Cultural Sacred Cows of American Education

As long as comparative studies show so many other countries outperforming American students, there will be those who dismiss the findings because of comparability concerns. The samples from other countries are more academically proficient, or societies in those countries value education more, or those education systems emphasize rote learning or.... The critics pull out the list anytime American students fare poorly, comparatively speaking. American students have been ranking low for a very long time now, so the list is pretty well memorized. The list has been repeated so often without dissent that its points are assumed to be true, whether they are or not.

The fact is there are comparability problems. In 1993, David C. Berliner tackled the topic in an article published by Phi Kappa Phi in their journal, National Forum. Significantly, he subtitled his article, “A False Guide for Reform.” Old stuff can be good stuff. Although Dr. Berliner wrote almost twenty years ago, he could have written yesterday.

To blame school failures on poor teachers, inadequate administrators, inappropriate curriculum, or uncaring parents is misleading. When children are poor, when they lack health care, when they come from dysfunctional families and dysfunctional neighborhoods, schools fail. When public schools do fail, it is because society has failed (bold added by S. Goya)....

International comparisons of achievement always will reveal differences because the economic support for schools in each nation, their curricula, the quality of the teachers, the health of their students, their administrative systems, the support for school by parents in each nation, the value of education in each nation, and job markets each nation prepares its children for all differ. Such variation in the national systems of education leads inexorably to variation in the performance of students in each nation.

In 1994, I wrote a short article, also published in the National Forum, addressing two differences between Japanese and American education that Americans generally accept as true. It is human nature to put superficially true statements through our cultural filters and end up with mistaken conclusions. First, because public schools do most of the educating in America, we automatically credit Japanese public schools for Japanese school achievement. If international studies intend to compare public school outcomes, then researchers will have a difficulty finding a comparable sample in Japan. Virtually every student in Japan has received substantial supplemental education from the ubiquitous private after-school schools (juku).

Second, we hear that the Japanese school calendar has 240 days. Our own American schooling leads us to assume Japanese students are “on-task” for 240 days. However, 100 days are only half days for one reason or another. Japanese annual public school instructional time measured in hours is actually quite similar to American instructional time, but because nearly all Japanese students also attend juku, they receive substantially more academic instruction than American students. Furthermore, there are some fundamental unquestioned cultural paradigms that influence the American view of what is possible and what is untouchable when it comes to education reform.

Attention Seeking

In America, there is an axiom that children of all ages crave attention. Therefore, Americans have unconsciously socialized their children to crave attention, similar to the unwitting differential treatment of boys and girls. Adults are generally unaware of the many ways they encourage even middle school and high school students to be attention seekers. Consequently, no one questions that part of every teacher's job is to give attention to every student. In fact, the main argument for reducing class size is smaller class sizes make it easier for teachers to give individual attention in an environment where the misbehavior of children is often interpreted as a bid for more attention from the teacher.

I did not question or even notice the unexamined attention seeking axiom until I taught in a society that does not socialize its children to be attention seekers. Teachers in these societies capably manage much larger classes even in preschool and the early grades. Most primary grades have an average of forty-five students per grade. Even more interesting, students from these societies generally outrank American students in comparative studies. While larger class sizes may not be a positive variable, it is at least not necessarily negative variable either. Of course, interpreting international comparisons is always a problem because of the complex interaction of variables. Even in the US, the research on class size is inconclusive and subject to confirmation bias.

For example, some Americans believe that societies with large class sizes post exemplary academic achievement because of an authoritarian school structure. One person wrote to me that they “knew” the Chinese government does not allow students to misbehave. While such a belief may be consoling, it is not true. Japanese education, especially in the elementary grades is very inquiring, active and hands-on. Furthermore, it does not occur to Japanese teachers that misbehaving students are seeking attention. They attribute misbehavior to other factors. If you have not created a room full of attention seekers, you can be a highly effective teacher with many more students in the classroom.

Contempt of High Achievers

American society is of two minds when it comes to high achievers. We say we value academic achievement, but what we say is betrayed by what we do. Our society routinely mocks and marginalizes high achievers. Tamara Fisher asked her gifted students to talk about how they felt about being high achievers. We did not need Ms. Fisher's class to tell us that while they were personally happy, they suffered socially. Nearly every American schoolchild has either been a victim or a perpetrator.

America says that one foundation of its education system is equal opportunity, that is, every child has a right to be educated to the extent of their potential. Then we undermine our grand values by charging high achievers with elitism. What exactly do we mean? That smart people can be smart as long as they hide it, so as not to hurt anybody's self esteem by their mere existence? There is an unresolved conflict between the values of meritocracy and egalitarianism.

Maltreatment of Substitute Teachers

One of the most appalling characteristics of American education is the routine poor treatment of substitute teachers and the commonplace administrative attitude that pranks and misbehavior come with the territory. Since when is it ever okay for students to mistreat another human being for a day. The substitute should be accorded the regard given to special guests for that is what they are. Nuff said.

Faculty Continuity

Everything about the American way encourages faculty longevity and discourages mobility. Teachers are certified at the state level. There are often silly, bureaucratic obstacles to re-certifying in another state. A teacher earning a Masters degree while teaching will receive a pay differential as long as they stay in the same district. Move to a new district and the Masters becomes an impediment to employment. Moving also turns experience into a disadvantage. Administrators are so adverse to paying for experience they will give credit for a maximum of only five years (in most districts). More often administrators simply pass over the experienced applicant in favor of the novice.

In Japan, for example, teachers are not only certified nationally, but they are also required to transfer schools every three years. Japanese administrators believes change keeps the staff fresh. The Japanese do not worry about the stability of school culture as Americans do. In fact, it could be argued that stability of school culture is actually a problem since the flip side of stability is resistance to improvements.

Instead of reflexively trotting out the tired list of reasons why international comparisons are flawed as if doing so somehow magically turns poor performance into acceptable performance, we should should be studying those reasons in detail to see what we can learn. It may be true that other societies value education more. Good for them. The lesson then is not to make an excuse, but to ponder what we could be doing to encourage American society to value education more, not only in word, but in deed.



Some Class Size Research Sources:

Counting Students Can Count http://nccic.acf.hhs.gov/node/28205

The Effect of Class Size on Student Learning http://livebinders.com/play/play_or_edit/31977

Class Size Research (List of Six Publications) http://www.bsd405.org/Default.aspx?tabid=5729

Class Size-Research Brief www.principalspartnership.com/classsize1110.pdf

Smaller Class Sizes: Pros and Cons http://www.publicschoolreview.com/articles/18

Making Enemies of ED Reform Allies

Alienating “ed reform” allies seems to be a counter-intuitive strategy, but one that “common-sense teachers” rely on more and more frequently. Anthony Cody summarizes the platforms of both “parties” in his biased Teacher Common Sense takes on Education "Reform" Nonsense. However, it is not like he did not give fair warning of his slant towards the “common sense teachers” party.

The past decade we have seen drastic changes affecting our schools, and many of these changes defy what we know as teachers and parents to be in the best interests of our children. We have allowed technocrats to drive our schools with data. It is high time for teachers and parents and students to challenge the reform nonsense that holds sway.

While he makes many valid points about poverty, teacher experience, tenure, test scores and data, I was hoping for an even-handed summary of the education reform conflict and the myriad ways the teachers' voices are ignored. What I see instead is subtle and not-so-subtle mocking of "ed reform" by using easy-to-demolish phrasing. The article also makes enemies of potential allies by redefining education reform as a political stance.

Plenty of experienced teachers and other stakeholders are passionate about education in America and want to see it reformed. If they make the mistake of calling themselves “education reformers”, by Mr. Cody's lights, they automatically oppose "common sense" teachers. We need to flee these sorts of useless and destructive either-or dichotomies when discussing issues as complicated and with as many self-interested stakeholders as education.

For example, ed reformers do not believe that “Class size does not matter.” It does matter in certain situations, but in most educational contexts, the research has not supported universally smaller classes. In fact, there are countries with normal class sizes of 45, even in the primary grades, where students consistently rank at the top of international standings. Even more telling, their below average students out perform our best students. Before someone rushes to defend American performance by discounting the achievement of these students, we must remember that like so much in education, international comparisons are complex.

It will not do to rely on tired defensive excuses. For example, claiming that our average kids have to compete against their superior kids obfuscates more than it clarifies. There are any number of opposing unexamined cultural assumptions operating within both the American education system and the systems of other countries that make it appear obvious that class size should be important. Appearances are deceiving. I will name just one American education axiom that may not necessarily be true: Children, by definition, seek attention from their teachers.

In another example, the statement "Large amounts of public funds should not be diverted to privately controlled institutions" promotes education partisanship and perpetuates charter school misconceptions. The premise ("So by the measure chosen by the reformers, (charter schools) fail") has merit, the implied conclusion does not follow. Charter schools are not "privately controlled institutions." They are a species of public school subject to most of the education code, and answerable to their public sponsor, generally a district or county education board.

The argument implies that by the "ed reformers" own criteria, charters are no better or worse than traditional public schools. Fair enough. Then let's do something about "bad" charters, instead of using them to excuse "bad" traditional public schools. Let "good" charters flourish alongside "good" traditional public schools. Furthermore, sponsoring public education entities actually profit by charter schools since they retain 15% of the charter's state funding. The charter school must meet its expenses with 85% of the funding. Some charters are cash cows for their public school sponsors, such as Hickman, which has hundreds more students in its charter school than in its sponsoring traditional public school.

We who are passionate about education must do more than reach across the aisle. We must rearrange the furniture, eliminate the aisle, and mingle.

I Love Math Manipulatives...But

I love math manipulatives. I really do. Manipulatives allow students to physically model mathematics concepts. But manipulatives are no panacea. Manipulatives have significant, often overlooked, limitations.

Mistaken Modeling

Many teachers view math instruction as teaching standard algorithms, that is, teaching students the conventional step-by step recipe for computing an answer. Thus teachers use manipulatives to model algorithms. However, teaching algorithms is not the same as teaching math. For example, the most common explanation for dividing fractions is to multiply by the reciprocal. Multiplying by the reciprocal works because something mathematical is going on. However, we usually teach the superficial procedure and ignore the mathematics. The purpose of manipulatives is to model the mathematics, not the algorithm. The difference is subtle, but crucial.

Manipulatives Cannot Model Everything

Math is far more powerful than physical manipulatives. Manipulatives are merely a bridge to that power. Manipulatives cannot model beyond three dimensions, but manipulatives can lead students to math beyond the three dimensions. Some Montessori schools have a manipulative that physically models a quadratic equation, Ax^2 + Bx + C. If the factors of the quadratic equation are equal to each other, the quadratic equation models a square. If the factors are unequal, the quadratic models a rectangle.

I first saw the intriguing quadratic equation model in a Montessori school in Japan where preschoolers were enthusiastically absorbing the geometry of the quadratic equation without resorting to pencil and paper. FOIL? Who needs it? The factors were perfectly obvious to them. Add a “height” factor to model three dimensions. If the height is “x,” we have a model of a third-degree equation. We have an “x-cubed.” Cubed! How cool is that? Can we build a model in of an equation in the fourth degree? Well, now we have bumped up against a limitation. Mathematical representations can express math much more powerfully than physical models.

The Training Curve

It can sometimes require substantial training in the symbolism and design of the manipulative before the child can use the manipulative. For some children, imagining that one thing stands for another can create an obstacle to the mathematics itself. It is an adult myth that children have superior imaginations. Children represent, pretend, or re-enact what they already know. They have trouble with pretending something they do not already know. Adults can manage with the incomplete sets of manipulatives often found in classrooms. Children may be stymied. Children especially have trouble with strings of representations. Dr. Kamii says manipulatives can end up being “abstractions of abstractions” rather than the concrete models usually intended. For example, a teacher might say “We do not have enough hundred-flats for every group to make their number. You can use a teddy bear to stand for a hundred-flat if you need to.” Such instructions only make things more perplexing for the kids.

Impractical for Problem Solving

If manipulatives are used as algorithm aids, students may not be able to solve problems when they have no manipulatives, like during a test. Constance Kamii, who researches the ways children learn math, found that when young children were given a problem for which they had received no instruction and free access to a variety of manipulatives, writing instruments and paper, children preferred their own constructions over those imposed by others. Children preferred to think their way through problems with pictures they draw themselves rather than with manipulatives.

Broken analogies

Math manipulatives are analogies. Every analogy breaks down at some point. Math manipulatives are no exception. Manipulatives have lots of features which may or may not be salient to the math. Children may have difficulty understanding which features to pay attention to and which to ignore. For example, Cuisenaire rods are different lengths. Each length is a different color, but the color is arbitrary and has nothing to do with the math. However, the colors are sure convenient because kids can use them to express math without numerals.

Too Much Fun

Perhaps the most dangerous limitation of manipulatives is the fun. Student teachers have often reported to me that their math methods courses were little more than a term's worth of “playing” with manipulatives. They loved their methods course, but when they got into a real classroom with real kids, they found to their chagrin that they were woefully ill-prepared to actually facilitate the acquisition of mathematics concepts. I have often observed teachers use manipulatives as a fun diversion without ever getting to the point of the mathematics involved. I have seen educators demonstrate the use of manipulatives without ever building the bridge to the concept.

Manipulatives cannot substitute for the teacher's own profound understanding of the fundamentals of mathematics (PUFM). Sadly, nearly every college of education has a version of the course “Principles of Mathematics for Elementary Teachers” because so many elementary education students lack PUFM.

The over exuberant adoption of manipulatives is yet one more instance of educational pendulum swinging. Good ideas get over-used and misapplied all the time, often turning what could have been promising strategies into just another education fad.

Patient vs. Impatient Problem Solving

According to Dan Meyer, the problem with a steady diet of TV sitcoms is students learn to expect easy problems resolved in twenty-two minutes “with a laugh track.” We have now raised several generations of “impatient” problem solvers, and typical math textbooks pander to the syndrome instead of challenging it.

Mr. Meyer has a prescription for what ails our math teaching.



According to Mr. Meyer, there are two kinds of mathematics: computation, or “the step you forgot” and math reasoning. Within computation, there are a lot of tricks and gimmicks, like counting decimal places. The tricks work because of the underlying math reasoning. We teach the tricks, the non-math, and call it math. Good grades for non-math amount to “congratulating students for following the smooth path and stepping over the cracks.” No wonder our students display symptoms of impatient problem solving syndrome:

Lack of Initiative,
Lack of Perseverance,
Lack of Retention,
Aversion to Word Problems, and
Eagerness for Formulas.

The older your students, the more likely you can be teaching math reasoning well and still encounter not only the symptoms, but also resistance to the cure. Your students have been so conditioned by previous experience, that like chemical tolerance, they do not believe they can function mathematically any other way. It might be a good idea to show this video the first day of class to shock their systems into even entertaining the idea that math could be different.

His description of his presentation of the water tank problem is very like the way Japanese elementary teachers have been teaching math for decades (that I know about). They can easily spend a whole period on a single problem, but they actually save time, because they are not wasting it practicing a forgettable blind procedure on twenty problems. They invest the time it requires to think about math, for as Mr. Meyer says, “Math is the vocabulary for your own intuition.”

Mr. Meyers suggests a five-part prescription:

Use Multimedia,
Encourage Student Intuition,
Ask the Shortest Possible Question,
Let Students Build the Problem, and
Be Less Helpful.

Teachers ignore many features of a problem as irrelevant without discussion as if we expect students to figure it out on their own. Many do, some do not. Asking what matters, says Mr. Meyer, is probably the most underrepresented question in math curriculum.

After, and only after, students have acquired the math reasoning should we give them shortcuts, tricks and mnemonics.This video is an excellent example of a math teacher receiving accolades for teaching non-math.




And finally, just for fun.

Review: Zeroing In On Numbers and Operations

Anne Collins and Linda Dacey. (2010). Zeroing In on Number and Operations: Key Ideas and Misconceptions. Portland, ME: Stenhouse Publishers.

This is a set of four books (Grades1-2, Grades 3-4, Grades 5-6, Grades 7-8 ) formatted as spiral-bound flip charts with each page longer than the one before.

According to the publisher's description,

(Each book of the set) provides thirty research-based, classroom-tested modules that focus on the key mathematical strategies and concepts... while highlighting the importance of teacher language in the development of those skills. The flipchart format makes it easy to access the key resources: summaries that identify the mathematical focus and associated challenges and misconceptions; instructional strategies and activities that develop conceptual understanding and computation skills; activities and ideas for adjusting the activities to meet individual needs; reproducibles for instructional use; and resources for further reading.

First, A Digression

Primary math can and should anticipate algebra.

One reason students have trouble with algebra is that teachers typically lead students to believe it to be a new and harder topic, a different math than arithmetic. Algebra should be taught as a natural problem-solving strategy, even in first grade. On the page entitled “Join and Separate” from the book “Grades 1-2” (there are no page numbers), the authors present this story problem: “Jake had 5 knights for his toy castle. His sister, Emma, gave him some more knights for his birthday. Now Jake has 11 knights. How many knights did Emma give Jake?”

How do we usually teach children to approach these kinds of story problems? We drill them on math fact families so they will recognize a math fact buried in words. Now I believe children should memorize their math facts, BUT I also think that language can be an ally rather than the enemy it usually becomes. The natural progressive analysis for this problem starts “5 knights (gave more) ?knights (so now) 11 knights,” proceeding to “5 knights plus ? knights equals 11 knights,” and finally “5 + ? (or box) = 11.” The “?” (or box) is what algebra calls “a variable” and if replacing the “?” or box with a lower case letter makes the expression look like algebra. Even first graders can set up the problem with a manipulative like the Algebra Gear by putting a turquoise piece (standing for the unknown) and five yellow cubes on one side of the equivalence mat and eleven yellow cubes on the other side. The child removes five yellow cubes from both sides to isolate the turquoise piece on one side, and voila! There are six yellow cubes on the other side. A big advantage is the lack of reliance on numerals.

We do not give children enough credit for their ability to think. We discourage thinking by presenting mathematics not as something that can be reasoned about, but as something that must be memorized and accurately recalled. If they do not remember, they have no recourse. If they fail to remember often enough, they soon conclude wrongly that they are bad at math. Math-phobia is just one more short step away.

The text's idea that join and separate problems both share the start-change-end structure is helpful, but the graphic organizer is not obvious or intuitive to children. The teacher would be better off going straight to the algebra gear which requires a lot less instruction and makes more intuitive sense. Then the problems can be “played” like a game.

On page A14 of Grades 1-2, there are three examples of sentences where all three components (start-change-end) are left blank. The idea is to play around with providing any two out of three. The authors rightly note, “leaving the initial state blank is the most challenging, as many students are uncertain where to begin.” The algebra approach addresses and eliminates this uncertainty. Students simply use the turquoise cube to stand for the blank and march on.

These Books Are Necessary

Teachers need a resource that explicitly addresses the common misconceptions children (and their teachers) hold about math. Sometimes teachers deliberately teach misconceptions because they do not know any better.

The set is comprised of four very slim volumes of fifteen informational pages and about fifteen pages of problems and exercises for a total of thirty pages printed on both side of the paper. Thus the entire set is about 120 pages. The list price per single book is fifteen dollars and sixty dollars for the set of four. In a strategic marketing maneuver, by dividing what normally would be one book into four, the publishers may be able to capture more income. Teachers are likely to be most interested in the information pertaining to the particular grades they teach. A teacher might not be inclined to pay sixty dollars for largely “irrelevant” material (although that point could be argued), but may willingly spend fifteen dollars for grade-specific content. The books could also be useful to education students.

I intended to read a sampling of pages from each book very carefully and peruse the rest. I wanted to get a feel for the quality of the information across the scope and sequence. I ended up reading all four books line-by-line, analyzing the references and working the problems. I made copious notes on every page.

A Selection of Some Glittering Gems

Grade 1-2, Counting by Tens and Ones: I like the concept of “counting the tens and the leftover ones.” In fact, I like to rename the “ones” place the “leftovers” because they are not in a group.

Grade 1-2, Writing Numbers: Children can learn a lot of math without numerals. This page has a good strategy for using cards to illustrate digit positions.

Grade 1-2, Equivalent Representations: This is a valuable trading exercise, all the better because it is done on the overhead, avoiding the possible “magic” of computer trading exercises. Computer simulations of physical activities often look like magic to students. They resign themselves to taking the teachers word instead of understanding for themselves.

I would only caution the teacher to make sure the students very intentionally see all aspects of the trade. Students need to be certain that the teacher added nothing nor removed anything. I actually prefer a manipulative like Digi-Blocks Each box can hold only ten units. Dumping the box to simulate “borrowing” makes the trade crystal clear. I have seen even junior high students incredulous that after dumping the box, the total number of packed and unpacked units did not change. These students have done trading activities with base ten flats, rods, and cubes without ever acquiring true conservation of number.

I also like the use of the term “equivalent” as opposed to “equal” because the form of 3 tens 2 ones is not identical to the form 2 tens 12 ones. Carefully distinguishing the difference implicitly anticipates “equivalent” fractions, where two fractions of differing appearance are equivalent because the underlying value is equal. The use of “equivalent” helps build consistency, for example, in geometry, when students must differentiate equal measure as opposed to identical and/or congruent. Perhaps the “equal” sign should be renamed the “equivalent” sign because equivalent is what we usually mean.

Another valuable way to exploit differing representations is to use different ways to record the model. What the authors call equivalent “representation” is actually equivalent variations of the model, in this case, base ten blocks. There are a number of ways to represent the model, drawing a picture or coloring preprinted diagrams of rods and cubes, using written words, numerals and symbolic language like 3r2c = 2r12c, where r stands for rods and c stands for cubes. Older students also benefit from using various types of representation.

Grades 1-2, Subtraction Is More Than Take Away: I like the discussion of the different meanings of subtraction. In keeping with the importance of language precision, teachers should say “three plus five equals eight,” not “three and five are (or is) eight.” Even better,”three plus five is equivalent to eight.”

Grades 1-2, Modeling Addition and Subtraction: Of course I like this page if only for the reference to Digi-Blocks. The Win 300 and Lose 299 activities are gratifyingly similar to my Chocolate Factory activity, inspired by an I Love Lucy episode



Grades 3-4, Helping Facts: Students who are acquiring profound understanding of fundamental mathematics still need fluency with facts. This page contains useful tips for recalling and reconstructing multiplication facts.

Grades 3-4, Meaning of Division is a good explanation of the various types of division. The authors did a good job with Remainders, even providing a nice segue into bases. I also liked the Multiplication Menu, and the discussion of the meaninglessness of “gozinta” and misconceptions inherent in the long division algorithm.



Grades 3-4: Number Lines and Benchmark Fractions: I like the emphasis on kids sharing and explaining their strategies to each other, but instead of singling a child out as the authors so often do, let the children work in groups and have a group spokesman present the group's findings to the class. The authors often state that “a student” did this or that, showing the individualistic bent of American education, as opposed to, for example, Japanese elementary schools, where math activities are generally group activities.

Grades 3-4: Finding Parts and Making Wholes contains a nice list of misconceptions.

Grades 3-4: Parts of a Group: American egg cartons are very useful for modeling fractions. Instead of putting any old counters in the egg cups, it is better to use plastic eggs in up to six colors. Then the ribbons are unnecessary and the egg cartons can be used to play fraction games with even first and second graders. As an aside, Japanese egg cartons hold ten eggs, making them ideal for place value lessons.

Grades 5-6 Greatest Common Factors and Least common Multiples:I like the Venn diagram for finding common factors.

The authors really shine when it comes to fractions, I liked six pages in a row:
Fractions on the Number Line “Fractions are used in three distinct ways: (1) as numbers, (2) as ratios, (3) as division.”
Adding and Subtracting Fractions with Pattern Blocks, good explanations and activities.
Modeling Multiplication of Fractions, good activities.
Modeling Division of Fractions with Pattern Blocks, avoids multiplying by the reciprocal.
Dividing Fractions with Area Model
Posing Problems With Fractions

Grades 5-6, Estimating Decimals: I like the emphasis on the significance of zero “placeholders” as indicators of precision because of the connection to measurement and data recording in science. The authors also point out the problems with “context-free” computation. Real math occurs in a context. Real math always has a story. Numbers have referents.

Grades 7-8, Analyzing Change: The story graphs nicely anticipate the early topics of physics.

Some of the Quibbles and Errors

Grades 1-2, Connecting Representations: I would have liked the confusion over the difference between number and numeral or other representations explicitly stated, however this major misconception is implied in the text and diagram. Whenever I show my Japanese rulers (which have no numerals) to kids, they wonder how it is possible to measure anything with such strange rulers. Letting them figure it out for themselves is quite a worthwhile group activity.

Grades 1-2, Counting by Tens and Ones: Students are asked to count the strawberries on page A6 of the appendix. There are forty-two strawberries arranged in a 7-by-6 array. Then students are asked where they see the 4 of forty-two in the strawberries, and then where they see the 2. I could understand if students had been asked to circle groups of ten, so I am not sure what the authors had in mind.

Grades 1-2, Along the Line and Open Number Line: Although the authors correctly describe the integer “2” as being units units away from zero, the origin (positive direction understood), they abandon origin two paragraphs later. Nearly every presentation of the number line in all four books fails to start from zero. It is important to emphasize that 3 + 5 does NOT mean “start at 3.” It means start at 0, and go 3 units in the positive direction, and then five more units in the positive direction. Maintaining a sense of origin helps students to understand absolute value later.

Digi-Blocks points out,

Note that with drawn number lines like this one, you are supposed to count the steps. Here we see that there are 3 steps between 0 and 3. But often times children try to count the hash marks. This becomes confusing. Do they count three hash marks or 4? With the Digi-Block number lines, it is entirely clear that there are 3 blocks.

I actually prefer Cuisenaire's “Rod Track” over Digi-Block's number line because you can turn one track vertical to model not only multiplication arrays but also distributive property and quadratic equations. Cuisenaire used to have a rod track for modeling negative numbers (I have one), but it is apparently no longer available. More's the pity.

Grades 3-4, Mental Computation: It is not true that when adding 56 +6, it requires greater skill to mentally perform the standard algorithm than to first add 56+4 = 60, then 60 + 2 = 62. Furthermore, the arrow code on this page adds an necessary layer of complexity. Finally, if the authors are worried that on a standard hundred chart, bigger numbers are below smaller numbers, try rewriting the chart with 1-10 at the bottom instead of at the top.

Grades 3-4, Column Addition: The authors present a trick for adding a column of numbers. Tricks work because of the math behind them, but they are no substitute for understanding the math. It is a neat trick, but should be introduced after scaffolding.

Grades 5-6, Fact Practice: There is indeed a difference between practice and drill, but practice is not “doing mathematics.” It is doing procedures that work because of the mathematics behind them. We have to constantly remind ourselves of the difference between procedure and concept. It becomes more clear when we remember that a procedural explanation is by no means mathematical. There is no math in telling a student to move the decimal two places to the left when multiplying by 0.01, regardless of the presence of numbers in the explanation.

Grades 7-8 Integers on the Cartesian Coordinate Plane: The Cartesian plane models the multiplication of variously signed integers only if ground rules are arbitrarily established first. The authors do not develop a rationale for the first and third quadrants containing positive products, and the second and fourth quadrants containing negative products.

A Sampling of Editorial Issues and Typos

Grades 1-2, Equality: The string has two “9”s, with one superscripted in a box. I suspect a misprint.

Grades 3-4, Two-Digit Multipliers: “Where are the 24 square feet for cucumbers...” should say “42 square feet.”

Grades 3-4, Problem Solving with All Operations: delete “this teacher read” in the phrase, “... an article this teacher read by Kim ...” so it reads “...an article by Kim...”

Grades 7-8, Finding Factors With Square Roots: This whole page is done completely wrong. I do not believe the challenge to “find a prime factor of a number that is greater than its square root” was ever issued by the teacher in the story. I do not believe the students looked all week without finding a single one, when there are millions of examples. It would not take them a minute to figure out that 5, a prime factor of 15, is greater than its square root of 3.87. It makes me wonder how many other stories are fabricated and do not represent the experience of real students at all. The page overlooks that pairs of factors align on both sides of the square root. The reason students have only to check the prime factors up to the integer of the square root, and that every prime so checked will pop out its corresponding friend on the other side of the integer of the square root. Some of these friends might also be primes greater than the square root. Also, there is a mention of an author named Zany, but no citation.

Grades 7-8, Unit Rates: The purported student quote under the table does not make sense in light of the data in the table. The student would not have said what he is reported as saying.

Grades 7-8, Exponents, (A16) Answer: A step is missing from the proof of Josh's conjecture in problem #5. The way it is presented, there is no obvious reason to add the exponents.
Solving Problems with Ratios (A30): Problem number 3 needs to be rewritten from scratch or deleted. It is nearly incomprehensible to junior high as is.
Making Rate Tables (A31): The answer in the back does not correspond to the first story problem. Also, there are some additions I would make to the graph designs to help anticipate graphing data in science classes.
Answers in the Back A28-2: Second sentence is the wrong reason.
A29: ¾ does NOT equal 2/3

Conclusion
Overall, the books could have used some serious pre-publication editing. There are some sparkling gems of insight sprinkled throughout. The authors' strong suit is clearly fractions. However, there are too many outright errors and too many missed fundamental misconceptions. The authors' use of number lines consistently overlooks the importance of starting at zero. Even though there are references to algebra, the books often miss opportunities to anticipate advanced material. Furthermore, the authors inconsistently evaluate the math skills of their target audience, elementary and junior high math teachers. The authors note that many misconceptions are shared by student and teacher alike, yet write as if these same weak teachers will be able to follow the many oblique references to specific math concepts. In “Grades 3-4: Adding Numbers in the Thousands,” the authors allude to the main problem with the spiral curriculum, but do nothing to challenge it. Sadly, the spiral curriculum is a major factor in students moving from grade to grade without learning the subject matter. Although the authors often mention the mistake of emphasizing procedure, “what is most important,” they write, “is that students develop a reliable technique...” Perhaps the authors are being practical. A reliable procedure is better than nothing, I guess.

The authors seem more at home with upper elementary math topics and a bit at sea with primary math topics and middle school topics. Since misconceptions, once acquired are difficult to unlearn, I would have preferred the strongest treatment of primary math, where foundations are laid, for better or for worse. The authors overlooked some important researchers. Jean Piaget and Constance Kamii come immediately to mind. On the other hand, there seems to be an implied rule: avoid references from pre-turn of the century, as if all important work is relatively recent. In-text citations are often missing. Although the teaching ideas are billed as being research-based, most of them look to be anecdotal accounts of one or another teacher's favorite lesson. Researchers are fond of denigrating “unscientific” research teachers do every day, forgetting that teachers do not have time to wait for the verdicts from “the ivory tower.” Lessons need to work immediately. Good teachers are constantly customizing, adjusting and refining.

I would like the appealing color scheme and the flip chart design of the books more if all the pages were the same length. Each page is about a quarter longer than the one before with the page topic as the footer on each page. The design is attractive and convenient because all the topics have the appearance of being tabbed on the first page. However, the design also guarantees some topics get short shrift simply because the page is half as long as other pages. I do wish the content pages were numbered. The many obligatory nods to what may turn out to be educational fads annoy me. Furthermore, it should not be necessary to explicitly market to RTI or promise standards alignment. The suggestions for calculator use add nothing. In fact, there is no evidence that calculators enhance number reasoning skills in the early grades, NCTM claims to the contrary notwithstanding. To their credit, the authors acknowledge the value of Montessori materials.

To summarize, the books could be useful resources for the novice teacher, but they are too expensive, and the novice teacher will likely not have enough experience to recognize the flaws. Even so, I might be willing to recommend the books if they were four or five dollars each instead of fifteen dollars. I had such high hopes for this material, and I regret I cannot give it a stellar recommendation.

The Agrarian Model Myth

The model of public education is not primarily agrarian, although the needs of a predominately rural population may have influenced the school calendar back in the beginning. It is not even predominately industrial, although the way factories were organized strongly influenced the organization of schooling.

The most salient model of public education is the model of the mind we inherited from the Age of Enlightenment.

Without further ado, I give you the animated illustration of an intriguing talk by Sir Ken Robinson.








Education reform is stuck in a rut because society has not confronted its most basic unexamined assumptions. I have often said we need a complete systematic overhaul. I was satisfied to mod the car, but no longer. Sir Ken goes further and says we need a new paradigm. He wants to throw the car out completely. Furthermore, he does not want to buy a new car. He wants to build something a completely different vehicle, perhaps one we have not imagined before.

Teach Tony Danza, Episode 2

In the second episode, Tony Danza gives his first quiz which half the class fails. When he hands back the quiz, a clash of expectations occurs. He expects the students to support their answers to the opinion questions. They complain that it is unfair for him to mark them off because opinion questions “do not have a right answer.” I do not blame the kids. Many years of lame critical thinking lessons have taught them that there is no wrong opinion, and that variations of the very popular “I think (fill in the blank) because I think (fill in the blank)” formulation is adequate support for an opinion.

Tony is sure they failed the quiz because they did not read the material; they insist they read it “five or six times.” He says out loud he does not believe it. Oops. But he knows they did not read because when he was in high school he did not read. One girl cries. Tony approaches her as if there is not another person in the room. If the class was inattentive before, they are all ears now. Tony has a lot to learn.

I am not impressed with Tony's instructional coach. He seems unwilling to give Tony any affirmations, is somewhat argumentative, and chooses to open emotional wounds, “Have you cried yet, Tony?” he asks. I am not impressed with the needlessly nasty assistant principal. I am not impressed with the overly harsh principal. Although they promised to support Tony, clearly their idea of what constitutes administrative support is far different from what teachers expect. The distinction is important because the number one reason teachers leave is lack of administrative support. “Mary,” a teacher quoted in the Chicago Studies, described what administrative support incarnate looked like.

I appreciate his early morning visibility and constant presence in the hallways every class period. He stands during all three lunches while we sit and enjoy our 30-minute meal. He writes personal notes when you do an excellent job on a project; he is open to suggestions that are results-oriented, and he chides negativity for negativity’s sake.

He keeps to the middle of the road and even if he has favorites, his choices are based on performance, not personality. In staff meetings, he does not preach, he shares. He has a sense of humor and attends most after-school functions.

He always greets you, and when he evaluates your instructional delivery, he stays the full 90 minutes. He actually reads over your plans to check for evidence of quality instruction, multiple tracks of learning, and assessment within your plans.

He learns the students’ names and jokes with them on their way to class or at lunch. At the same time he is firm and does not think twice about taking real troublemakers to our nearby town in handcuffs. He allows for flexibility some times in the teaching schedule to let kids display their talents, even in the midst of teachers complaining about instructional time lost. We are in a rural setting, so he realizes that for some students, school is the center of their total existence when it comes to cultural diversity and showcasing talents.

He reads a lot of different research and shares it with staff; he strives to establish some form of professional learning community in a school that knows very little about how it works. He meets with various groups repeatedly and has a 100% attendance rate except when he is at a workshop.

I have a different attitude about working for this principal because he actually notices how hard I work and lets me know that he sees what I do. He meets with every department to ask, what can I do to help you do a better job? What does your department need? How can we accomplish this or that?

In other words, supportive administrators act more like the teachers' servants than their overlords.

Reality Education: The Teach Tony Danza Show, Episode 1

Tony Danza, TV personality whose most memorable shows were probably Taxi and Who's the Boss, is only a couple years away from qualifying to draw his Social Security benefits. He says he always wanted to be a teacher, but boxing and acting derailed him. Quoting Robert Frost, Tony Danza is finally returning to the road not taken. He has become a 10th grade English teacher in an urban magnet school in Philadelphia. His road is a little different from most first year teachers. His first year is the subject of a reality TV show. He says he is terrified and he looks it.

We all know good and well that most reality shows are not really undirected slices of life. Real life is generally pretty uneventful, and in fact, we are shown less than twenty minutes of one week's class time. Although we abhor stress in our own lives, we love it other people's lives, even if the producers must create the conflict. Thus we have the scene starring the pointlessly nasty assistant principal. None of us knows what is going on “backstage” or what “stage directions” the students who volunteered to be in “Mr. Danza's” class have received.

Most viewers have never experienced the so-called reality of most reality TV. How many viewers have ever attended chef school, much less been stranded on an island? However, everybody has been to school. Everybody possesses a lens of personal experience, a frame of reference when it comes to education. Everybody's an expert. Funny thing is, we all have a different lens, and that makes the comments (on Hulu) about Tony Danza's show as interesting as the show itself. Furthermore, most people have a rather limited frame of reference, but that does not stop people from overgeneralizing, like the commenters who claim he should have picked a school more like their school if he really wanted to show what education in America is like. Nevertheless, as the show progresses, the comments should provide an interesting cross-section of society's attitudes toward education gathered together in one place. One thing I have already learned from the comments is that the general public does not know the difference between certification and an education degree.

When it comes to sheer numbers of frames of reference, I have more than most. I have taught in urban schools, suburban schools and rural schools, American schools overseas and in the good ole USA, Japanese schools, public and charter schools, religious schools and boarding schools, elementary, secondary, and post secondary schools. The show and Tony Danza have taken a lot of undeserved heat. I mean students do not usually sit around a cafeteria table and complain that they have not seen their teachers' resumes (as they did in this show). Every teacher has a first day, so whining about a teacher's lack of experience sounds specious. Students and Tony's colleagues complain about Tony talking too much, as if most classrooms are not dominated by teacher talk. When Tony is entertaining, students complain that it is not a teacher's job to entertain them, as if they have never complained about being bored to death by un-entertaining teachers.

Then there are those who resent the fact he is teaching without a state credential. A certified teacher sits in the back of the class every day, so it is more like an extended student-teaching placement . Did you know Tony is paying the school $3500/per class for the privilege? Mr. Danza's first day was no worse and no better than the first day of many, if not most, first year teachers. Many people seem invested in Tony's failure—but spoiler alert, the reviews are out, and his principal has gone on record saying she would hire him for real in a heartbeat because he proved to be a caring, gifted teacher. Apparently his on-the-job training was at least as effective as the course work for a state credential, maybe because the schools of education focus on the theoretical and neglect the practical aspects of teacher training. I am not willing to write off Mr. Danza. I am curious to see how he develops. He has the potential to do more for education in this country than all the PhDs put together.

Chancellor Rhee's Rock and Hard Place

When it comes right down to it, a lot of education stakeholders have an interest in preserving the status quo. Witness turf wars like the acrimonious debate about charter schools where one camp actually accuses the other of willfully intending to destroy public schools. All kinds of band-aid approaches have been tried and abandoned. Fads have come and gone. The window of opportunity for educating young children is quite small, and routinely squandered by partisan reformers. A recent New York Times/CBS News poll found that 58% of Americans do not like Democrats and 68% do not like Republicans. Obviously partisanship is a lose-lose proposition. So is framing every issue as an either-or dichotomy.

The public constantly seeks to attach a label even to nonpartisan educators. Those whose views are clearly not partisan, usually because they regularly and alternately offend one side or the other, get painted as wishy-washy wimps. I know because critical emails I receive fall into one of three categories: You Closet Liberal, You Closet Conservative, or You Fence-Sitter. Rarely are my positions critiqued on their merits, pro or con.

Education issues are systemic, and systemic overhaul requires someone with knowledge of the interrelationships between system components. Chancellor Michelle Rhee may not have many years experience as a teacher, but she has as much as many principals and administrators. In the partisanship climate of education today, whoever is serious about education will make bitter enemies in one camp or another. Guaranteed. They, like Rhee, will be damned if they do and damned if they don't. They will likely make many mistakes along the way. It is difficult to be your best self in the adversarial climate of education reform. Entrenched interests fight tooth and nail.

I have my own Rhee-like experience. More than ten years ago, in a county where there were serious problems with special education, the county superintendent of education approached me. He wanted to appoint me the county administrator of special education. I described my plan for reforming the county's special education programs. He loved it. Then I warned him to expect a political firestorm because what I was proposing would upset a lot of complacent and comfortable apple carts. I might not only rock a few boats, but capsize them. Unlike Rhee's boss when she similarly warned him, my prospective boss backed down. With an election coming up the next year, he decided he did not want to imperil the chances of his hand-picked successor. His designated successor won the election and decided he did not want to upset apple carts either.

Effective education reform requires a comprehensive overhaul of the system on a foundation of relational trust. Rhee pretty much admits she did not develop sufficient levels of relational trust. Ten years ago, if that superintendent had appointed me, I might have made the same mistake in my good-intentioned zeal to get things done yesterday with a minimum of schmoozing. I do agree with Rhee's critics that reform should not be something done to teachers. Teachers should be leading reform, but their efforts, and even their access, is blocked every day by administrators and researchers with minimal, even zero substantial, in-the-trenches responsibility for the academic achievement of students.

Reform is dangerous stuff. Teachers who drive small-scale reform in individual schools often become targets of not only the students and administrators, but even other teachers. Most schools have one or more teachers who are too busy being under-appreciated great teachers to be politically active. Some of them do not even have the time to write the multiple essays, arrange video-taping of their classes, and take time off to attend interviews in order to compete to be named Teacher of the Year. Teachers of the Year cannot simply be excellent teachers day in and day out, and be recognized. I admire Chancellor Rhee for stepping into fray. In the current political climate, it is not possible to be both serious about reform and harmonious with all stakeholders.

Effective ELL Science Intervention

My son read this article and said I was ahead of my time yet again. Fifteen years ago, I spent an important chunk of my career as the middle school science teacher in an international school whose students were 49% ELL. Although none, not one of the ELLs, spoke Spanish, they spoke many other languages, mostly East Asian languages. I quickly realized the old, time-tested sequence of “read the textbook, do a few labs, test the material” would not work. I created several interventions, all of which leveraged the native speaking skills of peers.

First, I started every unit with a series of labs, an intervention similar to having "students initially observe the process of osmosis with a tea bag and water" as the opener to a lesson about osmosis. Each lab team consisted of one native speaker and one ELL. The effect was that students gained experiential understanding of new vocabulary or schema before they encountered the vocabulary in printed form. Schema is the set of experience that informs comprehension. It is the frame of reference. For example, I would venture to guess that if you do not possess the schema of engineer, this sentence is gobbledygook, "A duct-less split can produce the exact amount of energy needed to temper an envelope.”* Developing schema is crucial to first language acquisition and just as important in second language acquisition.

Second, I adapted a primary school literacy program for use in my science class. The program came from Johns Hopkins University with the acronym CIRC (Cooperative Integrated Reading and Composition). I used my science text as a "basal reader" to create "Treasure Hunts" and other CIRC-based materials. Every student, even the native speakers, used these materials.

(The original design of CIRC provided templates for teachers to adapt their own school-adopted texts. It was later found that teachers lacked the will or the ability to create their own adaptations, so CIRC was reincarnated as the now-famous Success For All program. Today, teachers complain about expensive, scripted curriculum, but they did not take advantage of inexpensive, non-scripted curriculum when they had the chance. The creators of CIRC had no original intention of usurping teacher autonomy).

Third, I had students read their text aloud in class CIRC-style. Each lab team sat with their chairs next to each other and facing opposite directions so that the right ear of one student was close to the right ear of the partner. Each native speaker read one paragraph to their ELL partner, and then the ELL student read the same paragraph to their native speaking partner. The native speaking partner would supply words or correct pronunciation as needed. The team then repeated the process with the second and subsequent paragraphs. Thus, no student was a passive listener. At any moment, half of the students were reading aloud, and half were actively listening, either as ELLs preparing to read the same paragraph, or as native-speakers assisting their ELL partners.

Researchers say that the most valuable education research comes from teachers testing strategies in their own classrooms and reflecting on the results. However, when teachers report their own classroom research, it is often denigrated as being merely anecdotal or lacking sufficient sample size. Whatever. I am going to go ahead and report my results.

I gave the same unit tests to all students, native speakers and ELL students alike. Every single ELL student passed the tests, sometimes exceeding their own expectations. Even more remarkable, the native speakers' achievement skyrocketed. I was appalled to find that in the past I had denied native speaking students such high levels of achievement. The interventions worked so well with the first unit that they became my standard operating procedure ever after.

* Example from Marilee Sprenger, "Teaching the Critical Vocabulary of the Common Core"

No Swimming: Classroom Management and Rules

Have you ever read something, and then weeks later found that the author had made a bigger impression than you first believed? Sometime ago, I read the story of a teacher whose first name I believe was Deborah. She has one classroom rule, just one, which she absolutely insists upon, a rule she resolutely refuses to negotiate. What is her one ironclad rule? No swimming during class. That's it. She says she was thinking of an Anatole France quote, “The law, in its majestic equality, forbids the rich as well as the poor to sleep under bridges, to beg in the streets, and to steal bread."

Deborah's point is that it is counterproductive to make classroom rules out of everyday courteous behavior that applies whether in or out of school. Students, as reasonably socialized human beings, already know they are treat others with respect, keep their hands to themselves, etc etc etc. According to Deborah's imperfect analogy, the students are, or should be, the rich to whom such classroom rules apply. To illustrate her point, Deborah created a rule no one could break.

The very act of writing down and posting the rules of civilized behavior may invite rebellion. At the very least, it sends a subliminal message that the teacher expects these rules to be broken. As we know from Pygmalion effect research,students tend to rise (or fall) to expectations. The older the student, the more confidently the teacher can assume the student knows the norms of public behavior. After a cursory review, consequences should apply without the expectation of (sometimes numerous) second-chance warnings.

There is another kind of subliminal expectation, and because it is subliminal, it rarely rises to conscious realization. I first became aware of the power of these types of expectations while I was in Japan. There is a rule that shoes are to be removed whenever entering a home (and some other places, as well, the tip-off is usually plastic slippers in the entrance). In the twenty years I spent in Japan, I never saw anyone break this rule. I never heard anyone remind a child more than about three years old to “Take off your shoes” the way we routinely remind them to, “Say thank you.”

People do not often violate such “given” rules, or norms of behavior. I successfully used my observation of the power of “givens” with my own children. I established givens partly by modeling desired behavior and partly by sending non-verbal messages. In this way, I communicated to my kids, for example, that making a ruckus in public was unacceptable. Thus I never dealt with screaming kids in the grocery store, or anywhere else.

I tried to communicate certain so-called classroom rules the same way. For example, as a science teacher I mindfully and intentionally set up the room. I situated my desk so the back of my chair faced a wall and placing the chemical cabinet against that wall, so that chemical cabinet fairly screamed, “Off Limits!” Students do not like to go behind the teacher's desk. I wore my lab coat starting from the first day, and students “somehow” knew they would be doing real and serious science in my class. Similarly, this English teacher has her own ideas (such as the way she uses a seating chart) to non-verbally establish herself as the classroom manager.

Another problem with classroom rules is that rules, policies and routines are lumped together. Individual teachers may have different policies, but they generally share the same rules. A routine is not a rule; it is a procedure for efficiently accomplishing some repetitive task. The first day of class is the day to establish order from the outset by reviewing rules, communicating policies, and practicing routines. Classroom rules, policies and procedures are most effective in a climate of relational trust such as Dr. Pezz, who has no "rules," tries to establish.

...rules may not be necessary.
This may sound overly simple, but I tell my (high school) students that I only create rules if we need to have them. We only have them in my classes if students can’t respect one another and me.

How to Write Effective Progress Reports

"Parents these days just don't care,” a colleague complained to me one day. “I sent home progress reports two weeks ago, and so far only one parent has come in." The problem may not be the parents; it may be the progress reports.

Writing progress reports four or more times per year is probably one of the most time consuming duties teachers have. Ideally, every student should get a progress report, those that are doing great as well as those not doing so great. However, sending a progress report to every student is not always practical. If the student is doing well, the parents would love to hear it. Teachers may genuinely appreciate the chance to praise high-achieving students, but let's be honest. The main reason for progress reports is to alert parents that their student is on track to receive a poor grade come report card time. In some schools, progress reports are even called "deficiency reports." Supposedly if parents are notified in a timely matter, they will take steps to correct the problem. Yet most teachers do not expect, nor see, any real results in terms of student achievement.

How do you write a progress report that gets results? The secret is to write reports that are SPECIFIC and OBJECTIVE. This following sample progress report is easy to fill out, gets results and can be readily adapted for regular notification to parents even outside of progress report “season.”

A typical progress report might read, "Johnny is not doing well in class," a statement that is neither specific nor objective. It is not specific because a parent cannot tell from this report exactly what the child's problem might be. More than likely the parent will find getting additional accurate information from the child quite difficult, if not impossible. Such a report is also not objective because it expresses a judgment. It is possible that the parent has different goals than the teacher or draws a different conclusion from the same circumstances.

I once had a child from special education mainstreamed into my class without my knowledge. From the parent's point of view, this boy was "doing well" if he got through a school day without a violent outburst. His mother told me, "You should have seen him last year. He has really come a long way." The parent did not particularly care whether the boy did his homework or paid attention.

A better progress report might read, "Johnny isn't turning in his homework. He is disruptive in class." This report may seem to be both more specific and objective than the first one, but it actually gives very little useful information to the parent. If Johnny has turned in even one or two assignments, he will insist to his parents that he did so turn in his homework. If the parents come in at all, they will say, "But he says he has turned in his homework." The parent will likely have trouble dealing with the report of class disruption. The child will insist he has done nothing, or that the teacher doesn't like him. Parents need to know exactly what the child did that was disruptive in order to effectively discuss it with their child.

Some teachers are reluctant to be explicit because they do not want to drag out the heavy ammunition. They hope that a gentle, diplomatic hint will be enough, but it rarely is. I have read cumulative folders of troubled middle schoolers with copies of notes the first grade teacher wrote saying, "Sarah is working on socialization skills." Parents read that and think, "That's wonderful. Sarah is working on socialization skills. Very good." They often do not realize that the teacher is trying to say that Sarah is not getting along well with other children, or worse.

What can a teacher do to make sure progress reports get results?

1. HAVE A PLAN

Progress reports should be just one element of a well-thought-out classroom management plan, not an add-on. Some extra work in the first quarter will pay dividends the rest of the school year. Before the first day of school, write out your classroom policies, grading policies and consequences for misbehavior. Send these home with students with a tear-off slip at the bottom for parents to sign. Make the return of these signed slips the first homework assignment.

Ask the school to print three sets of class mailing labels for you. Or have the students address three envelopes to their parents. Or collect the email addresses of the parents as part of the contact information. There is really no point in sending a progress report home with the students; parents may never see them. Snail mail is only a little better, but it depends on who gets to the mailbox first.

2. COLLECT DATA

Teachers have usually figured out the class dynamics within the first couple weeks of school. Document this knowledge by keeping a record of who has their materials, who turns in their homework, who pays attention, etc. Make an informal tally sheet for checking off observations. Keep an anecdotal record of specific offenses, either written down or dictated into a tape recorder. It may sound like a mammoth bookkeeping job, and one thing teachers do not need is more paperwork. I give each student two lines in my grade book, one for grades and one for my private data coding and reporting system. It can be difficult in the beginning to keep the grade book handy and quickly code your observations as they occur or immediately after class. With time and practice it gets easier.

3. OFFER HELP EARLY

After two or three weeks, give students with missing assignments an opportunity to make up the work. Offer tutorial sessions for students who are behind. Keep a record of who comes in and what they accomplish.

4. PRE-FORMAT THE PROGRESS REPORTS

The progress report forms provided by most schools are inadequate. Design your own customized forms with fill-in blanks. Include the school's phone number and invite parents to make a conference appointment. If using email, it is a simple matter to attach the progress report to an email. Feel free to adapt the sample form below.

5. WRITING THE REPORT

The key is to be objective and avoid passing judgment. Give parents enough information to make their own judgments. Use the sandwich approach for criticisms: something positive, something negative, something positive. Be as specific as possible:

"Johnny did not bring his textbook to 4 out of 15 class meetings." NOT "Johnny comes to class unprepared."

"Peter threw spit wads in class on three occasions." NOT "Peter is disruptive in class."

Use positive sentence constructions whenever possible:

"Sarah has turned in 5 out of 20 homework assignments." NOT "Sarah has failed to turn in 15 out of 20 assignments."

"Sean has passed 4 out of 6 pop quizzes." NOT “Sean has failed 2 out of 6 pop quizzes."

Refer to the policy letter you sent home at the beginning of the school year. Tell parents whether the signed slip was returned or not. Mention any special efforts to help the student and the student's response:

"Mary attended 2 tutoring sessions during lunch and made up 3 missing assignments."

Even if the progress report is positive, be specific. Show, don't tell. An opening such as "Johnny is a pleasure to have in class" should be followed by an example, "He pays attention and asks insightful questions." An illustrative anecdote is best. “Johnny invented a creative new way to model negative numbers with the Algebra Lab Gear.

6. MAIL THE PROGRESS REPORTS

The whole point of progress reports is to keep parents informed. Therefore mail them directly instead of sending them home with students. Or email them. Your school may have its own progress report policies. Many schools require the distribution of hard copy progress reports to be signed by parents and returned. Normally you can customize your progress reports while accommodating school policies.

The first time I sent out progress reports according to these guidelines, the reaction was swift and sure. The day after the reports arrived home, several students appeared in my room at lunch time, lunch bags in hand. "My dad says I have to eat lunch with you until I catch up on all my homework," said one. "Yeah, me too," said another. The students came because their parents had sent them, and they came every day until the zeros were gone. They took their new-found diligence into the regular class as well, and they were rightfully pleased when their quarter grades showed it.



Sample Progress Report (on school letterhead)
PROGRESS REPORT TO PARENTS

STUDENT'S NAME: ______________________________ SUBJECT: _______________

DATE:___________________ GRADE TO DATE: _________
-----------------------------------------------------------------
CLASSWORK:
____ out of ____homework assignments completed.

Returned signed policy slip? ____Yes ____No

Passed ____ out of ____ quizzes.

Make up work: ____Completed ____Incomplete ____NA

Has participated in tutoring sessions? ____Yes ____No

Test Scores: ________

Participation:
____Excellent ____Satisfactory ____Needs Improvement

ATTITUDE AND CONDUCT:
____Well-mannered and courteous:
____Disruptive:


ATTENDANCE:
____ Unexcused Tardies ____Unexcused Absences

COMMENTS:




If desired, call xxx-xxxx to arrange a parent-teacher conference.

Date:__________ Teacher's Signature:____________________
-----------------------------------------------------------------
I have read and understood this progress report.

Student's Signature:________________________

Parent's Signature: ________________________

Date: _______________

Documenting Classroom Management

Education schools and professional development consultants have become fond of reward-based classroom management schemes. Most often these schemes rely on some sort of token economy, in which students earn or lose tokens based on their behavior. Later, students buy a reward with their accumulated tokens. In spite of the reams of research opposing extrinsic reward schemes, almost every teacher has a jar of marbles on their desk, or a rack of colored cards on the wall, or something.

The fact is token economies do work, at least in the short term. In some schools, getting through the day is all that matters anyway. Never mind loftier goals of helping students develop self discipline and satisfaction in their own learning, and countering the pervasive what's-in-it-for-me motivation. Problem is, extrinsic rewards lose force after just a few weeks. Furthermore, students have been known to turn the tables and begin blackmailing the teacher with threats to misbehave unless they get a reward. Then there is always the student who tests the scheme by creating a nothing-to-lose situation because any hope of reward has already been forfeited through misbehavior.

An even more vexing problem for teachers is the lack of administrative support. It is not fair, but administrators view a student in the office as a demonstration of teacher's lack classroom management skill. Calling parents is fraught with its own perils, especially since it is often a last resort. Teachers need a plan that answers all three concerns: promoting intrinsic motivation within students, securing administrative support, and avoiding calls of frustration to parents.

When teachers talk about making learning fun, they are hoping to tap into intrinsic motivation. Fun is only one type of intrinsic motivator, and possibly the least valuable, because it is easily converted into short attention spans, sound bites, and a desire for constantly new stimuli. There are other intrinsic motivators, deeper and more sustaining, such as those meeting the hierarchy of needs. Learning is accompanied by two drives, the drive to improve one's own knowledge and competency, and the drive to prove that competency to others. The first is intrinsic, and the one schools claim to promote. The second is extrinsic and the one schools actually promote through endless testing.

But I begin to digress. The point is classroom management should promote intrinsic rewards, in this case, disciplining of one's self.


First: Set Expectations

Instead of a long list of rules, most experts recommend focusing on the three most important to you, the teacher. Pick the three things that peeve you the most. It is not as if school were some other planet. Students (except the very youngest who may still be learning) already know the rules of socially acceptable and respectful behavior. The kid who disrupts because supposedly class is so boring sits quietly through an even more boring church sermon. The science teacher should probably be the only teacher with a list of rules longer than three because safety issues with equipment and supplies may be involved.

Second: Post Consequences

Think through your three most important rules and the consequences of infraction. Of course, natural consequences are the most effective, but school is not necessarily a natural situation. Be sure you choose consequences you have the will and the power to implement. Avoid decisions on the fly which students may consider open to negotiation. Of course, you will listen to students, but you will not be manipulated. You, the teacher, are the one with legal responsibility for students' safety and well-being. They are responsible for their behavior, not you.

Third: Follow Through Calmly assign consequences as soon as violations occur. Minimize warnings. For the most part, students were warned that first day when you detailed the rules and the consequences. Ignore the whining for second chances. Remember the three F's: Be fair, be firm, be friendly. You want to build a reputation for saying what you mean and meaning what you say. Keep records of what you do.

The following is sample record-keeping form suitable for secondary students:


CLASSROOM MANAGEMENT FORM

Student Name______________________ School Year _____________

Teacher _______________________________

This student's behavior has been disturbing the class. Specifically, the problem is:






As the classroom teacher, I have taken the following steps:

Step 1: LUNCHTIME DETENTION was assigned for __date____________. The
student (came) (on time) (late) (did not come). I discussed the problem with the student and reiterated future consequences.

Step 2: A SECOND LUNCHTIME DETENTION with written parent notification was held
_____date_______. I again discussed the problem with the student.

Step 3: A FORMAL TEACHER/STUDENT CONFERENCE was held on _____date_____.
I again discussed the problem with the student and warned that further misbehavior would result in an office referral. Student signed a memorandum of the meeting.

Step 4: PARENT PHONE CONTACT was made on ______date_______. I advised the parent of the problem and the steps taken thus far. The parent's support was requested.

Step 5: THE PROBLEM PERSISTS. Therefore, I am referring this student to the office.

Date: ____________ Time: ___________

Teacher Signature: _____________________



Features of the Classroom Management Form

All students received a detailed explanation of the due process the first day of school. I hold my detentions in my room at the very beginning of the lunch period BEFORE getting their lunch. They must come empty-handed. Lunch is prime social time that most students do not want to miss. Lunch time detention avoids many of the problems inherent with office-administered after-school detentions. I have students stand at casual attention, not leaning on anything for ten, only ten, silent minutes. If they utter a single word, even so much as “Is it time yet?,” they get another five minutes. Another word and they get detention the next day. Thus detention is never any more than fifteen minutes long.

I send a note home (by mail, not with the student) any time a student is assigned a second detention for the same problem. Students appreciate that the first time is “just between the two of us. Neither your parents nor the school need ever know.” I do not wait for issues to escalate before bringing the parents on board. Parents' number one complaint is that the teacher never informed them or did not inform them early “when we could have done something about it at home” whether they would have done anything or not. If I get around to step 4, the call to parents, it is not a cold call. They received a heads-up at step 2. Furthermore, the call is not made out of frustration, but part of an orderly due process.

I never assign more than two detentions. If you actually ever have to refer a student to the office, you have a complete record of the steps you took. You have documented a calm, competent approach that demonstrates you did not resort to office referral out of frustration. Make sure you do not send your only copy with the student. I start the file with the first detention and make a copy if and when I get to Step 4. The method I have outlined has worked well for me. I can count on one hand the number of times I actually had to send a student to the office. In fact, I rarely assigned even a second detention to any student.

Feel free to adapt the form to your own situation and personality.

Animals Smarter Than We Think

In a departure from the usual topics of a blog devoted to education, I would like to draw your attention to the fascinating title article in the August 16, 2010 issue of Time magazine, What Animals Think: New science reveals they're smarter than we realized. I feel quite confident that anyone who has ever loved and been loved by a dog, a cat or a horse never doubted the surprising cognitive and emotional intelligence of animals. Time drew a similar conclusion back in 1993.

My childhood dog, an Australian shepherd proud of the beautiful “feathers” festooning his legs and underbelly, hid behind the couch for an entire day in apparent humiliation after I trimmed those feathers. We were about to depart for my summer job at a YMCA camp and I wanted to spare him the discomfort of the inevitable burrs that would permanently lodge in his fur after his first romp through the monkey flowers.

Monkey flower oil is like super glue. I worried that perhaps he had forgotten the lesson of the previous summer. He had spent the entire first night trying to pull them out, keeping me and my cabin mates awake with his futile gnashing of teeth. With the dawn, I finally had enough light to cut the burrs out of his fur. He stayed out of the monkey flowers for the rest of that summer. Or maybe he was indignant that I though he forgot his lesson.

The first two weeks of camp were reserved by a program for developmentally delayed adults. Camp staff watched in amazement as that dog recognized, respected and then overcame every single camper's fear of dogs, or at least fear of this particular dog. In the first week of his first summer at camp, with no training whatsoever (in those days no one knew dogs could be trained for this), he became adept at warning me when a camper was about to have a seizure. Eventually he died, gray, arthritic and senile, at the age of seventeen.

Unlearning to Read

From the July 8, 2010 issue of the Economist, comes an intriguing story about learning to read. According to Stanislas Dehaene, a cognitive neuroscientist at the French medical-research agency, INSERM, learning to reading involves forcing the brain to unlearn an earlier pre-wired fundamental survival skill, the ability to recognize an object and its mirror image as identical. Dr. Dehaene believes learning to read also means sacrificing some facial recognition ability.

His studies suggest that one small area of the brain’s visual system is particularly activated by the written word. Dr Dehaene calls this the visual word form area (VWFA). Researchers debate the extent to which this area is specialised for word recognition, since it also responds to pictures. But Dr Dehaene thinks the VWFA evolved for object recognition and is requisitioned for word recognition. Unfortunately, it has one property that, though valuable when recognising objects, is not helpful for reading: more than other parts of the visual system it is activated both by an object and by that object’s mirror image.

Dr. Dehaene's theories shed new light on dyslexia.

It was thought that only dyslexic children were prone to confusing “b” and “d”, and “p” and “q”, and occasionally writing their names back-to-front, but Dr Dehaene has found that all children make this error.

If Dr. Dehaene is right, dyslexia is a consequence of normality, not an aberration. It is reading that is distinctly “abnormal.” The wonder may be that so many of us successfully learn to read.

(Dehaene) suggests the error happens because when learning to read children first have to unlearn that older survival skill. If he is right, then in adults the VWFA should be insensitive to which of two mirror images it is viewing when it comes to pictures, but sensitive to that distinction when viewing words and letters. This is indeed the case.

Dr. Dehaene's results could point to new reading instruction methods.

Obama's Speech Riles Educators

I read and listened to President Obama's speech to the Urban League defending RTTT. As "Master Educator" observed in the ensuing comments to an EdWeek blog post, “It is painstakingly clear that extraordinary measures need to be put in place to greatly improve classroom learning, strengthen school infrastructures and increase student achievement.”

The first part of the speech to rile some people is this:

“Part of (RTTT opposition), I believe, reflects a general resistance to change.  We get comfortable with the status quo even when the status quo isn’t good.  We make excuses for why things have to be the way they are.  And when you try to shake things up, some people aren’t happy.”

I have some grave misgivings about RTTT. That being said, when President Obama talks about a general resistance to change and being comfortable with the status quo, he is practically quoting from any Psychology 101 textbook. People do resist change and cling to the status quo, and surely some of those people are teachers. By no means is he indicting all teachers who oppose RTTT. There are legitimate criticisms. What concerns me is that Mr. Duncan, and by extension, the administration, seems to give lip service to listening to teachers, but teachers report that they do not feel heard, never mind agreed with.

After spending several paragraphs on the importance of teachers and the need for societal support and esteem of teachers, Obama said,

So I am 110 percent behind our teachers. But all I’m asking in return -- as a President, as a parent, and as a citizen -- is some measure of accountability. So even as we applaud teachers for their hard work, we’ve got to make sure we’re seeing results in the classroom.  If we’re not seeing results in the classroom, then let’s work with teachers to help them become more effective.  If that doesn’t work, let’s find the right teacher for that classroom.”

Accountability is always a reliable hot button. But as long as accountability is based on student test scores, there will be legitimate opposition, as expressed in the following EdWeek comments:

from Curiousidle:
1) Teachers have no voice in the system as it pertains to curriculum, materials, scheduling, educational philosophy, class size, etc. So, while we might have some "expertise" to bring to the mix, our input is not asked for or required by local, state or federal administrations. It's the ultimate catch22: literally no say in how schools function combined with all political responsibility for the effects of poverty on educational success.

2) The two goals of the education system: education and social engineering can and do conflict with one another at times... that is to say, not every policy decision feeds both priorities equally well. The public system tend to err on the side of social engineering... examples include requiring everyone to meet the same bar and dumbing down the curriculum so it can happen, removing important subject area skills that are necessary building blocks for later instruction so that students that don't have those blocks in place are able to remain at grade level, grade inflation, credit recovery, social promotion and other disreputable practices, heterogeneous grouping during the day for social development remediated by funded homogeneous grouping after school.

3) What happens OUTSIDE of school has a far more pervasive influence on preparation, willingness and academic success than what happens INSIDE the classroom. IF we don't address failure at the root, we're just playing politics and avoiding the really hard conversations.


From DDKona: We just don't agree with his administration's definitions of these ideas. Hold me accountable for planning and implementing lessons that engage students at their different levels. Hold me accountable for what I do as a professional. But the minute you define accountability as how my students do on a standardized test, that is the minute you ignite my opposition.

From MarkAHarris: What I find comical is that people love using the word "accountability" with teaching. Yet, no one uses it the way it should be: you hold teachers responsible for what they do. Testing does not do this.

From CEB: (Obama) dismisses legitimate concerns about his administration’s agenda as resistance to change or defense of the status quo. He is so insultingly wrong. Critics of RttT want to improve education just as much or more as he and the tycoons who pull Duncan’s strings.

Mr. Obama attempts to address testing:

When we talk about testing, parents worry that it means more teaching to the test.  Some worry that tests are culturally biased. Teachers worry that they’ll be evaluated solely on the basis of a single standardized test.  Everybody thinks that’s unfair.  It is unfair.
 
But that’s not what Race to the Top is about.  What Race to the Top says is, there’s nothing wrong with testing -– we just need better tests applied in a way that helps teachers and students, instead of stifling what teachers and students do in the classroom.  Tests that don’t dictate what’s taught, but tell us what has been learned.  Tests that measure how well our children are mastering essential skills and answering complex questions.  And tests that track how well our students are growing academically, so we can catch when they’re falling behind and help them before they just get passed along. 

I am pretty sure that if testing showed that American students were actually outperforming the world, no one would object to testing. A major impetus to RTTT is the poor comparative performance of American students. If students master what I teach as demonstrated by, AMONG OTHER MEASURES, the test scores on tests I write, then I am teaching successfully even in the face of outside influences I do not control. Of course, that assumes I am not gaming my tests as some teachers have done by handing out "study guides" that are nothing more than the test itself.

There is quite a small range of quality in the standards of different states. Furthermore, regardless of what individual state standards say, most teachers teach the curriculum as expressed by the textbook, not the state standards. Teachers tend to write their lesson plans based on the textbook, and then code those plans to the state standards. Very few teachers start their planning with the state standards, and very few teachers use the textbook as just one resource among many. My high quality lessons have sometimes been criticized as too textbook-independent. Students, parents and administrators do not believe that teachers have their own knowledge apart from the textbook.

In Japan, because the national standards drive the curriculum and the textbook material, Japanese teachers do not explicitly teach to the test. Testing and curriculum are automatically aligned. In fact, students' classroom tests are often written by someone other than their teacher. It works like this: There are six tests per subject in a Japanese academic year. The teachers take turns writing the tests. For example, there are three grades in junior high, so eighteen math tests will be written in an academic year. If there are ten teachers in a junior high math department, during the year each teacher will write one test for all math sections of a particular grade and most will write two.

The real problem, the one that goes unnamed, is anxiety. The number one reason teachers, many of them good teachers, leave teaching is lack of administrative support. There is simply no relational trust between teachers and administration that would reassure teachers of fair application of policy. Teachers have no reason to believe that

(RTTT's goal) isn’t to fire or admonish teachers; our goal is accountability.  It’s to provide teachers with the support they need to be as effective as they can be, and to create a better environment for teachers and students alike.

I once taught in a private school that was forced to shake things up. In its twenty-five year history, it had never sought accreditation. The headmaster decided to pursue WASC accreditation, but it was up to the teachers to do the boatload of extra work. They groused---loudly. It turned out I was the only one among them who had actually ever been through the WASC process, so I became the de facto leader. The very process of completing the self study forced the teachers to deeply examine themselves and their methods for the first time. Without spending an extra dime (although I think some overpay would have been in order), in less than one year, the teachers transformed the school from the lowest achieving school in the area to one on par with the best schools.