Mathematica Study Undermines Teacher Merit Pay

So often when I read what passes for news in education, I find myself thinking, “No surprise there.” I am thinking of starting a No Surprise There watch. A case in point is the latest news out of Chicago.

According to the study from Mathmatica:

Preliminary results from a Chicago program containing performance-based compensation for teachers show no evidence that it has boosted student achievement on math and reading tests, compared with a group of similar, nonparticipating schools, an analysis released today concludes.

The program also failed to improve teacher retention rates. Over the two years of the study, achievement gains from the first year evaporated in the second year. Researchers and commentators speculate at least three factors account for the disappointing outcomes:

1. Reform takes time. It is unreasonable to expect stable achievement gains after only two years.
2. Schools did not adhere to a standardized implementation of the plan. Since not everybody did it the same way, the averages may be washing out positive effects in some schools.
3. The basic design of the plan needs tweaking. Perhaps higher or “more meaningfully differentiated” payouts.

It is impossible to generalize from the mere handful of studies on the efficacy of merit-based or performance-based incentives. However, many researchers have studied extrinsic versus intrinsic rewards.* The meta-conclusion is that extrinsic rewards actually undermine achievement. What works is intrinsic, not extrinsic rewards.

Hardly anyone but teachers mention what may be the most salient factor. Merit pay did not lead to achievement gains as measured by higher test scores because teachers simply do not have control over the myriad of variables that affect student achievement.

*Results of Google search on “research extrinsic rewards”

Financial Aid—Shoot for the Moon

In what is being called landmark legislation, college loans must be converted from private lenders to the federal Direct Loan Program.

Campuses across the country are gearing up to meet the July 1 deadline to revamp student-loan programs, as required in the federal Health Care and Education Reconciliation Act of 2010.

Direct loans should be better for students. The fees banks had received to administer the loans can instead go to expanding Pell Grants. Furthermore, the lending relationship is more stable. The student loan will not be sold to another lender.

However, to call student loans “financial aid” is a bit of a misnomer. Nevertheless, the Free Application for Federal Student Aid (FAFSA) serves to qualify students for subsidized student loans. What high school guidance counselors know about, but we never see publicized are the lost opportunities to highly proficient and talented, but poor, students. Such students, after being accepted into a highly selective school, must await the financial aid award letter before deciding to to attend the school. Sometimes the financial aid package covers only half the cost. The aid package includes loans for both the student and the parents. The implication of the financial aid package is that it already includes the maximum loans for which they qualify. If students and parents are unable to borrow to make up the difference, then the student is effectively barred from attending the school to which they had been admitted.

The American Association of State Colleges and Universities (AASCU) documented the questionable practices of student loan lenders. A few years ago, Consumer Reports explained how some universities use insufficient financial aid to effectively nullify the academic acceptance of poor students. The practice has a name which I have forgotten and I have been unable to locate the original Consumer Reports article. Of course, colleges are not supposed to engage in such low-down tricks, but like any form of discrimination, it can be well nigh impossible to “prove.”

The institution a student attends is a track to future opportunities. It is not true that all a high-achieving low-income student has to do is get scholarships. If the financial aid package (scholarships, grants, loans, work-study) is insufficient, the low-income student loses access to opportunity. Frankly, loans are not financial aid, so it seems odd that students who do not qualify for financial aid do not qualify for student loans either. Students with no financial aid must go to the private loan market if they and/or their parents have insufficient funds.

But here's the thing: Many of the best schools are known for providing 100% financial aid. Harvard, for example, "guarantees to meet 100 percent of a student’s demonstrated financial need for all four college years based on information we receive from the family each year". So does the University of Southern California.

USC administers a robust financial aid program with a long tradition of meeting 100% of the USC-determined financial need for those undergraduate students who satisfy all eligibility requirements and deadlines.

Therefore, a high-achieving, low-income student might as well shoot for the moon, rather than economize at a school that is cheaper, but provides a lower percentage of financial aid.

Consumer Reports puts out a wonderful primer on financial aid that should be required reading for students and their parents.

Did Schools Hire Too Many Teachers?

Data from the U.S. Department of Education show that from 1999 to 2007 teachers were hired at more than twice the rate of the K-12 enrollment increases. When schools feel tremendous pressure to reform yesterday, they pick quick and dirty methods. For example, a school can look like it is raising student achievement by pushing first grade curriculum into kindergarten. See all the little kids with pencils and paper---yay, instant academic achievement.

Another easy reform instantly reduces teacher-student ratio by hiring more teachers. But if every classroom already has a teacher, where to put the extra ones. Schools responded by pulling experienced teachers out of classroom into professional development positions, and replacing them with new teachers. The rate of teacher hires far outpaced the increase in student numbers. Some schools even added teaching staff as enrollments declined.

The glut of new hires even overpowered the dreaded effect of boomer teacher retirements. Schools had anticipated a loss of one-third of the teaching force when baby boomers began to retire in 2008. Along about the time those teachers might have expected to retire, their retirement funds, if stock-based, as most are, were pummeled by the stock market. Teachers postponed retirement. As I have explained in previous articles, experienced teachers from out of district have a difficult time getting hired. No one wants someone with proven experience because it costs money.

Once in a while, a veteran gets in. For the lucky school, these veterans teachers are a bargain. Most schools give a maximum of only five years credit for experience in figuring wages. Any teacher with more than five years experience accepts a pay cut. If the teacher has twenty or more years of experience, the school gets all the proven competence for an outrageously low price. Nevertheless, in a fit of impressive shortsightedness, many schools consider that five years experience too expensive, passing over the grizzled veteran in favor of pink-cheeked new graduates.

During the hiring frenzy, schools may have hired some of these veterans. I am unaware of any demographic study, but I wonder how many got caught in the lay-off wave of 2009. You know, last in, first out. For a boomer teacher (or any boomer) to be laid off this late in their working life is disastrous. Those in their fifties may never be fully employed again. Yet Social Security benefits may be a decade or more away.

More and more school boards have noticed their hollow teaching cadres. Lots of young, inexperienced teachers, and declining numbers of mid-career and near-retirement teachers. Years and years of short range hiring policies based on minimizing salaries by sacrificing experience have produced schools without a solid core of highly experienced teachers. It is one reason why professional development contractors have secured such a foot-hold in the schools. Once the schools have signed a contract with one of these professional development outfits, they have no more money for the independent provider.

These virtually unemployable veteran teachers would be great local professional development providers. They are intimately familiar with local conditions, needs, and perceptions. They are uniquely positioned to provide customized professional development, the sort the big outfits advertise but rarely deliver.

College the New High School?

Long, long ago, American society decided that high school graduation represented the minimum amount of education to get a decent job. It used to be a person could graduate from high school and make a living. My childhood milkman (anyone remember those) graduated from high school and got a job with Foremost where he worked until he retired. He lived comfortably, bought (and paid off) a house two blocks from the nicest neighborhood in town, and saved enough to create a trust fund for his disabled daughter. He successfully kept his family smack dab within the middle class, all on “just” a milkman's salary, with just a high school education. His wife never worked outside the home.

Today, statistics show that a student with only a high school education has a slim chance of being able to support a family within the middle class. The Public Policy Institute of California (PPIC) recently released a report which says, among other things, that California needs educated workers and the high schools are not producing them. PPIC is calling for updates to California's Master Plan for Higher Education.

Currently the master plan establishes the top 12.5 percent of the state's high school graduates as eligible to attend the 10-campus University of California system, and the top 33 percent as eligible for the 23-campus California State University system. The PPIC projects a shortage of educated workers by 2025. High schools are not keeping up, but we have known that for a long time. Parents, teachers and guidance counselors have been advising students forever that if they want a decent job, one that will accomplish for their lives what my milkman's job accomplished for his, they had better graduate from college. High school has been insufficient for a long time.

So the PPIC proposes changing the Master Plan.

Eligibility goals for the CSU and UC systems should be gradually increased to new levels by
2025. The share of the state’s high school graduates eligible for UC should grow from the
top 12.5 percent to the top 15 percent of high school graduates. The share eligible for CSU
should grow from the top 33.3 percent to the top 40 percent.

Of course, California should expand college eligibility. In fact, PPIC”s recommendations may not go far enough. What with college being the new high school, everyone needs to go to college. If only it were so simple. Keeping students in school another four years effectively postpones childhood, an untenable position. Even now, since the age of majority was reduced to 18 (mostly in order to classify Vietnam war soldiers as adults), college from age 18 to 23 is a strange limbo where unready children are treated as adults.

Because any decent job requires college graduation just as decent jobs used to require high school education, college must be part of public education. We, as a society, have been down this road before. There was a time when an eighth grade education was sufficient, but when the necessity for high school was recognized, high school became publicly funded. College occupies the same place now.

What happens when college graduation cannot get you a decent job, say around the year 2075? Perhaps we need to get serious about upgrading high school---and junior high---and elementary school. We need to stop doing it wrong: adopting faddish bandaid reforms, testing to the moon, or shoving curriculum down the grades.

We need to begin with recognizing that crucial academic foundations are laid in the early grades in an atmosphere of relational trust.

Meanwhile, far from increasing enrollment, UC and CSU have cut courses, laid off faculty, and raised fees. The once nearly free public universities today charge upwards of $5000/term in “fees” because they do not charge “tuition,” doncha know.

Does teacher professional development work?

Apparently not. So concludes a pair of studies, one focused on middle school mathematics, and the other on early reading.

Results after one year of providing teachers math professional development (PD) indicate no improvement on their students' math achievement when compared to teachers who did not receive the study-provided PD.

The result is surprising and disconcerting. The professional development provided by the study emphasized fractions, decimals, percents, and ratios. Education students self-report these very topics as their number one weaknesses. Nevertheless, education students are sure to graduate and enter the classroom with their weaknesses intact, even after completing the mandated mathematics coursework.

The early reading study came to a similar conclusion.

Although there were positive impacts on teacher’s knowledge of scientifically based reading instruction and on one of the three instructional practices promoted by the study PD, neither PD intervention resulted in significantly higher student test scores at the end of the one-year treatment.

Eric A. Hanushek, from Stanford University, concluded, “...you can't change ineffective teachers into effective ones.” Hilda Borko, an education professor also from Stanford, counters with, “We know teacher change takes time.”

The truth is probably a blend of both assertions. A competent, reflective teacher is quick to adopt useful new skills, approaches, or tactics. The discovery of well-designed materials and curriculum induces nearly instantaneous change. Effective teachers are always looking for new tools to add to their every growing collection. If possible, the teacher will roll out the new tool the very next day. If the teacher finds the the new tool requires a major or even minor redesign of lesson plans, materials, and handouts, well, so much for summer vacation travel plans. Being the best that they can be is a core value of effective teachers.

Both studies tested for student improvement after one year and found none. But since both studies also found that the professional development did not increase teacher math knowledge or alter teacher practices, of course there would be no gains in student test scores.

The studies noted that participating teachers were “engaged” in the professional development, thus ruling out lack of engagement as a reason for the disappointing lack of results. However, as all teachers know, teachers can fully participate in professional development workshops, and still walk out thinking, rightly or wrongly, “Well, that was a waste of time.” Engagement is one of those necessary, but not sufficient conditions.

If we agree that effective teachers will readily adopt recognizably useful skills and concepts, why is professional development looking to be yet another waste of everyone's time, effort and money? Could it be that the schools of education need to be more selective in admitting education students? As it is, once a student is admitted, a high GPA at least in education courses and graduation is all but assured. Many states grant automatic teaching credentials to graduates of state education programs. Yet the National Bureau of Economic Research (NBER) reports that credentials make no difference.

One of the first things researchers did with the computed teachers' effects was investigate whether they were closely related to the teacher credentials upon which achievement was traditionally regressed. The answer was generally no: credentials do not explain teacher effects for the most part...differences in certification explain only a small fraction (if any) of the variation in achievement: differences among teachers with the same certification dwarf the differences associated with certification (or the lack thereof).

A study from New York found :

This evidence suggests that classroom performance during the first two years, rather than certification status, is a more reliable indicator of a teacher's future effectiveness.

Schools and universities continue to hype, and the public continues to buy, credentialing as some indication of quality.


Could it mean that society needs to demand more of its schools of education, and that in the short term, universities must be willing to forego the tuition cash cow the schools of education represent? I know that whenever I have suggested tougher requirements for student admission, the universities invariably respond that they cannot afford the loss of tuition. Thus the vicious circle never ends.

“We must break the cycle in which we find ourselves,” said William H. Schmidt...“A weak K-12 mathematics curriculum in the U.S., taught by teachers with an inadequate mathematics background, produces high school graduates who are at a disadvantage. When some of these students become future teachers and are not given a strong background in mathematics during teacher preparation, the cycle continues,”

Professor Schmidt was referring to the results of an international study on the preparedness of mathematics teachers, a study he supervised. Research is showing that when entry level pay for teachers is raised, the quality of education applicants increases. Perhaps society needs to agree to pay teachers more. One mechanism is a ballot referendum for higher taxes to pay teachers. Oh, that bad word—taxes.

The results of these studies raise many questions, and surely one is the reasonableness of expecting significant student improvement after just one year. Even if an effective teacher instantly adopts an improved practice, is a year long enough to effect student outcomes? Maybe, as excellent tutors have experienced. When a teacher fills a student's gap in “profound understanding of fundamental mathematics (Liping Ma),” the improvement in math scores can be dramatic.

In fact, teachers generally do not wait for annual bubble tests to decide if a new tool is worth keeping. They look for immediate effects based on criteria residing in their own head and nowhere else. If efficacy is not quickly apparent, teachers will abandon a new practice as quickly as they took it up. A school year is short, not long. Teachers do not have time to spin their wheels.

Once a student decides school is “doing time” or a particular subject is beyond them, once a student shuts down, it is very difficult, even for the best teachers, to reawaken wonder, interest, curiosity and the ability to persevere through a challenge.

All the foregoing being said, any analysis of the effectiveness on professional development suffers from the scarcity of rigorous studies of professional development efficacy.

The most recent review of studies of the impact of teacher PD on student achievement revealed a total of nine studies that have rigorous designs—randomized control trials (RCTs) or certain quasi-experimental designs (QEDs)—that allow causal inferences to be made (Yoon et al. 2007).*

Even fewer studies have examined the ways teachers incorporate and evaluate what they learn from professional development.

What surprised me most was the observation of teacher instructional practices:

To measure instructional practice for treatment and control teachers, one classroom observation was conducted for each teacher after the treatment teachers in that district had had at least 5 of the 8 scheduled days of institutes and seminars. The observations produced three primary measures of instructional practice, which documented the frequency with which the teacher employed several key behaviors encouraged by the PD program.13 The first measure, Teacher elicits student thinking, encompassed such behaviors as asking other students whether they agree or disagree with
a particular student’s response and also included behaviors elicited from the students such as offering additional justifications or strategies. The second measure, Teacher uses representations, counted the number of times the teacher displayed and explained a visual representation of mathematics, such as number lines or ratio tables, as well as the number of different types of representations the teacher used. The third measure, Teacher focuses on mathematical reasoning, counted the number of times that the teacher asked questions such as Why does this procedure work? Why does my answer make sense? or Why isn’t 3/4 a reasonable answer to this problem?

On average, teachers elicit student thinking about 3 times per class period, use representations twice and focus on math reasoning once. Me, I do all that all day long, so it seems to me that the problem with math education is far more fundamental than the study was designed to evaluate.

Generally speaking, middle school teachers are classified as secondary teachers and are expected to have a bachelors degree in the subject area they teach. Because of teacher supply and demographic issues, teachers are often assigned subjects outside their field. Even so, the percentage of studied teachers with a math or math related degree barely crested double digits. On a baseline test of the math covered in the professional development, the studied teachers “had a 55% chance of getting the right answer,” compared to 93% chance for the professional development facilitators. The average seventh- grade student of these teachers scored in the 19th percentile on a test of fractions.

Middle school math is a classic illustration of the old canard, the blind leading the blind. Math instruction at the elementary level, where fractions are introduced, is even worse. On the other hand, “more qualified teachers had a tendency to gravitate to schools that served students from more privileged backgrounds.” **

I am not saying that ALL PD is worthless and I have written about effective PD. Nor am I saying that these two studies are the be all and end all.

I am pointing out flaws in the study and flaws in the conclusions. I am saying that perhaps the designers of the study misunderstand how teachers adopt and/or reject what they learn from PD. Perhaps the designers did not adequately account for a host of other variables.

I am saying that what passes for improvement in eliciting student thinking is not much, just one more question in the class period.

I am also implying that student test scores do not necessarily measure of success of PD.



*Yoon, K.S., Duncan, T., Lee, S. W.-Y., Scarloss, B., and Shapley, K. Reviewing the Evidence on How Teacher Professional Development Affects Student Achievement (Issues & Answers Report, No. 033). Washington, DC: U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Southwest, 2007.

**J.E. Rockoff, "The Impact of Individual Teachers on Student Achievement: Evidence from Panel Data," American Economic Review, Papers and Proceedings, May 2004.

Smart Phones, Or Why Teachers Resent Education Research

It is not that teachers resent all research. But an extended advertisement posing as research? Or administrators mandating teachers implement new “researched-based” practices? Or research with questionable conclusions? Or research that ignores the day-to-day concerns of teachers? Or research on new ways to teacher-proof the curriculum?

Qualcomm funded a grant to provide smart phones to 100 ninth graders in North Carolina for algebra study. Guess what, the study found that smart phones aided algebra learning. So let's all run out and get smart phones for the kids.

The North Carolina Department of Public Instruction, Digital Millennial Consulting and Qualcomm Incorporated (Nasdaq: QCOM), a leading developer and innovator of advanced wireless technologies and data solutions, today announced the joint distribution of 100 Smartphones to four high schools in three school districts across the state of North Carolina.

The thing is these smart phones are little different from the ones in the store.

MobiControl enables teacher and administrators to restrict students from using the voice capabilities and instant messaging capabilities of the phone during primary instructional time.  Additionally, the devices route all requests for access to external Web sites via a Children’s Internet Protection Act (CIPA) compliant content filter.  Finally, all text-based communication through the closed social networking system are monitored to ensure appropriate use.  Students also are required to attend a training session related to an acceptable use policy under which a zero tolerance policy will be applied.  


...

Students are only given access rights to communicate with individuals participating within Project K-Nect.  Other social networking sites are blocked and all text based communication is monitored.  

Well, that's a relief. The Qualcomm smart phones are not exactly smart phones.

Okay, what, exactly, did students do with their student-safe smart phones that helped them learn algebra? According to an EdWeek report,

Students, some initially skeptical that a phone would help them do better in math, have been quick to embrace the idea of using the mobile device to learn, says Denton, who attends Dixon High School in the 24,000-student Onslow County, N.C., schools.
“At first, I was trying to figure out how a phone was going to help me with math,” she says. “I didn’t see a connection.”

But Denton, who started in the program with Algebra 1 and has since taken geometry and is now taking Algebra 2 through Project K-Nect, says she and her classmates soon saw many advantages provided by the phone, particularly being able to get help at any hour and using instructional videos for assistance.

So the main advantage of the smart phones were their Internet capabilities.

However the learning curve seems a little steep.

Intensive training for teachers—at least nine hours—is essential, says Gross, the technology consultant. Students need about four to six hours of training, he says.

It is not really the smart phones that made the difference. It is the way these customized smart phones address the digital divide, a modern incarnation of the old SES (socio-economic status) divide.

A 2005 Pew report defines the digital divide in terms of Internet access at home, and the differences are dramatic. Individuals in higher-income households are more likely to go online (93% access) and more likely to have high-speed connections (71%) that households with incomes below $30,000, where 49% have access and just 23% have high-speed connections.
 
The digital divide is significant by race as well, even when income levels are comparable. Both home computer use and home Internet access was 13% to 18% greater for Whites in lower-income brackets than for Blacks in the same income brackets.
 
Studies identifying this digital divide brought attention to these disparities in learning opportunities facing students already at high risk for academic failure. To address these disparities, the federal e-rate program was developed to invest public funds into hardwiring public schools for computer and Internet access. The result is that computers and Internet access are available in our schools. What hasn’t changed is that the digital divide continues after school hours, when children go home.
 
Once students in our country’s poorest families go home, they lose an important learning advantage, slipping further behind students who can extend their learning day into their home. The problem shifts from concerns about technical access to concerns about digital participation.

Smart phones are uniquely poised to address the digital divide because the target at-risk population already possesses cell phones.

A recent report released by NOP World Technology highlights cell phone penetration rates in the United States.
 
- 73% of 18 year olds have cell phones, a 15% increase from 2002 to 2004.
- 75% of 15 to17 year olds have cell phones, up 33% from 2004 to 2005.
- 40% of 12 to14 year olds have cell phones, up 27% from 2002 to 2004.
 

The main idea is to take a technology that has already crossed the digital divide and use it to give lower SES students access to resources that higher SES students already have.

But we must not lose sight of the fact that the smart phones are only as helpful as the Internet link. Some math links are wonderful, replete with clear explanations and videos that can help older students visualize the math concepts. Some math links are poor, incoherently designed, or procedure-based explanations. Perhaps before schools spend a lot of money on customized smart phones, they should check their records and see how many students have email. Presumably, if they have email, they have a way to access it. If they can access their email, they can use the Internet. Those students would not need smart phones.

In 2005, 75% of fifteen-year-olds had cellphones. How many have cellphones in 2010? Probably more than 75%. How many of those cell phones are Internet capable? Probably most of them. The Qualcomm study is but the most recent example of education research that only refreshes teacher mistrust of such research.

Lake Wobegone of the Future

What would happen if some popular policies of today were taken to their logical conclusion? If all the children are above average, would they not be “re-centered” like SAT tests? I do not know if the author, Richard Salsbury, pondered the question when he wrote his story Law of Averages. Maybe he did. But whether he did or not, the story reads like a parody of all that is wrong with education today.

It is the meritocracy turned on its head in the name of preserving the self esteem of all. (Snark alert)

“...how are other kids supposed to cope if they think you're above Average?"

Although the story takes place fifty years in the future, but even today there are many students who hide their academic achievement in self defense. Even if they go ahead and achieve, it may mean they are in the job market before society is ready for them, like the boy I know who graduated with a degree in chemistry when he was eighteen. No one wants an eighteen year old chemist, Doogie Howser not withstanding.

Girls have been playing dumb forever.

"Honey, think about this: what are you going to do if you score too highly in a knowledge test*?"
     "Well I haven't so far, have I? It's easy to fool them. I know how much the others know and I just answer the questions as if I were one of them."
     "That's not going to work forever. These tests are designed to catch you out...”


"The point is, Hannah, that people feel bad if someone else knows more than they do."

Because we all know how important self esteem** is. That is why everyone gets a certificate of participation at science fairs these days. Maybe the student's science fair project is nothing but an Internet cut-and-paste job, but as long as they feel good about themselves...

In the education system of the future, teachers can be called on the carpet for even so much as threatening to punish a student for misbehavior. But Hannah's teacher, a rebel in the mold of 1984's Winston Smith, recognizes Hannah's potential and takes the chance.

In the first private lesson (Hannah's teacher) ever gave me, she said, "If you are ever less than convincing (about publicly being only average) I will have you punished."
     That made me realise how serious she was, and how trusting - I could have reported her for threatening me.

...snip...

They called a trauma counsellor for me. She said it must have been a terrible shock to be punished for misbehaving...

There was one student who the teacher knew was below average.

Lois surreptitiously tore the sheet (upon which she had been skillfully sketching a portrait of the teacher) off her pad and screwed it up into a ball. "You think I'm stupid, don't you?" she said.
     There was an intake of breath from the class. They weren't used to hearing language like that.
     "No, Lois," Mrs. Jeffries said, "you're Average, like everyone else here...

You're all more clever than I am," (Lois) muttered.
     Mrs. Jeffries saw her chance, and replied thunderously. "I will not have language like that in my class, do you understand?""

In Mrs. Jeffries view, Lois is not merely below average, but a danger to everyone else. So she does something about it.

"Lois, listen to me. Your last score in the knowledge test was Average. No matter what else happens, that's what matters. You're no different from anyone else."

Ask any middleschooler. Being different from everyone else is the kiss of death.

"Listen, Hannah. If she fails a knowledge test then she'll be made to sit two more, and if her score is low on all three they'll take ... some very drastic measures."
     "How drastic?"
     "They can't make Lois any more intelligent, so they'll lower the standard across the country; they'll make Lois' level of ability the new Average. They think it's fair to do that. A computer will automatically rewrite the curriculum and ... young people will be even more stupid." She started chewing her lip. "You can see now why I changed her marks."
     "But ... there must be other children below Average."
     She nodded. "I think most of them skip school altogether - they can't face the shame. But Lois' parents think she's Average. They insist she attends."

Lois' parents remind me of parents we have all seen, except they insist that their children must participate in the gifted program. I don't know why. Society attributes no more genuine prestige to the gifted than it does to teachers.

But the teacher's efforts were in vain. She loses her job, and there is no one to change Lois' marks on the next test go-around. Hannah hears an announcement at an assembly and draws her own conclusions.

The presenter cheerfully called it "a set of improvements to the education system, designed to make it more fair."
     Improvements.
     What he meant to say was: "They tested Lois Durrell and found out she was stupid, so to make sure she doesn't feel bad about it, everyone else from now on will be stupid too."

Nevertheless, Hannah recognizes, if dimly that maybe Lois was above average after all.

When I saw that sketch you were doing of Mrs. Jeffries I felt jealous. That's why I said it was rubbish - to cover up for the fact that the exact opposite was true. I always wanted to be able to draw like that. I rescued that piece of paper from the bin and it's become my most treasured possession.

*I am not a Wikipedia fan, but this article is a comprehensive and well-cited overview of SAT history and issues. There has been so much tinkering, some justified, some questionable, that no knows for sure how to interpret them.

**A typical statement of the popular view of self esteem.