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Marsha Ratzel on Teaching Math

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The Great Fire Wall of China

As my regular readers know, I am writing from China these days, and have been doing so four years so far. Sometimes the blog becomes inaccessible to me, making it impossible to post regularly. In fact, starting in late September 2014, China began interfering with many Google-owned entities of which Blogspot is one. If the blog seems to go dark for a while, please know I will be back as soon as I can get in again. I am sometimes blocked for many weeks at a time. I hope to have a new post up soon if I can gain access. Thank you for your understanding and loyalty.

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Sunday, May 10, 2009

Why Standardized Testing Will Always Fail

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Friday, May 8, 2009

NOW They Notice That Teachers Will Go Missing

The most experienced teachers are retiring. Report Foresees Mass Teacher Retirements. No kidding. Back in the 1980's, the government noticed that baby boomers would start retiring in 2008, increased the percentage of social security withholding, and created the social security trust fund to hold the money. The point is not the current political debates about social security; the point is the foresight displayed. Our schools, as the educators of the nation's future, should be experts in foresight and preparation, but no.

As recently as 2003, according to a National Commission on Teaching and America's Future (NCTAF) report, retirement was not considered a factor. In fact, one chapter of the report is entitled, “It's Not About Retirement.”

The skeptical often ask: But don’t high retirement rates contribute to the high rate of teacher attrition? Not as much as we might think. More people are leaving teaching for non-retirement reasons (see figure 6) and available new entrants could easily offset the number of retirees if teacher turnover and attrition were not so high.

It is true that a large number of teachers currently in the classroom were hired in the late 1960s and the 1970s and that they are now approaching retirement. It is also true that retirement rates have been increasing each year. But the number of retiring teachers is far below the total number of teachers hired into our schools from all sources (see Table 2). Over the next 10 years, about 700,000 teachers are projected to retire, accounting for about 28 percent of hiring needs during that period.8 Teachers leaving the profession for reasons other than retirement (e.g., low pay, lack of professional support, poor school leadership) outnumber those retiring by almost 3-to-1. These reasons also drive some experienced teachers into early retirement.

In the end, the combined number of new entrants and re-entrants greatly exceeds the retirement rate. Even without drawing on potential re-entrants from the reserve pool of former teachers and those with teaching degrees who never entered teaching, our teacher preparation system could easily accommodate the current retirement rate. It is the high attrition rate among those who are not retiring that is fueling the teacher shortage.

For at least the last twenty-five years, schools have been rejecting mid-career expert teachers who move from one district to another. If, and that's a big if, a district hires an out-of-district teacher, the most credit for experience the teacher will get on the salary scale is a mere five years, if that.

So the expert essentially takes a big pay cut in proportion to experience. The more experience, the bigger the pay cut. Even so, districts have been routinely rejecting the expert teacher in order to save the extra few thousand that paying for a mere 5 years would cost.

So why the alarm now?

...a third of experienced teachers could retire. The problem is most dire in 18 states where half of all public school teachers are over age 50....To complicate matters, the report says, attrition rates among new teachers are as high as ever, with over a third of teachers leaving the profession within their first five years.

And what is the result? The old teachers are leaving, the new teachers are quitting, and the mid-career teachers are missing, working as insurance agents, receptionists, or tax preparers or whatever. What few mid-career teachers are left in the schools will be overwhelmed. Teachers with experience will be at a premium.

What should be done?

The first answer is usually to recruit more. But the problem is not so much recruiting as retention.

Districts are able to hire an adequate number of teachers, it says, but many turn over within three to five years, leaving schools with massive gaps to fill each fall. According to Carroll, attrition rates among career changers and alternative-pathway recruits are often the highest.

The report cited earlier agrees.

But in fact, we dramatically increased the supply of teachers during the late 1990s (see Table 2). The problem is that the teacher attrition rate has been increasing even faster. We are losing teachers faster than we can replace them. Teacher retention has become a national crisis.

How about emphasizing retention?

With the supply of new teachers “collapsing at both ends,” as the report describes, schools need to make a new effort toward retention.

To help solve the problem, the report suggests restructuring district staffing practices, by hiring retirees for flexible, part-time positions within schools and by replacing one-classroom-one-teacher models with cross-generational collaborative-learning teams. Such teams, NCAFT believes, could serve as an internal support network for new teachers, keep experienced teachers on staff to share their expertise, and provide a diverse set of experiences for students to learn from.

“We need to break out of the idea of classrooms altogether,” Carroll said. “It’s not one teacher per classroom, but a team that works with 150 or 200 students.” In NCTAF’s conception, learning teams would be led by National Board-certified or otherwise highly accomplished teachers and would incorporate community members, including adjunct content experts, and representatives from neighborhood agencies.

However, out-of-district teachers have become invisible. Many of these teachers were highly successful, went on to get their Master's degrees, love to teach, only to become virtually unemployable. No Child Left Behind may mandate highly qualified teachers, but these teachers have three strikes against them: education, experience, and possibly no certification in a new state.

These teachers are not asking for “alternative certification.” They just want recognition for what they have already accomplished. These highly qualified, but uncertified teachers, may be found in private schools all over the country. Sometimes a charter school will pick them up, but as more and more charter and private schools accept the conventional wisdom that somehow a teaching credential is an indication of quality, these teachers are nowhere. They want to teach, but society has thrown them away as just so much garbage.