**Editor’s Note**: Another installation in a series of posts evaluating the question: Has Indiana departed from the Common Core State Standards and its attempt to nationalize education in America?

Having been the first state to leave the Common Core,

…**Editor’s Note**: Another installation in a series of posts evaluating the question: Has Indiana departed from the Common Core State Standards and its attempt to nationalize education in America?

Having been the first state to leave the Common Core, the final draft of Indiana’s new K-12 content standards has been published and it will be brought to the State Board of Education on April 28 – ten days from now – for the final vote. Some reviews of this draft have been already published (e.g., here, here and here) but they focused mostly on the English and Language Arts (ELA) piece. I will focus on its mathematics and I will start with some general observations.

The drafting was done under a serious time pressure. There were only 12 weeks allocated for the standards-writing process that typically takes many months or even years. The writing panels should be commended for significant improvement of its early drafts, yet – as we shall see shortly — the final result is far from satisfying for Indiana, whose prior (pre Common Core) standards were highly praised as the best in the nation.

Previous drafts, particularly in K-8, were almost a carbon copy of the Common Core (CC), with a bunch of Indiana’s own addition on top of them. That created a bloated draft with numerous duplications and excessive number of standards. The final draft has most – but not all – of those duplications removed, and it seems to have a reasonable number of standards, between 21 and 36 per grade. Yet much of the draft is still made of Common Core standards even if their original language has been edited slightly to give the impression of change, and the excessive number of standards was hidden by sticking disparate standards together rather than by removing secondary content from the February bloated draft.

In terms of its language clarity, the final draft is somewhat improved yet still sloppy. It contains standards that are written in an obscure and difficult to comprehend language; standards that are so imprecise that they can be interpreted to mean anything; and standards that contain plain mathematical errors.

When it comes to rigor of expectations, the draft accelerated a couple of early arithmetic skills, yet when it comes to elementary school capstone standards such as fluency with multiplication and division of integers the draft ends up aligned with Common Core’s mediocre expectations and below Indiana’s 2006 standards. Similarly, Algebra 2 content present in Indiana’s 2006 standards has been now excised from Algebra 2 and moved to advanced courses like trigonometry or pre-calculus.

Finally, when it comes to pedagogy embedded in the standards, the situation has not improved much from the early drafts. The preamble to the final draft declares that (original emphasis):

While the standards demonstrate what Hoosier students should know and be able to do in order to be prepared for college and careers, the standards are not instructional practices. The educators and subject matter experts that worked on the standards have taken care to ensure that the standards are free from embedded pedagogy and instructional practices.The standards do not define how teachers should teach.

Unfortunately, this statement is simply untrue. The mathematics standards are infused with pedagogy and dictate – sometimes in painful detail, sometimes with experimental pedagogy – how to teach specific content, rather than leave the pedagogy to schools and classroom teachers.

Specific examples of each of the above mentioned problems are discussed below.

**Infusion with Common Core Pedagogy**

CC unreasonably and without any justification introduced counting to 100 in kindergarten, and 120 in the first grade. Prior to CC, almost universally, kindergarten counting expectation was 20, and counting to 100 was expected in the first grade. The Indiana draft adopts this baseless – and somewhat meaningless — CC characteristic, presumably as a mark of fealty.

Here is the CC standard 1.OA.6 that I previously used as an example of CC pedagogy:

1.OA.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

And here is its final Indiana draft equivalent:

1.CA.1: Demonstrate fluency with addition facts and the corresponding subtraction facts within 20. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). Understand the role of 0 in addition and subtraction.

Let us look carefully at what has happened here. First, Indiana slightly changed the language of the first sentence expecting fluency to 20 whereas CC expected it only to 10 (and less than fluency to 20). Nice but quite meaningless, as in the second grade both CC and the final draft already expect identical ability to fluently add and subtract within 100. The second part is identical, where CC pedagogy is carried intact into the final draft. Finally, the last sentence about the role of zero is carried over from the 2006 Indiana standards, nicely illustrating how the final draft achieved its seemingly-reasonable number of standards – the draft simply lumps distinct standards together to make them into one.

Here is the grade six ratio standard infused with pedagogy and copying Common Core prescriptiveness:

CC 6.RP.3:Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Draft 6.NS.10:Use reasoning involving rates and ratios to model real-world and other mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).

**Lowered Rigor**

Fluency with arithmetic of integers and fractions is frequently – and correctly – identified as the focus of elementary grades. Like CC, Indiana’s final draft expects fluency with addition and subtraction of integers by grade four, multiplication by grade five, and division by grade six. In contrast, Singapore is done with addition and subtraction by grade three and with multiplication and division by grade four. The 2006 Indiana standards expected both multiplication and division of integers to be completed by grade five, a year ahead of CC. Here is a small example of how the draft’s rigor and pedagogy compare internationally (grade three):

Draft 3.C.4:Interpret whole-number quotients of whole numbers (e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each).

Singapore, gr. 3:multiplication and division of numbers up to 3 digits by 1 digit (with remainder)

When it comes to fractions, the final draft defers fluency with the four arithmetic operations on fractions to grade six like Common Core. In contrast, the 2006 Indiana standards (and Singapore) expect it a year earlier, in grade five.

Studying circles is postponed to grade seven from grade six in 2006. Constructions with straight-edge and compass are postponed to high school from grade eight in 2006. Introducing and using the Pythagorean theorem is postponed to grade eight from grade seven in 2006.

Algebra 2 in the final draft excludes conic sections and doesn’t expect students to work with logarithms beyond just their definition – content that was present in the 2006 Indiana standards, and this content has been pushed in this draft to trigonometry and pre-calculus. Inductive proofs were completely eliminated from this draft.

**Sloppy and/or Erroneous Language**

There are too numerous cases where the draft’s language is sloppy and unclear to list them all here. A small selection is offered. · In numerous places the draft replaced CC language of arithmetic fluency “using the standard algorithm” with “using a standard algorithmic approach.” This seemingly innocuous alteration reflects a radical change undermining the expectation of students ever learning efficient and universally practiced standard arithmetic procedures for computation. While there is effectively a single “standard algorithm” for multiplication, “a standard algorithmic approach” includes, for example, also the inefficient diagonal lattice multiplication. Similarly, while we all know the standard vertical algorithm for addition, “a standard algorithmic approach” for addition may also include the abacus or systematic counting on one’s fingers and toes.

·

K.CA.3:Use objects, drawings, etc., to decompose numbers less than or equal to 10 into pairs in more than one way, and record each decomposition with a drawing or an equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). [In Kindergarten, students should see equations and be encouraged to trace them, however, writing equations is not required.]

How can one ”record each decomposition with … an equation” if “writing equations is not required”?

· *7.C.8:** Solve real-world problems with rational numbers by using one or two operations.*

Unclear if the intent is solving an expression with one or two arithmetic operations, or solving one- or two-step problems.

·

8.AF.8:Understand that solutions to a system of two linear equations correspond to points of intersection of their graphs because points of intersection satisfy both equations simultaneously.

A system of two linear equations typically has a single solution (two lines do not intersect at multiple points), while the standards implies multiple points of intersection.

Unfortunately, the selection above is just a sample of problems with the final draft.

**In Summary**

Until recently, Indiana standards were among the best in the nation. They were concise, clear, demanding, and mostly bereft of pedagogy. When Common Core was adopted, Indiana traded its excellent standards with mediocre, pedagogy-infused standards, written in Washington, DC. It is commendable that Indiana is the first state to realize the mediocrity of Common Core and abandon it, yet the proposed draft is far below the excellent quality Indiana has been used to.

There is an easy and obvious solution to this dilemma. Indiana should temporarily re-adopt its excellent 2006 standards. It already has a test aligned to those standards, and the only issue is to have those 2006 standards declared “college-ready” to preserve Indiana’s NCLB flexibility waiver. This should be an easy task given that the 2006 standards are of higher quality and higher rigor than the current draft, which has already been “blessed” as college-ready by Indiana’s universities and colleges.

Once the 2006 standards are re-adopted, Indiana should embark on a deliberate and unhurried process of improving its already-excellent standards.

In my previous post, I discussed the true meaning of Common Core’s “College Readiness” and I showed—using the words of Common Core’s own authors—the low level of its college-readiness definition and of its high school content in mathematics.

But what

…In my previous post, I discussed the true meaning of Common Core’s “College Readiness” and I showed—using the words of Common Core’s own authors—the low level of its college-readiness definition and of its high school content in mathematics.

But what about the plus (“+”) standards? As already mentioned, those “+” standards go beyond what every student is supposed to study. Perhaps, if students take all those, too, they will be prepared to study calculus in college and have a reasonable chance of success in STEM? No such luck, says Jason Zimba, the Bennington professor and lead writer of the math standards.

“If you want to take calculus your freshman year in college, you will need to take more mathematics than is in the Common Core,” he told the New Orleans *Advocate*.

What about highly motivated students who’d like to accelerate and take calculus before applying to the very selective colleges? No good news there, either. “AP Calculus is in conflict with the Common Core,” said the vice president in charge of AP courses at the College Board. It “lies outside the sequence” of the Common Core.

To longtime observers of the Common Core, none of this is too surprising. When the CCRS were written in 2009, Marc Tucker of the National Center on Education and the Economy had two representatives placed on the writing committees for ELA and math from day one. For a very long time, NCEE argued that American students are overeducated and that most of them should be steered into the workplace rather than into college. This pitch is also clear in NCEE’s recent report summarizing research that started in 2009, just as Common Core was being discussed:

Since a large fraction of community college students enrolled in the general studies track go on to four-year colleges, it is clear that for a substantial majority of high school graduates, being ready to be successful in the first year of a typical community college program is tantamount to being ready for both college and work. . . .

Indeed, community college first year programs of study typically assume that students have not mastered Algebra I. The most advanced mathematics content used in the vast majority of the first-year college programs we analyzed can reasonably be characterized as the mathematics associated with Algebra 1.25, that is some, but not all, of the topics usually associated with Algebra I, plus a few other topics, mostly related to geometry or statistics.

So there we have it. The Common Core from its inception has never been about true college readiness, despite its rhetoric. It never could have been, because those fake “college-ready” standards were planned to be high school graduation standards from the beginning. We know that only around a third of high school graduates are truly college-ready. It would be politically untenable for two-thirds of a high school cohort to fail graduation, and faking low-level “college-readiness” was the only way to avoid that disaster.

But what about the global competitiveness promised in *Benchmarking for Success*? What about preparing more students to earn science, engineering, technology, and mathematics (STEM) degrees? This question has baffled many. The recent NCEE report sheds some light on this question, too:

The high school mathematics curriculum is now centered on the teaching of a sequence of courses leading to calculus that includes Geometry, Algebra II, Pre-Calculus and Calculus. However, fewer than five percent of American workers and an even smaller percentage of community college students will ever need to master the courses in this sequence in their college or in the workplace.

In other words, the dumbed down high school expectations should be “good enough” for 95 percent of American students. They and their careers belong to the non-academic workplace. True academic education should be reserved only for the select 5 percent elite—the future managers, scientists and engineers. And government bureaucrats, one presumes.

It turns out there is no true STEM preparation in the Common Core, after all. Period. The elite will have been educated in select schools—whether private or public—that will go much beyond the Common Core. This gives an interesting new meaning to the “common” in Common Core, does it not? Jim Milgram and Sandra Stotsky, both members of Common Core’s Validation Committee, discuss the details at length in their recent report *Lowering the Bar: How Common Core Math Fails to Prepare High School Students for STEM**.*

Perhaps the most damaging aspect of the Common Core standards is not their low academic level, or the fact that they will likely result in less STEM preparedness in America rather than more. Their worst damage is bound to come from the confusion they sow among teachers and parents as to what it really means to be “college ready.” By interpreting that readiness in the narrow and non-standard sense of community college readiness, the Common Core falsely assures parents that their children are on a path to college when they are not, and removes parental pressure from schools and kids.

Of necessity this will be particularly damaging to low SES students and first generation college aspiring students, whose families heavily rely on the school system for this type of information.

**Indiana’s New Standards**

But there is hope. Recently, Indiana became the first state to reject the Common Core and embark on an effort to write its own standards. So far, the results have been mixed. I’ll reserve my remarks to mathematics.

The first draft, released in February 2014, had been haphazardly slapped together by taking Common Core and piling many other standards on top of them. This resulted in bloated standards of 40, 50, and even 60 standards per grade. Many of them duplicated each other, sometime at the same grade, sometime at other grades.

By mid-March there was a second draft. It improves on the first somewhat, yet it still suffers from significant bloat. Specifically, the language was cleaned up a bit, and the standards were reduced in number. Unfortunately, however, much of the reduction comes not from removing standards of secondary and tertiary importance, but from lumping together disparate standards into large “super-standards” containing multiple parts. Even more worryingly, very little content has been accelerated. In the larger sense, the K-8 draft released in March still reflects Common Core grade-level content and progressions, two to four years behind international top achievers. Finally, the overly didactic and repetitive nature of the underlying Common Core has not been reined in, and the draft still suffers from pedagogical over-prescriptiveness.

The high school standards second draft looks somewhat better. In contrast with elementary and middle grades, a significant amount of missing content has been added to most courses. Again, though, much of the overly didactic and detailed Common Core language has not been removed. Lastly, while the content of early high school courses is largely complete, trigonometry and pre-calculus are still rather weak.

Despite all that, the high school draft represents a reasonable effort to put in sufficient content to support STEM and non-STEM students alike.

From the production of these drafts, one sees a couple of things. First, the timeline for their development is clearly too short. Good standard-writing takes time and it would be a pity if Indiana, which had such a highly praised, clear, and high standard before the Common Core, would end up with muddled, wordy, obese and incoherent standards due to the rush to meet an unreasonable time-line.

Second, it seems as if two factions are fighting within these drafts. One seems to be pushing to take the Common Core “as is,” treating its every word and its every sub-standard and its every example as sacred and unalterable. The other apparently wants to add what the Common Core missed, but also wants to add content that Common Core intentionally—and wisely—left out of certain grades, like data analysis. In other words, the elementary and middle grades standards do not build on what the Indiana 2006 draft included, but rather throw together Common Core, Indiana 2006, and many additional bits and ends of unclear provenance.

To put it bluntly, these drafts not only look like the camel that resulted from the work of a committee, but they look like a double-humped camel.

Unless someone gives this ongoing effort a clear direction and reasonable interim deadlines, it is hard to see Indiana ending up with a product of which Indianans can be proud.

Supporters of the Common Core repeatedly claim that Common Core was a state-sponsored initiative, that the nation’s governors originated in 2007-8 this wonderful idea, and that the federal government had really – but really – nothing to do with these

…Supporters of the Common Core repeatedly claim that Common Core was a state-sponsored initiative, that the nation’s governors originated in 2007-8 this wonderful idea, and that the federal government had really – but really – nothing to do with these wonderful career- and college-ready standards that will propel many more of our students to be competitive in the global marketplace.

I will ignore for a moment what those supporters “forget” to mention – that the standards were produced in a secretive non-public process, that they were funded largely by the Bill and Melinda Gates Foundation and private DC-based lobbying organizations, and that they had little input from their actual stakeholders: teachers and the public.

Instead, I will focus on how well Common Core standards match their own claims and aspirations. And, as is usual for me, I will focus on mathematics.

The foundational document that Common Core promoters cite is *Benchmarking for Success*, published jointly by the National Governors Association (NGA), the Council of Chief State School Officers (CCSSO) and Achieve Inc. This 2008 report calls for, as its first and most important recommendations:

Upgrade state standards by adopting a common core of internationally benchmarked standards in math and language arts for grades K-12 to ensure that students are equipped with the necessary knowledge and skills to be globally competitive. (p.6)

To support this call, those three organizations described the **rigor** necessary from the proposed standards:

Rigor.By the eighth grade, students in top performing nations are studying algebra and geometry, while in the U.S., most eighth-grade math courses focus on arithmetic. … In fact, the curriculum studied by the typical American eighth-grader is two full years behind the curriculum being studied by eighth-graders in high performing countries.(p.24)

In September 2009, just three months after the Common Core State Standards Initiative (CCSSI) was publicly announced, it published its first major document, the *College and Career Readiness Standards* (CCRS). The CCRS required little more than the content of an authentic Algebra 1 course for their “college readiness.” Not for its 8th grade content as *Benchmarking for Success* promised, not even for high school graduation as used to be common twenty years ago, but for “College Readiness”!

This ultra-low definition of college-readiness in CCRS was challenged by some, yet the CCSSI never revoked these standards – it simply silently made them fade away from its web site as the K-12 grade-by-grade content was being worked on. When the final version of Common Core (CC) standards was finally published in June 2010, there was no clear definition set forth of what college-readiness is. For the high school, CC offered “regular” high school standards and some “plus” standards, declaring:

All standards without a (+) symbol should be in the common mathematics curriculum for all college and career ready students. Standards with a (+) symbol may also appear in courses intended for all students.

So are the “+” standards part of CC’s definition of college-readiness, or are they not? Nobody knows and CCSSI is not telling even five years after the CC’s publication. Based on various documents and “progressions” published since, it seems that everyone’s interpretation is that the “+” standards are not included in CC’s College Readiness, and they will not be assessed on CC grade 11 consortia assessments.

So what is the level of this *de facto*, if not *de jure*, Common Core College Readiness? How well does it fulfill the promise of *Benchmarking for Success* that they will be “internationally benchmarked” and ensure that our students will be “globally competitive”? This is easily answered, as CC itself squarely placed the first Algebra course in high school.

CC defenders argue that there is “a lot of algebra” in CC grade eight content. One can quibble about how much is “a lot,” but certainly there is a significant amount of algebra there. But there is a significant amount of algebra in 7th grade content, and in 6th grade content, and even in the first grade content! This is because CC defenders, probably intentionally, confuse the first algebra course with so-called (but ill-defined) “algebraic thinking” that has been present in every elementary grade of every state standard in this nation for a long time. Defenders can attempt to confuse between algebraic content and an algebra course until they are blue in the face, yet the fact remains – Common Core relegated its first algebra course to high school, unlike our global competitors. This is not rigor. Significantly, this refutes the notion of internationally benchmarked standards in math.

But does that mean that one cannot be college-ready in high school while taking Algebra 1 in 9th grade? Not necessarily. It depends on the other content taught in high school, and how that content is taught.

Common Core high school mathematics without the “+” standards contains what amounts to a weak Algebra 2 content, and to even weaker Geometry course. This is of critical importance because, overwhelmingly, 4-year state colleges expect at least Algebra 2 and Geometry as their admission requirement. In fact, a student taking Algebra 2 as the highest math course in high school has barely 39% chance of getting any bachelor’s degree (Tbl .5, p. 31 here), and somewhere between 2.1% and 15% chance of ending up with any STEM bachelor’s degree (Tbl. 7 here).

Here is what Jason Zimba, one of the three CC math standards’ authors, had to say about their college-readiness in 2010:

In my original remarks, I didn’t make that point strongly enough or signal the agreement that we have on this— the definition of college readiness. I think it’s a fair critique that it’s a minimal definition of college readiness.. . .Not only not for STEM, it’s also not for selective colleges. For example, for UC Berkeley, whether you are going to be an engineer or not, you’d better have precalculus to get into UC Berkeley”.

Translation: *Common Core’s “College Readiness” is good for Community Colleges, and for Non Selective 4-year colleges*. So much for the *Benchmarking for Success* promises that the standards will be “globally competitive.”

And here is what William McCallum, another author of the standards, had to say about the original CCRS at the 2010 joint Mathematical Association of America/American Mathematical Society meeting in San Francisco:

The level set by the [CCRS} document, I completely agree, it’s not what we aspire to for our children, . . . I completely agree with that and we should go beyond that. . . .We should expect our children to go beyond that level as the K-12 standards will go beyond the level set by the college and career-ready document. It will include standards about math permutations . . . The level that was set at the college and career ready document was not based on university admission requirements but was based on data about what students actually do, how well they succeed if they go to a certain level of mathematics.

It is worth noting that despite his promise, the final CC standards have a single reference to permutations, and it is a “plus” standard – apart from “college-readiness.” Also interesting is McCallum’s acknowledgement that the CCRS were not based on college admission requirements but rather on “some other data about what students actually do.” I will address this particular issue in my next post.

We must consider Common Core’s “college readiness” and what will be its likely impact on colleges.

We know that CC’s “college-readiness” is aimed only at community colleges and is below the minimum that most 4-year state colleges routinely require today. We also know that today roughly 2/3 of high school graduates continue to 2- and 4-year colleges, but only about half of them, roughly 35% of high school graduates, earn any degree. In other words, we will be forcing colleges to accept even less prepared students than today, but instead of sending them to remedial courses, state colleges will now have to enroll them directly in credit-bearing courses. Finally, we know that many state legislatures are putting into law requirements that anyone declared “college ready” by Common Core assessment will not face remedial courses in a 4-year state college. Much of this is pushed by the federal No Child Left Behind “flexibility waivers” (granted to 43 states and counting) that require states to align their K-12 system with their colleges.

What we don’t know is how colleges will react to a flood of underprepared students. We don’t know if they will simply bend at the knee and lower the meaning of their degrees, or will they extend the average time it takes students to earn a degree, or will they rebel and defend their autonomy to define what it means to be prepared for their institution. Both the second and third alternatives will mean an uphill battle with their state governments. However, unless academic faculties wake up and assert their authority one way or another, future degrees from state institutions will be worth even less than they are today.

One frequently hears that the Common Core standards are merely standards and expectations that do not dictate curriculum or pedagogy. Common Core proponents argue that those national standards do not interfere with the ability of teachers to use their preferred

…One frequently hears that the Common Core standards are merely standards and expectations that do not dictate curriculum or pedagogy. Common Core proponents argue that those national standards do not interfere with the ability of teachers to use their preferred pedagogical approaches, and do not further interfere with local autonomy over the curriculum. Here, for example, are Kathleen Porter-Magee and Sol Stern making the case why conservatives should support the Common Core:

Here’s what the Common Core State Standards are: They describe what children should know and the skills that they must acquire at each grade level to stay on course toward college- or career-readiness, something that conservatives have long argued for. . . . The Common Core standards are alsonota curriculum; it’s up to state and local leaders to choose aligned curricula.

Indeed, on the face of it, this is exactly what the Common Core standards claim to be. Its English Language Arts standards announce:

*A focus on results rather than means *

*By emphasizing required achievements, the Standards leave room for teachers, curriculum developers, and states to determine how those goals should be reached and what additional topics should be addressed . . . . Teachers are thus free to provide students with whatever tools and knowledge their professional judgment and experience identify as most helpful for meeting the goals set out in the Standards. (p.4)*

And they categorically state:

*The Standards define what all students are expected to know and be able to do, not how teachers should teach. (p.9)*

Similarly, the Common Core mathematics standards call themselves *content standards* – in other words, they dictate the “what” rather than the “how.”

Are these claims true? All around the country we hear of parents tearing their hair out after they look at what their children now bring home carrying the label “Common Core.” We hear stories of children providing correct answers to arithmetical problems and being marked down for using “improper procedures.” We hear about Common Core teacher training stressing the “how” rather than the correctness of students’ results. Are those anecdotes just isolated incidents and examples of wrong-headed interpretations of the standards?

If one reads the standards themselves, it quickly becomes obvious that they are *not* only about the “what” but rather include a lot of the *how*, despite their claim to the contrary. And that many of those anecdotes describe not a wrong-headed interpretation of the standards, but rather a faithful implementation of what they explicitly demand.

In English Language Arts much discussion occurred around the standards’ directive to share class reading time evenly between *informational texts* and *literary texts.* In high school, the standards insist on increasing the informational texts share to 70% (which may include also reading outside English class). I will not spend much time here on the foolish reasons for this change – that this is how the NAEP test splits its items, which has little to do with how to teach reading – but I’d simply point out that this is a *curricular directive par excellence*. It orders teachers how to structure their class time.

In mathematics, my own area of expertise, the examples of curriculum and pedagogy are numerous. Look, for example, on a first grade standard:

1.OA.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Were this a true content standard, it would have simply stopped after its first sentence: *Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.* Yet the standard continues and lists at least four different ways students must use to show … what? Can’t they simply show they can add and subtract, correctly and fluently?

And lest you think this is just a fluke, here is essentially the same standard in the second and third grades:

2.NBT.5: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

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.

In other words, students are not allowed simply to learn how to add and subtract in first grade, in second grade, or in third grade. No, they must use the training wheels that the authors want them to use, whether they can ride without them or not. What is this if not pedagogy, and a wrongheaded one to boot? Young children do not need four different ways to “explain” addition – at best, this could be guidance to teachers how to individualize teaching rather than expect children to know all these ways.

One can argue that those are just suggestions. Unfortunately, this is incorrect. The Common Core assessment consortia (PARCC and SBAC) will test these wrong-headed “strategies,” paying attention to the variety of ways problems are answered rather than to correctness of results.

Perhaps the most egregious case of imposing pedagogy occurs in Common Core geometry. It expects the teaching of triangle congruence in a particular and experimental way:

Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

A true content standard would simply say “Students prove triangle congruence” or, perhaps, “Students understand triangle congruence,” leaving the method of instruction to the teacher. Instead, Common Core not only dictates how to teach congruence, it insists on a specific experimental method of instruction that has *an established a track record of failure* where it was invented (pg. 33-35 here). Turns out that the authors of the standards were unaware of this record, and simply thought it mathematically “neat.” Talk about arrogance.

This example that has been making rounds on the internet beautifully illustrates the problems with the eclectic pedagogy dictated by the Common Core. The number line is strongly promoted by the Common Core for ordering numbers – fractions, decimals, integers, mixed – on it. It is actually well suited for that purpose. But while the number line can be also used in those “strategies” to explain the concept of addition and subtraction, it is ill-suited for doing the addition or subtraction itself – it is tedious, error prone, and not better than counting on one’s fingers. Yet here we have a third grade worksheet, clearly inspired by Common Core’s push for the number line, foolishly used not only to test a student’s actual performing of subtraction, it also expects this third grader to figure out where the notional Jack messed up on his finger counting.

Idiotic problems like this are likely to be found in many “Common Core aligned” textbooks and on the Common Core assessment – after all, they only follow the incessant exhortations found in the standards grade after grade to use “concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship … and explain the reasoning used” rather than simply expect a third-grader to fluently add and subtract. That fluency, Common Core declares, can wait until the fourth grade … while his Singaporean and Korean peers have learned it already in the second grade.