Holding the gate against ideas

“The government wastes hundres of millions of dollars on math and science programs that never seem to improve the test scores of American students,” writes Barbara Oakley in Take This Paradigm and Shove It in Psychology Today. She blames “intellectual gatekeepers” who keep unfashionable ideas from being debated and funded. 

. . . today’s K-12 educators—unlike educators in other high-scoring countries of the world—refuse to acknowledge evidence that memorization plays an important role in mastering mathematics. Any proposed program that supports memorization is deemed to be against “creativity” by today’s intellectual gatekeepers in K-12 education, including those behind the Math and Science Partnerships. As one NSF program director told me: “We hear about success stories with practice and repetition-based programs like Kumon Mathematics. But I’ll be frank with you—you’ll never get anything like that funded. We don’t believe in it.” Instead the intellectual leadership in education encourages enormously expensive pimping programs that put America even further behind the international learning curve.

“Pimping” programs? Hmmm.

In the education world, what potentially good ideas are outside the gate?

About Joanne


  1. Certainly there are gatekeepers of all kinds highly resistent to many kinds of ideas. It seems a fallacy to lay the blame on one end or the other of the spectrum–whether defined as memorization vs creativity, phonics vs whole language or any other of the dichotomies wh have identified as our ongoing battlegrounds.

    The real resistence–which as I think about it is hard to even discuss as all of the vocabulary of discourse has been pre-assigned to one side or the other–is to being scientific, collaborative, outcome-based, or otherwise simply thoughtful about what we are doing and how best to accomplish it–and why. Any new, old or present development is certain to be attacked by someone (who will claim that they were not a party to the discussion) as being thoroughly wrong-headed and merely a money-making ploy, part of a scheme to discount teacher’s opinions and training, or some other evilly intended something or other destined to ruin education.

    Our American frontier independence grants us the freedom to express an opinion and then close the classroom door. This ensures that the best of native skill and ability is seldom shared, and the worst is allowed to flourish.

  2. Am I the only one who thinks “creativity” in education is overrated? After reading this post, I’m relieved that I’m not.

  3. I’ve been saying that for decades. Phonics, spelling, grammar and arithmetic have already been discovered, their rules are well-known and should be taught as efficiently as possible. The same goes for science, geography and history. Until kids have a solid mastery of the basics of any subject, creativity is vastly overrated. On the part of teachers, I think the creativity argument goes hand-in-hand with a disinclination to follow a real curriculum or use teacher-centered instruction and a positive antipathy to the concept of mastery.

  4. Student of History says:

    Given the findings of the National Reading Panel Report, Jeanne Chall’s work and Marilyn Jager Adams extensive research as well, why do we still talk in terms of finding a “balance” between phonics and whole language?

    Given the extensive documentation in 2006 by Kirschner, Sweller, and Clark on why Minimal Guidance in instruction does not work, why do we still assert that math should be learned through exploration of new concepts rather than worked examples and sequential, explicit instruction?

    Why do we talk about balancing between what is researched, field tested and shown to work and what is wishful thinking?

    Where’s the balance in these bogus dichotomies?

  5. Good for Barbara Oakley. If what she says had been done in math, we wouldn’t have to be developing a non-credit course in arithmetic computation (add, subtract, multiply, divide, fractions, decimals, precents) for TEACHERS at my institution of (so-called) higher education.

  6. Richard Aubrey says:

    I have taught a couple of industry technical classes, and was an Infantry training officer back in the day.
    But I’m an outsider to education except for being the son, husband, father, father-in-law to teachers.
    As it happens, the wife and daughter teach Spanish, which requires memorization and nobody has tried to fancy up a way to teach language without requiring the students to know the words. The idea is silly, and self-refuting.
    What is interesting in the discussions, and I’ve watched them in other venues, is not the distaste for routine on the part of the teachers. That’s understandable, although the sergeant instructors who teach various skills do it in accord with an Army-wide syllabus, including, I think, some of the jokes. It is repetitive as hell, it is structured, and they do it over and over and over. Some may teach the same subject (i.e. Rifle Squad Tactics) to a new company every week for a year. Thing is, it works.
    But I can see a basic distaste for that, if there were alternatives.
    What eludes me is what seems to be a positive assertion that there is something wrong with memorization and detail mastery, something which keeps the kids from….something. As if the brain activity used in memorizing spelling precludes learning something else. It seems to be even ideological.
    I should say that language teachers have huge amounts of papers to do, because the progress has to be checked in small increments. It’s a burden on the teacher’s life.
    Many of the hot, new ideas don’t seem to be the kind that would generate a lot of homework to be checked, or tests to be written and corrected.
    Could that be it?

  7. All branches of the military use direct instruction to teach just about everything to just about everyone and it works.

    Some of the essential certification courses for physicians and surgeons (not just military) use direct instruction. Specifically, Advanced Trauma Life Support (ATLS), required for surgeons, ER physicians, all military physicians etc., and Advanced Cardiac Life Support (ACLS) both use this format.

    These two applications have proven effective and efficient in enormously varied classes for professionals with high-school through doctoral degrees, but k-12 kids are somehow supposed to discover arithmetic – and everything else – on their own? Please…just don’t go there.

  8. My kids hated Kumon, but as my daughter was counting on her fingers and her “progressive’ school didn’t seem to care, what was I supposed to do?

    In most things, you can’t get creative until you have the basics down pat.

  9. What eludes me is what seems to be a positive assertion that there is something wrong with memorization and detail mastery, something which keeps the kids from….something. As if the brain activity used in memorizing spelling precludes learning something else. It seems to be even ideological.”

    Did you see the movie Spellbound? Documentary about some kids preparing for the national spelling bee. Some different approaches. There was one young kid who struck me as likely on the ausperger’s spectrum–who was probably just incredibly efficient at either memorization or “seeing” the words. One little girl (the kid from DC–there have been some follow-up stories on her) was at a real disadvantage because she (and her school coach) relied on memorization of the word list–good for the local events, but the national doesn’t use a word list.

    The kids who were really effective were the ones who were studying multiple other languages, and understanding the structure and change of language over time–in order to be able to forecast (in cases where they had not memorized) which roots, prefixes and suffixes would go into making up an unfamiliar word–this is why they ask for the definition and the derivation. Far more sophisticated than memorization. My daughter had one elementary teacher who actually understood this. The rest all sent home ten words to memorize by Friday.

  10. Richard Aubrey says:

    Great for the geniuses and the Aspeger’s types and those coached and prepped for competition.
    How come it isn’t working for the rest of the kids?
    Jeez. You figured that would get by an adult?
    I picked up a lot of French and Latin and Vietnamese vocab by memorizing, and in the ninth grade it was ten words twice a week.
    It’s actually pretty easy. You write them down ten times. The muscle activity seems to groove the memory pretty deeply. And you don’t have brainsweat coming out your nose as you grind your eyeballs into the page. Takes less concentration and mental energy. I even got the words down using the exercise to improve my still-rotten handwriting, concentrating on the movements of the pen instead of the words. Simple.
    But, as I say, there seems to be a positive revulsion to memorization and mastery that goes beyond a teacher’s distaste for a routine and repetitive task.
    As if it’s fascist or something.
    Now, being married to a Spanish teacher would seem to have everything new and shiny built in, without all that nasty memorization.
    And about all I can do is order a couple of beers, find the bathroom, and read some directions on subway maps.
    Because I didn’t study Spanish in the traditional fashion as I did the other three languages.

  11. Margo says, “The kids who were really effective were the ones who were studying multiple other languages, and understanding . . . . . . . . . .” Isn’t that a tautology? The kids who were really effective were really effective. Good for them. I don’t teach many of them.

    Speaking of teachers Margo says, “The rest all sent home ten words to memorize by Friday”. I think I remember having 25 words to memorize by Friday when I was in elementary school. Maybe it was only 20. This was in the fifties, after all. But I know it was more than ten. It occurred to me many years ago that even 20 words a week doesn’t add up to all the words we need to be able to spell. Twenty words a week, for thirty-six weeks a year, times eight years of elementary school makes 5760 words. That’s a lot, but a long way from the number of words we know. I’m not a good speller, but I think I can spell more words than that. So how do kids really learn to spell? The advocates of creativity would argue, I think, that we therefore don’t learn to spell by memorization. I would not agree, but I can’t say that I can claim to understand how we do learn to spell. My gut instinct tells me that cutting down from twenty words a week to ten is not progress.

    Of course I’m all in favor of learning about word patterns, origins, and so on. I presume good teachers have always done that. I can also understand that many teachers might neglect it. And I can also understand that ten words a week with a good mix of associated learnings might be a lot better than 20 words without. But I do not agree with the perspective that nothing needs to be memorized. When I teach the quadratic formula I do my best to explain how we get it, but I still tell students to memorize it.

    As a math teacher I am aware of the disparagement of memorization in math. In 2003 I discovered that the NCTM (National Council Of Teachers of Mathematics) did not address, in their “Standards”, the need for practice in the learning of math. I wrote an article on that, “Some Disagreements With The Standards” It’s on my website at http://www.brianrude.com/disagr.htm. Practice may not be exactly the same thing as memorization, but it is closely related. And it is very important.

    I thought maybe my article would be published by “The Mathematics Teacher”, which is a magazine put out by the NCTM. I submitted it. They rejected it (in their own good time). Is that intellectual gatekeeping? Or was it just a mediocre article? You decide. My account of that affair is at http://www.brianrude.com/disdis.htm .

  12. Andrew Bell says:

    After basic arithmetic, math really isn’t about memorizing things. Sure, there are things that are easier if you have memorized them, but what often happens after arithmetic is that students want to solve problems using a memorized method instead of applying the tools one has learned to come up with a solution. This can quickly lead to failure.

    When I tutor math, I see this over and over. Unfortunately, many teachers don’t understand enough math to convey the essence of it to their students. Here is a simple example. You can memorize several forms of an equation for a line, and it is useful to do so. But it is more useful to be able to derive these for yourself, and it isn’t difficult. But you have to be taught that the formulas aren’t something mysterious that were created by Euler or Newton. You have to understand that they are within your grasp and come from simple things that you (hopefully) already understand.

    Math requires a set of tools. But it isn’t sufficient to acquire the tools, you have to learn how to use them.

  13. Richard Aubrey says:

    It isn’t sufficient….
    Some seem to be telling us it isn’t necessary.

  14. Andrew,

    Nobody argues that memorization is the end-all, be-all. What is argued is that memorization (in long-term memory) is critical for basic, pre-requisite, skills. And without those you can’t go anywhere else, as you keep being chained down by the hard effort to recall those basics.

    Ralph Raimi penned two short and beautiful pieces on this some time ago:


  15. Student of History says:

    “People untaught in mathematical reasoning are not being saved from something difficult; they are, rather being deprived of something easy”

    – Ralph Raimi, 1998 Fordham Math Standards Report

    Maybe every student should get the type of systematic and explicit math instruction recommended in the Response to Intervention practice guide published in April 2009.


  16. Oh my. Usually I’m in awe of the quality of the posts but not when this is the topic.

    There are many false assumptions here.

    It kind of scares me.

  17. Richard Aubrey says:

    Easy scared, huh, Robert?
    Is your fear supposed to make us do something?

  18. Student of History says:

    What a condescending comment Robert.

    Point out the false premises if you can.

    Please do not simply allude to an intellect too superior to indulge us.

  19. The whole “math wars” boil down to parents, who want their children to learn math, and Professional Educators (PhD!), who want to try the latest educational fad.

  20. Margo –
    Your spelling bee example does in fact display higher level functions than memorization… but they cannot occur until that first step of memorization has been completed. While those students were able to reasonably guess at spellings using root words, they could only do this after memorizing those root words and numerous examples of each.
    In other words, for a student to be competent at algebra, they need to be extremely familiar and able to easily perform all the basic mathematical functions. This, of course, they can only achieve through completing hundreds of example problems correctly.

  21. today’s K-12 educators—unlike educators in other high-scoring countries of the world—refuse to acknowledge evidence that memorization plays an important role in mastering mathematics.

    This just goes to show how little the author knows. K-12 Educators have little to no say so on what curriculum they will be using, when and how the lessons are taught.

  22. tim-10-ber says:

    Great comments —

    Mike in Texas — I beg to differ with your comment about educators having little to say in what curriculum will be used, how or when the lessons will be taught…

    I believe educators if you want to be viewed as true professionals can figure out how to have a voice (and a strong one) in this process. It starts one school at a time. It starts with strong leadership. It is done in the corporate world through the voice of the client (student and their family), the voice of the associate( everyone in the school), 360 feedback and the voice of the shareholder (the community). This is one thing educators need to figure out because it truly works in the business world…

    There are more educators than administrators in a given city, county or state. Coming together you can and will make a difference. Now…figure out how to find your voice, stop hiding behind tenure (geez…wish I had that after 35 years in my profession!!) and stop your whining.

    Look at the private schools in your communities…what curriculum do they use? When are they teaching physics (it is becoming a freshman level course and an advanced course), when is Algebra I offered, when are languages offered…what is done in the lower grades to prepare the students for high school rigor, etc…there are plenty of good examples…look at the suppose top schools in the country according the US News…share this information with your board, your principals, your fellow teachers, administrators, etc…hurry before it is too late…

    We have a two tiered education system with the elite private schools in any given city and the default government schools…what is being done to close this gap and elevate the default schools to true choice schools — all of them…

  23. Super Sub:

    I think that you are making my point (the one from my first post). But we have an incredibly difficult time having conversations that don’t dichotomize. Why must we always think in terms of creativity (or understanding or curiosity, or whatever) vs memorization? Or phonics vs whole language?We go on about education as if there are always two camps and one must declare allegience to one or the other and any movement towards the center will bring about dire consequences.

  24. Richard Aubrey says:

    We dichotomize because that’s the way the pros want it.
    You won’t find many whole language proponents saying there’s a place for phonics, and creativity people will actively state that memorization is, at best, useless.
    Even having a place for both is chancy because you can’t do creativity if you don’t have a clue about the issues. That means knowing stuff and that means memorization.
    I have a fraternity brother who’s made a good living as a bassoonist. Has played in some big symphony orchestras and has a couple of chamber quartets he can put together for private functions.
    He spent hours–probably still does–doing the scales in the furnace room of the fraternity house, the tootling coming weirdly up through the walls at two in the morning. His point was that if you don’t know how to blow, it doesn’t matter how the ideas flow.

  25. Michael E. Lopez, Esq. says:

    Hear, hear, Mr. Aubrey.

    Basoons, sports, math, reading… it’s all of a kind.

    You can’t make it in basketball if you haven’t spent the hours and hours and hours practicing freethrows and layups until they become second nature.

    Similarly, times tables can’t just be memorized. They need to be ingrained. They need to be second nature. The first step to that is memorization. Them lots and lots of practice using them. Over and over and over again till the brain hurts.

    The same with reading: memorization of phonics is only the first step. If you want to be a proficient reader, and not stumble over pages one word at a time for the rest of your life (justifiably feeling as if you were an ignorant failure at school), then you need to practice, practice, practice. I’d say that by the time you finish high school, you probably should have read at least 1000 books. (My estimate might be more accurate if I said something like 140,000 pages — so that Harry Potter actually gets you closer than one volume of Sweet Valley High.)

    Well, you ain’t gonna be able to do that unless you get the phonics crap done and behind you early. If you’re still decoding in fifth grade, you’re on your way to being totally screwed and it’s time to spend three hours a day every day doing nothing but working on the basics.

    If you’re still decoding in ninth grade, it’s over. You’re done. No one is going to want to put in the time and effort needed to bring you up to speed. If you want to read proficiently at that point, you’re going to need to do it yourself, or hire a very specific type of private tutor.

    But one thing that is NEVER going to work is attempting to push you into advanced reading without having mastered the basics, and practiced them to the point where they are second nature.

    Yet that is precisely what many of our teachers today either want to see done, or don’t care enough to object to. And, frankly, it’s because a lot of them are ignorant and they can’t really read proficiently, either. We’ve actually failed at this education thing for a long enough period of time that now a lot of our teachers don’t have the necessary basic skills to move on to higher levels of proficiency.

    That means it’s the teachers, too, who need to go out and drill, drill, drill till this stuff becomes second nature. But why would they want to do that? They’ve already GOT the job for which their education was supposed to prepare them. There’s no more carrot.

    Somebody get me a stick.

  26. Andrew Bell says:


    I agree with Mr. Raimi. But we must separate the idea of memorization of basic and useful things, such as the trig identities he describes, from the actual doing of math, which is quite a different thing. Most teachers believe that memorization is valuable to some degree, don’t they? But perhaps what teachers should convey to students is this: if they have memorized frequently used facts, they will be able to do math more easily, which is to their benefit.

    I think what good teachers might disdain is time spent memorizing things that aren’t generally useful when that time could be spent either memorizing useful things or applying what one has learned and memorized.

    I don’t regret not having spent time learning how to spell many of the words that are spelling-bee worthy.

  27. I regularly see (admittedly anecdotal) evidence that there must be a huge number of teachers/schools who disdain memorizing useful things. For instance, the two deli clerks (late teenage and about 40) who assured me that their digital scale couldn’t measure 2/3 of a pound of turkey and 1/3 of a pound of ham. Neither had a clue about the relationship between decimals and fractions, but they finally consented to place the meats on the scale until I said “stop.” Another instance was the bakery clerk (mid 30s) who entered into her cash register the $4.00 I gave her for a $3.20 order but had no idea what to do when I gave her the $.20, even with the “assistance” of a calculator. Then there was the vendor at a mall kiosk who was unable to calculate the 5% sales tax on a $10.00 purchase, again with a calculator’s “help.” These incidents occurred in three different states, so the disdain for memorization isn’t localized.

  28. “I’d say that by the time you finish high school, you probably should have read at least 1000 books. (My estimate might be more accurate if I said something like 140,000 pages — so that Harry Potter actually gets you closer than one volume of Sweet Valley High.”

    A page in a book like “The Book of Three” or “The Black Cauldron” runs about 250 words. 140,000 pages works out to 35 million words in 13 years (I’m counting kindergarten). But your typical high schooler can/should read many more words/year than your typical KG-3rd grader. Even one million words/year is an enormous amount for a typical 3rd grader.

    So … simplifying a bit and assuming that all the reading is done in the last ten years, we get 3.5M words/year. I’ll assume that a year has 350 days to make the math easier and we get 10,000 words/day (every day, not just school days).

    200 words/minute works out to 50 minutes/day of reading. Every day. For ten years.

    Is this what you think is required to be a “proficient reader”?

    -Mark Roulo

  29. Actually, textbooks and other non-fiction sources should count also, since content knowledge across the disciplines is critical to reading comprehension and proficiency, so 50 minutes doesn’t seem to be a totally unreasonable average. At least, one could strive for that.

  30. Michael E. Lopez, Esq. says:

    Mr. Roulo-

    After reading your post, I realized I’m wrong. 140,000 pages isn’t really enough. (I take it that the point of your comment was to show that it was too much. What follows is based on that interpretation. If I have misunderstood and you think there should actually be MORE reading, I’m open to the suggestion.)

    It should probably be 160,000 pages, not 140,000.

    Now, let’s re-run the numbers.

    First, I think 11 years for the average works… K-2d can probably be counted as a single year for these purposes, but by 3rd grade you need to be starting in on things around the Hardy Boys/Nancy Drew level. Or at least Encyclopedia Brown. And we’re talking averages here.

    But you wanted 10… so we’ll run it both ways. Model A will be 10, Model B will be 11.

    You took out like 4% of the year when you cut down to 350. I want those two weeks back. We’ll compromise and go with a bank year of 360 days. Model B will be 3960 days. Model A will be 3600 days.

    Lloyd Alexander is probably a good proxy. Some books have more, and probably even more have less, but most of the reading is probably going to be done at or around this level on average. (Remember… we don’t need to be reading fine literature here: Sweet Valley High *is* good enough for practice at the 7th grade level!)

    So 250 words per page it is. 160K * 250 = 40 million words on the nose.

    Model A: 11,111 words per day
    Model B: 10,101 words per day

    Now… you used a 200 wpm reading speeding. That might be a *temporal* average… as in that might be the average reading speed of a child taken as a function over the time period ranging from Kindergarten to high school graduation.

    In Kindergarten, reading speeds are going to be fairly low, even though the material is going to be much easier. We’re probably looking at somewhere around 20 words per minute. It’s going to go up fairly rapidly with consistent practice, though. 200 words should be obtainable by 6th or 7th grade (around the temporal midpoint of the education).

    A proficient reader should be somewhere around 300-350 wpm.

    BUT: the majority of the material (in terms of page count) is, as you concede, going to be read at a much higher speed. So I’m going to go ahead and help myself to a 225wpm reading level over the course of the whole 160,000 pages.

    But, you wanted 200… so let’s do Model A00, Model A25, Model B00, and Model B25, just to be thorough.

    Model A00: 11,111/200 = 55.55 minutes
    Model A25: 11,111/225 = 49.38 minutes
    Model B00: 10,101/200 = 50.51 minutes
    Model B25: 10,101/225 = 44.89 minutes

    Wow. We increased it up to 160,000 words and it’s STILL all coming in at around 45 minutes to an hour. (Note, by the way, that these figures are at or around the magic 10,000 hour number that we’ve heard about lately with respect to things like figure skating and playing musical instruments. Coincidence? I THINK NOT!!!!!!)

    An hour a day. Every day. For Eleven years. That’s an average: it should probably be 2-3 hours a day every day during the high school years, and at least 90 minutes during the junior high school years. Much of it, I might add, will DONE IN CLASS while school is in session.

    So, yes. That is how you get good at something. If you aren’t willing to put in that kind of work, then you’re not serious about whatever it is that you’re supposedly doing.

  31. Mike in Texas, “This just goes to show how little the author knows. K-12 Educators have little to no say so on what curriculum they will be using, when and how the lessons are taught.”

    I don’t know about anybody else but myself, but I (high school educator) do have a tremendous amount of say in the curriculum that I use and when and how the lessons are taught. I would not teach in a situation where I did not.

  32. Richard Aubrey says:

    Ref reading and phonics.
    It appears–to me, anyway–that alphabets were designed as a quick and dirty way to reduce spoken sounds to symbols. That way, you can repeat the sound, out loud or to yourself mentally; and hear that it resembles a word you already know.
    We only have twenty-six letters, most of which have only two sounds, determined by context.
    The key is knowing the words first.
    That means a word-rich and context-rich environment growing up.
    Ideographs, as in Chinese, are the ultimate whole language concept, accessible only to a class of mandarins who can afford to devote their entire lives to learning them. I think they were designed because the various languages and dialects the ancient Chinese emperors ruled were mutually unintelligible, while a picture of a horse is a picture of a horse, and when reduced to ideographs, still a horse, however the locals pronounce it.
    We don’t need that.

  33. Mark Roulo says:

    “I take it that the point of your comment was to show that it was too much.”

    Actually, no. I wasn’t making an argument for either too much or for not enough. I just wanted to be sure that you were, in fact, taking a position that 45-60 minutes/day of reading for 10-11 years is what you felt was required to achieve proficiency.

    Your answer is, basically, “Yes.” (to within rounding).

    Which is what I wanted to know 🙂

    I’ll suggest that 1 hour/day for 10-11 years is more concrete for most people (although less accurate because of the implied words/minute rate) than 140,000 to 160,000 pages.

    -Mark Roulo

  34. Mark Roulo says:

    Wow. We increased it up to 160,000 pages and it’s STILL all coming in at around 45 minutes to an hour. (Note, by the way, that these figures are at or around the magic 10,000 hour number that we’ve heard about lately with respect to things like figure skating and playing musical instruments. Coincidence? I THINK NOT!!!!!!)

    I think we’ve dropped about a figure of three.

    One hour of reading per day for 365 days a year for ten years is:

    365×10 = 3,650

    Not 10,000.

    We’d need closer to 3 hours/day for ten years to get to 10,000 hours of reading. No?

    -Mark Roulo

  35. Michael E. Lopez says:

    Bah! You’re right.

    I was looking at the wrong number.

    OK, scratch that part.

  36. It’s a poorly written piece which did not actually appear in the magazine.

    The writer claims that her point of view, that there isn’t enough memorization in math classes, is suppressed by the same people who believe that global warming is a fact.

    In Fox News logic, it all fits.

  37. Other places where new ideas have not gotten through? How about special education, as I point out in Fixing Special Education–12 Steps to Transform a Broken System. http://www.schoollawpro.com and http://www.parkplacepubs.com.

    There’s lots of stuff that needs to see the light of day! Thank you for bringing out this need.

  38. Today’s newspaper announces a “program designed to teach students how to think strategically instead of strictly through memorization,” partially funded by six million dollars of federal stimulus money. Seems like we’re behind the research here in Texas.

  39. It’s not the gatekeeping against good ideas that’s the real problem – it’s the headlong embrace of bad ideas that’s the real problem.

  40. Mr. Lopez,

    Do you have some research that you could cite to back up the need for an hour of reading per day.

    A year ago or so I read that the most proficient students read 4-5 million words per year from 3rd grade forward, while the least proficient read 150,000. I’d like to substantiate those numbers but am running into dead-ends. Any sources you might point out would be very appreciated.


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