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Posted at 11:30 AM ET, 12/13/2010

Willingham: What causes performance decline across grades?

By Valerie Strauss

My guest today is cognitive scientist Daniel Willingham, a psychology professor at the University of Virginia and author of “Why Don’t Students Like School?”

By Daniel Willingham
An “absolute wake up call.”

That’s what Education Secretary Arne Duncan called the latest results of the the PISA test, which measures 10th grader’s achievement in reading, math, and science.

If we’ve all been asleep up until now, we’ve really got trouble.

U.S. kids did not shine, but the latest round of results of PISA, formally known as the Program for International Student Achievement, don’t look that different than what we’ve seen in the last decade.

On the PISA, U.S. kids typically score about average relative to kids from other participating countries. They rank in the middle of the pack, around 20th.

What’s notable to me is that U.S. fourth graders have usually done better.

Those tests (the TIMSS for science and math, and the PIRLS for reading) are not directly comparable, of course. That said, U.S. fourth graders have typically scored above the mean of participating countries, and typically rank somewhat above the middle of the pack, usually about 10th, noticeably different than 10th graders.

What might cause this decline across grades?

In the early grades we emphasize the skills that are tested at the early grades, but we fail to build knowledge that---although it’s not measured early on---will be important later.

In reading, the emphasis is on decoding, and our kids are pretty good decoders.

But by 10th grade, being a good reader no longer means being a good decoder. Most kids are good decoders by this time. Instead, reading tests emphasize comprehension, and comprehension is mostly driven by prior knowledge--knowing a little bit about the subject matter at hand. (I’ve emphasized the importance of prior knowledge in reading here and here.)

All that time spent on decoding in the early grades, (and time not spent on history, geography, science, music, art, etc.) comes back to haunt kids in 10th grade and beyond.

A parallel phenomenon is happening in math. In the early grades U.S. kids are not very strong on conceptual understanding, but they are pretty good at learning math facts and algorithms.

That’s sufficient to produce good test scores in the early grades. Kids can recognize problem types and know which algorithms to apply.

But once you start algebra, the absent conceptual knowledge really starts to hurt you.

So again, what was missing in the very early grades doesn’t come home to roost until high school.

The international comparisons show us that we still have work to do in the upper grades. The pattern of performance tells me that the work must begin in early elementary school.


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By Valerie Strauss  | December 13, 2010; 11:30 AM ET
Categories:  Daniel Willingham, Guest Bloggers  | Tags:  arne duncan, daniel willingham, pirls, pisa, pisa scores, test scores, timss  
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Thank you, Dr. Willingham.

I haven't read anyone else who makes these points, regarding the discrepancies between the elementary and high school scores and some of the missing pieces in elementary education.

Dr. Willingham mentions the lack of emphasis on an expanded curriculum (history, geography,science, music, art, etc.) as the most likely culprit in diminishing scores.
I think he's right; two other culprits, from my experience, are:
- too much emphasis on technology;while
it opens many doors and does wonderful
things, the sheer speed of it all has
to make young children depend on an
'easiness' in learning; there is not
the difficult grappling with concepts
one has to do to build the mind's

- too many young administrators and
teachers who have not had a solid
grounding in the liberal arts and don't
understand what we are missing by their
decline; to wit:

TRUE story - an experienced English
and Literature teacher from High School
sat in a Middle School English
department meeting where the (very
young) head of the department was
tasking the teachers to increase the
students' skill levels. The High
School English teacher asked the dept.
head what they were to do about
improving the understanding of

The dept. head's response: "Who cares
about content? All the kids need are

Very scary.

Posted by: PLMichaelsArtist-at-Large | December 13, 2010 12:13 PM | Report abuse

Dr. Willingham makes some excellent points, but he paints a picture that students are doing just fine learning the algorithms in the lower grades, but may be missing the conceptual understanding. High school math teachers may tell a slightly different story. They may talk about students who don't even have mastery of the basic skills. Teachers talk of students who don't know how to multiply fractions, nor how to operate with decimals, and who are dependent on calculators.

A student who has mastery of basic algorithmic procedures and number facts, and can apply these to various types of word problems is generally on a path toward algebra. To be more specific, if a student knows that to find how many 2/5 inch intervals are contained in3/2 inch you divide 3/2 by 2/5, he/she does not really have to be able to explain the derivation of the invert and multiply rule for dividing fractions in order to succeed in algebra. But there are some who place a premium on conceptual understanding. Programs like Investigations in Number, Data and Space, as well as Everyday Math are two programs that purport to provide the conceptual understanding and sacrifice procedural fluency in the process. There is a prevailing belief that knowing how to find three ways of finding the answer to 112 x 23 (as well as illustrating it with a picture) will place them on the road to algebra. This emphasis on process over content has hurt many students.

Posted by: BGarelick | December 13, 2010 5:54 PM | Report abuse

@BGarelick: I hear you. Your point--that US kids are not where they should be on basic computation--is well taken. My point would be better put as saying that we have gotten as far as we have in the early grades through some competence in computation. On the conceptual piece, we have much farther to go.

It's also been brought to my attention that Rick Hanushek and colleagues have offered a different interpretation of PISA performance--they argue that the particulars of the sample is crucial. There paper can be found here

Posted by: DanielTWillingham | December 13, 2010 7:08 PM | Report abuse

Perhaps Professor Willingham missed the call and is sleeping late. Todays elementary students are not taught math facts with fluency and efficient algorithms are avoided like the plague. I htink it Willingham reads Professor Wu's paper, "What's so difficult about elementary school math?..." in the American Educator (fall 2009).

Todays students are schizophrenically "discovering" inefficient strategies that are not tied with any facts of substance such as efficent algorithms.

And, schools of education promote these ideas as if they were fact and research supported. They are not.

Posted by: kltroidle | December 13, 2010 7:40 PM | Report abuse

Interestingly enough I was having this conversation with a colleague today. Why do we have children reading and doing math on grade level, getting good grades and achieving honor roll or credit roll in the primary grades, then when they get to third grade everything falls apart? I have no definitive answer, but there is a major shift in the curriculum, especially in math.
Previously we taught math using the constructivist Every Day math series in the primary grades only, then shifted to a home grown program called LL Teach. Unfortunately,in Everyday Math, there was not ENOUGH focus on basic skills, so the children advancing to third grade could not do the basic computation required in the LL Teach program. They had not mastered the skills or concepts necessary to be successful at more advanced math. My only conclusion is that there must be a focus on basic skills in the primary grades while asking the children to demonstrate their understand and use the skills in real life applications. I like our new program because it focuses on the required basic skills using a multi-sensory approach, language development and then the application of the skills. It's only our second year, so the effects of the new program won't be known until the end of next year when the first group of students enter third grade.

Posted by: teachermomnj | December 13, 2010 7:43 PM | Report abuse

It is very difficult for Dr. Willingham, or any one else to discuss student achievement without admitting that almost all of our teachers are competent, and one-half of our students are below average. I do appreciate his efforts.

Posted by: jseddinsok | December 13, 2010 8:13 PM | Report abuse

There definitely has been a phenomenon occurring in math, but I doubt it is parallel to reading.

The early grade competence in computation seems to lose ground for many students as they move up the grade levels. I hope it is different in other schools and for other teachers, but my experience found only 25% of students entering my sixth grade class year after year were proficient enough with basic multiplication facts to be successful. Valuable class time was used developing basic fact proficiency in order to be successful working with fractions. Many students could explain how something worked but could not perform the computations and had yet to learn efficient algorithms. What may hurt students in algebra more than “absent conceptual knowledge” is poor proficiency with basic facts. Without that proficiency students have difficulty with fractions and without an ability to work with fractions they have no hope of being successful.

Posted by: ChasC | December 13, 2010 8:58 PM | Report abuse

I work with elementary school children who have been identified as "gifted." I'm sick of teachers referring first graders to me who are proficient word callers, but who cannot read for comprehension.

Here's a typical example: a first grade teacher came to me last week very excited about a student who supposedly reads on a fifth grade level. When I asked her how his comprehension was, she replied "Oh, he has some of that, too." Sadly, the child was able to pick his way through a chapter of "Frog and Toad," but had no idea what any of it meant. His supposed fifth grade reading level was based on his ability to decode a list of words, with no regard for comprehension.

Here's the way I test for reading--I find an engaging, grade-level appropriate picture book and sit down with the child to share it. I have him read to me and we talk about what's going on in the book. I can get a feel for whether he understands the book, what reading difficulties he has, and whether he needs something more challenging. I don't need to find the child's Star reading level or a PALS or DRA score to figure out how well he reads.

But we can't allow teachers to evaluate reading levels this way because then the companies that produce the reading level data lists would go out of business.

Children learn to read well by reading and sharing good books, not by practicing decoding in a vacuum.

Posted by: aed3 | December 13, 2010 9:49 PM | Report abuse

Regarding math skills--every year, I find that the kids I work with are less and less able to solve story problems. I suspect it's at least partly because of their poor reading comprehension. They have a lot of trouble following a line of logic. They do great with SOL tests because they learn so many skills for backing into a multiple choice response. But when confronted with a multi-step open ended problem, they are baffled. Right now I'm struggling to get fourth graders to work with materials I used for second graders a few years back. The slide seems to get worse very year. We now have a whole generation that has been taught nothing but multiple choice test taking skills and decoding.

Posted by: aed3 | December 13, 2010 10:04 PM | Report abuse

"we have gotten as far as we have in the early grades through some competence in computation. On the conceptual piece, we have much farther to go."

Fair enough, but I have two concerns with this statement. One is that it seems to dichotomize computation skills and conceptual understanding. Don't they feed off one another?

The other is that it will be cited by Reform Math advocates as further support for the use of their pet programs (Investigations, Everyday Math, and the like), which, they claim, emphasize conceptual understanding and critical thinking skills in ways that, they claim, "traditional math" failed to do.

But specific comparisons of Singapore Math, traditional pre-1960s math, and Reform Math (see the comparisons at strongly suggest that the continued spread of the latter, this uniquely American approach to k12 math, is probably perpetuating and exacerbating our academic decline--in conceptual understanding and in computational skills alike.

Katharine Beals

Posted by: KatharineBeals | December 13, 2010 10:25 PM | Report abuse

Whoa...whoa...whoa... with all due respect Dr. Willingham you have it exactly backwards.

I have taught high school algebra for more than 20 years and the kids who do poorly in algebra, do poorly because of lack of basic skills. The basic skill level of students has never been lower.

Any student who arrives at high school fluent in basic skills sails through algebra yet at least 50% of our incoming freshman either fail or do poorly. This can be directly correlated to their lack of basic skills, especially the inability to use basic algorithms.

You can’t learn how to manipulate in the abstract when you don’t understand how to do it with real numbers. I can guarantee any student who is close to grade level in basic math skills will be an above average student in Algebra.

Through testing we have verified that at least 50% of our students are entering high school with math skills below the 5th grade level. Many do not know their basic math facts and can't do the simplist long division problem. They can't do anything with fractions and can't find a common demoninator without a calculator. This is attibutable to reform math curricula that ignores foundational basic skills in favor of trying to teach students to become problem solvers.

The main problem these students have to solve is how to get through life being mathematically illiterate.

I find the same problem in my AP Calculus courses. It is not the the deep calculus concepts that baffle them, it is the inability to do calculus level fractions. Again, in order to do abstract math you must understand algorithms using real numbers. This simply isn't being emphasized in the early grades anymore.

Tom Loveless had it exactly right when he addressed the problems of trying to teach Algebra to kids who are far behind in basic skills:

"In eighth grade they are now expected to
learn, in a single year, the six years of math that they have not yet learned along with a full year of algebra. No one—no teacher, no researcher, no governor, no school board member, no philanthropist—knows how to teach in one year what has not been learned in six and then how to teach algebra on top of that. Algebra teachers are being asked to do the impossible. The greatest teachers in
the world do not know how to teach algebra
to students who do not know basic arithmetic."

Posted by: BobDeantalkdotcom | December 13, 2010 10:48 PM | Report abuse

Amen BobDeantalkdotcom! I have been baffled this year trying to teach algebra to kids without any mastery of or fluency in basic math facts. One student answered two math facts in a two minute time trial. He missed 8x0=?? So solving systems of equations . . . . . . not so much.

In his recent book, Dr. Willingham emphasizes the importance of fluency for ameliorating working memory limitations. He explains that practice helps with generalization as well building fluency. I believe the lack of proficiency in basic skills is a better explanation for lower skills at the high school level.

I think that background knowledge is a factor in lower scores in math among high school students. Part of this is related to reading comprehension of word problems. However the deeper the repertoire of background knowledge and skills, the better students will be able to solve new problems.

Posted by: bcollom | December 14, 2010 12:05 AM | Report abuse

"In the early grades U.S. kids are not very strong on conceptual understanding, but they are pretty good at learning math facts and algorithms." - I think not.

The ugly truth is that the direction of mathematics learning in US public schools is to embrace the "anti-math" approach to the discipline. The basics in math are no longer taught at the elementary school level (despite Dr. Willingham's beliefs to the contrary) - instead the body of "learned educrats," cognitive scientists, and psychology experts have brought us cognitively debilitating elementary mathematics curricula like "TERC Math Investigations" and "Every Day Math." Yet these same "experts" decry the decline in US student performance in math; amazing!

Perhaps rather than focusing on "Why Don't Students Like School" US public education might instead take a cue from those nations whose children are excelling in academic disciplines. One cannot move on to higher mathematics if not allowed to learn the basics, and the focus in elementary education has taken an ugly turn in the last 20 years courtesy of fuzzy math programs that deny children the opportunity to learn. Want to see achievement levels that top performing nations reach? Then put aside the psychology and cognitive science books and LEARN from what these countries are doing - teaching math basics to mastery starting at the elementary level. None of these countries is as vested in the psychology and cognitive science as the US - they simply teach math.

Dr. Willingham ought to visit the elementary schools in the northern Virginia area - in Prince William County VA for one he'd find educrats gushing over "tremendous conceptual understanding" but thousands of children unable to put pen and pencil to paper and solve basic arithmetic problems.

Children tend not to learn that which they are not taught and the volume of what is not taught these days - particularly in elementary math - is staggering. The sad truth is that US public schools have embraced a slow burn of dumbing down math with fuzzy curricula sponsored by cadres of well-intentioned educrats and we are reaping the fruits of these labors.

Posted by: 2plus2equals5 | December 14, 2010 8:39 AM | Report abuse

My point was not that US schools ought to scale back on instruction in computation or instruction in decoding. My point was not that US students are highly proficient in either of those skills. (And maybe kids math skills have gotten worse in the last decade, as some claim here. The NAEP scores paint a different picture.)
I was pointing out that US 10th graders rank worse than US 4th graders. Claiming that our kids have terrible basic skills doesn’t really account for the drop between 4th and 10th grade. If you think the TIMMS scores mean anything, they are doing better than their peers from many other countries at 4th grade. . . some of whom will outscore them by the 10th grade. So why are these other kids who were scoring worse than US kids now scoring better?
The conceptual side is separable from computation. A lot of kids can perform two digit addition and subtraction problems, but have only a fuzzy understanding of place value. In one study, a majority of sixth graders did not really understand that an equal sign signifies equality. I am suggesting that this matters, and that the dearth of conceptual knowledge becomes more and more troubling to performance as kids get to more and more advanced topics.
Singapore kids do so well not only because of their mastery of the basics, but because the model system teaches the conceptual side from the start.
The heart of flexibility and of good transfer in any skill is deep understanding. It’s also a whole lot easier to make content interesting if the learner understands it.
Because I pointed out a problem in US kids conceptual knowledge of math does not mean I am a fan of any curriculum that claims to teach concepts. I am aware that many school systems are using lousy curricula that claim to teach concepts.

Posted by: DanielTWillingham | December 14, 2010 10:14 AM | Report abuse

You mean by 3rd grade they are pretty good decoders. If not, you need to hustle to get the student up to par. Don't waste precious time on garbage curriculum (Reading Recovery). And don't let the student fall farther and farther behind. By 4th grade, they need to read to learn - ie social studies, science.

Posted by: harriska2 | December 14, 2010 2:20 PM | Report abuse

I fail to find how the author can state "A lot of kids can perform two digit addition and subtraction problems".

The problem is that they can't. Apparently, I'm not the only one that thinks that.

Everyday Math states in the teacher guide (or used to) that you don't need to teach math facts because it will come along over the years.

They don't. Many students (20%? 40%?) need to be explicitly taught. They are NOT.

Posted by: harriska2 | December 14, 2010 2:37 PM | Report abuse

In the reading domain, decoding remains an issue for older students.

Older students with reading difficulties benefit from interventions focused both at the word level and at the text level. Identifying need and intervening accordingly in the appropriate areas (e.g., vocabulary, word reading, comprehension strategies, and so on) is associated with improved outcomes for older students with reading difficulties.
Scammacca, N., Roberts, G., Vaughn. S., Edmonds, M., Wexler, J., Reutebuch, C. K., & Torgesen, J. K. (2007). Interventions for adolescent struggling readers: A meta-analysis with implications for practice. Portsmouth, NH: RMC Research Corporation, Center on Instruction.

Phonological decoding made a significant unique contribution to reading comprehension for the eighth/ninth-grade group, to spelling for the fourth/fifth- and eighth/ninth-grade groups, and to the decoding rate and accuracy measures for all three groups, with only three exceptions.
Nagy, W., Berninger, V.W., & Abbott, R.D. (2006). Contributions of morphology beyond phonology to literacy outcomes of upper elementary and middle-school students. Journal of Educational Psychology, 98(1), 134-147.

Even among experienced readers individual differences in comprehension of text reflect efficiency of phonological processing at the word level.
Shankweiler, D., Lundquist, E., Dreyer, L. G., & Dickinson, C. C. (1996). Reading and spelling difficulties in high school students: Causes and consequences. Reading and Writing: An Interdisciplinary Journal, 8, 267-294.

In this group of high school students who have been continuously and prospectively monitored since kindergarten, our findings indicate that difficulty with phonologic awareness represents the most robust characteristic of reading disability.
Shaywitz, S. E., Fletcher, J. M., Holahan, J. M., Shneider, A.E., Marchione, K., Stuebing, K. K., Francis, D. J., Pugh K.R., Shaywitz, B. (1999). Persistence of dyslexia: The Connecticut longitudinal study at adolescence. Pediatrics, 104, 1351-1359.

“Together, these findings provide evidence that dyslexic adults are not, as may have been assumed, unable to profit from remedial practice," wrote the researchers. "In fact, the same strategies that are effective in teaching children phonological awareness skills are helpful in adults. Further, they are accompanied by neural changes known to underlie reading remediation of developmental dyslexia in childhood combined with those previously observed during the rehabilitation of adults with acquired dyslexia [due to brain damage].”
Eden, G. F., Jones, K.M., Cappell, K., Gareau, L., Wood, F.B., Zeffiro, T.A., Dietz, N.A.E., Agnew, J.A. and Flowers, D.L. (2004). Neurophysiological recovery and compensation after remediation in adult developmental dyslexia, Neuron, 44, 411–422.

Posted by: kerryhempenstall | December 14, 2010 4:46 PM | Report abuse

American kids don't need to learn history, geography, science, music, art, etc. because they are learning to be leaders instead.

Posted by: harrumph1 | December 14, 2010 7:18 PM | Report abuse

This has been one of Daniel Willingham's most thoughtful posts, and he is making an excellent point explaining why our PISA math scores are bad, for 15 years old students, while our TIMSS scores are relatively good for 4th grade math students.

In essence, the TIMSS test does not capture and test the math skills that need to be built up by the 4th grade - in familiarity with formal expressions and in abstraction - that are necessary for success in later math classes.

So while our young math students may be proficient with calculations and may score ahead of their international peers in the small grades, they do not acquire the same conceptual proficiency and fall behind form their counterparts in later grades.

The curricula most widely used in our schools, Everyday Math and TERC Investigations, popular in wake of the NCTM 'reforms' of the 1990s, are not helping kids become proficient quickly with the standard arithmetic algorithms so they can move on quickly to more formal and more logical-style problems.

The Everyday Math student workbooks pre-write all the '+', '-', 'x', ':' operation signs and the '=' equality symbol in the solution of the exercises, in effect leaving just space for the students to 'fill' the numbers. This way students never really practice to write complete and formally correct mathematics. Using these curricula students don't get a chance to learn to express formal mathematical language, and that hurts in the more abstract later stages in high school.

Andrei Radulescu-Banu

Posted by: iubica2 | December 17, 2010 11:18 PM | Report abuse

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