Place Value Part 3: The Bake Sale

Place value is such a fundamental concept that we should ensure the students recognize place value and its significance wherever it occurs. An activity I call “The Bake Sale” highlights place value in the operation of division. I will present just one example. Of course, teachers can have as many examples as groups within the classroom. The groups should not be too large, not more than three of four students per group.

The scenario: They are getting ready for a bake sale. They have a platter of cookies and they want to make sure they will have enough cellophane bags to package the cookies. In today's example, the platter has 173 cookies and they will be packing 6 cookies to a bag. I use beans for cookies and little squares of paper for the bags. So the students would start with 173 precounted beans.

The first concept I want them to see is division as repeated subtraction. They are to remove 6 beans at a time, just as if they were really packing cookies, and place them on a square of paper. As they do so they place a tally mark. Very young children would have a specially designed “worksheet” for recoding each “bag.” For example, a page of squares that the students color as they “pack” each “bag.” When they are through, the number of squares with beans and the number of tally marks or colored squares on the worksheet should be the same.

Older students will want to cut to the chase and simply perform the long division. But one purpose of this activity is to help students see the math behind the procedure, and besides in real life, they really would be subtracting 6 cookies at a time, repeatedly, until there were no longer enough cookies to pack a bag.

They should have 28 bags with 5 cookies left over. Some older students already know that the “real” answer is 28 and 5/6, or maybe 28.83 or ... depending on what decisions they make. Some will be sure that the answer is 29 because they learned to round somewhere along the way. Some of them may believe an answer with a remainder (as in 28 R5) is juvenile, and not as good an answer as some of the other possibilities. Students must always be reminded that math is the servant, not the master.

Later in the activity students will see that the “juvenile” answer is the most useful answer.

Once they have determined the answer, it is time to revisit the standard algorithm with a variation. Rewrite the division problem like this:




The green lines show the place value columns. In a class discussion, we establish that a 2 goes above the 7, not because 6 goes into 17 twice, but because the 7 is in the tens’ place, 6 is going into 170 (17 tens) 20 times. The 2 is really a twenty. Students need to be reminded continually what the numerals really signify as they complete calculations. Otherwise, students are merely manipulating abstract, meaningless symbols.

Because we are writing the division problem with Arabic numerals, naturally each digit and its columns represent a place value. Since 6 roundly goes into 170 twenty times, meaning we can show 20 repeated subtractions in one step, we write a 20, not a 2, over the 173. Since we have filled 20 bags at once with 6 cookies per bag, we have removed or subtracted 20 x 6, or 120 cookies from the platter. We show this very concrete action by subtracting 120 from 173, leaving 53 cookies on the platter. We remove enough cookies to fill eight more bags, that is 48 cookies, leaving 5 cookies on the platter, not enough to fill a bag. We needed 28 bags.

Although not “wrong,” 28 and 5/6, 28.833, 28.83 or 29 have no practical utility in this scenario. Students will have an easier time evaluating the reasonableness of an answer if they are encouraged to keep the context and the numbers together. When they round to 29, they are saying 29 what? 29 bags. By the end of the activity, it should be clear that 5/6 of a bag is not helpful and that typical rounding serves no useful purpose. I require students to write their answers in complete English sentences. The answer to this problem is not “28,” or even “28 bags,” but something like “we needed 28 bags to pack the cookies.”

The finished problem would look like this:






The format looks a little different than the standard algorithm, but the significance of place value is preserved. This type of format did not have a name when I first started using it, or perhaps I mistakenly thought at the time that it was an innovation of my own. I was little surprised when the format began appearing in textbooks as “scaffolding.”

Incidentally, at every opportunity we should insist that students read numerals correctly. Simply reading numerals correctly can prevent confusion. “And” marks the spot between “wholes” and “parts.” Although the answers with fractional parts served no real purpose in this activity, of course there are other contexts where the fractional part is important. In any case, some of the other possible answers would be read “twenty eight and five-sixths,” “twenty eight and eighty three hundredths.” I would use “twenty eight point eight three” only for dictation purposes, not for mathematical purposes.

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?