Did the Common-Core Math Writers Accidentally Drop a Standard?
This week, I wrote a story about reported problems with the high school common-core math standards. Some of the most ardent supporters of the Common Core State Standards, including people who helped write them, have said the high school standards are weaker than those for K-8. Several experts told me that's in part because the high school standards were rushed out the door after they were written, and weren't as thoroughly reviewed as the earlier standards.
Within that story, there's an interesting tidbitin fact, it's arguably what journalists might call a buried lead.
Richard Askey, a professor emeritus at the University of Wisconsin-Madison, who was a member of the common-core feedback group, told me that somewhere within the many drafts of the document, the writers lost a geometry standard.
Here's the full quote from my conversation with Askey:
"There was one thing that dropped out and was in the draft. Bill McCallum says it dropped out between one draft and the next and he doesn't know how. When you have a similar object and look at the area and you double the size, area goes up by a factor of 4, and volume goes up by a factor of 8. Area scales by squares and volume by cubes. It's mentioned in Appendix A but isn't in the standards. And it was there in one of the drafts."
The standard is, as Askey pointed out, in the appendix, which is not technically part of the standards. (Appendix A offers suggestions for how schools can organize the standards into courses, and was written by a different team.) On pages 32 and 71, it states:
Informal arguments for area and volume formulas can make use of the way in which area and volume scale under similarity transformations: When one figure in the plane results from another by applying a similarity transformation with scale factor k, its area is k2 times the area of the first. Similarly, volumes of solid figures scale by k3 under a similarity transformation with scale factor k.
Such phrasing does not appear within the standards themselves.
In an interview, McCallum, one of the three lead writers for the Common Core State Standards for mathematics, chose not to comment on the supposed missing standard. However, he pointed out later by email that states can add standards to the common coreand that California has added a standard quite similar to the one Askey said was missing. McCallum highlighted the following standard on p. 24 of California's version of the common core:
Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k2, and k3, respectively; determine length, area and volume measures using scale factors.
It's worth noting that, after telling me about the missing standard, Askey quickly went on to defend the writers. "The people who were doing this were working 15 hours a day," he told me. "You take things, you pull them out, and put them somewhere else, and every once in a while things get lost."
The mathematician has also maintained his adamant support for the standards. "These are the best that have been done in the U.S.," he said. "I want them to succeed."
The fact remains, though, that 43 states and the District of Columbia are now implementing the common standardsand that students in many of those states may miss out on this standard if teachers and curriculum writers don't fill in the skill gap.