academic abilities and experience camaraderie outside the classroom. All in all, Japan's schools have been remarkably good at enabling their charges to develop all-round mental and social capabilities that stand them in good stead as individuals and contributors to society...


...snip...


I confidently expect continued sensationalist and misguided deploring of the shortcomings of Japanese schools and young people - either as undisciplined know-nothings or fact-stuffed robots - because "crisis" makes copy that sells. But the more mundane reality is that Japanese education does a pretty good job of turning out young people who are thoughtful, hard-working, energetic, knowledgeable, and often, remarkably creative - even if it could do still better.

The Japanese themselves are not wholly satisfied with their education system. They worry because their ranking in international comparisons is slipping. However, it is foolish to dismiss good ideas from Japan because of an American educational ethnocentrism that grasps at any reason to discount and then ignore valuable lessons from the Japanese education system.

“Education... From Cradle Through a Career”

I appreciate that the President talks so often about the importance of education, most recently at the Centennial of the NAACP.

All of us can agree that we need to offer every child in this country -- every child --
...every child in this country the best education the world has to offer from cradle through a career.

No argument there. The debate centers around how to do it while still allowing competing interests to perpetuate and prosper. There are reasons society has settled for the current education system. One other thing we can agree on is the value of excellent teachers.

the job of a teacher is too important for us to accept anything less than the best. 

It may surprise you to learn that many, maybe most, school districts have a pernicious policy of rejecting the best school teachers. If a teacher moves from one community to another, that teacher has become what is called an “out-of-district” teacher. These teachers are proven successes with demonstrated competence and experience. They face a good chance of being rejected when they apply for teaching position in their new district. Most districts have a policy of rejecting applicants with more than around five years of teaching experience. And even if they hire the applicant, they will start the teacher on the pay scale at no higher than the five-year-experience level.

If America adopts nothing else from the Japanese education system, America needs, NEEDS, to adopt the idea that teachers are among the most esteemed members of society and teaching is among the most prestigious of professions, a profession capable of attracting our best students.

We need to walk back from the increasingly prevalent idea in American society that teachers are mere technicians. The Alternative Education Resource Organization (AERO) recently held a conference. One of the workshop presenters, Susan Ohanian, addressed the trend toward making teachers technicians. From a description of her workshop:

19. Teacher Professionalism At Risk
Presenter: Susan Ohanian
Description:
Teacher professionalism is at risk, under bombardment by Democratic and Republican corporate-politicos. When a teacher becomes a technician whose existence is dependent on directives from the State, then the very term 'teacher professionalism' becomes an oxymoron. This jeopardizes alternative schools as well as public schools. We are all At Risk.

 
What Ms. Ohanian is referring to is the increasing desire of schools to have their teachers become “facilitators” who manage computer-based courses, or deliver prepackaged curriculum. Schools have begun making teachers into technicians as a way to overcome the problem with teacher quality. Every teacher hates these scripted packages precisely because using them infringes on teacher autonomy and professionalism. Schools feel they have no choice. Schools feel that entrusting teachers (autonomy) is too risky because too many teachers lack quality (professionalism). Allowing the trend toward teachers as technicians to continue will only debilitate our education system further by making what some believe to be true to become really true, that anyone can be a teacher.
Any parent is witness to the learning power of babies and toddlers. Another thing we can agree on is that the earliest years are the foundational years.

And we should raise the bar when it comes to early learning programs.  It's not enough just to have a babysitter.  We need our young people stimulated and engaged and involved. .. some (early learning programs) are wasting what studies show are by far a child's most formative years.

But we cannot rely on the government. Nor should we.

Government programs alone won't get our children to the Promised Land.  We need a new mind set, a new set of attitudes -- because one of the most durable and destructive legacies of discrimination is the way we've internalized a sense of limitation; how so many in our community have come to expect so little from the world and from themselves.

That's a description of one mindset. I encountered that mindset in the person of a junior high boy at an urban school. He was in my science class. I was constantly encouraging students to use education as the way out of the ghetto. This boy said, “Why bother? My father is a janitor and that's all I'll ever get to be.”

But there's another mindset he did not mention, a competing mindset no less debilitating. That is the mindset of entitlement manifested by students who believe that they do not need an education, their future as members of a privileged group is assured, and school is for meeting friends, playing around, and messing with the teacher. They think they are rich, but do not perceive their poverty.

The key to students with a positive attitude towards school is parents.

You can't just contract out parenting.  For our kids to excel, we have to accept our responsibility to help them learn...  And by the way, it means we need to be there for our neighbor's sons and daughters... That's the meaning of community.

With the support of parents, children can aspire to their potential.

It also means pushing our children to set their sights a little bit higher... I want them aspiring to be scientists and engineers -- (applause) -- doctors and teachers -- (applause) -- not just ballers and rappers.  I want them aspiring to be a Supreme Court Justice.  (Applause.)  I want them aspiring to be the President of the United States of America.  (Applause.)

America needs an attitude makeover. Society needs to respect and esteem teachers. The colleges of education need to turn out teachers worthy of esteem and respect. Many disruptive students yearn to have a teacher who is worthy of their respect. Oftentimes their disruption is a search for someone, please, anyone to earn that respect. Schools need to pay teachers a salary befitting a professional. Once the esteem of society is the norm, colleges of education will have no difficulty attracting a full cohort of the the best and the brightest.

kids are smarter than we give them credit for

Kids ARE smarter than we give them credit for. In America, we really do not believe in our children. By an interesting turn of circumstances, I once found myself teaching high school biology to a multi-age group of students from second grade through high school. I found the youngest children could responsibly handle the equipment, record data, and discuss the implications of their data as well as the oldest students. Where the older students excelled was in writing the lab report. The children loved learning biology. It was fun, challenging and built real self-esteem, not the specious self-esteem so common in schools.

At the conclusion of his speech, the President waxed poetic:

One hundred years from now,
on the 200th anniversary of the NAACP,
let it be said that this generation did its part;
that we too ran the race;

that full of the faith that our dark past has taught us,
full of the hope that the present has brought us,
we faced, in our own lives and all across this nation,
the rising sun of a new day begun.

Incidental Oversight or Deliberate Social Engineering

America is full of sober, responsible people who tried very hard to do the right thing financially. They got their education, got a job, bought a house, stayed out of debt and saved for retirement. They followed all the rules only to wake up one fine morning and find themselves in serious financial trouble. What did they learn? They did not necessarily do the right things after all. They, meaning we, found that very often our financial teachers gave us advice that benefits them rather than us. Yet even now, our financial teachers, wherever they may be found, are advising us to do what we have so long been taught to do: go to school, work hard, stay out of debt, save for retirement, and hope things will be okay. Once the crisis is over and things are back to normal, doing all those old right things will work---except when they don't.

Every financial adviser strangely urges relying on the same failed strategies to work in the future, the strategies that enrich them instead of us. And why not? Most so-called financial advisers are really financial sales people. We should expect what they say to benefit mostly themselves. It seems each financial adviser has a pet financial instrument. For some, no matter what the financial problem is, the solution is life insurance. For others, the solution is an annuity. Still others, it's the stock market. For yet others...whatever it is they are licensed to sell. Once they have been paid, it little matters how their advice impacts their clients for good or ill.

Given the importance of finance in every single person's life, it is astonishing that finance is not generally taught in schools, nor is there much public demand to make finance part of the school curriculum. Teachers may read and groan, Oh, please, do not add even one more burden to the teaching load or one more excellent subject to be neglected in favor of NCLB testing. Even so, finance should be part of the curriculum, perhaps within the math curriculum. To be sure, many math textbooks touch on financial topics, especially when looking for real world applications of the math students are supposed to be learning. But these incidental financial topics are taught by the same elementary math teachers whose lack of a profound understanding of fundamental mathematics has already been well-documented.

Robert Kiyosaki, taking some cues from John Taylor Gatto, believes that keeping our children in ignorance about money and how it works is evil. We are in the information age when knowledge about all kinds of things, including money, is crucial. Yet as any history of education shows, our education system still operates in the industrial age. During the most recent presidential campaign we heard that education and the economy are intertwined and interdependent. However, there are no broad-based initiatives to include finance in the curriculum.

A program to teach financial literacy is probably more important than the technology literacy schools were more than happy to integrate into their curriculum, especially since technology in schools was often generously funded by the foundation arm of corporations in a position to profit. Thus Apple put free computers in many schools. Nearly every foundation's Request for Proposals (RFP) for grant funding requires a computer/technology component. Financial literacy is even better, because almost by definition, financial literacy would enhance that darling of all educators, CRITICAL THINKING. Financial literacy is all about evaluation, the very top level of cognitive knowledge.

What would a curriculum of financial literacy include? Robert Kiyosaki, writing about this very topic, would probably say a curriculum* of financial literacy would include:
1.The language of money.
2.The difference between capital gains and cash flow.
3.The fairytale aspect of most financial advice.
4.The influence of attitude on reality.
5.Selling yourself.

In other words, students need a new mind set, a different frame of reference, a modified set of pegs for organizing the basics of financial knowledge, such as rate of inflation, compound interest and tax strategies, just to name a few. Those basics need to be taught within a different frame of reference, because clearly the old frame of reference further enriches the already rich at our expense. Schools need to prepare students for the information age where knowledge is king. So far, schools seem uninterested in the task, perhaps because teachers with the new, different, modified mindset are so rare, and because the usual, but flawed advice, is not only everywhere, but everywhere accepted as correct. I am not necessarily recommending Mr. Kiyosaki's work. He has his own agenda. However, finance is such an integral part of the adult life for which we are supposed to be preparing students, we need to get serious about including it in the curriculum.










*Robert Kiyosaki spelled out his curriculum in chapter 12 of his new online book. The chapter did not exist when I first wrote the post, and the link is now broken.

“History of money...
Understanding a financial statement...
Difference between asset and liability...
Difference between capital gains and cash flow...
Difference between fundamental and technical investing...
Measuring an asset's strength...
Know how to choose good people...
Know which assets are best for you...
Know when to focus and when to diversify...
Minimize risk...
Know how to minimize taxes...
The difference between debt and credibility...
Know how to use derivatives...
Know how your wealth is stolen...
Know how to make mistakes...”

The Education Train May Have Left the Station

The education train may have left the station, leaving traditional educators still groping their way blindly to the platform.

New, innovative, non-educators are poised to blaze the new education trails needed to help America reclaim its status as the world class education system. These new style educators usually have not earned education degrees, have not taught school, and do not possess any state teaching licenses. All that stuff is so last century. Nevertheless, they may be at the forefront of the education reform so many of us yearn for.

I am not talking about technology, a relatively recent buzzword near and dear to education writers and grant-funding foundations. A Request for Proposal without a technology piece is getting pretty rare. However, technology is often nothing more than gussied-up drill-and-kill.

The people currently studying the dynamics of learning are not necessarily publishing in journals, but they are implementing what they learn in domains outside of traditional education settings. Second Life just held its first commencement ceremony honoring virtual students who earned degrees entirely in the virtual world. Talk about online education. I just want to know if the real person behind the Second Life avatar has acquired real-life marketable skills. I mean if the avatar had to complete assignments and pass tests to earn a virtual degree, is it possible the person behind the avatar acquired that knowledge. And if not, could the concept be designed so that the puppetmaster, so to speak, does acquire the puppet's skills? Intriguing.

The government has commissioned Visual Purple to create training simulations that put participants in decision-making roles to maximize learning by doing. Robert Kiyosaki, of Rich Dad, Poor Dad fame, has a game, The CashFlow Game, out to help people master his strategies and tactics. The idea behind these simulations is the the puppet represents the puppetmaster, and the puppetmaster must learn and integrate knowledge and skills in order for the puppet to succeed. The acquired knowledge and skills is then directly useful in real life work.

So am I just talking about games and simulations? No. Games and simulations are nothing new. I used Reader Rabbit, Oregon Trail, Operation Frog, Sim Ant, and other programs with positive effects many, many years ago. But those programs were supplemental to my main teaching agenda, and compared with some of the new developments, frankly clumsy and primitive. With a well-designed curriculum, some of the new games can BE the teaching environment.

To be clear, I am NOT saying you have to subscribe to the opinions of any of the purveyors of games and simulations. I AM saying that Confucius was right. The amount remembered depends on the level of processing. The simulations seek to maximize learning at the active, 90% level.

Uncontrollable Variables Muddy Evaluations

Does Jonathan Alter at Newsweek really know what he wants? His recent article, Peanut-Butter Politics, rightly pinpoints teacher effectiveness as a crucial component of classroom effectiveness, but accuses the teachers union of reluctance to actually hold teachers accountable. The problem is he has no viable accountability plan except a nebulous call for measuring teacher effectiveness in the classroom.

Teacher effectiveness–say it three times. Last week a group called the New Teacher Project released a report titled "The Widget Effect" that argues that teachers are viewed as indistinguishable widgets–states and districts are "indifferent to variations in teacher performance"–and notes that more than 99 percent of teachers are rated satisfactory. The whole country is like Garrison Keillor's Lake Woebegon, except all the teachers are above average, too.

Why? The short answer is teachers' unions. Duncan complained recently that the California school system has a harmful "firewall" between student evaluation and teacher evaluation. In other words, teachers can't be evaluated on whether their students actually learned anything between September and June. The head of the San Francisco union says it's nuts to judge teachers on whether there's evidence that shows improvement in their classrooms. An A for accountability, eh?

...snip...

It takes a tough man to say, in the middle of a recession, "no improvement, no check." But if not now, when?

I addressed The Widget Effect a couple weeks ago. It is not so much that there is a lack of desire to hold teachers accountable. The main problem is that there are simply too many variables the teacher does not control. No one has yet proposed any fair way of evaluating teachers. And no teacher can or should be held responsible for (for example) the drunken uncle who lives in the student's home.

The worthlessness of evaluations creates a major disconnect in the school policy.

Though it is widely accepted that a teacher’s effectiveness matters more than any other school factor in student success or failure, it is almost never considered in critical decisions such as how teachers are hired, developed or retained.

Teacher effectiveness cannot be considered because teacher effectiveness is unknown. What's more, researchers have no consensus as to the characteristics of an effective teacher.
I would like to address the first two points.

It is easy to be negative and overlook the legions of highly motivated, highly competent, and highly effective teachers in our classrooms. In spite of the evaluation difficulties, we know they are there. here's the thing: many are recognized only years after a student has benefited from their influence. At the time, their students, with their lack of life experience, may not have realized what a treasure their teacher was. In fact, they may have even “hated” their teacher. Nevertheless, great teachers populate our classrooms in great numbers. A commonly appearing estimate is 50%. Around 50% of education students have the right stuff, but nearly all students will graduate and end up in our schools. Any college of education cohort can differentiate the more able from the less able among their peers. Maybe our colleges of education should be more selective, evaluating teaching candidates for suitability long before they have invested four plus years of time and money in becoming teachers.

Students (and Teachers) Do Not Understand Math

Three weeks ago educators wondered if conclusions from the Response to Intervention (RTI) research might be applicable to mathematics.

Educators gathered here last week to discuss a recent federal “practice guide” on response to intervention for students struggling in mathematics agreed that applying the RTI approach to that subject is challenging. But they also suggested that doing so was worth the effort.

It is instructive to discover the reasons applying the RTI approach to math is challenging.

Response to Intervention involves six steps: Screen, Teach, Intervene, Probe, Chart and Adjust.

Screen
Valid screening measures predict who is, and who is not, at risk for future reading difficulty. These measures are administered to determine if a child is at risk for failing a state's "high stakes" end of year achievement test, by which the state measures a school's overall performance. Children considered to be "at risk" are expected to experience difficulty responding (not keeping up) in the core curriculum as traditionally delivered in the regular general education classroom. Note: Due to the desire to capture all children who are truly "at risk," the false positive rate of early screening may be as high as 50 percent. In other words, as many as half of all the children who are identified as "at risk" by early screening may not be truly "at risk."
Teach
Core curriculum in the regular general education class should be research-based and field tested. This means, based on evidence from converging research, that the core curriculum contains all the elements found necessary to effectively teach reading and has a known track record of success. Such curriculum is to be delivered by "highly qualified" teachers sufficiently trained to deliver the selected instruction as intended, i.e., with fidelity to design. My note: Notice the language says, “trained to deliver the selected instruction as intended.” I knew one highly competent first-grade teacher in California that refused to deliver the selected instruction (whole language) as intended. It was a good thing because her students ALL learned to read even as California fell to 49th place in reading during the whole language period. The fad lasted until 1995 when phonics was reinstated in the curriculum. The change in the role of the teacher as indicated by the language I have noted is problematic.
Intervene
Provide "at risk" children with enhanced opportunities to learn, possibly including, but not limited to, additional time exposed to the core curriculum in small groups (3-6 students), other supplementary instruction, or special education.
Probe (progress monitoring)
Progress monitoring tests are brief measures of specific reading skills that are administered to determine if the child receiving intervention is responding as intended. They are given frequently, at least once every two weeks.
Chart
Progress is regularly charted to provide a visual record of actual rate of gain in specific reading skills in relation to a specified goal. The goal of intervention is for the child to improve relative standing and perform at or closer to grade level standards and is individualized according to the unique needs of the child.
Adjust
Depending on whether the child is achieving a rate of progress determined by his or her individualized goal, the manner and intensity of intervention will be adjusted. The cycle of progress-monitoring and adjustment of intervention will continue, even if a determination for special education eligibility is made.

Math educators met June 10, 2009 to explore whether the same six steps would be just as effective in math as in reading.

Educators at last week’s event said that fitting math into an RTI framework is hard, but that they believe it is now vital to improving math performance for struggling students.

One of the main difficulties is finding suitable math education materials.

Judith Russ, the mathematics curriculum supervisor for the 134,000-student Prince George’s County district in Maryland, said for her part that finding the right materials is hard.
The instructional materials “are not looking at building conceptual understanding. That’s one of the challenges we have,” she said.

The first step is to screen.

Karen D. Cheser, the assistant superintendent for learning support services for the 20,000-student Boone County district in Florence, Ky., said her school system started using RTI in reading two years ago, and had initially planned to leave math for later. But indications that students were becoming weaker as they reached higher-level math classes, among other factors, pushed the district to act.

Ms. Cheser said the district created its own universal screening program, which allows teachers to dig into what was going wrong for many students. It turned out that many students needed to focus so hard on computation that they were unable to grasp more sophisticated concepts, she said.

The panel found that children's gaps in mathematical understanding were fairly predictable.

... remediation for students in grades K-5 should focus on the properties of whole numbers, like counting, addition, and subtraction. Older students, up to 8th grade, should learn rational numbers in depth, including the meanings of ratios, decimals, and percentages, the panel recommends.

Another recommendation is that all students who need extra math assistance should work on fluent retrieval of basic arithmetic facts, like simple addition and multiplication. Higher-level mathematics often assumes that students can quickly recall facts like “3 times 9” or “11 minus 7,” when such operations may be difficult for those lagging behind their peers, the panel found.

The current reliance on the calculator does nothing to promote fluency with math facts. In fact, some teachers say that, with the ubiquitousness of calculators, it is no longer necessary to memorize math facts. But I know that students who cannot readily retrieve math facts struggle with algebra, and the research is confirming my observations.

Mathematics instruction has emphasized procedural competence over conceptual understanding. You do not necessarily have to understand the mathematics underlying long division as long as you can perform the operation. Sadly, students who perform mathematical operations reliably are told (through test grades) that they understand math when the reality is that they may have no idea why they do what they do. They do not “understand” math. The math materials in our schools “are not looking at building conceptual understanding,” as Judith Russ, mathematics curriculum supervisor, noted. But at least in times past, students were expected to memorize math facts in order to complete the procedural operations. So the situation is that students are not understanding math concepts, nor do they have the basic tools, math facts, for mechanically solving problems.

Years ago we used to call screening “diagnosis” and the best teachers have always made diagnosis part of their teaching practice. I used to diagnose struggling algebra students one-by-one. I still diagnose one-by-one, but nearly always I find the same gaps. They do not understand the function of place value (even if they can name a digit's place). They do not understand whole number properties (and fail to apply properties to numbers that do not look like “numbers,” especially numbers containing variables. They do not understand the difference between one and zero (such as when the “cancel” and say something like, “That's zippo.” They certainly do not understand fractions. Once I address these four abysses of knowledge, algebra suddenly becomes straightforward and even beautiful.

Is Quality Education a Lost Cause?

I love reading old stuff. Did some expert pundit's analysis and future projections come to pass or not? A quarter century ago, there were lots of articles wondering what we would do with all our future free time. The answer turned out to be---work even more. A quarter century ago, lots of articles wondered how America would solve its looming math and science teacher shortage. The answer turned out to be ---not much. Many universities are importing math and science professors from other countries because America is not producing its own. So it was interesting to reread an old article from Time entitled "Help! Teacher Can't Teach" dated Monday, Jun. 16, 1980, nearly thirty years ago. It could have been written yesterday.

Like some vast jury gradually and reluctantly arriving at a verdict, politicians, educators and especially millions of parents have come to believe that the U.S. public schools are in parlous trouble. ..Experts confirm that students today get at least 25% more As and Bs than they did 15 years ago, but know less.

Society holds the teachers responsible.

the new complaints about teachering also arise from a dismaying discovery: quite a few teachers (estimates range up to 20%) simply have not mastered the basic skills in reading, writing and arithmetic that they are supposed to teach.

Even as criticism abounds, Time (and all of us) recognize that 20% is quite a bit less than 100%.

Of course, among the 2.2 million teachers in the nation's public schools are hundreds of thousands of skilled and dedicated people who, despite immense problems, manage to produce the miraculous blend of care and discipline, energy, learning and imagination that good teaching requires. ...The best-educated and most selfless teachers are highly critical and deeply concerned about the decline in teaching standards and educational procedures. Their frustration is perhaps the strongest warning signal of all.

Testing tends to be the first line of defense. Many states began mandating teacher competency tests, only to find that far too many practicing teachers were unable to pass these tests. Lest one should think that teacher competency tests were perhaps too hard, most required math typically taught between the eighth and tenth grades, and English at corresponding levels. Any teacher, presumably all of them college graduates, should be able to pass easily. But they do not.

I was astonished to be the first one finished with the California Basic Educational Skills Test (CBEST). I put that test away in less than two hours. It was supposed to be a four-hour test. I once took the National Teachers Examination (NTE) in early childhood education cold, no study, review or preparation of any kind. I had been a secondary teacher for many years. I scored at the 86th percentile. I was not happy. My score was too good for someone like me who had taken a test outside of my field. According to the normative data on my score report, the vast majority of test takers were graduates of early childhood education programs. I did better than 86% of them. Not good.

Education Secretary Arne Duncan's support of merit pay for teachers, though framed as a way to pay teachers more, is really just a disguised way of saying if teachers taught better, our schools would be better, and so maybe more money would motivate teachers to teach better. One of the problems of merit pay is the unstated assumption that teachers are not already doing their best.

Okay, let's face the issue of teacher quality head on.

1.Teaching credentials are no assurance of teacher quality.
2.Schools do not hire the best qualified candidates, but the cheapest.
3.School of education attract students of lower academic ability than other academic departments.
4.Graduates of colleges of education must often take basic teacher competency tests many times before they pass.
5.Math teachers often do not possess a profound understanding of fundamental mathematics.

Some schools, like The Equity Project charter school in New York*, is determined to acquire high-quality teachers. They are offering $125,000 per year and the application process is a grueling four-step process. The charter school has created such a grueling process because the usual documentation, university degree with or without a state teaching credential, is worthless.

It did not used to be like this.

In 1900, when only 6% of U.S. children graduated from high school, secondary school teachers were looked up to as scholars of considerable learning.

Things were going swimmingly as high schools graduation rates steadily improved to a high of 70% by the 1960's. Sputnik was a huge surprise in 1957.

Almost overnight, it was perceived that American training was not competitive with that of the U.S.S.R. Public criticism and government funds began to converge on U.S. schools. By 1964, achievement scores in math and reading had risen to an alltime high.

Let's repeat that: Public criticism and government funds began to converge on US schools. Though only a child, I remember that time well. Society did not simply complain and moan; society demanded action and the government responded. The result, which directly benefited me, was that by 1964 achievement scores in math and reading had risen to an all time high. Only genuine achievement would do because society had a stake in knowing accurately if education was working. There was no interest in the statistical juggling so common now. Want SAT score improvement? In 1995, the College Board simply added 100 points** to everyone's score.

Over the last thirty years, there has been plenty of societal moaning and complaining, but no demand, no collective will. So society had the education system it wants. What did now Research Professor of Education at New York University Diane Ravitch say thirty years ago?

Diane Ravitch: "It is really putting things backward to say that if children feel good about themselves, then they will achieve. Instead, if children are learning and achieving, then they feel good about themselves."

Colleges of education are still teaching a backwards concept of self-esteem.

Although the driving motivation to beat the Soviets to the moon was not the noblest, my generation was the last beneficiary of America's once legendary education system.

Ever since the mid-1960s, the average achievement of high school graduates has gone steadily downhill.

...snip...

Many teachers have come to see themselves as casualties in a losing battle for learning and order in an indulgent age. Society does not support them, though it expects them to compensate in the classroom for racial prejudice, economic inequality and parental indifference.

In 1957 it was Sputnik. What will it take today for society to set aside complacency, ideological wrangling, or perpetuation of social status quo?


*The Equity Project's 4-stage application process

**To be fair, the purpose of recalibrating scores was not to artificially raise scores, but to realign the scores to the population so that a score of 500 would once again be average. According to the New York Times article,

The average verbal score today is 424; the average math score, 478.
So the College Board officials have decided to "recenter" the scale, changing it so the average student will once again get scores of 500 on the verbal and math tests...
In 1941, when the current norms were established for scoring the S.A.T., the world was a very different place. A small group of middle- and upper-class Americans attended college...

As colleges diversified in the 1960's, opening their doors to more poor and first-generation Americans, S.A.T. scores began a steady drop. By 1969, the average verbal score was 462; today, it is 424.

Teachers are Widgets

So President Obama wants to get rid of the bad teachers.

"We need to make sure our students have the teacher they need to be successful. That means states and school districts taking steps to move bad teachers out of the classroom. Let me be clear: if a teacher is given a chance but still does not improve, there is no excuse for that person to continue teaching. I reject a system that rewards failure and protects a person from its consequences. The stakes are too high," Obama said.

Nobody wants bad teachers. But exactly who are the bad teachers? How do we go about identifying them? Oh, I know. Let's take a look at the teacher evaluations. Surely the evaluations, many of them professionally designed, will point out the bad teachers. After the bad teachers are identified, all that remains is the battle with the teacher's union, whose mission is to make sure bad teachers teach until retirement. (snark alert).

Every school I have ever seen has a program (at least in the employee handbook) for annual evaluations. In my whole career, I have been evaluated just five times by supervisors (principal, vice principal, or department chair). And here is something else everyone knows: the evaluations are worthless. Now a new study by the New Teacher Project confirms what everyone knows. Entitled “The Widget Effect,” the study show that teachers are fungible.

The study illustrates that teacher evaluation systems reflect and codify the “Widget Effect”—the fallacy that all teachers are essentially interchangeable—in several major ways:

All teachers are rated good or great. Less than 1 percent of teachers receive unsatisfactory ratings, even in schools where students fail to meet basic academic standards, year after year.

Excellence goes unrecognized. When excellent ratings are the norm, truly exceptional teachers cannot be formally identified. Nor can they be compensated, promoted or retained.

Professional development is inadequate. Almost 3 in 4 teachers did not receive any specific feedback on improving their performance in their last evaluation.

Novice teachers are neglected. Low expectations for beginning teachers translate into benign neglect in the classroom and a toothless tenure process.

Poor performance goes unaddressed. Half of the districts studied have not dismissed a single tenured teacher for poor performance in the past five years.

The worthlessness of evaluations creates a major disconnect in the school policy.

Though it is widely accepted that a teacher’s effectiveness matters more than any other school factor in student success or failure, it is almost never considered in critical decisions such as how teachers are hired, developed or retained.

Teacher effectiveness cannot be considered because teacher effectiveness is unknown. What's more, researchers have no consensus as to the characteristics of an effective teacher.
I would like to address the first two points.

All teachers are rated good or great. And because all teachers are good or great, excellence goes unrecognized.
At best, evaluations are worthless. In many schools, an evaluation is a pro forma process, if it happens at all. The busy administrator visits the class for a few minutes, walks out and writes the glowing report.

At worst, the evaluation is a retaliatory or evidence-fabrication tool. I am reminded of the young elementary art teacher whose reputation for excellence was well-known by staff and parents alike. Teachers dropping off their class at her classroom often lingered and teachers retrieving their class often came early to observe and hopefully glean some useful tips. One fine April morning the vice principal came to observe a class period and stayed for the whole class. His one and only comment after the class left: he did not like that the students were allowed to chat with their neighbors as they worked on their art.

The resulting evaluation was a disaster. On a 5-point scale, her average came to 2.7. She objected to the principal and he allowed her to write a rebuttal. But the rebuttal went nowhere. All that survived of the evaluation was the average which appeared on a list of all the teachers with all their 4.X averages. The school submitted the list to the district office.

She complained bitterly to the principal who told her not to worry—it would have no effect on her future career. She complained to her colleagues, some of whom interceded for her with the principal. You see, this young teacher had rebuffed the vice principal's advances at the school Christmas party. Her colleagues suggested the principal replace the vice principal's evaluation with one of his own, but he refused, saying it would be unseemly to override the vice-principal.

This story is not a fluke. Evaluations, if done at all, are often undertaken only because the teacher has entered the administrator's radar for some reason. In such situations, greatness cannot help but go unrecognized. I would go so far as to say that Teachers of the Year are not necessarily the top teachers. They are teachers with spare time. Many of the best teachers are simply too busy to fulfill the onerous essay and video requirements to be considered for a Teacher of the Year award.

What, you say. You thought Teachers of the Year were nominated for doing their jobs every day. Most Teachers of the Year are self-nominated. Typical is the application for the Arizona Teacher of the Year.

Teacher nominees/applicants must submit a written application that is reviewed by a panel of judges consisting of educators, students and members of the business community. Ten finalists are selected from the written applications.

The 10 finalists are asked to prepare a 15-minute videotape. The final selection process includes review of the videotape, an interview and an impromptu speech by each of the 10 finalists. Following that process, the Teacher of the Year is selected along with four “Ambassadors for Excellence” and five finalists. The Teacher of the Year and Ambassadors have multiple opportunities during the year to make public appearances throughout the state, speaking to professional, civic, educational, parent and student groups. (my bold)

The written application includes 13 double-spaced pages of essay material:

Educational History and Professional Development Activities (2 double-spaced typed pages) – 5 points
Professional Biography (2 double-spaced typed pages) – 5 points
Community Involvement (1 double-spaced typed page) – 5 points
Philosophy of Teaching (2 double-spaced typed pages) – 15 points.
Education Issues and Trends (2 double-spaced typed pages) – 15 points
The Teaching Profession (2 double-spaced typed pages) – 20 points
National Teacher of the Year Message (1 double-spaced typed page) – 10 points
Arizona Teacher of the Year Message (1 double-spaced typed page) – 10 points

The school administrator must agree in writing to approve up to 30 days for a substitute teacher to allow for newly-minted teacher of the year public appearances.


You may be the greatest teacher in the world, but if you are, and you are honest, you are very likely not going to write essays that will get you selected as teacher of the year, especially when you write about “education issues and trends” and “the teaching profession.” John Taylor Gatto was voted New York's Teacher of the Year in 1991 and immediately, with his acceptance speech, began telling everyone about the insidious goal of compulsory education to de-educate students. He has written several books, all with the same message. Somehow I have trouble believing the message he proclaimed from the Teacher of the Year platform was the same message he told the committee he would proclaim when he wrote his application essays.

Neither the complicated, multifaceted, self-selected Teacher of the Year evaluations nor the run-of-the-mill annual evaluations performed (or not) in most schools succeed in any meaningful way.

Can the Top-Scoring State Beat International Scores?

How does the math covered in the highest-ranking American state stack up against that of a top-scoring international performer?

International comparison studies typically focus on the comparing the scores achieved by same-age students in different countries. Also typically, students from Asian countries tend to outperform US students over and over again. Each time a report like that comes out, just as predictably there will be an out-pouring of the same old tired excuses. Their students are different from our students. Their culture is homogeneous whereas ours is diverse. Their schools are allowed to teach whereas our schools must meet social, medical and nutritional needs. Their parents value education whereas our parents, not so much. On and on. The excuses act as a sedative to put society back to sleep. Okay, society says, there are understandable reasons for the differences in performance. The results are not really comparable. Apples to oranges. What a relief. So we stop thinking about it.

Could there be something more?

Sean Cavanaugh of Edweekreports:

A host of recent studies have examined how U.S. students’ mathematics skills compare against those of their foreign peers. Now, a new analysis probes a more precise question: How does the math covered in the highest-ranking American state stack up against that of a top-scoring international performer?

Let's repeat the question: How does the math covered in the highest-ranking American state stack up against that of a top-scoring international performer? It does not matter whether the results are comparable or not. No matter the reason our kids come out second rate, other kids are beating our kids in the worldwide competition. Remember, President Obama said that if we want our kids to out-compete the world, we must out-educate them.

So how does the math covered stack up?

A study released last week finds that elementary students in Hong Kong are exposed to more difficult and complex math than pupils in Massachusetts, an elite scorer on national and international exams. The analysis, published by the American Institutes for Research, in Washington, examines the math content of Hong Kong and Massachusetts by comparing the two jurisdictions’ standardized tests in 3rd grade math.

We're talking about third grade, part of the foundation of the rest of a child's academic career. The study did not look at scores on a specially designed test for international comparison purposes. The study did not look at the content of such a specially designed test. The study examined the respective jurisdiction's in-house test, the standardized test for Massachusetts and Hong Kong. Even more interesting, the study had no interest in the children's scores on these tests. The study studied the test content itself. And why Massachusetts?

Massachusetts is also a consistent elite-scorer on the primary U.S. domestic test, the National Assessment of Educational Progress.

What the study found is that the Hong Kong test emphasizes number and measurement concepts. The test also contains a larger percentage of constructed responses rather than chosen responses. The Hong Kong test questions were more complex, requiring the application of knowledge and non-routine, multi-step solutions over simple recall. From the foundations, children in Hong Kong are tested on higher-order thinking skills than American children, even “elite” American children.

Do Chinese teachers teach to the test?

(Steven Leinwand, one of the study's authors), said the authors chose to examine test content in Hong Kong and Massachusetts because the two jurisdictions' early-grades math curricula were relatively similar—and because state tests in the United States tend to guide math instruction.

American educators “pay attention to the tests,” he observed. “If you change the state tests, it’s a powerful lever for what goes on in the classroom.”

In the US, the favorite quick and dirty way to reform education is to redesign the tests. That's what Arizona did in the 1990's with their AIMS test. Arizona created high-stakes tests for fifth, eighth and eleventh grade, as if new tests automatically change educational philosophy and encourage innovation. Even honor students flunked these tests. The overwhelming response to high-stakes tests is to teach to the test, a response well-documented by No Child Left Behind. When a test reflects existing educational philosophy, there is no need for sample tests or practice materials.


Liping Ma has documented the emphasis Chinese teachers place on concept development over computational procedures. James Stigler reiterated many of the same points. Chinese math education, exemplified by Hong Kong, already valued conceptual understanding and the test reflects that value. The US, regardless of all the pretty talk in the media, values computational procedures and the Massachusetts test reflects that value.

How did Mr. Leinwand put it? “... state tests in the United States tend to guide math instruction.” That is the large part of the problem. We are suppose to test what we teach, not teach what we test. The US mistakenly thinks testing drives instruction.

The Uncomfortable Conclusion

Laying solid foundations in the early years matters.

Hong Kong’s use of more difficult and complex test items could be connected to a higher proportion of its test-takers, 40 percent, scoring at the “advanced” TIMSS level, than Massachusetts, at 22 percent. Just 10 percent of American students, on the whole, reached that level, the authors argue. In addition, research shows a “strong correlation” between nations’ math performance in early and later grades, they say.

Why Standardized Testing Will Always Fail

The most basic characteristic of any test is validity, that is, whether the test actually tests what it purports to test. Everyone, from the “professionals” who write standardized tests, to the everyday classroom teacher putting together a five-point quiz, learns that a test that does not actually test what it claims to test is worthless. They all learned about validity in the colleges of education.

So John Pearson makes a great point when he observes that every test is a reading test.

TAKS is stressful enough to prepare for at the 3rd grade level, and our kids at least can get reading assistance on the math test! There has been a little bit of debate over exactly what that means, but at least it is specified that, on an individual basis, a student may ask to have a word or a question read aloud. This helps immensely, especially with a child who is a struggling reader and/or an English Language Learner.

However, after 3rd grade, the kids are completely on their own for every TAKS test -- excepting those kids with special modifications, of course. The vast majority of kids taking these tests every year cannot ask to have a word read, cannot ask for clarification on a question, cannot ask ANYTHING except a question about the directions, and the directions are usually "Pick the best answer."

So what it comes down to is that these kids are taking a series of reading tests. Some of them are ABOUT math or ABOUT science, but they don't strictly assess those subject areas as much as they assess whether or not the child can read the questions, some of which are highly complicated.

I knew a little boy in Japan who was completely bilingual in both Japanese and English, but who had attended only Japanese preschool and kindergarten. The first thing to understand about his situation is that the Japanese kindergarten ends near the end of March, so when he “graduated” from kindergarten, his parents decided to enroll him in an international school where instruction was conducted in English. The principal said the first grade teacher needed to access the boy's readiness.

On the appointed day in March, this boy sat down with a clearly unhappy first grade teacher. She did not want any new students entering her class so close to the end of the school year, especially one whose parents had the idea the child would go on to second grade after less than three months in first grade. The teacher asked a number of questions about fairy tales and a few addition problems and announced that the boy was “marginal.” She would allow him into her first grade class on the condition that the parents understood that in September he would very likely have to “repeat” the first grade. The parents accepted the condition.

In April, the school gave the annual Stanford 9 bubble tests. The first grade teacher made a copy of this boy's answer sheets to hand grade, because the score reports would not be available before the end of the school year. She needed ammunition for the parent-teacher conference she was sure she would need when she planned to tell the parents that yes, indeed, their son would have to repeat first grade.

To her utter astonishment, the boy had almost a perfect set of answer sheets. The score report, when it eventually arrived, placed the boy in the 99th percentile on every battery. Obviously he went to the second grade along with his class. Eventually the same boy graduated from an American university at age eighteen with a degree in chemistry.

So why did the teacher consider the boy marginal? Mostly because he did not know who Rumpleskilskin was. The boy could have told her all about Momotaro, a Japanese fairy tale character the teacher had never heard of, if only she had known to ask, except Momotaro was not included in the school's first grade curriculum anyway.

Imagine going to live in Russia for a year and taking a math class. After 3 months, you are given a math test in Russian, consisting of word problems and lengthy questions. I don't know about you, but I would fail that test miserably. Would ANYONE in their right mind think that that means I don't know math?? Or that that test accurately gauged my knowledge??

I was a teacher in that international school in Japan. I taught math and science to the middle-schoolers. Every year fully 50% of my students were non-native speakers of English. One year four of my students were non-English speakers who had transferred from the Japanese school just that year. Lucky for me I also speak Japanese. I was the only American teacher in the school who spoke Japanese. There were a few Japanese-speaking teacher's aides.

I made all kinds of accommodations to help my non-native English-speaking students. I paired each one with a native speaker for labs. I translated my instruction to Japanese on the fly on a regular basis. I adapted reading instruction techniques usually used in much lower grades to the science book as if the science book were a basal reader. I read words or whole questions from my tests for any student who asked. And for those four non-English speakers, I translated the whole test to Japanese. I did all these things because I knew what every tester should know, that is, the purpose of the tests. The purpose of my tests was to evaluate the student's mastery of my instruction with the corollary purpose of giving the students the best chance for success.

We may think the purpose of standardized is to evaluate individual student's knowledge, but in reality, the tests serve to rank students compared to the norming population, and then by extension, to rank the quality of the school relative to the norming population. The reality will always frustrate because the nature of norming means that half will be above the 50th and half will be below the 50th percentile when compared to the total population.

If some schools can attract an overabundance of topside students, obviously other schools will end up with an overabundance of bottomside students. Testing can, by design or not, perpetuate the inequality of educational opportunity and undermine any promising efforts of school reform.

So who would want to perpetuate inequality of educational opportunity? Sadly, dear parents and other adults, Lake Wobegone does not exist.