The New York Times Discovers Educational Public Health!

I'm racing to read my huge stack of student papers before Wednesday's grading deadline, but I have to note an excellent post that went up at the NYT this past weekend.  It's from a Stanford professor who's doing good work on income inequality and education--good work that would fit well into my fantasy graduate school of educational public health.  The post is called "No Rich Child Left Behind", and it makes the very important points that:

A) Educational outcomes are and have always been very, very dependent on class.

B) The disparity in achievement between rich and poor has increased over the past fifty years, with the big difference coming because the performance of rich kids has significantly increased since the 1980s, so that whereas in 1980 there wasn't much difference between the rich and the middle class, now there is a significant gap.

C) Test scores of poor kids are not dropping--on the contrary, they are increasing, and the widening gap between rich and poor is because the test scores of the poor and middle class are not improving as quickly as those of the rich.

D) School narrows the gap: over the nine-months of the school year, the gap narrows, but then it increases again (and a bit more) in the summer.

E) According to the author, some of the growing gap comes because of the significant increase in inequality over the last few decades, but some of it also comes because the rich have been devoting ever more resources to the support and have been engaging in, to borrow a phrase from other researchers, "concerted cultivation" of their children's cognitive resources.

In a wonderful section of the post, Reardon writes:

It’s not clear what we should do about all this. Partly that’s because much of our public conversation about education is focused on the wrong culprits: we blame failing schools and the behavior of the poor for trends that are really the result of deepening income inequality and the behavior of the rich.

[...]

Meanwhile, not only are the children of the rich doing better in school than even the children of the middle class, but the changing economy means that school success is increasingly necessary to future economic success, a worrisome mutual reinforcement of trends that is making our society more socially and economically immobile.

We need to start talking about this.

Yes, we do need to start talking about it, and Reardon starts talking about it in a very important way: rather than talking about how schools can narrow the gap, for instance by using schools to provide social services (something I've argued is silly), he talks about, not only  investing in quality early childhood care for  kids of working parents, but also on providing families with the time and resources to take better care of their own kids.  "Let’s invest in parents so they can better invest in their children," he writes, and goes on to suggest the eminently sensible idea of providing more support for parental leave from work. In this spirit, I have suggested that raising the minimum wage and having a better national health insurance system should also be seen as important educational initiatives.

Reardon also mentions that the American Educational Research Association has decided to make the theme of its annual conference this year be "Education and Poverty: Theory, Research, Policy and Praxis."  That is of course good news, and although the conference's theme is a bit mealy-mouthed, some of the responses to the theme are interesting--my favorite of the ones I've read so far is the obvious but necessary "The Poverty of Capitalism" by a UCLA prof named Peter McClaren, who says important things even as he conforms touchingly, as I think Noel Coward once wrote, to type (check out his picture in the appendix below), but I also like the idea that we have conversations with our poor students about how "poverty is a prejudiced construct sustained by those who are led to believe that “venerated” institutions are the preferred, superior and normative legislator for values and morals because of their power to grant and reproduce intellectual, academic, able-istic, gendered, classed, religious, environmental, ethnic, linguistic and heternormative capital within dominant culture."

Overall, however, what I'm seeing on the conference website looks a bit more like a backwater of clever theory than anything that will build the institutions we need to combat either capitalism or its constructs.  Again, what we need is a proper, scientific graduate school of educational public health. I think we need to speak the language of the society we live in, not plan for a revolution that may never come, and which, if it did come, would have nothing at all to do with our planning.  That's why I prefer Sean Reardon over Peter McClaren.  But I could be wrong!

In any case, I'm very glad to see the post at the Times, and I'm glad that some people are thinking and talking about the way poverty matters.  I look forward to reading some of McClaren's research.

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Appendix:

For those who like visuals and want to be touched in that Noel Coward way, here's Peter McClaren, the revolutionary critic of Capitalism (or has Tom Petty found a second career?):

Peter McClaren

And, in a picture conforming a bit less touchingly to type, here's Sean Reardon, the Director of Stanford's Interdisicplinary doctoral Training Program in Quantitative Educational Policy Analysis and my hero for this week:

Sean Reardon

Students who need to read in school

It works to make kids do their homework in school

Leafstrewn has just gone through a remarkable episode in which the headmaster's proposal to cut the administrator of an alternative program for kids who are having a lot of trouble in school was met with such opposition from the faculty that she changed her mind.  The episode was remarkable mostly for the teachers' support for a program serving a small fraction of our students, support that will mean losing teacher jobs, but also because the headmaster admitted, quite gracefully, that she had made a mistake.  Everyone came out looking pretty good, and I was proud of our school.

The episode also reminded me of how effective this particular alternative program has been. Five students from my ninth grade classes last year are now in the program, and four of the five have spoken to me positively about it (the fifth I haven't happened to bump into). As the potential cut to the program was in the balance over the past week, I've been thinking a lot about what has made it so successful for my former students.  It certainly helps that the program has very good teachers and a caring and very hands-on administrator, but perhaps the key element of the program is that the students are made to do their homework in school.  As one of them told me recently, after I'd asked if he was doing the assigned reading, they have to get the work done, or they don't get to go home at the end of the day.

This is a simple but extremely important practice.  It seems indisputable that the number one proximate cause (as opposed to indirect factors like poverty) of student failure at Leafstrewn is failure to do homework.  Having an even better teacher might help, being more genetically gifted might help, and coming from a richer and more educated family certainly helps, but the line separating passing from failing is basically whether kids get their homework done. Certainly for my five students from last year who are now in our alternative program, had they all done their homework, they all would easily have passed English for the year.  (Another program here, the "Tutorial" program, essentially gives students time, space and encouragement to do their homework in school.) This makes me wonder, again, about the value of homework, and it makes me think that Bruce Baker is right and the (modest) success of programs like KIPP is mainly due to spending more money on, among other things, a longer schoolday.  It also makes me think, again, about the value of reading in school.

A student who doesn't read

I had a chat today with a former student who isn't in this alternative program.  I'll call him "Billy."  Billy is a bright, polite, very appealing kid whose family has not had it easy, to put it mildly.  When he was in my ninth grade class two years ago, Billy told me regularly that he wanted to drop out of school so that he could get a job and help support his family.  Like everyone else, I told him that he would be able to help his family better if he stayed in school.  Billy passed my class, barely.  He read virtually none of the assigned reading or our whole-class texts.  He did, however, read four or five Alex Rider books (which are at about a fifth grade level).  Those may have been the only books he has completed in high school.

Billy told me he had failed English in 10th grade and he was in danger of failing this year as well. I asked why. He said: "Because I don't do my homework."  I said, "Do you do the reading?"  He said, "No.  Never."  I said, "But you read in my class.  I remember you reading Alex Rider."  He said, "Yeah, because we read in class. I don't read at home.  I never read at home in your class either."  I don't think that's strictly accurate--I remember him reading Alex Rider at home as well--but it gets at an important truth.

Reading is the most important academic skill.  As I wrote last year, "Our school has kids under its control for over six hours a day.  There is no good reason we can't have them sitting and silently reading books for at least an hour each day.  Nothing else we do with them is as important; nothing else would be as efficient, productive, and individualized." Or, as a Mexican novelist recently wrote in the New York Times, "One cannot help but ask the Mexican educational system, “How is it possible that I hand over a child for six hours every day, five days a week, and you give me back someone who is basically illiterate?”"

If we think reading is valuable, we should be using time in school to have them do it. That a child as bright and wonderful as Billy--a student who devoured Alex Rider books during a six-week independent reading unit--can have read fewer than ten books over his whole high school career is shameful for our school.  We have taken care of Billy in many ways, and we have always treated him with gentleness and respect, but we have mostly not done for him what we would do for our own children--given him books he can read and time to read them.

Homework in School and Social Justice

The proximate cause of these students' failure is that they don't do their homework, but they all share a deeper cause as well: Billy, the students I had last year who ended up in the alternative program, and every student I have this year who is in danger of failing, all come from families that are at the low end of the economic spectrum.  If we really want to "reform" education in a way that will help poorer children succeed, we should start by finding a way to do what our excellent alternative program here at Leafstrewn does, and give kids time to do their homework--especially their reading--in school.

For vocabulary, input volume matters

A recent issue of Edweek has another lame article purporting to connect research to the Common Core--again, most of the "research" is incredibly weak and the experts say silly things.  Nevertheless, the article does mention one classic piece of research, and looking back at that study leads, as usual, to the conclusion that reading volume matters a lot.

Unnecessary new research...
According to the first paragraph of the article:

     Children who enter kindergarten with a small vocabulary don't get taught enough words—
     particularly, sophisticated academic words—to close the gap, according to the latest in a
     series of studies by Michigan early-learning experts.

Well, duh.  Anyone who had looked carefully at the vocabulary research, or indeed simply thought logically about the matter, would know that no scientific studies are necessary to conclude that kids with small vocabularies can't possibly be "taught" enough words to close the gap, since the only truly significant way kids learn words is through reading them and hearing them used.  I have never yet read a study purporting to show that any class of students, anywhere, has been "taught" enough words to make a significant increase in their vocabularies.  The main study discussed in the article found limited vocabulary instruction across the board, and less instruction in "academically challenging words" at high-poverty-schools.  Neither of these findings is necessarily significant, because vocabulary instruction just doesn't make much of a difference.

...and humorless experts!
Throughout the article, ostensible experts are quoted saying silly things.  For instance, one scholar says that Kindergarteners should be taught academic words like "predict."  That might be reasonable, but then she goes on, "Why would you choose to emphasize the word 'platypus'? It makes no sense."  Hm.  What makes no sense to me is that someone who can't imagine a reason to emphasize a really interesting, cool, loveable word like "platypus" would have anything to do with children's education, let alone be on the faculty at the University of Michigan.

What we should be thinking about
The article spends a fair amount of space, and a cool decision tree sidebar graphic, on which words to teach.  Thinking a lot about this is probably a waste of time, since teaching words doesn't make much of a difference, except, perhaps, insofar as kids enjoy them.  What then should we be thinking about?  Well, the only decent piece of research cited by the article is the classic 1995 study by Hart and Risley that reveals the remarkable disparities in the numbers of words heard by kids from different socioeconomic backgrounds.  Upper-middle class kids hear 11 million words per year, while poor kids hear 3 million; by the age of three, upper-middle class kids know twice as many words.  The  two "key conclusions" of the Hart and Risley study are the following:

• The most important aspect of children’s language experience is quantity.
• The most important aspect to evaluate in child care settings for very young children is the amount of talk actually going on, moment by moment, between children and their caregivers.

These conclusions do NOT say that we should be spending our time deciding which words to "emphasize" or "prioritize" or teach; instead, what matters is how many words kids are hearing or reading.  In fact, I see no reason not to transfer the second conclusion of the Hart and Risley study to schools of older children, too, with only slight modifications. As children get older, we need to add reading to our model, since as we get older reading is essential for experiencing high volumes of sophisticated language, and the quality of the input may become more important, since you do want them to hear or read words thast they don't actually know, but the quantity is still much more important than the Edweek article acknowledges.  So I would extrapolate thus:

• The most important aspect to evaluate in child-care settings for older children (i.e., schools) is the amount of sophisticated language actually experienced by the children, whether from a caregiver (i.e. teacher) or by reading.

Of course, I suspect reading is probably more important than teacher-talk. The Hart and Risley study focused on talk among families, which is primarily one-on-one, and the best way to simulate that in a classroom with a student-teacher ratio of at least 20:1 is by having each child reading a book. So I'll conclude where I always do, with another form of my usual hypothesis:

• The most important aspect to evaluate in child-care settings for older children (i.e., schools) is the amount of reading actually going on.

Poverty matters in Wisconsin: No poor school achieves as well as any rich school

Corporate ed reformers like Joel Klein and Michelle Rhee always argue, as in their "manifesto" on "How To Fix Our Schools," that poverty can be overcome by schools and teachers.  That manifesto asks us to start with what they call "the basics" of what they call "failing schools":

     "the single most important factor determining whether students succeed in school is not
     the color of their skin or their ZIP code or even their parents’ income—it is the quality
     of their teacher.”

This is, of course, a straight-out lie.  Unfortunately, lies this convenient are zombies that need to be disproved over and over again. I recently saw, on the blog of a retired math teacher, a graph that (re-)does the job quite neatly.

The graph, gratefully reproduced below, shows very clearly the relationship between poverty and educational achievement.

The state of Wisconsin makes available a lot of data about all of its schools, and the retired math teacher blogger has made a chart comparing the average "student achievement score" for a school (a composite of the math and reading scores on the state tests for all students in a school) with the % of students who are eligible for free or reduced-price lunch.  Each blue dot represents a school; its vertical position represents student achievement, while its left-right position represents the % of "economically disadvantaged students."  (The curved lines are the first and third-degree functions that fit the data best--you can ignore them if you like.)

(From http://gfbrandenburg.wordpress.com/2013/01/21/poverty-isnt-destiny/)

What I like about this graph is its beautiful symmetry. Look at the top left hand corner of the graph, and you will see that there is not a single rich school (i.e. less than 10% of students eligible for free or reduced price lunch) in the entire state of Wisconsin whose "student achievement" the state measures at less than 54.  Similarly, there is not a single poor school (i.e. FRPL>90%) whose student achievement is above 53. In other words, there is ZERO overlap between the rich schools and the poor schools.

This graph, like the compelling ones compiled by UT physicist Michael Marder, shows that in the real world there is no school--not a single one!--that has succeeded in educating its poor kids to the level of even the lowest-achieving rich-kid schools.  It may be theoretically possible, but as far as I can tell it has never been done, and to say, as Klein, Rhee and their ilk do, that "the single most important factor" determining success in school is not parental income but teachers is offensive to teachers, to kids, and to anyone who cares about truth, science, data, or reality.

Educational Public Health and the "Broader, Bolder Approach"

A hundred years ago this year, in 1913, Harvard and MIT, in a joint venture, founded the first American school of public health.  That same year, the Rockefeller foundation sponsored a conference that led to the expansion of Harvard’s school of public heath and the founding of another school at Johns Hopkins.  Over the past century, the field of public health has made amazing progress—arguably, far more than medicine—in improving and expanding American lives.  Now, a hundred years later, it’s time for a similar effort in education.  Along with graduate schools of education, which focus mainly on in-school factors of our educational life, we also need graduate schools that would study the many significant out-of-school, society-wide factors in education. 

I wrote a post a few months ago outlining this idea of educational public health.  That original post is here.  I also got in touch with some of the very few Americans who work on these issues full-time.  Elaine Weiss, who runs an effort called the "Broader, Bolder Approach to Education," liked my post well enough to put an edited version of it up on her Huffington Post blog, under her and my byline.  You can find it here. 

The Broader, Bolder Approach, affiliated with the worthy Economic Policy Institute, is one attempt to do some of what I have suggested a graduate school of public education might do.  You can support them by visiting their website and reading about their work, and by joining luminaries like Linda Darling-Hammond and Diane Ravitch, and teachers like me, and signing on to the BBA's mission statement.

Literacy by any means necessary: the Malcolm X method of learning vocabulary

As an American literature teacher, I'm used to thinking of classic American literature as a treasure trove of extremely thoughtful meditations about almost everything, so I'm very interested in what the American canon has to say about education in general, and about reading in particular.  I've written about To Kill a Mockingbird's caustic portrayal of school and its loving celebration of a Frank Smith-like culture of reading, and about the great scene in which Huck Finn's father castigates his son for learning to read.  American autobiographies are full of wonderful descriptions of coming into literacy (in Smith's words, of joining the literacy club)--sometimes by reading books on your own (Ben Franklin), by reading aloud as a family (Henry James), by using the library (Richard Wright).

These American autobiographies are especially good on reading as a form of self-definition and self-discovery.  Most of the richest and most poignant examples of this that I can think of happen to be from autobiographies of Black Americans--from Frederick Douglass to Richard Wright to Barack Obama. I love Frederick Douglass's story of deliberately making friends with poor white boys and bribing them with bread so that they would teach him to read--but Malcolm X's story is the one I'm going to focus on today.  I'll talk about Malcolm's efforts in more detail, but I want to note first that for all of these extraordinarily gifted and amazingly determined men, the journey to literacy was, in Douglass's words, "a long, tedious effort for years."  We should not kid ourselves; even as we try to help make the process as easy and painless as possible, we need to remember that learning to read and write well is not always easy, especially for those suffering from their place in an oppressive social system.

The Malcolm X method of vocabulary instruction
If we want our kids to learn vocabulary, maybe we should think about people who have actually done it.  We've probably all read the part of The Autobiography of Malcolm X in which Malcolm describes teaching himself to read, but I hadn't reread it for years, and it's worth looking at again.  In prison, Malcolm (I call him by his first name with all respect) had started corresponding with Elijah Muhammad, and he became frustrated with his inability to express himself clearly.  He also found that when he tried to read, he didn't know many of the words.  He ordered a dictionary from the prison library and looked at it.  Not knowing what to do--since there were so many words he needed to learn, he just started writing, and he copied the down the first page of the dictionary: definitions, punctuation and all.

It took him all day to copy out that first page.  Then he re-read what he had written down.  He was fascinated.  He liked the word "aardvark."  So he copied down the next page.  And he filled tablet after tablet of paper, and in the end he COPIED OUT THE ENTIRE DICTIONARY!

According to Malcolm X, copying out the dictionary was a great way to learn words, and as he learned more words, he was able to understand the books he tried to read, and as he could understand the books better, he came so to love reading that he read non-stop, and you couldn't have gotten him "out of books with a wedge." And the famous clincher: reading was liberating. Although he was in prison, he had "never been so truly free."  For Malcolm, every page of his books was what Richard Wright called it: a "ticket to freedom."

When the work becomes their own
Copying out the entire dictionary worked very well for Malcolm X.  Should we have our students do it?  Maybe. But I think, looking at this story, the main lesson I take away is that of motivation.  Malcolm was obviously gifted--but he had always been gifted.  He had a lot of time--but so did every other prisoner.  The determination to improve his vocabulary came only when he was (a) highly motivated and (b) face to face with his own poor ability (1).  He was very interested in writing to Elijah Muhammad, and he realized that he could not, in his letters, say what he wanted to say.  When motivated to read and write, and aware that he needed to improve, he figured out a method that worked for him.

Is it possible to create, for our students, conditions similar to those that led Malcolm X to copy out the dictionary?  (Our students are certainly not imprisoned, but they are under the supervision of the state for several hours a day, for many years.)  How can we ask them to do writing that they actually care about doing?  The student newspaper is an excellent way--for the kids who work on it. What can we do in our classes? Creative writing?  Sure--for some.  Have them write letters?  Have them write opinion pieces?  We do that stuff...  How can we have them do more writing that they actually really want to do?  The second condition--that they be confronted with their own poor ability--we arguably already try to do, in our grades and comments.

So one thing we could try is giving the students more freedom in what they write and harsher grades on their writing.  Another thing we could try is giving significantly less feedback on their writing and how to improve it.  This would feel extremely unnatural to us, and would probably be really difficult, and our students might hate us for it--but it might work.  (Is that crazy?  Maybe.  It's been a long week...)  I remember my father's telling me he only learned to write when he was a freshman in college and had a choice: learn to write better, or fail out.  My wife, too, only really learned to write when she was a freshman in college and had to work really hard on revising her own papers.  The burden needs to be on the students, not on us.  How do we put it there?

I don't know how to do it, but I have seen the results. Tonight I watched the Shakespeare play at my school. It was wonderful.  The students did amazing work, and they took full responsibility for it.  In fact, they took so much responsibility that in the talk-back after the play, the teacher who directed the play was not even mentioned--not even once.  Now that is a triumph of teaching! The play couldn't have happened without her, but for the students the work became their own.



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Footnote:

(1)
These two factors are exactly parallel with the ones that spurred Ben Franklin to extraordinary efforts at self-improvement.  Franklin was having a debate in letters with a friend of his on various hot topics of the day--like whether it was worth educating women (Ben said yes)--and his father happened to see a few of the letters.  His father told Ben that while Ben often had stronger arguments, the friend was a better writer.  This criticism so wounded Ben's vanity that he went to extraordinary lengths to try to improve his writing: first he took articles from his favorite magazine, the Spectator, made notes on their content, and then tried to reconstruct the article from his outline; second, he took Spectator articles and tried to turn them into rhyming verse; third, he took the rhyming verse versions of the articles and put them back into plain prose.  This is not even to go into the lengths he went to obtain books (after he "borrowed" one in the evening he would stay up all night to read it by candlelight so as to be able to return the book before it would be missed in the morning, and he became a vegetarian and subsisted on a "bisket" or "a handful of raisins" in order to save money to buy books).  Ben Franklin, like Malcolm X, had a powerful practical reason to want to be good at writing (to best his friend Collins) and was confronted with his own poor ability (when his father said Collins wrote better than he did).

Election special: Presidential Prep Schools (Part I)

Our presidential candidates, like most of the US plutocracy, attended private high school.  I'm interested in the differences between the education and literacy of the elite and the education and literacy of the masses, so I spent an hour or so looking at the Presidential prep schools: the Punahou Academy (Obama) and the Cranbrook school (Romney), and another hour or so trying to think about the differences between these schools and public schools.  I find it troubling that our elites are withdrawing more and more from the spheres that the rest of us inhabit, and the private school/public school divide is just one rift among many.  What does this divide look like, and what does it mean?  I'm not really sure, but I've written two posts trying to explore the matter.  This first post is about Punahou and Cranbrook in general, and I'll post something tomorrow about what the schools' English departments say they're doing.

General differences between private high schools and public high schools
These high schools are different from public high schools mainly in their student populations.  The main reason Obama, Romney, Gates and other elites go to private school is that private schools are allowed to exclude kids who are less docile, less privileged, and less able.  Good public schools are mostly "good" because they enroll more docile, privileged and able students, and low-performing public schools are mostly bad because they enroll less docile, less privileged, and less able students. Elite private schools take this difference between "good" public school and "bad" public school to a whole different level, since even at Leafstrewn we don't actively select our students. Punahou and Cranbrook are able to hand-pick their students, and their enrollments are made up almost entirely of extremely privileged and genetically fortunate children (according to an interesting study differences in academic ability among rich kids are at least 50% genetic, whereas among poor kids environment accounts for 90% of academic ability).  At Punahou or Cranbrook, the few scholarship kids, like the young Barack Obama, are rare birds completely unrepresentative of their poorer peers (and Obama was hardly poor).  This hand-picked student body is by far the most important difference between a private and a public school, since students are the most important factor in student achievement at any school, more important than the curriculum, the teachers, or even the budget. .

Non-academic factors also matter
The student population is also important for non-academic reasons, of course. Just as I myself prefer public schools (as a teacher and a parent) for non-academic reasons, many people prefer private schools for non-academic reasons.  Having different populations means that the friends children make are different; the parent population is different; and the culture is different.  But the differences go beyond population.

For one thing, the physical plant is usually dramatically different.  My son goes to public school in a scary, depressing, prison-like structure:
 

Our President and his opponent, on the other hand, went to lushly landscaped academic chateaux.  (Cranbrook's campus, below left, was called, by the New York Times's architecture critic, "one of the greatest campuses ever created anywhere", and Punahou, at right, reminds me somehow of the Hearst castle at San Simeon):

Academic differences beyond the student population
Aside from the populations, and aside from the culture and the architecture and the groundskeeping, these private schools are also dramatically different from public schools in two ways: (1) they have lower student-teacher ratios; (2) they are not bound by governmental curriculum and testing requirements.

The student-teacher ratios at wealthy private schools are dramatically different from those even at public schools in wealthy towns.  The public schools in leafy Bloomfield Hills, where Cranbrook is located, are relatively well-funded, and have extremely low numbers of students receiving free or reduced-price lunch.  While nationwide about 50% of students are eligible for Free or Reduced Price lunch, the number in our own wealthy Leafstrewn is 13%, and in the Bloomfield Hills public schools it's even lower, somewhere between 2 and 8%.  Nevertheless, whereas the public schools in Leafstrewn and Bloomfield Hills have student-teacher ratios of between 11 and 15, Cranbrook has a student-teacher ratio of 8.

Private schools are also not bound by nearly as many government rules.  Punahou and Cranbrook both require standardized tests to get in, and both brag about their SAT results and their National Merit Semifinalists, but neither school subjects its students to the battery of standardized tests that are a yearly disruption of the routine at Leafstrewn and every other public school in the country.  They are also free to run their schools, including their English departments, however they wish--but I'll wait until tomorrow's post to address that.

What do these differences mean?
One thing they mean is that when politicians or billionaires talk about school reform, it is hard for me to take their words at face value.  If standardized testing is so important for improving schools, why don't elite parents push for their own children's schools to give the same tests?  My son went to a private quaker school for a couple of years in between public schools, and he did not take the MCAS.  Malia and Sasha do not have to take standardized tests every year.  Why not? And if class size doesn't matter much, as Bill Gates is so fond of saying, why is it that Punahou and Cranbrook and Lakeside (Gates's alma mater) have dramatically lower teacher-student ratios than public schools do? (In fact the data is pretty clear: as you would expect, class size does matter, and it matters more for poor kids. The chair of Obama's council of economic advisors, Alan Krueger, has done great work on this--see his 2003 article, available here--but Arne Duncan has said that larger classes in high school might be a good idea.)  So in my eyes, neither Presidential candidate has much credibility on education, and both ignore the most important factors in our country's educational health.

Another thing these differences mean is that we public school teachers might look at the curriculum and teaching at private schools, since they probably do things slightly differently.  I've been thinking a lot about how we English teachers can learn from looking at doctors, at literature, at homeschooling, at international differences, and so on; prep schools are another interesting outside comparison. So tomorrow I'll say something about the way the two Presidential Prep schools say they handle reading, and I'll say which candidate I would vote for if all I knew was their high school's English department mission statement.

More on the non-golden age of the 50s...

This is not directly literacy-related, but it supports and confirms what I was talking about in my last post, so I'll just mention it quickly.  Richard Rothstein, who has for years and years been doing a great job of patiently and repeatedly dismantling the idea that schools and teachers are the best way to overcome poverty, has a wonderful, entertaining and painful article in The American Prospect. I'll give the basic story here, but it's worth reading the whole thing.

I. Joel Klein's non-evidence-based BS
Joel Klein--who represents better perhaps than anyone else (see footnote) the idea that if only we put billionaires in charge of our schools and gave them a free hand to hire, fire and generally wreak havoc, then public education will be able to cure all of our country's social ills (which are now largely the result of incompetent, undisciplined teachers who have read too much Paulo Freire)--Joel Klein is always citing his own life story to show that all you need are good teachers to lift you out of inner-city poverty and public housing.  According to Klein, he himself grew up poor and in public housing, in a family that offered him no support for reading or other cultural activities, but his public school teachers held him to high standards, and he went to Columbia and on to a successful career, so therefore poverty is not an insurmountable impediment, and his story shows that "you'll never fix poverty in America until you fix education."

The most obvious problem with this story is that one anecdote does not prove much of anything.  A larger problem is that the nation's schools were not, by any objective measure, any better overall in the 50s or 60s than they are now. But the biggest problem with the story is one you wouldn't know unless you did what Richard Rothstein did and actually looked into it: Klein's account of his own childhood is essentially untrue in every particular.

Klein was not in fact poor: his postal-worker father and bookkeeper mother probably made significantly more than the national median household income.

Klein's family did offer him culture and literacy.  In fact, Klein was inspired to become a lawyer because his father would take him to the federal courthouse in Manhattan to watch cases, and if his family was like many other middle-class Jewish New York families of his era, education was probably valued as much as life itself.

Klein did grow up in public housing, but it was in no way like public housing as we have become accustomed to think of it.  The words "public housing" for most evoke notions of crime-ridden wastelands, subsidized permanently by the government, inhabited by single parents and terrified children who are mostly people of color.  The public housing Klein grew up in, by contrast, was not rent-subsidized, and in fact could be seen as a bastion of white middle-class privilege: the application process excluded single-parents, anyone with a criminal record, anyone with an out-of-wedlock birth, anyone with a history of drug addiction or mental illness, and most people of color (there was essentially a quota system intended to keep the neighborhood balance the same as it was before). In other words, the social problems, as Rothstein puts it, were "weeded out by the Housing Authority."  This is not what most people think of when they hear "public housing."

So Joel Klein's biography does not actually provide any evidence that a poor kid growing up in a dangerous and unhealthy neighborhood with little family support can be saved by a good teacher.  Instead, it reinforces the obvious truth that a middle-class kid growing up in a safe and healthy neighborhood with significant family support will do well in school and will appreciate a good teacher when he gets one--as Klein appreciated his high school physics teacher.

II. Parallel Childhoods
One of the strengths of Richard Rothstein's article exposing Klein's BS is that Rothstein and Klein turn out to have had parallel childhoods.  Like Klein, Rothstein grew up in a middle class neighborhood in New York with a postal worker father and a bookkeeper mother, went to public school and went on to an Ivy League college. The two men even had the same physics teacher. But while Klein complains about not having a Mitt-Romney-like childhood and pretends that schools in the fifties were so great as to make up for his deprivation, Rothstein is aware that it was his family support that made the difference.  Rothstein even tells us that when he wanted to apply to Harvard, his high school refused to process the application (because "boys from here don't go to Harvard") until Rothstein's father took the day off from work to come in and talk to the Principal.  So much, as Rothstein says, for the golden age of the 50s.

For most people, as for Rothstein and probably Klein, education in the 1950s was no better than it is now.  Then, as now, there are lots of kids from middle-class homes and parents without college degrees who are pushed and supported by their families and go on to great academic success.  My father and stepfather are both examples of this: both grew up in stable middle-class homes, with parents who hadn't been to college; both were pushed and supported by their parents.  My father, who went to a small rural high school in the midwest, was one of two kids in his high school class to go to college, but he ended up at MIT.  My stepfather grew up in a Mitchell-Lama building in Washington Heights, with parents who hadn't gone to college, and he went on to be valedictorian at Bronx Science; he also went on to MIT.

Neither my father nor my stepfather would ever say that their 50s and 60s public schools were responsible for their success.  Their schools were OK, but most students in those schools did not achieve such dramatic success. Instead, what allowed my father and stepfather to excel so remarkably was the support and encouragement of their middle-class parents, the fact that they were not surrounded by miserable poverty, and probably the fact that they themselves were pretty gifted.

III. Rothstein's concluding peroration
Again, it's worth reading the whole article, but here are a couple of paragraphs from the end of it:

"It would be obscene for me to claim I overcame severe hardship and was rescued from deprivation by schoolteachers. It is more obscene for Klein to do so, because his claim supports attacks on contemporary teachers and a refusal to acknowledge impediments teachers face because of their students’ social and economic deprivation. It’s a deprivation that he never suffered but that many children from public housing do today.
"A few superhuman teachers may lift a handful of children who come to school from barely literate homes, hungry, in poor health, and otherwise unprepared for academic instruction. But even the best teachers face impossible tasks when confronted with classrooms filled with truly disadvantaged students who are not in tracked special-progress classes and don’t arrive each morning from families as academically supportive as mine. Instead, they may come from segregated communities where concentrated and entrenched poverty, unemployment, and social alienation over many generations have been ravaging."

IV. My own conclusion: the subtext of Klein's and others'  master narrative
(I don't have time to write this in an articulate way, since I have to enter interim progress reports, but I'll take ten minutes and make an attempt.)

Klein's story is obscene, but its obscenity is not unique to Joel Klein; in fact, it is part of a larger cultural phenomenon, the anxious attempts by our ruling classes to assert that they deserve their own extraordinary privileges,  and I think we need to understand the current emphasis, by these ruling classes, on education and education reform as a part of this larger cultural phenomenon.

This need to deny one's own cultural advantages can be seen not only in Klein's absurd story, but in the absurd assertions by successful aristocrats like Mitt Romney that they are self-made men ("I inherited nothing").  Our society is in many ways less a meritocracy than it was 50 years ago, but the ruling classes want to pretend that it is.  (This is, I believe, the thesis of a book I haven't read, The Twilight of the Elites: America After Meritocracy, by the estimable Christopher Hayes.)  The ruling elites know they are smart and have worked hard, and they want, perhaps understandably, to pretend that their success is due to their own efforts.  The elites' emphasis on education has to be seen in the light of this pretense.

Every time a politician pays lip service, as Obama did in his disastrous debate, to the idea that education is the best way to rebuild our economy and create jobs, we should remember that this is a self-serving argument, and one that implicitly blames the poor for their own condition. When we see articles that say that even high-priced colleges are a great investment, we should consider that college, for many students in a country whose top college major is "Business", may be as much a matter of what I think Jane Jacobs calls "credentialing" and what I always think of as analogous to a guild system; that is, a college degree functions as a class marker, and the four years of hard work or debauchery at an expensive campus is less about education than about your parents trying to ensure that you remain in the upper middle class.

What we are living in is less meritocracy than plutocracy, and saying that our educational system is failing is a way of displacing blame for the increasing inequality whose effects are all around us, if we only have eyes to see. (This is not to say that education doesn't matter, nor to say that individual teachers can make a difference--and in fact I am trying my best, but we teachers can't do it all by ourselves.)



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Footnote: Joel Klein's career

Hired in 1998 by billionaire Mayor Bloomberg, Joel Klein was for years the Chancellor of the largest public school system in the country despite having no prior experience in education (he was counsel for a huge corporation); after resigning in 2010, Klein now works for two other billionaires Rupert Murdoch (Klein is trying to sell media to public schools) and for Eli Broad (Klein is in charge of Broad's massive effort to put "reform"-minded (anti-union, pro-privatization) superintendents in place across the country).

Social class and reading

I've been worrying recently about the ways in which reading is social, cultural, and deeply influenced by one's social class.  Below are a few attempts to start to think this through.


Images of Reading: solitary, but also social

Reading is in many ways a solitary activity.  People tend not to read in large groups, and when they do (reading rooms; subway cars), reading often seems to wall off the self from the group.  When I think of images of reading, I think of those portraits of female readers, in which the reading is nearly always shown as an activity of almost circular self-sufficiency.  Here's a picture by Fragonard:

It's a lovely picture, and we like it partly because it makes makes us imagine what it's like to be the young woman. We want to be her because reading looks so pleasant, so private, so self-sufficient--not necessarily passionate, not necessarily joyful, but reasonable, calm, and, despite the pillow against which she is propped up so straight, wakeful.  We put ourselves in her place, we want to know what the book is about, we imagine such a wonderful self-sufficiency (perhaps we are enjoying the painting in the same way the young woman enjoys the book), and the picture is so much about at-one-ness that viewer and subject partly merge. 

But the picture is more complicated, and the apparent solitude is less solitary, than it might seem. It is also less self-sufficient, and it is embedded in a pretty distinct social and cultural context.  First, and most obviously, such a celebration of privacy, such solitary self-sufficiency in a young woman,  may seem, as in Vermeer paintings, to have (that pillow!) an erotic tinge. The young woman in Fragonard's picture is both attractive and quite fetchingly dressed, and if reading might seem a solitary activity, she is less alone than she thinks, for both painter and viewer may play the role of peeping Tom.  

(Here's one, by Renoir, in which the inherent eroticism of the subject is a bit more obvious:

!)

The eroticism of the picture is merely the most obvious way in which reading is never completely solitary.  These young women, like reading itself, are also clearly of a certain class--or rather, are distinctly not of a certain class--that is, they are not poor.  The woman in the Fragonard painting is probably richer than Renoir's subject--by Renoir's time, reading, or leisure, had filtered down to the middle class---but both have had time in their childhoods to learn to read, someone to help them learn, and maids and servants to clean the house, shop for and cook the food, put on their dresses, tie their ribbons and plump their pillows.  While their servants were doing such work (you might argue that Renoir's girl looks like she might have to do some housework herself, but then Renoir is an inveterate fantasist), these non-poor women enjoyed available books to choose from, an undistracting space and continuous leisure time in which to read the books they choose, and friends with whom they could discuss the stories.  In nearly every way, reading was an upper-class pursuit. 

Reading and social class in To Kill a Mockingbird 

The situation is similar in To Kill a Mockingbird. The book paints a wonderful picture of an apparently self-sufficient childhood culture of reading.  Jem, Scout and Dill don't need school--Harper Lee seems deeply skeptical of the idea that reading can be taught--and the children's summer world, a combination of unsupervised outdoor play and passionate engagement in Tom Swift and Tarzan books, seems as beautifully self-sufficient as Fragonard's idyll of solitary reading.  Anyone should be able to read, it seems, and when the book's villain, Bob Ewell, is asked by the book's hero, Atticus Finch, whether he can write, Mr. Ewell is indignant, but in the joke he makes (or should I say the joke the author has at his expense), we are given to understand that his level of literacy is despicably low.  "Of course I can write," Mr. Ewell says.  "How do you think I sign my relief checks?"  We laugh, but we understand that the Ewells probably can't read, as we would think of reading, and that their illiteracy is a part of their separateness, their subhumanness.  According to Atticus, it's not even worth making the Ewell children go to school, because the Ewells are the Ewells and will never change.

I'm dwelling at length on to Kill a Mockingbird because it presents such a clear picture of a good reading culture and such a clear picture of the all-important social divisions.  In Maycomb, one is almost completely defined by one's family and one's class. Jem, Scout and Dill are good readers, but nearly every other upper-class character, that is to say, everyone who lives on the town's "main residential street," is also a member of the reading club: even the mean, racist Mrs. Dubose kicks her morphine habit with the assistance of a Walter Scott novel; and even Boo Radley likes to cut out newspaper articles for his scrapbook.  

The poor farmers, on the other hand, who occupy the next rung down on the social ladder, may be literate, but they are not readers.  Of the farm children who make up most of her class at school, Scout tells us that "the ragged, denim-shirted and floursack-skirted first grade, most of whom had chopped cotton and fed hogs from the time they were able to walk, were immune to imaginative literature."  The Cunninghams and their neighbors were not raised by lawyers who are professional readers and writers, they did not see their parents sitting in the armchair reading every night, and they were provided neither the books nor the time to read even if by some form of extra-sensory perception they had somehow gotten it into their heads that reading was a worthwhile pursuit.

The social groups who occupy the bottom two rungs of the social hierarchy, the African-Americans and the poor white trash, are mostly illiterate--not only immune to imaginative literature, but hardly able to read or write at all.  Bob Ewell may be able, barely, to scratch out his name, but his son Burris, who at eight or nine years old has only spent two full days in school, can't spell his, and his nineteen-year-old daughter Mayella, the best of the bunch, has only been to school for two years and can read and write only as well as her father.  Most of the African-Americans in the town are also illiterate; of the large congregation in the First Purchase church, only four or five, including Calpurnia and her son Zeebo, know how to read.

That African-Americans, and poor Whites, are still less literate than the upper classes is completely to be expected.  The Fragonard picture was painted about 250 years ago.  To Kill a Mockingbird takes place less than a hundred years ago. Cultures usually change very, very slowly.  Burris Ewell was younger than my grandfather; his grandchildren could be my students. We, like them, are living with the inheritance of centuries and centuries of social divisions.  For centuries in Europe, only the clergy knew how to read. In England, your crimes were treated much more leniently if you could prove you could read (they'd ask you to read Psalm 51, the "Neck Verse," and if you could read about God's mercy, then the powers that be would offer mercy as well).  In the American south, education for slaves was prohibited by law. This was all very, very recent, and since we are still living in a culture shaped by this history, we can most effectively make progress by accepting that our work is not only "instructional," not only about "skills," but is primarily social and cultural. 

Family, Peers, and School

The point I am laboriously making here is that reading is not only solitary, and it is not a "skill" that can be isolated, taught and tested in the way that perhaps long division can (though I wonder);  no, reading is social and cultural, and we teachers of reading must keep that uppermost in our minds.

We often assume that all parents want their kids to succeed, to become readers, but some of them probably don't.  There's a funny and horrifying scene in The Adventures of Huckleberry Finn in which Huck's absent, illiterate father comes back to find that while he's been away his son has learned to read.  Pap is upset:  "Looky here -- you drop that school, you hear? I'll learn people to bring up a boy to put on airs over his own father and let on to be better'n what he is. You lemme catch you fooling around that school again, you hear? Your mother couldn't read, and she couldn't write, nuther, before she died. None of the family couldn't before they died. I can't; and here you're a-swelling yourself up like this. I ain't the man to stand it -- you hear?"

When Huck reads a bit, Pap knocks the book across the room and warns Huck that if he catches him at school again, he'll beat him.  The scene is funny partly because Pap's attitude is so counter to all the middle-class bromides (Stay in school, etc.), but it's also funny because it expresses something real: there is a real anti-academic feeling in a lot of people.  Sure, nearly every parent genuinely wants his or her child to succeed in school--but a lot of them have mixed feelings.  They may have hated school themselves.  A part of them may feel that they didn't succeed and don't want their kids to succeed.  I had mixed feelings about school myself, and I know I have transmitted those feelings to my children.

It's not only parents, but peers, who work against creating a culture of reading.  In To Kill a Mockingbird, the only two readers in the First Grade classroom are Scout and the teacher, and even if they could work together it would be difficult for them to move the great mass of the rest of the class. The greatest obstacle to student success is often the students.  Not the student, singular, but his or her peers.  It takes more than one person to create a culture--and a teacher is only one person.  True, she has a vested authority, but she is competing against a score of other people, many of whom are not yet initiates into the society of readers.

This is a huge, and potentially growing problem

In the United States, despite the constant talk of our weak performance and the "crisis" in education, the situation is roughly what it's been like for decades.  The rich kids do very well, even by international standards, and the poor kids don't.  Recent results on the OECD's PISA tests make this clear: in 2009, US schools with less than 10% poor kids had reading scores averaging 551, significantly better than the scores in any other country (schools with more than 75% of students receiving Free or Reduced Price Lunch averaged 446, significantly worse than Turkey), but US poverty rates are among the highest in the OECD.

In any case, US schools with few poor kids do very well, and this has been clear at least since 1972, when Christopher Jencks and his colleagues published their magisterial Inequality: A Reassessment of the Effect of Family and Schooling in America (and every year other writers like Richard Rothstein and Gerald Grant make the same obvious point). Oddly, it was also in 1972, or thereabouts, that the economic fortunes of the bottom 50% took a turn for the worse.  Median wages, adjusted for inflation, peaked in the early 1970s and have been flat or declining since, even as the incomes of the upper-middle-class have grown quite a bit and the incomes of the rich have grown enormously.

This inequality has large educational effects.  Robert Putnam (of Bowling Alone fame) gave a talk recently on inequality that has been getting a lot of press (David Brooks, whom I usually loathe, wrote a somewhat reasonable column about it this week).  The basic idea is that poor kids grow up in dramatically different environments, and are given much, much less attention and fewer resources (like books!) than their higher-SES peers.  The inequality among children, according to Putnam, is getting dramatically worse.  I look forward to Putnam's book, but we teachers should be taking this stuff into account every day, trying to provide, in school, the cultural and social education that our students are missing outside of school.

We can't make up for cultural gaps by mechanical means.  Instead, we should be doing just what the Deweyan teacher in To Kill a Mockingbird is trying and failing to do: we should be reading to our students--but reading them stories they like.  We should be modeling our love for reading and thinking. We should be providing them with books to read, and time in which to read them.  We should be fostering student discussion in lit circles and the like.  What we should not be doing is what we too often are doing: giving our students the educational equivalent of Scout's classmates daily chores: drudge-work, like feeding hogs and chopping cotton, that keeps them from the valuable, mind-growing work of leisure-reading.  School should look like this:

...or even like this:

Two curricula: one for the elite, another for the masses

     The elite are "nurtured"and "inspired" toward a "love" for reading

Like Barack Obama and Arne Duncan, Bill Gates did not go to a public high school.  Instead, Gates, a scion of an elite Seattle family, went to a fancy prep school called Lakeside.  Lakeside's English curriculum is quite different from the Common Core Standards that Gates paid millions to have created and is spending millions now to promote, and that Obama and Duncan are pushing as well, through their "Race to the Top" (sic) program.  The Common Core standards suggest long and detailed classroom analyses of extremely difficult texts, and offer absolutely nothing in the way of requiring extensive reading or encouraging a love of reading.  This curriculum is dramatically different from the ones offered at Lakeside, where Bill Gates's kids now go, but I wouldn't expect Lakeside to change its ways anytime soon.

Here are the mission statements for Lakeside's English programs at the middle school and high school levels:

    "The Middle School English Department is dedicated to nurturing a lifelong love of reading
    and writing. We strive to create a community of readers and writers that inspires students to
    experiment with a variety of written forms."

    "Lakeside’s [High School] English Department’s highest goals are to inspire in students a 
     love of literature and to help students become great writers."

Both the middle school and high school statements use the word "love" and emphasize writing in an "authentic voice" and "artistically."  The curriculum is notably literary and cultural, and not narrowly designed to ready students for the business or political world.

It's also notable that these English departments aren't afraid to talk about encouraging a love of reading.  Encouraging a love for reading might seem like an obvious goal of English class, but in the Orwellian world of the Education-Industrial-Complex that goal is controversial.

     The masses are given "instruction" aimed at "proficiency"

This Orwellian madness surfaced in 2006, when the new President of the International Reading Association came out against encouraging a love for reading.  Professor Tim Shanahan, one of the biggest names int he reading world, had already made clear that he was against natural reading: he was a prominent member of the "National Reading Panel" (2000) that after a cockeyed look at the evidence, argued at length for explicit instruction and dishonestly claimed that there was no evidence that independent silent reading was effective.  In 2006, he became President of the International Reading Association, which has as one of its three stated purposes, in addition to improving reading instruction and promote reading proficiency, to "encourage reading and an interest in reading" (Reading Today, June 2006). Shanahan's first move as President of the Association was to say that while he could support improved instruction and promoting proficiency, he was not in favor of "encouraging reading and an interest in reading."  Although Shanahan can be eloquent and passionate about why reading is important, he apparently thinks it's inappropriate and dangerous to encourage interest in it.

For this, Shanahan was not laughed out of the profession; he remains one of the big shots of the reading world. This past week, the thoughtful, intelligent instructor of my PD workshop referred to Shanahan in glowing terms and gave us a couple of his articles.  How could this be?  How could the President of the International Reading Association argue against teachers' trying to encourage "an interest in reading"?!  Bill Gates's kids have teachers that nurture a lifelong love of reading, but the rest of us can't even encourage an interest in reading?  Are there different rules for private and public schools?  Well, yes--according to Shanahan.

     Interest in reading and "freedom of choice"

For, although his central (if insane) argument is that encouraging an interest in reading is somehow inimical to effective teaching, and that we should be "jealous of instructional time" which would apparently be wasted by encouraging student interest in our subject, Shanahan also argues at length that it is beyond a public school teacher's mandate to encourage interest in his subject.  In order to make this argument, Shanahan shifts the terms of the debate from the words "interest" to "pleasure" and then to "desire" and then to "love", and argues suggests that as "institutional beings," teachers have no right to try to instill love or desire in anyone.  A teacher's "public responsibility," according to Shanahan, does not include "encouraging reading," which is, he says, a "personal goal" that might carry "danger."  What danger?  Apparently encouraging reading would limit "freedom of choice."

That encouraging an interest in reading could be considered as limiting to freedom of choice is obviously Orwellian.  As Bill Gates found when he went from public school to private school, and as Shanahan should know, given his explanation of why he is passionate about teaching reading, encouraging an interest in reading actually promotes freedom of choice, while merely teaching it dispassionately as a useful skill is usually a good way to limit freedom. For Shanahan public schools, although obligated to impose explicit instruction of the kind Bill Gates found so tedious when he went to public elementary school, are not allowed to offer students encouragement and nurturing of the very practices that will allow freedom.

     Conclusion: We need to create a culture of reading, even in public schools


Why is Shanahan so uncomfortable with the notion of encouraging interest in reading, even though he acknowledges that reading is important?  Why does Gates spend his billions to promote increased class size and increased testing, even though he sends his kids to a school that brags about its average class size of 16 and that manages to have 40% of its Seniors be National Merit Scholarship Finalists without having done any of the kind of high stakes testing Gates is working to impose on the rest of us?  The obvious answer for Shanahan is that he has spent his career promoting explicit skill instruction, and for Shanahan to admit that it's important to teach reading as an organic, pleasurable experience, or to admit that reading is largely a socially mediated activity, might seem to him to call into question his life's work.

As for Gates, perhaps he doesn't know how to address the social and cultural aspects of learning, or perhaps he thinks the changes he's pushing will lead indirectly to an improved cultural and social environment in the classroom.  My guess is that Gates sees public school as properly different from what he offers his own children. When Gates himself switched from public school to private school, he noticed a dramatic cultural shift.  As he recalls, "it was a change at first.  And the idea of just being kind of a goof-off wasn't the sort of high reward position like it had been in public schools." It seems possible that, partly based on this experience, Gates doesn't think it possible to change that culture.

But he should think so, for in the same interview I quoted before, he offers an excellent example of a public institution that encourages reading. Gates remembers that when he was a kid, the library would give you a gold star if you read ten books over the summer, and two stars if you read twenty.  According to Gates, he and "five or six girls" would compete to see who could read the most books.  For reading is a solitary activity, but reading is also a social activity, and it can be encouraged.

The first job of every high school English class should be creating a culture of reading.  This is difficult to do when many of our expert authorities don't believe that interest matters, and think that human beings are mechanisms that have only to be properly programmed for "proficiency." The best way make sure that our public schools are not like the one Bill Gates went to, where "being a goof-off was more socially rewarding," is to replace the interest in goofing off with an interest in reading and thinking, and that can only happen if we encourage that interest.  We must make sure that our public schools do "encourage reading"--even inspire a love for it.  If reading is, and has always been, strongly linked to social class, we don't have to accept the social class divisions that we are given.