The article

Common Core Standards: The New U.S. Intended Curriculum by Andrew Porter, Jennifer McMaken, Jun Hwang, and Rui Yang

doi: 10.3102/0013189X11405038 *Educational Researcher* 40(3):103–116, May 5, 2011.

has an analysis of the new Common Core Standards, comparing them to existing state standards, standards in other countries, and a few well-known assessments or standards documents. (I’ve blogged about a different comparison almost a year ago in California standards vs. Common Core.)

The method published in *Educational Researcher* attempts to reduce the complexity of comparing huge, complex documents down to single numbers measuring similarity, which loses a lot of the information. Saying that California shares 0.27 similarity (on a scale of 0 to 1) with the Common Core for kindergarten math standards, or 0.31 for high-school math, does not tell me whether the Common Core is better or worse, just that it is different.

The similarity measure is computed from comparing the weights given to each of 1085 cells of an array in math (815 for language arts). The arrays are 2-dimensional, crossing topics with cognitive demand. The projections onto the cognitive demand axis are shown for “state” standards (which I assume are the sum over all grades and states for which they have data) and the Common Core. Later on in the paper, they imply that the tables are just for grades 3–6, but they failed to have any caption on the table (so much for “Data displays” being taught to educational researchers).

level |
state |
CC |

Memorize |
12.11% |
9.50% |

Perform Procedures |
48.82% |
43.74% |

Demonstrate understanding |
28.66% |
35.65% |

Conjecture |
7.78% |
5.96% |

Solve non-routine problems |
2.63% |
5.16% |

Of course, this comparison is for all states and some subset of grades, not specifically for any one state, which is where the comparison might be useful. Still, I’m glad to see an increase in “demonstrate understanding” and “solve non-routine problems”, and a decrease in “memorize” and “conjecture”. (Note: conjecturing is a useful thing, but grade schools and high schools confuse it with guessing, so students are better off not being taught to do it wrong.)

A more informative table is the one that breaks things down by major topic area:

Topic |
state |
CC |

Number sense |
13.84% |
32.75% |

Operations |
15.08% |
22.72% |

Measurement |
0.00% |
17.79% |

Consumer applications |
11.58% |
0.05% |

Basic algebra |
0.03% |
13.40% |

Advanced algebra |
14.47% |
0.00% |

Geometric concepts |
0.24% |
5.73% |

Advanced geometry |
9.27% |
1.64% |

Data displays |
2.83% |
2.76% |

Statistics |
4.72% |
3.16% |

Probability |
0.15% |
0.00% |

Analysis |
0.03% |
0.00% |

Trigonometry |
0.64% |
0.00% |

Special topics |
0.32% |
0.00% |

Functions |
1.09% |
0.00% |

Instructional technology |
25.71% |
0.00% |

This table tells me more about the weaknesses of their method than it does about the standards, though. I see no way that one set of standards can be all “basic algebra” and no “advanced algebra” while the other is all “advanced” and no “basic”. I also have no idea what they mean by “analysis”, but it is almost certainly not the topic that mathematicians call “analysis”, which is a more advanced form of calculus. The numbers in both columns look ludicrous (25.7% on “instructional technology”, which probably means use of calculators? 32.75% on number sense?). Quite frankly, after seeing this table, I do not believe anything the authors have to say about the standards—the numbers look cooked to make their point, rather than being a dispassionate analysis of the data. Looking further in their paper, I see that this is just incompetent proof-reading, as their graphs show low “advanced algebra” content in both columns, and do not show huge bump for “instructional technology” in the state column

So, the one interesting table in their paper is clearly garbage. What a waste of effort, doing all that work then failing to proofread the paper and printing trash. Other incompetent editing: some tables have states labeled with names, others have “State A”, “State G”, … .

I think that *Educational Researcher* needs to retract the paper and have the authors redo the paper with proper proofreading and captioning of their tables and figures—this is unacceptably bad work for an academic publisher.

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