Common Core: A House that Doesn’t Make Sense
The Common Core Core-ites constantly ask those opposed to show them a standard “they don’t like”. Taken out of context, it might be difficult to take umbrage to specific standards, but taken as a whole, it is easier to determine if they make sense or not. This is a tactic to divert the main issue that the CCSSI circumvented the political process of state and federal statutes, but let’s play the Core-ite game and talk about why the standards should be discarded because of their content and/or lack of content.
Think of the Common Core State Standards Initiative as if you are looking for a new house in which to live:
- You drive up to it and think, “this looks like a great house”. The landscaping is pristine and it’s in a great neighborhood.
- The real estate agent lets you in and you notice the ceilings are a bit too low but you can work with them. Just don’t invite tall people to visit.
- The dining room is more like a sitting room as only a small table and a few chairs will fit in there, but formal dining is so out of date anyway, who needs a large dining room?
- The rooms are small and you could take out a wall to expand, but uh oh….that looks like a load bearing wall. Maybe those small rooms should be renamed “cozy”. You can work with this.
- The kitchen is a bit out of date but you can take care of it later. This would necessitate complete renovation.
- The granite countertops in the bathrooms are nice and new cabinets can be installed later since the homeowner renovated on the cheap. So what’s wrong with nice countertops over cabinets that don’t close anymore?
- The tacked on family room is really awful with the 80’s rock facade on the wall and the tiki bar needs to be ripped out but hey, what’s a few additional thousand dollars?
- The third bedroom is really, really tiny but those guests won’t stay too long that way!
- Garage? Who needs a garage? The bonus room that was renovated via the garage space is really needed now that you don’t have small children in the house.
- FINALLY! The selling point of the house! It has a lovely, lovely pool! That’s worth something!….just as long as it doesn’t rain too much….
You would be foolish to buy a house with such major issues. From the outside the house looks awesome. It has great street appeal and a wonderful pool. But when you get into the house itself, it just doesn’t work. You could certainly live there but it would not fit your needs.
The same can be said about the Common Core Math standards. The letter below, from Dr. James Milgram who refused to sign off on the standards, details specific issues with the math standards he found objectionable. He enters the house of mathematics and explores the various rooms of arithmetic operations, geometry and fractions. All the rooms taken together, he decides this is a house that cannot be inhabited.
The pdf of his letter can be found here:
Excerpts (areas are bolded by MEW):
Review of Final Draft Core Standards
R. James Milgram
What follows are my comments on the nal draft of the CCSSI Core Mathematics
Standards. There are a number of standards including, but not limited to 1-OA(6), 2-
OA(2), 2-NBT(5), 3-OA(7), 3-NBT(2), 4-OA(4), 4-OA(6), 4-NF(1), 4-NF(2), 5-OA(3),
8-G(2), 8-G(4), F-LQE(5), G-SRT(4) that are completely unique to this document, and
most of them seem problematic to me. I have repeatedly asked for references justifying
the insertions of these or similar standards in previous drafts, but references have not been
provided. Consequently, to my knowledge, there is no real research base for including any
of these standards in the document.
Arithmetic operations: page 2/13:
Note that most of these standards have some sort of
uency requirement for operations in a range, but no requirement that the algorithm being used is either general or general-izable. Also, note the extremely excessive pedagogical constraints in 1-OA(6), 3-OA(7).
Note that 3-OA(6) is actually a denition, and part of a denition that is given at
least one year earlier in virtually all the high achieving countries at that.
Specically, subtraction is dened in the following way: a – b is that number c,
if it exists, so that b+c = a, while division is dened by ab is that number, c,
if it exists, so that b c = a.
With these understandings, the students in the high achieving countries only have
to learn and master two operations, addition and multiplication, since the other two
come along for free. Moreover, this is a key piece of the underpinnings for their
success. But we are, instead, given 3-OA(6) which is neither fish nor fowl.
The seven standards above would have been exemplary if they had not occurred after the
“fluency” standards for unconstrained algorithms that I had objected to at the beginning
of this discussion. Within the document itself, there seems to be a minor war going on,
and this is not something we should hand over to our teachers. (MEW note: dark humor here. The Core-ites accuse the opponents as ‘politicizing’ the standards. Seems as if that political war is embedded in the standards themselves)
The above standards illustrate many serious aws in the Core Standards. Also among
these difficulties are that a large number of the arithmetic and operations, as well as the
place value standards are one, two or even more years behind the corresponding standards
for many if not all the high achieving countries. Consequently, I was not able to certify
that the Core Mathematics Standards are benchmarked at the same level as the standards
of the high achieving countries in mathematics. (MEW note: is this why the ‘internationally benchmarked’ claim was withdrawn from the standards’ talking points?)
Fractions: page 7/13:
The next problem is with the standard 4-NF(2) Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark
fraction such as 1=2. Recognize that comparisons are valid only when the two fractions
refer to the same whole. Record the results of comparisons with symbols >, =, or <,
and justify the conclusions, e.g., by using a visual fraction model.
The rest part of this standard is exemplary, but it is completely distorted by what follows.
What does in mean to compare to “a benchmark fraction?” And this is only made worse
by the requirement that students “recognize that comparisons are valid only when two
fractions refer to the same whole.” This is an entirely unappetizing admixture of apples
and spoiled oranges.
Geometry: page 8/13
The approach to geometry in Core Standards is very unusual, focusing in eighth grade
and beyond on using the Euclidian and extended Euclidean groups to dene congruence
and similarity as well as develop their key properties. Mathematically, this approach is
rigorous, but it would generally be regarded as something that would be done in a college
level geometry course for math majors. The exposition at the high school level seems
plausible, and may well work. However, to my knowledge, there is no solid research that
justifies this approach at the K-12 level currently.
It is also worth noting that a similar approach was taken in Russia about 30 years back,
but was quickly rejected. It wasn’t that the teachers were not capable of teaching, though
this may well be a problem for most middle school and many high school math teachers
here. The problem was that it was way too non-standard, and basic geometric facts and
theorems had to be handled in entirely new, untested, and ultimately unsuccessful ways. (MEW note: News flash! It’s NOT necessarily ‘just’ an implementation issue!)
In fourth grade we have
4-MD(1) Know relative sizes of measurement units within one system of units including km,
m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement,
express measurements in a larger unit in terms of a smaller unit. Record measurement
equivalents in a two-column table. For example, know that 1 ft is 12 times as long as
1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet
and inches listing the number pairs (1, 12), (2, 24), (3, 36), …
This is the summative standard for a whole sequence of standards that start in the earliest
grades but continue through grade 5 or even grade 6. It is far too complex to be listed
only in grade 4. But that is exactly what is done in Core Standards. It is as though the
authors had a master-list of topics and felt free to sprinkle them wherever there might
have been room. (MEW note: It reminds me of that tacked on family room with the tiki bar. It just doesn’t work with the flow of the house, but hey, the idea of another room sounded good).
5-MD(3) Recognize volume as an attribute of solid figures and understand concepts of volume
a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic
unit” of volume, and can be used to measure volume.
b. A solid figure which can be packed without gaps or overlaps using n unit cubes
is said to have a volume of n cubic units.
Partly, I feel that this standard is occuring too early. It takes some time and effort for
students to appreciate the complexity of visualizing solid gures through plane sections
or possibly nets. Partly, as before, this standard is avoiding the real issues, namely,
determining the volumes of figures that can not be decomposed into n cubes without gaps
or overlaps, such as triangular prisms or rectangular cones. When we look at this pair of
issues together, we can begin to see why I feel so uncomfortable with these standards. (MEW note: the house is not flowing well.)
It is at the point above, and even more so with the corresponding similarity standard
8-G(4) Understand that a two-dimensional gure is similar to another if the second can
be obtained from the rst by a sequence of rotations, reflections, translations, and
dilations; given two similar two dimensional figures, describe a sequence that exhibits
the similarity between them
where I feel that we are dealing with an experiment on a national scale. There are even
more difficulties with the statement “given two similar two dimensional figures, describe
a sequence that exhibits the similarity between them” than was the case with the corre-
sponding statement in 8-G(2).
Dr. Milgram ends his letter asking why the main author of the geometry standards is supporting a theory of standards:
Before we dare to challenge teachers and students with standards like these, we ab-
solutely have to test the approach in more limited environments, and I find it highly
disturbing that H.-H. Wu, the main author of the greometry standards in Core Standards,
feels able to make the following statement in a recent article:
The mathematical coherence of CCMS also lies at the heart of the discussion of high
school geometry. Briefly, the better standards, such as California’s, insist on teaching
proofs. This is a good thing, but it does place an unreasonable burden on a high
school course on geometry as the only place where any kind of proof can be found
in school mathematics. As a result, some of these courses begin with formal proofs
based on axioms from the beginning, with no motivation. There is another kind of
reaction, however. Giving up entirely on proofs as unlearnable, some courses treat
plane geometry as a sequence of hand-on activities that do not mention proofs. In
addition, both kinds of courses are disconnected from the teaching of rigid motions
(translations, rotations, and reflections) in middle school. What CCMS does is to add
the teaching of dilations to rigid motions in grade 8 using hands-on activities, and on
this foundation, develops high school geometry by proving all the traditional theorems.
For the first time, the school geometry curriculum provides a framework in which all
the apparently unrelated pieces of information now begin to form a coherent whole.
It holds the promise that learning geometry in K-12 can finally become a reality.
Over the last 12 years Wu and I have collaborated on the California Framework, a number
of other states standards, and on a number of nationally influential documents. Normally,
Wu is very careful about distinguishing between what one hopes is true and what one
knows will work, but in this instance I feel he has allowed his innate hope to overwhelm
A good real estate agent wouldn’t talk a client into buying a house that doesn’t fit the family’s needs. Why would the author of the geometry standards (and those signing on to the standards) agree with standards that are not verifiable and research based? He is similar to a house buyer who likes the idea of buying a house but doesn’t perform the due diligence to ascertain whether the foundation is solid or the cost of renovating that which does not work.
Unlike a house buying expedition, however, parents and taxpayers didn’t go out looking for new standards from non-governmental organizations which we are being forced to use in our schools. We didn’t particularly want move from our previous state standards to live in Common Core land (no one asked the voters or legislators) but we were forced to live there. It’s as if the education reformers masqueraded as Common Core land real estate agents and did not disclose the house’s deficiencies. Now we know what is in the standards and how our kids are living with them. We want to tear up the deed we never signed and want a house that makes sense.