Part II of the 2015 Brown Center Report on American Education

Over the next several years, policy analysts will evaluate the impact of the Common Core State Standards (CCSS) on U.S. education.  The task promises to be challenging.  The question most analysts will focus on is whether the CCSS is good or bad policy.  This section of the Brown Center Report (BCR) tackles a set of seemingly innocuous questions compared to the hot-button question of whether Common Core is wise or foolish.  The questions all have to do with when Common Core actually started, or more precisely, when the Common Core started having an effect on student learning.  And if it hasn’t yet had an effect, how will we know that CCSS has started to influence student achievement? 

The analysis below probes this issue empirically, hopefully persuading readers that deciding when a policy begins is elemental to evaluating its effects.  The question of a policy’s starting point is not always easy to answer.  Yet the answer has consequences.  You can’t figure out whether a policy worked or not unless you know when it began.^[i] 

The analysis uses surveys of state implementation to model different CCSS starting points for states and produces a second early report card on how CCSS is doing.  The first report card, focusing on math, was presented in last year’s BCR.  The current study updates state implementation ratings that were presented in that report and extends the analysis to achievement in reading.  The goal is not only to estimate CCSS’s early impact, but also to lay out a fair approach for establishing when the Common Core’s impact began—and to do it now before data are generated that either critics or supporters can use to bolster their arguments.  The experience of No Child Left Behind (NCLB) illustrates this necessity.

After the 2008 National Assessment of Educational Progress (NAEP) scores were released, former Secretary of Education Margaret Spellings claimed that the new scores showed “we are on the right track.”^[ii] She pointed out that NAEP gains in the previous decade, 1999-2009, were much larger than in prior decades.  Mark Schneider of the American Institutes of Research (and a former Commissioner of the National Center for Education Statistics [NCES]) reached a different conclusion. He compared NAEP gains from 1996-2003 to 2003-2009 and declared NCLB’s impact disappointing.  “The pre-NCLB gains were greater than the post-NCLB gains.”^[iii]  It is important to highlight that Schneider used the 2003 NAEP scores as the starting point for assessing NCLB.  A report from FairTest on the tenth anniversary of NCLB used the same demarcation for pre- and post-NCLB time frames.^[iv]  FairTest is an advocacy group critical of high stakes testing—and harshly critical of NCLB—but if the 2003 starting point for NAEP is accepted, its conclusion is indisputable, “NAEP score improvement slowed or stopped in both reading and math after NCLB was implemented.” 

Choosing 2003 as NCLB’s starting date is intuitively appealing.  The law was introduced, debated, and passed by Congress in 2001.  President Bush signed NCLB into law on January 8, 2002.  It takes time to implement any law.  The 2003 NAEP is arguably the first chance that the assessment had to register NCLB’s effects. 

Selecting 2003 is consequential, however.  Some of the largest gains in NAEP’s history were registered between 2000 and 2003.  Once 2003 is established as a starting point (or baseline), pre-2003 gains become “pre-NCLB.”  But what if the 2003 NAEP scores were influenced by NCLB? Experiments evaluating the effects of new drugs collect baseline data from subjects before treatment, not after the treatment has begun.   Similarly, evaluating the effects of public policies require that baseline data are not influenced by the policies under evaluation.   

Avoiding such problems is particularly difficult when state or local policies are adopted nationally.  The federal effort to establish a speed limit of 55 miles per hour in the 1970s is a good example.  Several states already had speed limits of 55 mph or lower prior to the federal law’s enactment.  Moreover, a few states lowered speed limits in anticipation of the federal limit while the bill was debated in Congress.  On the day President Nixon signed the bill into law—January 2, 1974—the Associated Press reported that only 29 states would be required to lower speed limits.  Evaluating the effects of the 1974 law with national data but neglecting to adjust for what states were already doing would obviously yield tainted baseline data.

There are comparable reasons for questioning 2003 as a good baseline for evaluating NCLB’s effects.  The key components of NCLB’s accountability provisions—testing students, publicizing the results, and holding schools accountable for results—were already in place in nearly half the states.  In some states they had been in place for several years.  The 1999 iteration of Quality Counts, Education Week’s annual report on state-level efforts to improve public education, entitled Rewarding Results, Punishing Failure, was devoted to state accountability systems and the assessments underpinning them. Testing and accountability are especially important because they have drawn fire from critics of NCLB, a law that wasn’t passed until years later.

The Congressional debate of NCLB legislation took all of 2001, allowing states to pass anticipatory policies.  Derek Neal and Diane Whitmore Schanzenbach reported that “with the passage of NCLB lurking on the horizon,” Illinois placed hundreds of schools on a watch list and declared that future state testing would be high stakes.^[v] In the summer and fall of 2002, with NCLB now the law of the land, state after state released lists of schools falling short of NCLB’s requirements.  Then the 2002-2003 school year began, during which the 2003 NAEP was administered.  Using 2003 as a NAEP baseline assumes that none of these activities—previous accountability systems, public lists of schools in need of improvement, anticipatory policy shifts—influenced achievement.  That is unlikely.^[vi]

Unlike NCLB, there was no “pre-CCSS” state version of Common Core.  States vary in how quickly and aggressively they have implemented CCSS.  For the BCR analyses, two indexes were constructed to model CCSS implementation.  They are based on surveys of state education agencies and named for the two years that the surveys were conducted.  The 2011 survey reported the number of programs (e.g., professional development, new materials) on which states reported spending federal funds to implement CCSS.  Strong implementers spent money on more activities.  The 2011 index was used to investigate eighth grade math achievement in the 2014 BCR.  A new implementation index was created for this year’s study of reading achievement.  The 2013 index is based on a survey asking states when they planned to complete full implementation of CCSS in classrooms.  Strong states aimed for full implementation by 2012-2013 or earlier.      

Fourth grade NAEP reading scores serve as the achievement measure.  Why fourth grade and not eighth?  Reading instruction is a key activity of elementary classrooms but by eighth grade has all but disappeared.  What remains of “reading” as an independent subject, which has typically morphed into the study of literature, is subsumed under the English-Language Arts curriculum, a catchall term that also includes writing, vocabulary, listening, and public speaking.  Most students in fourth grade are in self-contained classes; they receive instruction in all subjects from one teacher.  The impact of CCSS on reading instruction—the recommendation that non-fiction take a larger role in reading materials is a good example—will be concentrated in the activities of a single teacher in elementary schools. The burden for meeting CCSS’s press for non-fiction, on the other hand, is expected to be shared by all middle and high school teachers.^[vii] 

Table 2-1 displays NAEP gains using the 2011 implementation index.  The four year period between 2009 and 2013 is broken down into two parts: 2009-2011 and 2011-2013.  Nineteen states are categorized as “strong” implementers of CCSS on the 2011 index, and from 2009-2013, they outscored the four states that did not adopt CCSS by a little more than one scale score point (0.87 vs. -0.24 for a 1.11 difference).  The non-adopters are the logical control group for CCSS, but with only four states in that category—Alaska, Nebraska, Texas, and Virginia—it is sensitive to big changes in one or two states.  Alaska and Texas both experienced a decline in fourth grade reading scores from 2009-2013.

The 1.11 point advantage in reading gains for strong CCSS implementers is similar to the 1.27 point advantage reported last year for eighth grade math.  Both are small.  The reading difference in favor of CCSS is equal to approximately 0.03 standard deviations of the 2009 baseline reading score.  Also note that the differences were greater in 2009-2011 than in 2011-2013 and that the “medium” implementers performed as well as or better than the strong implementers over the entire four year period (gain of 0.99).

Table 2-2 displays calculations using the 2013 implementation index.  Twelve states are rated as strong CCSS implementers, seven fewer than on the 2011 index.^[viii]  Data for the non-adopters are the same as in the previous table.  In 2009-2013, the strong implementers gained 1.27 NAEP points compared to -0.24 among the non-adopters, a difference of 1.51 points.  The thirty-four states rated as medium implementers gained 0.82.  The strong implementers on this index are states that reported full implementation of CCSS-ELA by 2013.  Their larger gain in 2011-2013 (1.08 points) distinguishes them from the strong implementers in the previous table.  The overall advantage of 1.51 points over non-adopters represents about 0.04 standard deviations of the 2009 NAEP reading score, not a difference with real world significance.  Taken together, the 2011 and 2013 indexes estimate that NAEP reading gains from 2009-2013 were one to one and one-half scale score points larger in the strong CCSS implementation states compared to the states that did not adopt CCSS.

As noted above, the 2013 implementation index is based on when states scheduled full implementation of CCSS in classrooms.  Other than reading achievement, does the index seem to reflect changes in any other classroom variable believed to be related to CCSS implementation?  If the answer is “yes,” that would bolster confidence that the index is measuring changes related to CCSS implementation. 

Let’s examine the types of literature that students encounter during instruction.  Perhaps the most controversial recommendation in the CCSS-ELA standards is the call for teachers to shift the content of reading materials away from stories and other fictional forms of literature in favor of more non-fiction.  NAEP asks fourth grade teachers the extent to which they teach fiction and non-fiction over the course of the school year (see Figure 2-1). 

Historically, fiction dominates fourth grade reading instruction.  It still does.  The percentage of teachers reporting that they teach fiction to a “large extent” exceeded the percentage answering “large extent” for non-fiction by 23 points in 2009 and 25 points in 2011.  In 2013, the difference narrowed to only 15 percentage points, primarily because of non-fiction’s increased use.  Fiction still dominated in 2013, but not by as much as in 2009.

The differences reported in Table 2-3 are national indicators of fiction’s declining prominence in fourth grade reading instruction.  What about the states?  We know that they were involved to varying degrees with the implementation of Common Core from 2009-2013.  Is there evidence that fiction’s prominence was more likely to weaken in states most aggressively pursuing CCSS implementation? 

Table 2-3 displays the data tackling that question.  Fourth grade teachers in strong implementation states decisively favored the use of fiction over non-fiction in 2009 and 2011.  But the prominence of fiction in those states experienced a large decline in 2013 (-12.4 percentage points).  The decline for the entire four year period, 2009-2013, was larger in the strong implementation states (-10.8) than in the medium implementation (-7.5) or non-adoption states (-9.8).  

This section of the Brown Center Report analyzed NAEP data and two indexes of CCSS implementation, one based on data collected in 2011, the second from data collected in 2013.  NAEP scores for 2009-2013 were examined.  Fourth grade reading scores improved by 1.11 scale score points in states with strong implementation of CCSS compared to states that did not adopt CCSS.  A similar comparison in last year’s BCR found a 1.27 point difference on NAEP’s eighth grade math test, also in favor of states with strong implementation of CCSS.  These differences, although certainly encouraging to CCSS supporters, are quite small, amounting to (at most) 0.04 standard deviations (SD) on the NAEP scale.  A threshold of 0.20 SD—five times larger—is often invoked as the minimum size for a test score change to be regarded as noticeable.  The current study’s findings are also merely statistical associations and cannot be used to make causal claims.  Perhaps other factors are driving test score changes, unmeasured by NAEP or the other sources of data analyzed here. 

The analysis also found that fourth grade teachers in strong implementation states are more likely to be shifting reading instruction from fiction to non-fiction texts.  That trend should be monitored closely to see if it continues.  Other events to keep an eye on as the Common Core unfolds include the following:

1.  The 2015 NAEP scores, typically released in the late fall, will be important for the Common Core.  In most states, the first CCSS-aligned state tests will be given in the spring of 2015.  Based on the earlier experiences of Kentucky and New York, results are expected to be disappointing.  Common Core supporters can respond by explaining that assessments given for the first time often produce disappointing results.  They will also claim that the tests are more rigorous than previous state assessments.  But it will be difficult to explain stagnant or falling NAEP scores in an era when implementing CCSS commands so much attention.   

2.  Assessment will become an important implementation variable in 2015 and subsequent years.  For analysts, the strategy employed here, modeling different indicators based on information collected at different stages of implementation, should become even more useful.  Some states are planning to use Smarter Balanced Assessments, others are using the Partnership for Assessment of Readiness for College and Careers (PARCC), and still others are using their own homegrown tests.   To capture variation among the states on this important dimension of implementation, analysts will need to use indicators that are up-to-date.

3.  The politics of Common Core injects a dynamic element into implementation.  The status of implementation is constantly changing.  States may choose to suspend, to delay, or to abandon CCSS.  That will require analysts to regularly re-configure which states are considered “in” Common Core and which states are “out.”  To further complicate matters, states may be “in” some years and “out” in others.

A final word.  When the 2014 BCR was released, many CCSS supporters commented that it is too early to tell the effects of Common Core.  The point that states may need more time operating under CCSS to realize its full effects certainly has merit.  But that does not discount everything states have done so far—including professional development, purchasing new textbooks and other instructional materials, designing new assessments, buying and installing computer systems, and conducting hearings and public outreach—as part of implementing the standards.  Some states are in their fifth year of implementation.  It could be that states need more time, but innovations can also produce their biggest “pop” earlier in implementation rather than later.  Kentucky was one of the earliest states to adopt and implement CCSS.  That state’s NAEP fourth grade reading score declined in both 2009-2011 and 2011-2013.  The optimism of CCSS supporters is understandable, but a one and a half point NAEP gain might be as good as it gets for CCSS.

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This post continues a series begun in 2014 on implementing the Common Core State Standards (CCSS).  The first installment introduced an analytical scheme investigating CCSS implementation along four dimensions:  curriculum, instruction, assessment, and accountability.  Three posts focused on curriculum.  This post turns to instruction.  Although the impact of CCSS on how teachers teach is discussed, the post is also concerned with the inverse relationship, how decisions that teachers make about instruction shape the implementation of CCSS.

A couple of points before we get started.  The previous posts on curriculum led readers from the upper levels of the educational system—federal and state policies—down to curricular decisions made “in the trenches”—in districts, schools, and classrooms.  Standards emanate from the top of the system and are produced by politicians, policymakers, and experts.  Curricular decisions are shared across education’s systemic levels.  Instruction, on the other hand, is dominated by practitioners.  The daily decisions that teachers make about how to teach under CCSS—and not the idealizations of instruction embraced by upper-level authorities—will ultimately determine what “CCSS instruction” really means.

I ended the last post on CCSS by describing how curriculum and instruction can be so closely intertwined that the boundary between them is blurred.  Sometimes stating a precise curricular objective dictates, or at least constrains, the range of instructional strategies that teachers may consider.  That post focused on English-Language Arts.  The current post focuses on mathematics in the elementary grades and describes examples of how CCSS will shape math instruction.  As a former elementary school teacher, I offer my own personal opinion on these effects.

Certain aspects of the Common Core, when implemented, are likely to have a positive impact on the instruction of mathematics. For example, Common Core stresses that students recognize fractions as numbers on a number line.  The emphasis begins in third grade:

CCSS.MATH.CONTENT.3.NF.A.2
Understand a fraction as a number on the number line; represent fractions on a number line diagram.

CCSS.MATH.CONTENT.3.NF.A.2.A
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

CCSS.MATH.CONTENT.3.NF.A.2.B
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

When I first read this section of the Common Core standards, I stood up and cheered.  Berkeley mathematician Hung-Hsi Wu has been working with teachers for years to get them to understand the importance of using number lines in teaching fractions.^[1] American textbooks rely heavily on part-whole representations to introduce fractions.  Typically, students see pizzas and apples and other objects—typically other foods or money—that are divided up into equal parts.  Such models are limited.  They work okay with simple addition and subtraction.  Common denominators present a bit of a challenge, but ½ pizza can be shown to be also 2/4, a half dollar equal to two quarters, and so on. 

With multiplication and division, all the little tricks students learned with whole number arithmetic suddenly go haywire.  Students are accustomed to the fact that multiplying two whole numbers yields a product that is larger than either number being multiplied: 4 X 5 = 20 and 20 is larger than both 4 and 5.^[2]  How in the world can ¼ X 1/5 = 1/20, a number much smaller than either 1/4or 1/5?  The part-whole representation has convinced many students that fractions are not numbers.  Instead, they are seen as strange expressions comprising two numbers with a small horizontal bar separating them. 

I taught sixth grade but occasionally visited my colleagues’ classes in the lower grades.  I recall one exchange with second or third graders that went something like this:

“Give me a number between seven and nine.”  Giggles. 

“Eight!” they shouted. 

“Give me a number between two and three.”  Giggles.

“There isn’t one!” they shouted. 

“Really?” I’d ask and draw a number line.  After spending some time placing whole numbers on the number line, I’d observe,  “There’s a lot of space between two and three.  Is it just empty?” 

Silence.  Puzzled little faces.  Then a quiet voice.  “Two and a half?”

You have no idea how many children do not make the transition to understanding fractions as numbers and because of stumbling at this crucial stage, spend the rest of their careers as students of mathematics convinced that fractions are an impenetrable mystery.   And  that’s not true of just students.  California adopted a test for teachers in the 1980s, the California Basic Educational Skills Test (CBEST).  Beginning in 1982, even teachers already in the classroom had to pass it.   I made a nice after-school and summer income tutoring colleagues who didn’t know fractions from Fermat’s Last Theorem.  To be fair, primary teachers, teaching kindergarten or grades 1-2, would not teach fractions as part of their math curriculum and probably hadn’t worked with a fraction in decades.  So they are no different than non-literary types who think Hamlet is just a play about a young guy who can’t make up his mind, has a weird relationship with his mother, and winds up dying at the end.

Division is the most difficult operation to grasp for those arrested at the part-whole stage of understanding fractions.  A problem that Liping Ma posed to teachers is now legendary.^[3]

She asked small groups of American and Chinese elementary teachers to divide 1 ¾ by ½ and to create a word problem that illustrates the calculation.  All 72 Chinese teachers gave the correct answer and 65 developed an appropriate word problem.  Only nine of the 23 American teachers solved the problem correctly.  A single American teacher was able to devise an appropriate word problem.  Granted, the American sample was not selected to be representative of American teachers as a whole, but the stark findings of the exercise did not shock anyone who has worked closely with elementary teachers in the U.S.  They are often weak at math.  Many of the teachers in Ma’s study had vague ideas of an “invert and multiply” rule but lacked a conceptual understanding of why it worked.

A linguistic convention exacerbates the difficulty.  Students may cling to the mistaken notion that “dividing in half” means “dividing by one-half.”  It does not.  Dividing in half means dividing by two.  The number line can help clear up such confusion.  Consider a basic, whole-number division problem for which third graders will already know the answer:  8 divided by 2 equals 4.   It is evident that a segment 8 units in length (measured from 0 to 8) is divided by a segment 2 units in length (measured from 0 to 2) exactly 4 times.  Modeling 12 divided by 2 and other basic facts with 2 as a divisor will convince students that whole number division works quite well on a number line. 

Now consider the number ½ as a divisor.  It will become clear to students that 8 divided by ½ equals 16, and they can illustrate that fact on a number line by showing how a segment ½ units in length divides a segment 8 units in length exactly 16 times; it divides a segment 12 units in length 24 times; and so on.  Students will be relieved to discover that on a number line division with fractions works the same as division with whole numbers.

Now, let’s return to Liping Ma’s problem: 1 ¾ divided by ½.   This problem would not be presented in third grade, but it might be in fifth or sixth grades.  Students who have been working with fractions on a number line for two or three years will have little trouble solving it.  They will see that the problem simply asks them to divide a line segment of 1 3/4 units by a segment of ½ units.  The answer is 3 ½ .  Some students might estimate that the solution is between 3 and 4 because 1 ¾ lies between 1 ½ and 2, which on the number line are the points at which the ½ unit segment, laid end on end, falls exactly three and four times.  Other students will have learned about reciprocals and that multiplication and division are inverse operations.  They will immediately grasp that dividing by ½ is the same as multiplying by 2—and since 1 ¾ x 2 = 3 ½, that is the answer.  Creating a word problem involving string or rope or some other linearly measured object is also surely within their grasp.

I applaud the CCSS for introducing number lines and fractions in third grade.  I believe it will instill in children an important idea: fractions are numbers.  That foundational understanding will aid them as they work with more abstract representations of fractions in later grades.   Fractions are a monumental barrier for kids who struggle with math, so the significance of this contribution should not be underestimated.

I mentioned above that instruction and curriculum are often intertwined.  I began this series of posts by defining curriculum as the “stuff” of learning—the content of what is taught in school, especially as embodied in the materials used in instruction.  Instruction refers to the “how” of teaching—how teachers organize, present, and explain those materials.  It’s each teacher’s repertoire of instructional strategies and techniques that differentiates one teacher from another even as they teach the same content.  Choosing to use a number line to teach fractions is obviously an instructional decision, but it also involves curriculum.  The number line is mathematical content, not just a teaching tool.

Guiding third grade teachers towards using a number line does not guarantee effective instruction.  In fact, it is reasonable to expect variation in how teachers will implement the CCSS standards listed above.  A small body of research exists to guide practice. One of the best resources for teachers to consult is a practice guide published by the What Works Clearinghouse: Developing Effective Fractions Instruction for Kindergarten Through Eighth Grade (see full disclosure below).^[4]  The guide recommends the use of number lines as its second recommendation, but it also states that the evidence supporting the effectiveness of number lines in teaching fractions is inferred from studies involving whole numbers and decimals.  We need much more research on how and when number lines should be used in teaching fractions.

Professor Wu states the following, “The shift of emphasis from models of a fraction in the initial stage to an almost exclusive model of a fraction as a point on the number line can be done gradually and gracefully beginning somewhere in grade four. This shift is implicit in the Common Core Standards.”^[5]  I agree, but the shift is also subtle.  CCSS standards include the use of other representations—fraction strips, fraction bars, rectangles (which are excellent for showing multiplication of two fractions) and other graphical means of modeling fractions.  Some teachers will manage the shift to number lines adroitly—and others will not.  As a consequence, the quality of implementation will vary from classroom to classroom based on the instructional decisions that teachers make.  

The current post has focused on what I believe to be a positive aspect of CCSS based on the implementation of the standards through instruction.  Future posts in the series—covering the “bad” and the “ugly”—will describe aspects of instruction on which I am less optimistic.

This is part two of my analysis of instruction and Common Core’s implementation.  I dubbed the three-part examination of instruction “The Good, The Bad, and the Ugly.”  Having discussed “the “good” in part one, I now turn to “the bad.”  One particular aspect of the Common Core math standards—the treatment of standard algorithms in whole number arithmetic—will lead some teachers to waste instructional time.

In 1963, psychologist John B. Carroll published a short essay, “A Model of School Learning” in Teachers College Record.  Carroll proposed a parsimonious model of learning that expressed the degree of learning (or what today is commonly called achievement) as a function of the ratio of time spent on learning to the time needed to learn.     

The numerator, time spent learning, has also been given the term opportunity to learn.  The denominator, time needed to learn, is synonymous with student aptitude.  By expressing aptitude as time needed to learn, Carroll refreshingly broke through his era’s debate about the origins of intelligence (nature vs. nurture) and the vocabulary that labels students as having more or less intelligence. He also spoke directly to a primary challenge of teaching: how to effectively produce learning in classrooms populated by students needing vastly different amounts of time to learn the exact same content.^[i] 

The source of that variation is largely irrelevant to the constraints placed on instructional decisions.  Teachers obviously have limited control over the denominator of the ratio (they must take kids as they are) and less than one might think over the numerator.  Teachers allot time to instruction only after educational authorities have decided the number of hours in the school day, the number of days in the school year, the number of minutes in class periods in middle and high schools, and the amount of time set aside for lunch, recess, passing periods, various pull-out programs, pep rallies, and the like.  There are also announcements over the PA system, stray dogs that may wander into the classroom, and other unscheduled encroachments on instructional time.

The model has had a profound influence on educational thought.  As of July 5, 2015, Google Scholar reported 2,931 citations of Carroll’s article.  Benjamin Bloom’s “mastery learning” was deeply influenced by Carroll.  It is predicated on the idea that optimal learning occurs when time spent on learning—rather than content—is allowed to vary, providing to each student the individual amount of time he or she needs to learn a common curriculum.  This is often referred to as “students working at their own pace,” and progress is measured by mastery of content rather than seat time. David C. Berliner’s 1990 discussion of time includes an analysis of mediating variables in the numerator of Carroll’s model, including the amount of time students are willing to spend on learning.  Carroll called this persistence, and Berliner links the construct to student engagement and time on task—topics of keen interest to researchers today.  Berliner notes that although both are typically described in terms of motivation, they can be measured empirically in increments of time.     

Most applications of Carroll’s model have been interested in what happens when insufficient time is provided for learning—in other words, when the numerator of the ratio is significantly less than the denominator.  When that happens, students don’t have an adequate opportunity to learn.  They need more time. 

As applied to Common Core and instruction, one should also be aware of problems that arise from the inefficient distribution of time.  Time is a limited resource that teachers deploy in the production of learning.  Below I discuss instances when the CCSS-M may lead to the numerator in Carroll’s model being significantly larger than the denominator—when teachers spend more time teaching a concept or skill than is necessary.  Because time is limited and fixed, wasted time on one topic will shorten the amount of time available to teach other topics.  Excessive instructional time may also negatively affect student engagement.  Students who have fully learned content that continues to be taught may become bored; they must endure instruction that they do not need.

Jason Zimba, one of the lead authors of the Common Core Math standards, and Barry Garelick, a critic of the standards, had a recent, interesting exchange about when standard algorithms are called for in the CCSS-M.  A standard algorithm is a series of steps designed to compute accurately and quickly.  In the U.S., students are typically taught the standard algorithms of addition, subtraction, multiplication, and division with whole numbers.  Most readers of this post will recognize the standard algorithm for addition.  It involves lining up two or more multi-digit numbers according to place-value, with one number written over the other, and adding the columns from right to left with “carrying” (or regrouping) as needed.

The standard algorithm is the only algorithm required for students to learn, although others are mentioned beginning with the first grade standards.  Curiously, though, CCSS-M doesn’t require students to know the standard algorithms for addition and subtraction until fourth grade.  This opens the door for a lot of wasted time.  Garelick questioned the wisdom of teaching several alternative strategies for addition.  He asked whether, under the Common Core, only the standard algorithm could be taught—or at least, could it be taught first. As he explains:

Delaying teaching of the standard algorithm until fourth grade and relying on place value “strategies” and drawings to add numbers is thought to provide students with the conceptual understanding of adding and subtracting multi-digit numbers. What happens, instead, is that the means to help learn, explain or memorize the procedure become a procedure unto itself and students are required to use inefficient cumbersome methods for two years. This is done in the belief that the alternative approaches confer understanding, so are superior to the standard algorithm. To teach the standard algorithm first would in reformers’ minds be rote learning. Reformers believe that by having students using strategies in lieu of the standard algorithm, students are still learning “skills” (albeit inefficient and confusing ones), and these skills support understanding of the standard algorithm. Students are left with a panoply of methods (praised as a good thing because students should have more than one way to solve problems), that confuse more than enlighten. 

Zimba responded that the standard algorithm could, indeed, be the only method taught because it meets a crucial test: reinforcing knowledge of place value and the properties of operations.  He goes on to say that other algorithms also may be taught that are consistent with the standards, but that the decision to do so is left in the hands of local educators and curriculum designers:

In short, the Common Core requires the standard algorithm; additional algorithms aren’t named, and they aren’t required…Standards can’t settle every disagreement—nor should they. As this discussion of just a single slice of the math curriculum illustrates, teachers and curriculum authors following the standards still may, and still must, make an enormous range of decisions.

Zimba defends delaying mastery of the standard algorithm until fourth grade, referring to it as a “culminating” standard that he would, if he were teaching, introduce in earlier grades.  Zimba illustrates the curricular progression he would employ in a table, showing that he would introduce the standard algorithm for addition late in first grade (with two-digit addends) and then extend the complexity of its use and provide practice towards fluency until reaching the culminating standard in fourth grade. Zimba would introduce the subtraction algorithm in second grade and similarly ramp up its complexity until fourth grade.

It is important to note that in CCSS-M the word “algorithm” appears for the first time (in plural form) in the third grade standards:

3.NBT.2  Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

The term “strategies and algorithms” is curious.  Zimba explains, “It is true that the word ‘algorithms’ here is plural, but that could be read as simply leaving more choice in the hands of the teacher about which algorithm(s) to teach—not as a requirement for each student to learn two or more general algorithms for each operation!” 

I have described before the “dog whistles” embedded in the Common Core, signals to educational progressives—in this case, math reformers—that  despite these being standards, the CCSS-M will allow them great latitude.  Using the plural “algorithms” in this third grade standard and not specifying the standard algorithm until fourth grade is a perfect example of such a dog whistle.

It appears that the Common Core authors wanted to reach a political compromise on standard algorithms. 

Standard algorithms were a key point of contention in the “Math Wars” of the 1990s.   The 1997 California Framework for Mathematics required that students know the standard algorithms for all four operations—addition, subtraction, multiplication, and division—by the end of fourth grade.^[ii]  The 2000 Massachusetts Mathematics Curriculum Framework called for learning the standard algorithms for addition and subtraction by the end of second grade and for multiplication and division by the end of fourth grade.  These two frameworks were heavily influenced by mathematicians (from Stanford in California and Harvard in Massachusetts) and quickly became favorites of math traditionalists.  In both states’ frameworks, the standard algorithm requirements were in direct opposition to the reform-oriented frameworks that preceded them—in which standard algorithms were barely mentioned and alternative algorithms or “strategies” were encouraged. 

Now that the CCSS-M has replaced these two frameworks, the requirement for knowing the standard algorithms in California and Massachusetts slips from third or fourth grade all the way to sixth grade.  That’s what reformers get in the compromise.  They are given a green light to continue teaching alternative algorithms, as long as the algorithms are consistent with teaching place value and properties of arithmetic.  But the standard algorithm is the only one students are required to learn.  And that exclusivity is intended to please the traditionalists.

I agree with Garelick that the compromise leads to problems.  In a 2013 Chalkboard post, I described a first grade math program in which parents were explicitly requested not to teach the standard algorithm for addition when helping their children at home.  The students were being taught how to represent addition with drawings that clustered objects into groups of ten.  The exercises were both time consuming and tedious.  When the parents met with the school principal to discuss the matter, the principal told them that the math program was following the Common Core by promoting deeper learning.  The parents withdrew their child from the school and enrolled him in private school.

The value of standard algorithms is that they are efficient and packed with mathematics.  Once students have mastered single-digit operations and the meaning of place value, the standard algorithms reveal to students that they can take procedures that they already know work well with one- and two-digit numbers, and by applying them over and over again, solve problems with large numbers.  Traditionalists and reformers have different goals.  Reformers believe exposure to several algorithms encourages flexible thinking and the ability to draw on multiple strategies for solving problems.  Traditionalists believe that a bigger problem than students learning too few algorithms is that too few students learn even one algorithm.

I have been a critic of the math reform movement since I taught in the 1980s.  But some of their complaints have merit.  All too often, instruction on standard algorithms has left out meaning.  As Karen C. Fuson and Sybilla Beckmann point out, “an unfortunate dichotomy” emerged in math instruction: teachers taught “strategies” that implied understanding and “algorithms” that implied procedural steps that were to be memorized.  Michael Battista’s research has provided many instances of students clinging to algorithms without understanding.  He gives an example of a student who has not quite mastered the standard algorithm for addition and makes numerous errors on a worksheet.  On one item, for example, the student forgets to carry and calculates that 19 + 6 = 15.  In a post-worksheet interview, the student counts 6 units from 19 and arrives at 25.  Despite the obvious discrepancy—(25 is not 15, the student agrees)—he declares that his answers on the worksheet must be correct because the algorithm he used “always works.”^[iii] 

Math reformers rightfully argue that blind faith in procedure has no place in a thinking mathematical classroom. Who can disagree with that?  Students should be able to evaluate the validity of answers, regardless of the procedures used, and propose alternative solutions.  Standard algorithms are tools to help them do that, but students must be able to apply them, not in a robotic way, but with understanding.

Let’s return to Carroll’s model of time and learning.  I conclude by making two points—one about curriculum and instruction, the other about implementation.

In the study of numbers, a coherent K-12 math curriculum, similar to that of the previous California and Massachusetts frameworks, can be sketched in a few short sentences.  Addition with whole numbers (including the standard algorithm) is taught in first grade, subtraction in second grade, multiplication in third grade, and division in fourth grade.  Thus, the study of whole number arithmetic is completed by the end of fourth grade.  Grades five through seven focus on rational numbers (fractions, decimals, percentages), and grades eight through twelve study advanced mathematics.  Proficiency is sought along three dimensions:  1) fluency with calculations, 2) conceptual understanding, 3) ability to solve problems.

Placing the CCSS-M standard for knowing the standard algorithms of addition and subtraction in fourth grade delays this progression by two years.  Placing the standard for the division algorithm in sixth grade continues the two-year delay.   For many fourth graders, time spent working on addition and subtraction will be wasted time.  They already have a firm understanding of addition and subtraction.  The same thing for many sixth graders—time devoted to the division algorithm will be wasted time that should be devoted to the study of rational numbers.  The numerator in Carroll’s instructional time model will be greater than the denominator, indicating the inefficient allocation of time to instruction.

As Jason Zimba points out, not everyone agrees on when the standard algorithms should be taught, the alternative algorithms that should be taught, the manner in which any algorithm should be taught, or the amount of instructional time that should be spent on computational procedures.  Such decisions are made by local educators.  Variation in these decisions will introduce variation in the implementation of the math standards.  It is true that standards, any standards, cannot control implementation, especially the twists and turns in how they are interpreted by educators and brought to life in classroom instruction.  But in this case, the standards themselves are responsible for the myriad approaches, many unproductive, that we are sure to see as schools teach various algorithms under the Common Core.

The release of 2015 NAEP scores showed national achievement stalling out or falling in reading and mathematics.  The poor results triggered speculation about the effect of Common Core State Standards (CCSS), the controversial set of standards adopted by more than 40 states since 2010.  Critics of Common Core tended to blame the standards for the disappointing scores.  Its defenders said it was too early to assess CCSS’s impact and that implementation would take many years to unfold. William J. Bushaw, executive director of the National assessment Governing Board, cited “curricular uncertainty” as the culprit.  Secretary of Education Arne Duncan argued that new standards typically experience an “implementation dip” in the early days of teachers actually trying to implement them in classrooms.

In the rush to argue whether CCSS has positively or negatively affected American education, these speculations are vague as to how the standards boosted or depressed learning.  They don’t provide a description of the mechanisms, the connective tissue, linking standards to learning.  Bushaw and Duncan come the closest, arguing that the newness of CCSS has created curriculum confusion, but the explanation falls flat for a couple of reasons.  Curriculum in the three states that adopted the standards, rescinded them, then adopted something else should be extremely confused.  But the 2013-2015 NAEP changes for Indiana, Oklahoma, and South Carolina were a little bit better than the national figures, not worse.[i]  In addition, surveys of math teachers conducted in the first year or two after the standards were adopted found that:  a) most teachers liked them, and b) most teachers said they were already teaching in a manner consistent with CCSS.[ii]  They didn’t mention uncertainty.  Recent polls, however, show those positive sentiments eroding. Mr. Bushaw might be mistaking disenchantment for uncertainty.[iii] 

For teachers, the novelty of CCSS should be dissipating.  Common Core’s advocates placed great faith in professional development to implement the standards.  Well, there’s been a lot of it.  Over the past few years, millions of teacher-hours have been devoted to CCSS training.  Whether all that activity had a lasting impact is questionable.  Randomized control trials have been conducted of two large-scale professional development programs.  Interestingly, although they pre-date CCSS, both programs attempted to promote the kind of “instructional shifts” championed by CCSS advocates. The studies found that if teacher behaviors change from such training—and that’s not a certainty—the changes fade after a year or two.  Indeed, that’s a pattern evident in many studies of educational change: a pop at the beginning, followed by fade out.  

My own work analyzing NAEP scores in 2011 and 2013 led me to conclude that the early implementation of CCSS was producing small, positive changes in NAEP.[iv]  I warned that those gains “may be as good as it gets” for CCSS.[v]  Advocates of the standards hope that CCSS will eventually produce long term positive effects as educators learn how to use them.  That’s a reasonable hypothesis.  But it should now be apparent that a counter-hypothesis has equal standing: any positive effect of adopting Common Core may have already occurred.  To be precise, the proposition is this: any effects from adopting new standards and attempting to change curriculum and instruction to conform to those standards occur early and are small in magnitude.   Policymakers still have a couple of arrows left in the implementation quiver, accountability being the most powerful.  Accountability systems have essentially been put on hold as NCLB sputtered to an end and new CCSS tests appeared on the scene.  So the CCSS story isn’t over.  Both hypotheses remain plausible. 

Reading Instruction in 4^th and 8^th Grades

Back to the mechanisms, the connective tissue binding standards to classrooms.  The 2015 Brown Center Report introduced one possible classroom effect that is showing up in NAEP data: the relative emphasis teachers place on fiction and nonfiction in reading instruction.  The ink was still drying on new Common Core textbooks when a heated debate broke out about CCSS’s recommendation that informational reading should receive greater attention in classrooms.[vi] 

Fiction has long dominated reading instruction.  That dominance appears to be waning.

After 2011, something seems to have happened.  I am more persuaded that Common Core influenced the recent shift towards nonfiction than I am that Common Core has significantly affected student achievement—for either good or ill.   But causality is difficult to confirm or to reject with NAEP data, and trustworthy efforts to do so require a more sophisticated analysis than presented here.

Four lessons from previous education reforms

Nevertheless, the figures above reinforce important lessons that have been learned from previous top-down reforms.  Let’s conclude with four:

1.  There seems to be evidence that CCSS is having an impact on the content of reading instruction, moving from the dominance of fiction over nonfiction to near parity in emphasis.  Unfortunately, as Mark Bauerlein and Sandra Stotsky have pointed out, there is scant evidence that such a shift improves children’s reading.[vii]

2.  Reading more nonfiction does not necessarily mean that students will be reading higher quality texts, even if the materials are aligned with CCSS.   The Core Knowledge Foundation and the Partnership for 21^st Century Learning, both supporters of Common Core, have very different ideas on the texts schools should use with the CCSS.[viii] The two organizations advocate for curricula having almost nothing in common.

3.  When it comes to the study of implementing education reforms, analysts tend to focus on the formal channels of implementation and the standard tools of public administration—for example, intergovernmental hand-offs (federal to state to district to school), alignment of curriculum, assessment and other components of the reform, professional development, getting incentives right, and accountability mechanisms.  Analysts often ignore informal channels, and some of those avenues funnel directly into schools and classrooms.[ix]  Politics and the media are often overlooked.  Principals and teachers are aware of the politics swirling around K-12 school reform.  Many educators undoubtedly formed their own opinions on CCSS and the fiction vs. nonfiction debate before the standard managerial efforts touched them.

4.  Local educators whose jobs are related to curriculum almost certainly have ideas about what constitutes good curriculum.  It’s part of the profession.  Major top-down reforms such as CCSS provide local proponents with political cover to pursue curricular and instructional changes that may be politically unpopular in the local jurisdiction.  Anyone who believes nonfiction should have a more prominent role in the K-12 curriculum was handed a lever for promoting his or her beliefs by CCSS. I’ve previously called these the “dog whistles” of top-down curriculum reform, subtle signals that give local advocates license to promote unpopular positions on controversial issues.

Event Information

The Common Core State Standards have been adopted as the reading and math standards in more than forty states, but are the frontline implementers—teachers and principals—enacting them? As part of the 2016 Brown Center Report on American Education, Tom Loveless examines the degree to which CCSS recommendations have penetrated schools and classrooms. He specifically looks at the impact the standards have had on the emphasis of non-fiction vs. fiction texts in reading, and on enrollment in advanced courses in mathematics.

On March 28, the Brown Center hosted an online discussion of Loveless's findings, moderated by the Urban Institute's Matthew Chingos.  In addition to the Common Core, Loveless and Chingos also discussed the other sections of the three-part Brown Center Report, including a study of the relationship between ability group tracking in eighth grade and AP performance in high school.

Watch the archived video below.

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Check out Reading and Math in the Common Core Era on Spreecast.

The 2016 Brown Center Report (BCR), which was published last week, presented a study of Common Core State Standards (CCSS).   In this post, I’d like to elaborate on a topic touched upon but deserving further attention: what to expect in Common Core’s immediate political future. I discuss four key challenges that CCSS will face between now and the end of the year.

Let’s set the stage for the discussion.  The BCR study produced two major findings.  First, several changes that CCSS promotes in curriculum and instruction appear to be taking place at the school level.  Second, states that adopted CCSS and have been implementing the standards have registered about the same gains and losses on NAEP as states that either adopted and rescinded CCSS or never adopted CCSS in the first place.  These are merely associations and cannot be interpreted as saying anything about CCSS’s causal impact.  Politically, that doesn’t really matter. The big story is that NAEP scores have been flat for six years, an unprecedented stagnation in national achievement that states have experienced regardless of their stance on CCSS.  Yes, it’s unfair, but CCSS is paying a political price for those disappointing NAEP scores.  No clear NAEP differences have emerged between CCSS adopters and non-adopters to reverse that political dynamic.

"Yes, it’s unfair, but CCSS is paying a political price for those disappointing NAEP scores. No clear NAEP differences have emerged between CCSS adopters and non-adopters to reverse that political dynamic."

TIMSS and PISA scores in November-December

NAEP has two separate test programs.  The scores released in 2015 were for the main NAEP, which began in 1990.  The long term trend (LTT) NAEP, a different test that was first given in 1969, has not been administered since 2012.  It was scheduled to be given in 2016, but was cancelled due to budgetary constraints.  It was next scheduled for 2020, but last fall officials cancelled that round of testing as well, meaning that the LTT NAEP won’t be given again until 2024.  

With the LTT NAEP on hold, only two international assessments will soon offer estimates of U.S. achievement that, like the two NAEP tests, are based on scientific sampling:  PISA and TIMSS.  Both tests were administered in 2015, and the new scores will be released around the Thanksgiving-Christmas period of 2016.  If PISA and TIMSS confirm the stagnant trend in U.S. achievement, expect CCSS to take another political hit.  America’s performance on international tests engenders a lot of hand wringing anyway, so the reaction to disappointing PISA or TIMSS scores may be even more pronounced than what the disappointing NAEP scores generated.

Is teacher support still declining?

Watch Education Next’s survey on Common Core (usually released in August/September) and pay close attention to teacher support for CCSS.  The trend line has been heading steadily south. In 2013, 76 percent of teachers said they supported CCSS and only 12 percent were opposed.  In 2014, teacher support fell to 43 percent and opposition grew to 37 percent.  In 2015, opponents outnumbered supporters for the first time, 50 percent to 37 percent.  Further erosion of teacher support will indicate that Common Core’s implementation is in trouble at the ground level.  Don’t forget: teachers are the final implementers of standards.

An effort by Common Core supporters to change NAEP

The 2015 NAEP math scores were disappointing.  Watch for an attempt by Common Core supporters to change the NAEP math tests. Michael Cohen, President of Achieve, a prominent pro-CCSS organization, released a statement about the 2015 NAEP scores that included the following: "The National Assessment Governing Board, which oversees NAEP, should carefully review its frameworks and assessments in order to ensure that NAEP is in step with the leadership of the states. It appears that there is a mismatch between NAEP and all states' math standards, no matter if they are common standards or not.” 

Reviewing and potentially revising the NAEP math framework is long overdue.  The last adoption was in 2004.  The argument for changing NAEP to place greater emphasis on number and operations, revisions that would bring NAEP into closer alignment with Common Core, also has merit.  I have a longstanding position on the NAEP math framework. In 2001, I urged the National Assessment Governing Board (NAGB) to reject the draft 2004 framework because it was weak on numbers and operations—and especially weak on assessing student proficiency with whole numbers, fractions, decimals, and percentages.  

Common Core’s math standards are right in line with my 2001 complaint.  Despite my sympathy for Common Core advocates’ position, a change in NAEP should not be made because of Common Core.  In that 2001 testimony, I urged NAGB to end the marriage of NAEP with the 1989 standards of the National Council of Teachers of Mathematics, the math reform document that had guided the main NAEP since its inception.  Reform movements come and go, I argued.  NAGB’s job is to keep NAEP rigorously neutral.  The assessment’s integrity depends upon it.  NAEP was originally intended to function as a measuring stick, not as a PR device for one reform or another.  If NAEP is changed it must be done very carefully and should be rooted in the mathematics children must learn.  The political consequences of it appearing that powerful groups in Washington, DC are changing “The Nation’s Report Card” in order for Common Core to look better will hurt both Common Core and NAEP.

Will Opt Out grow?

Watch the Opt Out movement.  In 2015, several organized groups of parents refused to allow their children to take Common Core tests.  In New York state alone, about 60,000 opted out in 2014, skyrocketing to 200,000 in 2015.  Common Core testing for 2016 begins now and goes through May.  It will be important to see whether Opt Out can expand to other states, grow in numbers, and branch out beyond middle- and upper-income neighborhoods.

Conclusion

Common Core is now several years into implementation.  Supporters have had a difficult time persuading skeptics that any positive results have occurred. The best evidence has been mixed on that question.  CCSS advocates say it is too early to tell, and we’ll just have to wait to see the benefits.  That defense won’t work much longer.  Time is running out.  The political challenges that Common Core faces the remainder of this year may determine whether it survives.

The Supreme Court today decided that Congress meant what it said when it enacted the Affordable Care Act (ACA). The ACA requires people in all 50 states to carry health insurance and provided tax credits to help them afford it. To have offered such credits only in the dozen states that set up their own exchanges would have been cruel and unsustainable because premiums for many people would have been unaffordable.

But the law said that such credits could be paid in exchanges ‘established by a state,’ which led some to claim that the credits could not be paid to people enrolled by the federally operated exchange. In his opinion, Chief Justice Roberts euphemistically calls that wording ‘inartful.’ Six Supreme Court justices decided that, read in its entirety, the law provides tax credits in every state, whether the state manages the exchange itself or lets the federal government do it for them.

That decision is unsurprising. More surprising is that the Court agreed to hear the case. When it did so, cases on the same issue were making their ways through four federal circuits. In only one of the four circuits was there a standing decision, and it found that tax credits were available everywhere. It is customary for the Supreme Court to wait to take a case until action in lower courts is complete or two circuits have disagreed. In this situation, the justices, eyeing the electoral calendar, may have preferred to hear the case sooner rather than later to avoid confronting it in the middle of a presidential election.

Whatever the Court’s motives for taking the case, their willingness to hear the case caused supporters of the Affordable Care Act enormous unease. Were the more conservative members of the Court poised to accept an interpretation of the law that ACA supporters found ridiculous but that inartful legislative drafting gave the gloss of plausibility? Judicial demeanor at oral argument was not comforting. A 5-4 decision disallowing payment of tax credits seemed ominously plausible.

The Court’s 6-3 decision ended those fears. The existential threat to health reform from litigation is over. But efforts to undo the Affordable Care Act are not at an end. They will continue in the political sphere. And that is where they should be. ACA opponents know that there is little chance for them to roll back the Affordable Care Act in any fundamental way as long as a Democrat is in the White House. To dismantle the law, they must win the presidency in 2016.

But winning the presidency will not be enough. It would be mid 2017 before ACA opponents could draft and enact legislation to curb the Affordable Care Act and months more before it could take effect. To borrow a metaphor from the military, even if those opposed to the ACA win the presidency, they will have to deal with ‘facts on the ground.’