On January 11, I spoke to the annual meeting in Chicago of the Modern Language Association about the Common Core. My talk was titled “Common Core: Past, Present, Future.”

I think readers of this blog will find it of interest.

It is about 17 pages long, so sit down.

I explain the background of the standards and explain why they have become so controversial, with critics and supporters on all points of the political spectrum–right, left, and middle.

I recommend decoupling the standards from the testing. And I recommend that the standards be reviewed, corrected, and updated on a regular basis by panels of teachers and scholars. No set of standards should be considered so sacrosanct that they can never be revised. These arrived encased in concrete.

Monica Garcia is president of the Los Angeles school board and Superintendent John Deasy ‘s strong supporter in Los Angeles. She supports charter schools and evaluating teachers by test scores. Los Angeles has more charters than any other city in the nation. They have little supervision. They get public money to do as they please (in reformer-speak, that is called “innovation”).

Garcia’s friends do not want to take any chances.

Here are the latest campaign contribution reports. They do not include Mayor Bloomberg’s $1 million or Michelle Rhee’s $250,000 or other gifts from big-time corporate interests.

‘Rigor’ is in, and the common core standards promise to raise the achievement in this country by raising expectations which students always rise to meet.

As a staunch “status-quo defender,” it might surprise ‘reformers’ that I have some pretty radical ideas about how I’d change the math curriculum in this country if I could. While they tinker around with teacher evaluation formulas which could, at best, raise test scores by a little, I would like to see a complete overhaul of what we teach in math.

When I heard that the common core was going to address the problem that the math we teach is “a mile wide and an inch deep” and that we need to teach fewer things, but better, I thought that this was an excellent idea. It was something I was thinking about for a while. It is not possible to deeply teach too many topics in a year. It would be like trying to have a class read fifty novels in a year in an English class. It would not be possible to cram that much in and do it well.

As I learned more about the common core, I got concerned since they didn’t really seem to be removing many topics from the curriculum. Instead math teachers are told to teach to a greater depth of understanding in the same time frame. Another important issue is how students will be assessed to see if they have achieved a deeper understanding.

Since I teach at one of the top high schools in the country, Stuyvesant High School, and since I try to usually teach to encourage a deep understanding, I wanted to share with Diane Ravitch’s vast audience what a common core math activity could look like, what the assessment might be, and why the actual assessments will never accomplish what they were supposed to.

I chose 8th grade geometry standard 8.G.B.6 which states “Explain a proof of the Pythagorean Theorem and its converse.”

Now the Pythagorean is probably the most famous thing in all of math. In Gilbert and Sullivan’s Pirates of Penzance they even refer to it in “I Am the Very Model of a Modern Major General”.

I’m very well acquainted, too, with matters mathematical,
I understand equations, both the simple and quadratical,
About binomial theorem I’m teeming with a lot o’ news,
With many cheerful facts about the square of the hypotenuse.

At the end of ‘The Wizard Of Oz,” The Scarecrow, after receiving his ‘brain’ even takes a crack at it.

OK. So after that gentle introduction, I’m going to remind anyone who might have forgotten that the Pythagorean Theorem describes a relationship between the lengths of the three sides of a right angled triangle. Specifically, if you add together the squares of the two shorter sides it will equal the square of the longest side.

In the diagram below, AC is 5 units and BC is 12 units. To use the Pythagorean Theorem to determine the length of AB, you would calculate 5*5=25 then add to that 12*12=144 to get 25+144=169. Then you would have to find the square root of 169, which is 13 since 13*13=169.

Generally students are ‘told’ the Pythagorean Theorem. Sometimes they are shown a formal proof of it using something called similar triangles, but that proof is not very convincing or memorable.

When I make a math lesson, my goal is for it to be thought provoking, relevant, or both. So when I teach the Pythagorean Theorem in common core style, I’d want to get my students thinking about why the relationship is true, and a good way to do this is with some very cool geometric diagrams. In the old days (300 B.C.) when people would say “In a right triangle the sum of the squares on the legs equals the square on the hypotenuse,” they meant it literally. ‘Square’ did not mean to multiply something by itself, but the four sided shape that we learn about as toddlers. So saying “a squared plus b squared equals c squared” in this context means that the combined areas of the yellow and blue squares are equal to the area of the orange square.

To get kids thinking about why this might be true, I’d have them examine a few pictures. Here’s one that should keep any curious person staring and thinking for at least ten minutes.

I’d ask students to try to justify why the five pieces that make up the big square are identical to the five pieces that make up the small and medium sized squares.

I’d then have them think about, and then discuss in pairs, this famous image.

My hope is that most of the class would be intrigued by this image to realize that since the left hand square is made up of four triangles and the orange square and the right hand square is made up of the same four triangles and the yellow and light blue squares, then the orange square must have the same area as the yellow and light blue combined.

For my ‘assessment’ which is also what would be natural on the common core, I’d present another picture kind of like these, only harder.

Now here’s where the common core assessments will break down. As a teacher the way I’d assess my students would not just be if they “figured it out.” While I’d be pretty happy if some students figured this one out, I could be satisfied if nobody figured it out. If I saw my students concentrating on it, talking about it with their neighbors, thinking about it and not giving up for twenty minutes, making some progress, developing some theories and then testing those theories, smiling — enjoying this challenge. That’s what I’d want to see and I seriously doubt that the common core will, or can, accomplish this.

By the way, in case you’ve been intrigued by this, I’m going to put the answer down so you have to scroll to it.

Jeannie Kaplan is an elected member of the Denver Board of Education. She has been critical of corporate-style reform and of the heavily-funded effort to persuade the public that it is successful. When she heard that Jonah Edelman of Stand for Children told an audience in Tulsa recently that Denver was a national model of success, she decided to review the score card for the district. (Stand for Children boasts of its civil rights credentials but supported a slate of Republican candidates for the state legislature in 2012, as part of its campaign for corporate reform).

Kaplan wrote for this blog:

So Much Reform. So Little Success

Denver, Colorado is a poster child for much of what reformers like to see: standardized testing, teacher accountability, charter schools, choice, co-location, and oh, did I mention testing? Denver Public Schools is trying or has tried almost all of them. Why, even Jonah Edelman, founder of one of the most well-funded, prominent reform organizations, Stand for Children, just today, January 10, 2013, pointed to Denver as a leader in reform because of its “portfolio” of school choice led by its charter schools. So, how is reform really working in Denver?

Let’s start by focusing on achievement, meaning test scores, since that is the focus of all things reform. (This post will have a lot of data since reform and data go hand in hand these days, especially data that can be spun). Denver Public Schools have been rated by the Colorado Department of Education as “Accredited with Priority Improvement Plan,” for the last three years. Out of five grades this is the second to the bottom. To be fair, DPS is inching toward the next category, “Accredited with Improvement plan.” The cut point is 52% of eligible points; Denver is at 51.7%. I am not sure how meaningful this data point is, since the GROWTH points count for 35 points out of 100 and ACADEMIC ACHIEVEMENT, meaning proficiency, counts for only 15.

Colorado now places enormous emphasis on “the growth model.” While no one would contest you need to have growth to get to proficiency, I believe this model masks what is really happening, and so the data I am citing is all about proficiency. To further emphasize how growth can mask proficiency, allow me to quote from one of Denver’s most ardent reformers, Alexander Ooms, who said on in a commentary on EdNewsColorado:

I could not have said it better. The data I cite are proficiency numbers, not growth numbers.

In 2005, when reform was in its infancy, Denver Public Schools hired its first non-educator superintendent: Michael Bennet, former businessman/lawyer, former mayoral chief of staff . Mr. Bennet’s childhood friend and fellow businessman, Tom Boasberg, was hired to replace him when Bennett became a Senator. Denver has been experimenting with reform since then. Oh, and BTW, Jonah Edelman grew up as Tom Boasberg’s neighbor in Washingon, D.C.

After 8 years, what academic changes has reform produced?

The following data is from 2005 through 2012, according to Colorado standardized tests. Here is the website for a deeper delve into the data

We can’t leave achievement without looking at the State of the Union shout-out school, Bruce Randolph. Bruce Randolph Middle School in 3 years of state tracked data shows a gain of 2% in reading to 28%, stayed at 19% in math, increased by 3% in writing to 17%, and increased 7% in science to 17%. It is tied for last in proficiency – 52nd – for all of Denver’s middle schools.

Bruce Randolph High School has declined 10% to 33% in reading, declined 3% in math to 10%, declined 2% in writing to 14% increased 1% to 12% in science. Bruce Randolph is 24th out of 27 high schools in academic achievement.

ACHIEVEMENT GAP increases based on 7 years of CSAPs/TCAPs

Elementary School

Reading 4.17

Writing 5.78

Math 6.46

Middle School

Reading 3.23

Writing 4.71

Math 6.72

High School

Reading 3.01

Writing 5.82

Math 6.30

According to DPS data, the gap between FRL and paid-lunch students has widened by 9% since 2005. In 2005, percent proficient for FRL was 29%, paid was 58%. In 2012 the numbers were 41% for FRL, 79% for paid. The gap has grown to 38%.

ACT RESULTS: (A composite score of 21 is generally accepted as a college readiness benchmark)

From a DPS presentation of September 2012

2005 17

2012. 17.6

GRADUATION for 2011 – we are still waiting state numbers for 2012 but the number of students graduating increased from 2,642 in 2005 to 3,414 in 2012, for a total of 772 more graduates in 8 years…or an average of 96.5 more graduates each year.

Here is how Denver Public Schools compares with the state:

State 73.9%

Denver 56.1%

REMEDIATION (from Fall of 2010)

From the Fall of 2007, when this data was first available to the Fall of 2010 (the latest data available, remediation numbers have increased from 57.1% to 59.7%. The state of Colorado is at 31.8%.