Algebra For All Eighth Graders

Here we go again. Another example of education reform by fiat . Another example of education reform without supporting infrastructure.

California 8th graders will be required to take Algebra 1 and be tested on it as part of the state’s accountability system, under a controversial decision made by the state board of education last week after last-minute pressure from Gov. Arnold Schwarzenegger.

Why don't we just fail the kids right now and save some money?

Mr. O’Connell said in his own letter to the state board that requiring all 8th graders to take algebra would especially be hard on African-American and Hispanic students who, as demographic subgroups, are still not even scoring at the proficient level “on what amounts to 7th grade standards.”

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Education officials so far have offered no details about any budget impact from the move. But providing support to get teachers ready to teach algebra to all 8th graders could be difficult given a California budget deficit estimated at $17 billion at one point, which has forced cuts in all departments, including education.

Don't get me wrong. I am all for higher standards and greater expectations. It is not surprising that studies show “that taking algebra in middle school is linked to higher mathematics achievement in high school.” The problem is that students lack the “foundational skills” for algebra such as fractions and (believe it or not) place value.

The students who struggle the most with the abstract nature of algebra are those who tend to lack “understanding around the key big ideas” throughout elementary math, said Terry Vendlinkski, a senior researcher at the National Center for Research on Evaluation, Standards, and Student Testing at the University of California, Los Angeles.

Liping Ma has famously documented that American elementary math teachers lack “profound understanding of fundamental mathematics”. How are these teachers supposed to teach what they themselves do not know ?

James M. Rubillo, the executive director of the Reston, Va.-based National Council of Teachers of Mathematics, pretty much agrees.

”We’ve seen a lot of schools trying to mandate Algebra 1, and the failure rates are very high,” he said. “It doesn’t necessarily take into account the readiness of the students or the capability of the teaching force.

Gifted Smifted

TAG (Talented and Gifted, or GAT, Gifted and Talented, or GATE, or just GT, depending on the school) teacher, Tamara Fisher, corrects common misunderstandings in her lengthy and detailed description of what “gifted” is and is not. I have a ton of experience with the gifted issue so I am interested in her take. I can tell you right off the bat that I got sick and tired of the Salem witch trials. Our family moved around a lot and it seemed every GT program was inordinately fond of the Salem witch trials. All told, my own children covered four topics in their years of GT participation: Salem witch trials, bridges, French, and Russian.

GT is NOT a reward for kids who behave well in class and turn in perfect work. Rather it IS an academic necessity for children who learn differently….
GT is NOT a program for kids with exceptional grades...
GT is NOT fun for fun's sake…
GT is NOT extra work to fill extra time…
GT is NOT for kids who are "better" or "more special” than other kids…
GT is NOT about fun and games...
GT is NOT a program only for good kids…
GT is NOT a test of what the kid does know…
GT is NOT NOT NOT NOT NOT a privilege!!!!! Rather, it IS an essential need for children whose pace of learning dramatically out-steps other kids …
GT is NOT a self-esteem booster for children who seem to need one. Rather, it IS a sincere validation of ability(bold added)...
GT is NOT about preparing kids to “save the world” someday..
GT is NOT a “club” to belong to. Rather, it IS a peer group where gifted kids can feel like they actually belong…
GT does NOT address only academic needs. Rather, it ALSO addresses social and emotional needs and validates gifts and talents. (bold added)…
GT is NOT about pressure to fit a label or stereotype…
GT should NOT be an experimental group led by whoever is available….
GT should NOT be an optional offering, if convenient. Rather, it SHOULD BE a high priority because there are kids who need it (bold added)..
GT is NOT an easy A…

I bolded several of the statements because they allude to a very specific issue of academic achievement in our schools. Regardless of all our fine talk about academic achievement, society does not value academic achievement. Students perceive the hypocrisy every day at school. In predominately black schools, classmates often accuse the high achievers of acting white. In some schools, students hide their achievements and engage in theatrical misbehavior in order to protect “street cred.” I have been known to participate in these little conspiracies with some students.

Every state has laws that mandate the education of every child according to the child’s needs. Practically speaking, what really happens is that only children who have been labeled into a specifically funded program get that extra attention. Normally, these special programs are for students who have been deemed “deficient” in some respect.

In my state, where both state law and state accreditation standards mandate that schools identify and provide services for gifted students, only about 40% of schools claim they actually do so. There is no consequence for the schools that do not meet that portion of the accreditation standards. The only consequence falls onto the shoulders of the gifted students who are at the mercy of luck that they will get a teacher who recognizes their learning needs and does something on her own to try to reach them. Educating kids should not be an optional convenience. It should be a high priority. We SAY it is a priority. But when it comes to our nation’s gifted students, are we really educating them if research shows that they already know, on average, about half the year’s material before the school year even begins?

One of my main themes is that US society does not really want a world-class education system. If we did, nothing would stop us. It may be a trivial example, but is there anyone in the US who DOES NOT KNOW that their analog TVs will not work in six months? The point is when we want people to learn something, we make sure they do.

GT is NOT a surplus offering for kids who have surplus knowledge. Rather, it IS an academic intervention...

“Some States Said to Share 'Core' Standards”

So concluded an analysis by Achieve(Aug 13, 2008), an organization dedicated to raising “academic standards and achievement so that all students graduate ready for college, careers, and citizenship.”

The academic standards for secondary English/language arts and math were analyzed for Arkansas, Georgia, Indiana, Kentucky, Louisiana, Maryland, Michigan, New Jersey, Ohio, Oklahoma, Rhode Island, Tennessee, and the math standards for Arizona, Minnesota, New Mexico, and Texas.

Achieve found that independently-formulated state standards tend to be more similar than different.

There is a clearly identifiable common core across the states. It’s not that they have identical standards, but there’s a high degree of commonality,” said Michael Cohen, the president of Achieve…

I am not surprised. My undergraduate curriculum students found the same thing five years ago when I assigned them the project of investigating the state standards of at least ten states for one subject in one grade of their choice. Among them all, they managed to cover most of the states, most of the grades and most of the subjects. It was eye-opening for them to realize that no matter how strongly states insist that their standards are somehow better than the standards of other states, overall it simply was not true. The various state standards are more alike than different.
My students guessed at why this might be true. Their hypothesis closely matched that of the president of Achieve:

“The common core reflects the reality of the world—that there is fundamental knowledge in English and mathematics that all graduates must know to succeed…

Such a finding has several implications:
1. A national curriculum is very feasible. In fact, a sort of de facto national curriculum already exists by way of nationally adopted textbooks. Regardless of published standards, the scope and sequence for any particular content area is mostly predetermined by the textbook.

2. States wasted a ton of money hiring high-priced educational consultants to reinvent the standards wheel one state as a time. This money could have been used, for, I don’t know, hiring the proven, competent teaching veterans who are a bit more expensive than the novices schools hire instead.

3. State teacher subject-area tests are another waste of money. The National Teacher Exam (NTE) will suffice for all states. I was surprised when I found out that many states require teachers to take the state’s own tests even if they have scores from the NTE or other state tests. Teachers have to pay for these tests out of their own pocket.

4. States waste a ton of money separately creating high-stakes tests. I remember when many states used the Iowa Test of Basic Skills. Now every state thinks they have to have their own test.

5. Probably there is plenty of money for school budgets if special interest, politically-motivated, and, in fact, all expenditures were carefully and impartially scrutinized.

Another Educational Fad Bites the Dust

Funds to continue the once popular “Reading First” are shriveling up.

Timothy Shanahan, a reading researcher at the University of Illinois at Chicago who has worked as a consultant to the Reading First program in several states, called the program “politically toxic.”

“Reading First is dead,” he writes on his blog, www.shanahanonliteracy.com. “It could have withstood the corruption described in the inspector general’s report or the interim impact study—but not both!”

So what went wrong?

Reading First “has been plagued with mismanagement, conflicts of interest, and cronyism, as documented by the inspector general,” Rep. Obey said, referring to a series of reports released by the Department of Education’s inspector general in 2006 and 2007 that suggested some federal officials and contractors involved in implementing the program had conflicts of interest and appeared to favor some commercial products over others.

“Moreover, a scientifically rigorous study released by the Department of Education found that the program has no discernible impact on student reading performance,” Rep. Obey, who is also the chairman of the Appropriations subcommittee that handles education funding, said in a reference to the evaluation released May 1 by the Institute of Education Sciences, an arm of the department. ("‘Reading First’ Research Offers No Definitive Answers," June 4, 2008.)

Reading First went the way of most fads. What usually happens is something that may have started as a good idea when first implemented by enthusiastic early adopters gets watered down by mediocre professional development training by independent contractors hired to digest and then spit out the training. I know how this works; I have sometimes been one of the independent contractors hired to present someone else’s ideas. I do not do well at this. I usually cannot refrain from incorporating my own ideas, normally because the canned presentations do not respect the intelligence and feelings of the intended audience. Once the special interests get involved, it is generally all over. Besides, later implementations have difficulty replicating the results of the enthusiastic early adopters.

What the most skillful teachers usually do is incorporate the best, or at least the most workable, ideas from any fad into their eclectic bag of tricks. Even without special funding, some aspects of every fad usually survive in some form in the teaching repertoire of some teachers where it becomes impossible to isolate from everything else the most effective teachers do.

Teacher Shortage: Could It Be a Myth?

I wonder because veteran teachers have such a hard time finding work. Are there really so many teacher applicants that districts feel that there is no problem with rejecting competent proven veterans of the classroom?

I appreciate Christine Denman, the district administrator who admitted to what is a dirty secret in districts all over America.

Hi - as a district administrator, I can definitely give you some of the reasons you are not getting interviews. Many districts are not considering anyone with more than 5 years of experience because they have to pay more. I was directed by our school board not to consider anyone with more than 3 years experience! This, in the long run, may not be the best practice because you have to provide alot of inservice training in many cases.

Over the years, many administrators have told me of the same policy, usually in confidence. “Between you and me and the lamppost,” they begin. I first heard of this short-sighted policy 13 years ago from a member of a district hiring committee.

Veteran teachers traditionally have provided most of the inservice training on a daily, informal basis. After years of turning away veteran teachers, schools are realizing their shortsightedness. The baby-boomers begin retiring, some of whom are being encouraged to retire early to make room for cheaper teachers, leaving a gaping hole in the teaching staffs of many schools. There are a lot of novice teachers, the old warhorses are retiring, and there is a shortage of mid-career teachers to carry on the traditional mentoring of novices.

The Importance of Relational Trust

Neither governance, nor money, nor curricula nor any of the other usual elements make the difference. Without a certain element not normally identified or considered in reform studies, the achievement gap will be unlikely to narrow substantially. According to Parker J. Palmer, author of “The Courage to Teach,” education is a perennially tweakable political hot button. Political initiatives equal quick fixes, and quick fixes do not work. Even sincere reform efforts are doomed by the emphasis on symptoms rather than root causes.

Mr. Palmer was the guest on NPR's New Dimensions, July 22, 2008. He described the results of Chicago's education mandate of 1988. The researchers found that deprivation in any of the elements usually targeted for reform did not explain shortcomings in education quality. One element, more than any other, explained and predicted education quality. That element the researchers called “relational trust.”

When I reflect on the various educational settings in which I have taught, I find I agree completely with Mr. Palmer. Settings characterized by trust in the good faith motivations and efforts of all the stakeholders led to high achievement and satisfaction levels. Other types of settings produced less achievement and satisfaction regardless of whether every other element was in place or not.

Relational trust in Japanese and American schools looks a little different, but produces the same high results. Reports comparing the Japanese education system with the American education system typically focus on the same superficial elements with perhaps an analysis of portability. The concept of relational trust integrates what we know, and helps us understand that importing some Japanese ways of doing things, in the absence of relational trust, will likely result in just one more doomed reform effort.

Relational trust clarifies the conundrum of why certain reforms seem to work great in some schools, but fail in other schools. During the 1980’s there was a popular method for organizing and presenting curriculum “Workshop Way.” It is just one example of an implementation that I observed working great in some schools and having no effect in others. Inconsistent results rendered even good ideas mere fads.

According to Mr. Palmer, every interaction asks the question, “Is what I see what I get?” Every relationship, every interaction is about trust. He believes our institutions cannot be changed from the outside, that they must be changed by insiders. I once observed insider change completely transform a school from a low achieving school to a high achieving school in less than two years. The change required no new money, no additional testing, and no new curriculum. The change happened under the nose, but completely out of the radar of the superintendent. If he had known, he would have sabotaged our efforts. By the time he became aware, it was a fait accompli.

So what is relational trust? The "vital signs" of relational trust are respect, competence, personal regard and integrity.

Can excellent work be coerced from principals, teachers, and students simply by withholding diplomas, slashing funds, and publishing embarrassing statistics in the newspaper?...

Bryk and Schneider contend that schools with a high degree of "relational trust," as they call it, are far more likely to make the kinds of changes that help raise student achievement than those where relations are poor. Improvements in such areas as classroom instruction, curriculum, teacher preparation, and professional development have little chance of succeeding without improvements in a school's social climate...

What is relational trust? Bryk and Schneider readily admit it is "an engaging but also somewhat elusive idea" as a foundation for school improvement. But after thousands of hours spent observing schools before, during, and after the school day they suggest four vital signs for identifying and assessing trust in schools:

 Respect. Do we acknowledge one another's dignity and ideas? Do we interact in a courteous way? Do we genuinely talk and listen to each other? Respect is the fundamental ingredient of trust, Bryk and Schneider write.
• Competence. Do we believe in each other's ability and willingness to fulfill our responsibilities effectively? The authors point out that incompetence left unaddressed can corrode schoolwide trust at a devastating rate.
• Personal regard. Do we care about each other both professionally and personally? Are we willing to go beyond our formal roles and responsibilities if needed to go the extra mile?
• Integrity. Can we trust each other to put the interests of children first, especially when tough decisions have to be made? Do we keep our word?

Mr. Palmer integrates human relationships, education, health care, institutions and politics. I invite you to listen to the entire program.

“Ed. Schools Flunking Math Prep”

According to a study released on June 26, 2008 by National Council on Teacher Quality, colleges of education are doing a terrible job of preparing teachers to teach elementary math. In many universities, the professors in the college of education do not teach the math for elementary teachers; usually the professors are from the math department, and those math professors agree that newly-minted elementary teachers are poorly skilled at teaching math.

The report looked at 77 elementary education programs around the country, or roughly 5 percent of the institutions that offer undergraduate elementary teacher certification.

It found the programs, within colleges and universities, spend too little time on elementary math topics.

Author Julie Greenberg said education students should be taking courses that give them a deeper understanding of arithmetic and multiplication. She said the courses should explain how math concepts build upon each other and why certain ideas need to be emphasized in the classroom.

The fact is many education programs already require students to take courses intended to “explain how math concepts build upon each other and why certain idea need to be emphasized in the classroom.” Other researchers (i.e. Liping Ma, James W. Stigler, James Hielbert, Harold W. Stevenson) have found that American teachers compare poorly with teachers of other countries both in their understanding of math and their ability to teach it. So what is the problem?

Any of the math professors could have told you, but a study is more convincing. A PhD candidate at the University of Arizona is working on a dissertation about the attitudes of pre-service elementary teachers in the "math for elementary teachers" course. The candidate video-taped students in their elementary math classes, conducted interviews of students and their math professors, and analyzed the students evaluations of the class. She found that students approach the elementary math courses with one of two attitudes: either they consider themselves a math learner and see the course as an opportunity to learn more, or more commonly, they see the course as a waste of time because they already studied the material in elementary school and think their understanding is already more than sufficient.

The dissertation confirms what professors of these courses have observed again and again. Students tend to be hostile because they believe the courses are nothing but meaningless university hoops. Nevertheless, alarming numbers fail the classes. Some universities have a 50% fail rate. Students retake the course until they barely pass and then they move on, eventually becoming certified teachers, even though their math understanding is still woefully inadequate.

The report also criticized the tests education students take when they complete their coursework, and on which states rely when granting teacher licenses. In many cases, the prospective teachers are judged on the overall score only, meaning they could do badly on the math portion but still pass if they do well in the other areas.

Truth be told, the math professors do play a role in the problem. Many of them do not want to teach this kind of low-level content, deeming it a waste of their expensive and prestigious PhD's. Besides, they know students tend to down-rate the instructors of these courses, hurting the instructor's evaluation mean. Furthermore, math professors often fail to customize the course for education students. One way to motivate the unmotivated is to present the material in the context of anticipating and preventing children's math misconceptions. But since nearly all the math professors have never taught young children, they are unable to provide the information the future teachers want.

Without the misconception frame, students may believe that there is something wrong with them, an idea that is very hard for them to accept after twelve years of gratuitous self-esteem building. Even when a math educator with experience teaching children explicitly teaches the class in terms of children's misconceptions, students often remain hostile and become even more resentful when they perceive that for some reason unknown to them they are not succeeding in what they believe should be a “skate” class. They will often punish the instructor with unfairly harsh evaluations. No worries about the instructor's self esteem.

College students are naive if they believe that a professor cannot match up anonymously written student evaluations to the individuals who wrote the evaluations, especially in a class of around 25 students or less. The dissertation video-taped fraction lessons. Pre-service teachers, even when gently confronted with conceptual errors, grouse, “So what? What difference does it make?” and other similar responses. The same students inexplicably writes in the evaluation that they did not get much out of the class. No wonder, with the bad attitude going in.

American children are especially weak in fractions, so it should come as no surprise that elementary pre-service teachers, given that they are often among the least scholastically able in the university, are especially weak in fractions as well.

"Almost anyone can get in. Compared to the admissions standards found in other countries, American education schools set exceedingly low expectations for the mathematics knowledge that aspiring teachers must demonstrate," said the report.

One of the main reasons American children do poorly in international comparisons is because their teachers are ill-prepared to teach them.

(Francis) Fennell, who instructs teacher candidates in math at McDaniel College in Westminster, Md., said a common area of weakness among his students is fractions—the same subject the national math panel described as a weak area for kids. "Part of the reason the kids don't know it is because the teachers aren't transmitting that," he said.