Common Core and Programs Used in “High-achieving Countries”

In debates about the Common Core State Standards for Mathematics (CCSS), one sometimes sees the following type of claim:

This is fully two to three years behind what is expected from students in high-achieving countries.

For example, this claim is made for Common Core standards for addition and subtraction with whole numbers, multiplication with whole numbers, and division with whole numbers (see pp. 16, 17 here).

But a look at “standards” (e.g., courses of study) and textbooks of countries commonly considered high-achieving does not show these gaps.

Easter Eggcorns from The Math Myth

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.

Grade 4 and 8 NAEP Objectives Outside the Common Core

This is a guest post by Jason Zimba.

Created in the late 1960s, the National Assessment of Educational Progress (NAEP) today measures U.S. achievement in mathematics, reading, science, U.S. history, and other subjects. The most recent framework for the mathematics assessment is described in a document published in 2014 by the National Assessment Governing Board and entitled Mathematics Framework for the 2015 National Assessment of Educational Progress. Below, I list assessment targets from the NAEP Mathematics Framework that are outside the expectations in the Common Core State Standards for Mathematics (CCSS-M).

Unfinished Business from 300 BC

The double meaning of “ratio” in U.S. school mathematics is a phenomenon that goes back as far as Euclid. On the one hand, a ratio of two numbers is written as a pair, e.g., 3 to 1. On the other, a trigonometric ratio is a single number, e.g., the sine of pi/6 is one half—not 1 to 2. (Ratios of more than two numbers do not have this double interpretation, so are not part of this discussion.)

Comments on Ravitch’s MLA Speech

The historian Diane Ravitch gave a speech to the Modern Language Association on January 11 about the past, present and future of the Common Core State Standards which was posted on a Washington Post blog. There’s a lot to like about the speech when it comes to rethinking uses of tests and test scores. I’ve been in favor of caution about testing since at least 1999 (see my article here).

However, the speech has some statements that are unclear, appear unaware of research in mathematics education, or seem uninformed. Some concern:

Characteristics of standardized tests.

Field testing standards.

Developmental appropriateness of the CCSS.

Development of the CCSS.

Details are below.

Comments on Goodman’s “Comparison of Proposed US Common Core Math to Standards of Selected Asian Countries”

Summary. In July of 2010, Jonathan Goodman published a comparison of Common Core State Standards with curriculum documents from several Asian countries (China, Hong Kong, Japan, Singapore, Taiwan). In my opinion, his analysis has some serious flaws. In this post, I give some examples. In an earlier post, I have given a brief overview of differences in national context, noting the different uses of standards and other documents in the U.S. and elsewhere. These different contexts and uses suggest how a U.S. reader’s expectations may lead to misinterpretation of documents from outside the U.S. In this post, I compare some of Goodman’s statements with the content of these documents in two ways: comments and detailed side-by-side comparisons.

Comments on Milgram’s “Review of Final Draft Core Standards”

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Summary. In 2010 (apparently in June), Jim Milgram posted a review of the Common Core State Standards, comparing them with standards of high-achieving countries. In my opinion, his review misses some important details and makes some incorrect conclusions. In this post, I give some examples. In an earlier post, I have given a brief overview of differences in national context, noting the different uses of standards and other documents in the U.S. and elsewhere. These different contexts and uses suggest how a U.S. reader’s expectations may lead to misinterpretation of documents from outside the U.S. In this post, I discuss some assertions in the review and give some detailed side-by-side comparisons of comments with standards, teacher’s guides, and other documents.

Update. More details about Milgram’s assertions are discussed in my October 12, 2022 post here.

Interpreting Standards from Other Nations: Considerations of National Context

Over the past decade, comparisons of U.S. standards for mathematics have been made with “standards” from other countries, e.g., national curriculum standards, syllabuses, or courses of study. Some of these comparisons overlook important details, resulting in conclusions whose accuracy could be improved considerably without much additional effort. This post gives a brief overview of two differences in national context that affect interpretation of documents from other countries, in particular, China, Hong Kong, Japan, Korea, Singapore, and Taiwan. (Further details are in an appendix at the end of this post.) The two posts that follow (here and here) discuss comparisons that have been made by (respectively) the mathematicians James Milgram and Jonathan Goodman.

Considering What Evidence?

In February, the Brookings Institution released its 2012 Brown Center Report on American Education. These comments concern Part 1 of the Brookings Report, “Predicting the Effect of the Common Core State Standards on Student Achievement,” especially those pertaining to the Common Core State Standards for Mathematics.

A minor oddity is that this section of the report begins by describing the CCSS as “written by teams of curriculum specialists.” This statement has a footnote which gives this URL. But the information at the URL says no such thing and is contradicted by the list of members of the writing groups here at the same web site.

Strange Accounts of the Common Core State Standards

The mathematicians Sol Garfunkel and David Mumford discuss the Common Core State Standards for Mathematics (CCSS) in their August 24 New York Times editorial “How to Fix Our Math Education,” concentrating their remarks on high school.

In contrast, the education researcher Andrew Porter and colleagues concentrate on Grades 3–6 and 8 in “Common Core Standards: The New U.S. Intended Curriculum” in the April issue of Educational Researcher. In August, Porter described these findings in his Education Week article “In Common Core, Little to Cheer About.”

As someone who has read the CCSS, I find these articles peculiar. (Disclosure: I edited the penultimate version of the CCSS and am the editor for the CCSS Progressions.)

Here’s why.