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The Common Core’s Pedagogical Tomfoolery

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 also not a 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.

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