Mathematics and Education

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Easter Eggcorns from The Math Myth

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In her article for Slate, Evelyn Lamb points out that parts of Andrew Hacker’s book The Math Myth are not exactly Easter eggs—although they function as jokes for numerate people, their humor seems unintended.

Instead, they might be dubbed “Easter eggcorns.” The word “eggcorn” arose from “acorn” and now means:

A series of words that result from the misunderstanding of a word or phrase as some other word or phrase having a plausible explanation, as free reign for free rein, or to the manor born for to the manner born (from William Shakespeare’s Hamlet). American Heritage Dictionary

Thus an “Easter eggcorn” combines the hidden surprise of an Easter egg with the misunderstanding and plausible explanation of an eggcorn.

Along with Easter eggcorns for numerate people, The Math Myth has joke-like surprises for people familiar with K–12 mathematics education in the United States. (For my background in mathematics education, see this page.) This post is devoted to examples of the latter. Because parts of these examples may seem like misquotations or misreadings, I have included scans of pages from the book.

Standards are test questions?

Chapter 1 begins with a brief discussion of concerns about mathematics education in the United States. It says that “calls are heard to return to rigor and end feel-good rostrums” (p. 5). We are told:

Scan p.5(bottom of p. 5)

Scan p.6(top of p. 6)

As noted several chapters later in The Math Myth (Chapter 8, p. 124), these “questions” are “selections” from the Common Core State Standards for Mathematics (CCSS), a 93-page document which can be downloaded here. In particular, they come from two standards for high school (Functions, Interpreting Functions 8b; and Algebra, Arithmetic with Polynomials and Rational Functions 5).

The CCSS are expectations for what students should know, not tests of whether they meet those expectations. Such tests have been developed by two consortia formed by groups of states, Smarter Balanced Assessment Consortium (SBAC) and Partnership for Assessment of Readiness for College and Careers (PARCC). Examples of the types of test questions that students will actually face are here (SBAC) and here (PARCC, Question 9 involves an exponential function).

It’s instructive to compare The Math Myth version of the second “question” with the original:

a-apr 5

There are several differences: the 5 (which is the number of the standard); the footnote; and the plus sign in parentheses “(+).” The plus sign indicates that the standard is “Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics” (see p. 57 of the Common Core Standards for Mathematics).

Unlike the “plus standards”:

All standards without a (+) symbol should be in the common mathematics curriculum for all college and career ready students.

Thus the title of Chapter 8 is another Easter eggcorn:

scan chap8

A more accurate title would be:

chap title

Standards are lesson plans?

Chapter 8 begins by describing the Common Core State Standards (CCSS) as being developed under—confusingly—“the aegis of a transcontinental conglomerate called the Common Core State Standards” (p. 117). It refers to the Common Core as “this curriculum” (p. 118, line 1) and states that:

Ultimately, the Common Core morphed into a full set of K–12 lesson plans, spelling out what every teacher was expected to impart and every student to learn. (pp. 120–121)

When I first read the sentence above, I thought “a full set of K–12 lesson plans” was a reference to the outcome of a project (e.g., EngageNY) which provides instructional materials aligned to the CCSS. (An example of an EngageNY plan for a lesson on exponential functions is here.) A typical lesson plan is at least one page long (often much longer), but the document that delineates the Common Core Standards is only 93 pages. Surely The Math Myth did not mean to imply that this document was “a full set of K–12 lesson plans.”

However, I changed my mind several pages later (p. 123). In the same paragraph, the Common Core (I think this means the “transcontinental conglomerate”) is said make assertions about “its lesson plans,” which are countered—according to The Math Myth—by examination of “its 1,386 standards.”

Does this mean that The Math Myth considers a standard to be a lesson plan? It’s not uncommon for standards documents to be misinterpreted in various ways, e.g., as dictating instructional sequence, or being instructional materials.

Making sense (and nonsense) of these examples

Considering the Common Core State Standards as a collection of test questions, collection of lesson plans, or transcontinental conglomerate may have a certain plausibility if each meaning is taken individually.

Although standards themselves are not test questions, they determine the content of test questions. Similarly, standards are not lesson plans, but they set goals to be reached via lesson plans. Although a set of standards is not a transcontinental conglomerate, a transcontinental conglomerate (Pearson) administers the standards-aligned tests created by PARCC.

Taken together, however, these different meanings for “standards” are likely to be unhelpful for readers who are not already familiar with mathematics education in the United States.

 

 

 

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Written by CK

July 31, 2016 at 3:43 pm