Tag Archives: algebra one

Bush/Obama Ed Reform: Zenith

(This is part 2 of my brief (hahahah) history of the rise and fall of modern education reform. This part is longer because much more happened. Unlike the events in part 1, I experienced the Obama reforms as a teacher, having graduated from ed school the year of his inauguration. I began blogging the year he was re-elected.)

Bipartisan Achievements

Barack Obama won the presidency in 2008 while simultaneously blasting NCLB and praising charters and merit pay for teachers. In practice, he and Secretary of Education Arne Duncan kept giving reformers everything they wanted–although in fairness, reformers got increasingly nervous about their gifts as his presidency matured.

Ironically, given the general sympathy that the Obama administration had for education reform, a new version of the ESEA was impossible throughout most of the Obama presidency. This proves to be an extremely significant limitation.  Arne Duncan and Obama, rather than force states to live with the unpopular mandates, invited the states to submit waivers asking to be exempt from the penalties. This gave the Obama administration considerable power to force states to adopt policies the federal government wanted. Conservatives were unnerved by what most would considera a violation of Section 438 of the General Education Provisions Act banning any federal control over state educational choices.

Bribing the States, round I: Race to the Top, Waivers

First up was Race to the Top, enacted as part of the economic stimulus plan of 2009, in which over $3 billion was set aside for rewards to competitive bids. Compared to the moon shot by Arne Duncan, the competition demanded compliance with most key aspects of education reform. Of the 500 points awarded,  313 of them (63%) were for teacher effectiveness (138 points), adopting “common core” standards (70 points), supporting the growth of “high quality” charters (55 points) and intervention into low-performing schools (50 points).  Schools that didn’t promise to  fulfill ed reformers’ wildest dreams didn’t stand much of a chance. From the link above: “Between 2001 and 2008, states on average enacted about 10 percent of reform policies. Between 2009 and 2014, however, they had enacted 68 percent. And during this later period, adoption rates increased every single year.”

Around 2010, it became possible to observe two developments that were in fact completely forseeable to everyone back in 2001, when NCLB was signed.

First, NCLB allowed states to define proficiency and then penalized schools that didn’t meet that definition.  That might not have been a problem except for the second development:  no matter how easy the tests got, 100% proficiency never happened. And the gaps were the usual ones.

But now  2014 was squarely in sight and closer and schools well outside the usual urban dystopias were getting hammered into program improvement.

Since a new ESEA was still politically impossible, the Obama administration began offering “waivers” from the consequences of extended failure to meet NCLB,   in exchange for setting their own higher, more honest standards for student success:

  • State must adopt college and career ready standards
  • Schools must be held accountable
  • Teacher and principal evaluation systems

Some education reformers (the conservatives) were concerned about the quid pro quo nature of the waiver requirements.   Other education reformers (the neoliberals) pishtoshed those concerns, saying (much as they said later about immigration) that Congressional gridlock made the waivers and demands logical and reasonable. A typical debate, in which  Andrew Rothernam, neoliberal reformer from the Clinton administration, rationalized the Obama waivers  “This dysfunction matters because when NCLB was passed in 2001, no one involved imagined the law would run for at least a decade without a congressional overhaul.” (translated, good god, no one took that nonsense about 100% proficiency, we expected to modify it before then!)

Obama announced the waivers in February, 2012, and by July of that year 26 states had waivers, with another 9 awaiting approval. A year later, all but seven states had waivers. Jerry Brown and the California team flatly refused to intervene in “failing schools” or evaluate teachers by test results and never got a waiver (although a few districts applied separately and got one).

While we refer to the testing consortiums (consortia?) as the Common Core tests, I was surprised to learn that the original competition for the grants was part of Race to the Top. Arne Duncan announced the winners, PARCC, which had 26 states signing on, and SBAC, which had 33 (some states joined both), in 2010.

The tests, almost more than the standards, excited education reformers. No more would individual states be able to dumb down their tests to reach NCLB standards. All the states would be held to the same standard.

But it wasn’t federal mandates, of course. No, no. This was all voluntary!

Bribing the States, round II: Common Core

The Common Core initiative was originally the brainchild of Janet Napolitano when she heading up the National Governor’s conference, documented in 2007’s Benchmarking for Success: Ensuring US Students Receive a World-Class Education (note: it’s kind of amazing how hard this document is to find. All the links to it reference the NGA doc, but that’s been deleted. I think this is the only existing online copy). She convened a group, and they came up with a set of five action items, three of which you can see reiterated above in the Obama waiver, because they were basically copied.

But it would never have gone anywhere had not Gene Wilhoit (head of school superintendant organization) and David Coleman, described in the link ahead as “emerging evangelical of standards” but actually little more than an ex-McKinsey guy with an assessment display (display. not design) startup  went to see Bill Gates, whose enthusiasm should have been a big neon light of warning, given his track record. Gates funded the development of standards. Coleman used the money to start “found” Student Achievement Partners and hire Jason Zimba, an ex-business partner who now worked for Coleman’s mothert(or, was a professorat Bennington College, where Coleman’s mom was president). Zimba, Phil Daro, and William McCallum wrote the math standards. Coleman and Susan Pimental wrote the ELA standards. The original Benchmarking report stated that the standards would be based on the American Diploma Project, but for reasons I don’t understand and might be interesting for someone else to explore, Coleman and crew rewrote a lot of it.

As the history shows, education reformer groups–those involved with accountability and choice–weren’t directly involved in the birth of Common Core, although it’s also clear from the verbiage in the Benchmarking report that education reform initiatives like teacher value-added measurement, charters, and school takeovers were very much in political parlance at that time, and very much bipartisan.

But education reformer groups loved the Common Core because they saw it as a way to bail them out of the two serious failures of NCLB described above. As Rick Hess observed in a five-year retrospective of Common Core, “The problem with that is if you had hard tests or hard standards you made your schools look bad. So there was a real, kind of perverse incentive baked into NCLB [to make the tests easier]“.  Hilariously, Michael Petrilli, who was in the Bush administration and was a key bureaucrat in the passage, has often said he disagreed that the 100% proficiency goal but “his boss” forced it on him. So now that NCLB was in a bind, the ed reformers were all for Common Core bailing them out.

The waiver process is often blamed for the rapid adoption, but in fact every state but Alaska, Texas, Nebraska, and Virginia had adopted Common Core standards by  2012, and all of those but Wyoming had done so long before Obama announced the waivers. Apart from the conservatives “in principle” objections, the original hullaballoo over heavy-handed federal interference was teachers’ outrage at a president–a Democrat, no less–using money to bribe states into evaluating teachers by their students’ test scores.

Regardless, states eagerly adopted the Common Core standards and in 2012, all seemed right in the world of education reform.


Technically, all of the above was the Obama Administration’s bribes to the states to change their governance.  These are just some specific cases or other items of interest.

Tennessee won the Race to the Top, getting $500 million to enact First to the Top. Initiated by Governor Phil Bredesen, a Democrat, carried through by Bill Haslam, Republican. Tennessee’s application promised two things of note, First, it would use its existing, longstanding teacher evaluation system (TVAAS) and use it as a formal evaluation tool, responsible for 35% of teacher evaluations. Then, in order to invervene in “failing” schools,  it set up a state-run district, the Achievement School District, creating a  as opposed to a state taking over a district. The lowest performing schools were simply placed in that district. The stated goal of the ASD was to take schools from the bottom 5% and “vault” them to the top 25%.  In 2011, Haslam appointed Kevin Huffman, ex-TFA teacher and executive, as well as Michelle Rhee’s ex-husband,  as Commissioner of Education.  The first ASD superintendent was Chris Barbic, former TFA teacher and founder of Yes Prep, another charter system in Houston.

Mark Zuckerberg went on Oprah in 2010 and, with great fanfare, donated $100 million to Newark, New Jersey schools.  Chris Christie appointed Cami Anderson, alumni of TFA management,  as superintendent of the district in May 2011. A year later, Anderson signed a contract with the Newark Teachers Union giving bonus pay for higher test scores or teaching math and science (although teachers could choose to be paid traditionally). The pot was sweetened with a lot of back pay which, to put it mildly, was not what Zuckerberg wanted the money to be spent on.

Michelle Rhee got a lot of attention, bragging of giving DC schools a “clean sweep”, dumping all the “bad” teachers and administrators who didn’t get test scores up. Eva Moskowitz was dumping students who didn’t get test scores up. Joel Klein left his NYC post in 2011; Bloomberg’s pick of Cathy Black, a woman with no teaching or administrative experience, was extremely unpopular. Bloomberg gave up on Black after four months and appointed Dennis Walcott, who was accepted at face value as an improvement. School turnaround consultant Paul Vallas ran the Louisiana Recovery District (mostly New Orleans Schools) for 4 years.

Education reform generally became more popular in Democratic circles, given Obama’s strong support.  Steven Brill’s article The Rubber Room called attention to NYC’s practice of housing teachers who’d been removed from the classroom but couldn’t actually be fired.  Waiting for Superman, a documentary promoting choice and blasing unions and tenure, opened to universal praise by media, politicians, and other thought leaders. In 2010, Obama openly supported the dismissalof a Rhode Island high school’s entire staff, saying, “our kids get only one chance at an education, and we need to get it right.”

All this criticism kept building. 2012 was a nadir year terms of establishment discourse about public school teachers, although their reputation among the public seemed largely unchanged. It became increasingly popular to attack teacher tenure, again by both Democrats and Republicans, and certainly in the generally left of center media. Many states had agreed to evaluate teachers by test scores and both major unions had signed onto the Common Core standards, although teachers themselves were very doubtful.  A preponderance of politicians and academics were more than willing to agree that teacher quality needed to improve, that tenure might be problematic, and that teachers should be judged at least in part on test scores.  The Chicago Teachers Union went on strike, pitting union president Karen Lewis against Rahm Emmanuel, and media sympathies were entirely with Rahm. Governor Scott Walker ended collective bargaining for public workers (except cops and firefighters!).

One major setback: DC’s 2010 election, in which black voters booted Adrian Fenty, the media-popular mayor, largely because they wanted to get rid of Michelle Rhee, who stepped down the day after the election. Her successor, Kaya Henderson, kept firing teachers, but she’s black, which might have made a difference. Rhee immediately announced a new organization, Students First, and let Richard Whitmire write an admiring biography.


In 2008, California made algebra I the “test of record” for eight graders, meaning that 8th graders would take an algebra end of course test or the schools would receive a penalty towards average yearly progress.

High school exit exams mostly held constant; this 2008 Edweek article actually says that fewer than half of the states required exams, but that may be because of lawsuits. California, for example, was sued constantly about the use of the CAHSEE in the early 2002.

Charter Growth, Choice, TFA

Just one state, Washington, authorized charters during the Obama administration. Absolute growth was still slow through  2011,  but then recovered from 2012 to 2017. As a percentage, though, the decline from 2001 to 2011 was steep, slowed slightly but still declined through 2017.  By 2012, charter advocates began pushing the suburban progressive charter, realizing that growth would continue to slow if they couldn’t disengage white folks from their beloved public schools. Suburban charters were (and are) popular with whites in racially diverse areas, particularly in the south; for example, Wake County charter schools were 62% white in 2012.

When the 2007-2008 meltdown hit, TFA recruitment soared ever higher as elite grads sought shelter from a horrible job market. Relay Graduate School began in 2011, basically providing a teaching credential for new hires of inner city charters.

In 2010, Douglas County (major Colorado suburb) began a highly contested investigation into a voucher program, one that would give public money for all private schools, including religious ones. The school board ultimately supported a move forward, despite a split community.

And that’s the end of the very nearly straightforward rise of education reform. It’s impossible to cover every major development, but I really tried to look at advances in every major area.

I’m going to call 2012 as the peak of the era, for reasons I’ll go through in the next post. It’s not that all progress stopped. It took four more years before education reformers even began to consider how badly they’d been beaten. But most of them would realize that they were now fighting significant opposition that they couldn’t easily dismiss.

Something I’ve mentioned before: it’s amazing that Republican media folk, as opposed to education reformers and even politicians, still talk like it’s 2008-2012. There’s really no understanding in the pundit world how badly they’ve been beaten.

Working on the next; hoping to get it done before the new year. I will go back and edit these if something significant occurred to me.



The Product of Two Lines

I can’t remember when I realized that quadratics with real zeros were the product of two lines. It may have been this introductory assessment that started me thinking hey, that’s cool, the line goes through the zero. And hey, even cooler, the other one will, too.

And for the first time, I began to understand that “factor” is possible to explain visually as well as algebraically.

Take, for example, f(x)=(x+3) and g(x)=(x-5). Graph the lines and mark the x-and y-intercepts:


Can’t you see the outlines of the parabola? This is a great visual cue for many students.

By this time, I’ve introduced function addition. From there, I just point out that if we can add the outputs of linear functions, we can multiply them.

We can just multiply the y-intercepts together first. One’s positive and one’s negative, so the y-intercept will be [wait for the response. This activity is designed specifically to get low ability kids thinking about what they can see, right in front of their eyes. So make the strugglers see it. Wait until they see it.]

Then onto the x-intercepts, where the output of one of the lines is zero. And zero multiplied by anything is zero.

Again, I always stop around here and make them see it. All lines have an x-intercept. If you’re multiplying two lines together, each line has an x-intercept. So the product of two different lines will have two different x-intercepts–unless one line is a multiple of the other (eg. x+3 and 2x+6). Each of those x-intercepts will multiply with the other output and result in a zero.

So take a minute before we go on, I always say, and think about what that means. Two different lines will have two different x-intercepts, which mean that their product will always have two points at which the product is zero.

This doesn’t mean that all parabolas have two zeros, I usually say at this point, because some if not all the kids see where this lesson is going. But the product of two different lines will always have two different zeros.

Then we look at the two lines and think about general areas and multiplication properties. On the left, both the lines are in negative territory, and a negative times a negative is a positive. Then, the line x+3 “hits” the x-axis and zero at -3, and from that zer on, the output values are positive. So from x=-3 to the zero for x-5, one of the lines has a positive output and one has a negative. I usually move an image from Desmos to my smartboard to mark all this up:


The purpose, again, is to get kids to understand that a quadratic shape isn’t just some random thing. Thinking of it as  a product of two lines allows them to realize the action is predictable, following rules of math they already know.

Then we go back to Desmos and plot points that are products of the two lines.


Bam! There’s the turnaround point, I say. What’s that called, in a parabola? and wait for “vertex”.

When I first introduced this idea, we’d do one or two product examples on the board and then they’d complete this worksheet:


The kids  plot the lines, mark the zeros and y-intercept based on the linear values, then find the outputs of the two individual lines and plot points, looking for the “turnaround”.

After a day or so of that, I’d talk about a parabola, which is sometimes, but not always, the product of two lines. Introduce the key points, etc. I think this would be perfect for algebra one. You could then move on to the parabolas that are the product of one line (a square) or the parabolas that don’t cross the x-intercept at all. Hey, how’s that work ?What kinds of lines are those? and so on.

That’s the basic approach as I developed it two or three years ago. Today, I would use it as just as describe above, but in algebra one, not algebra two. As written,I can’t use it anymore for my algebra two class, and therein lies a tale that validates what I first wrote three years ago, that by “dumbing things down”, I can slowly increase the breadth and depth of the curriculum while still keeping it accessible for all students.

These days, my class starts with a functions unit, covering function definition, notation, transformations, and basic parent functions (line, parabola, radical, reciprocal, absolute value).

So now, the “product of two lines” is no longer a new shape, but a familiar one. At this point, all the kids are at least somewhat familiar with f(x)=a(x-h)2+k, so even if they’ve forgotten the factored form of the quadratic, they recognize the parabola. And even better, they know how to describe it!

So when the shape emerges, the students can describe the parabola in vertex form. Up to now, a parabola has been the parent function f(x)=xtransformed by vertical and horizontal shifts and stretches. They know, then, that the product of f(x)=x+3 and g(x)=x-5 can also be described as h(x)=(x-1)2-16.

Since they already know that a parabola’s points are mirrored around a line of symmetry, most of them quickly connect this knowledge and realize that the line of symmetry will always be smack dab in between the two lines, and that they just need to find the line visually, plug it into the two lines, and that’s the vertex. (something like this).

For most of the kids, therefore, the explanatory worksheet above isn’t necessary. They’re ready to start graphing parabolas in factored form. Some students struggle with the connection, though, and I have this as a backup.

This opens up the whole topic into a series of questions so natural that even the most determined don’t give a damn student will be willing to temporarily engage in mulling them over.

For example, it’s an easy thing to transform a parabola to have no x-intercepts. But clearly, such a parabola can’t be the product of two lines. Hmm. Hold that thought.

Or I return to the idea of a factor or factoring, the process of converting from a sum to a product. If two lines are multiplied together, then each line is a factor of the quadratic. Does that mean that a quadratic with no zeros has no factors? Or is there some other way of looking at it? This will all be useful memories and connections when we move onto factoring, quadratic formula, and complex numbers.

Later, I can ask interested students to sketch (not graph) y=x(x-7)(x+4) and now they see it as a case of multiplying three lines together, where it’s going to be negative, positive, what the y-intercept will be, and so on.


At some point, I mention that we’re working exclusively with lines that have a slope of positive one, and that changing the slope will complicate (but not alter) the math. Although I’m not a big fan of horizontal stretch outside trigonometry, so I always tell the kids to factor out x’s coefficient.

But recently, I’ve realized that the applications go far beyond polynomials, which is why I’m modifying my functions unit yet again. Consider these equations:


and realize that they can all be conceived as as “committing a function on a line”. In each case, graphing the line and then performing the function on each output value will result in the correct graph–and, more importantly, provide a link to key values of the resulting graph simply by considering the line.

Then there’s the real reason I developed this concept: it really helps kids get the zeros right. Any math teacher has been driven bonkers by the flipping zeros problem.

That is, a kid looks at y=(x+3)(x-5) and says the zeros are at 3 and -5. I understand this perfectly. In one sense, it’s entirely logical. But logical or not, it’s wrong. I have gone through approximately the EIGHT HUNDRED BILLION ways of explaining factors vs. zeros, and a depressing chunk of kids still screw it up.

But understanding the factors as lines gives the students a visual check. They will, naturally, forget to use it. But when I come across them getting it backwards, I can say “graph the lines” instead of “OH FOR GOD’S SAKE HOW MANY TIMES DO I HAVE TO TELL YOU!” which makes me feel better but understandably fills them with apprehension.

Two Math Teachers Talk

Hand to god, I will finish my post about the reform math fuss I twittered in mid-week, but I am blocked and trying to chop back what I discuss and I want to talk about something fun.

So I will discuss Dale, a fellow math teacher who was a colleague at my last job. Dale is half my age and three days younger than my son. Yes. I have coworkers my son’s age. Shoot me now.

He and I are very different, in that he is an incredibly hot commodity as a math teacher, whose principal would offer him hookers if he’d agree to stay, and gets the AP classes because he’s a real mathematician who majored in math and everything. He turns down the hookers because he’s highly committed to his girlfriend, who is an actual working engineer who uses math every day. I am not a hot commodity, not offered hookers, and not a real mathematician. I also don’t have a girlfriend who is an actual working engineer using math every day, but there’s a lot of qualifiers in that last independent clause so don’t jump to too many conclusions.

He and I are similar in that we both were instantly comfortable with teaching and the broad requirements of working with tough low income kids who don’t want to be in school, and extremely realistic about cognitive ability. We also don’t judge our students for not liking math, or get all moral about kids these days. (Of course, he is a kid).

We are also similar in that we like beer and burgers (he has a lamentable fondness for hops, but no one’s perfect), and still meet once or twice a month at an appropriate locale to talk math. I tell him my new curricular ideas, which he is kind enough to admire although his approach is far more traditional, and ask him math questions, particularly when I was teaching precalc; he tells me that most of the department wants him to be head, despite his youth and relative inexperience. We also talk policy in general. It’s fun.

“I have some news for you,” I told him, “but you will laugh, so you should put down your beer.”

He obligingly takes a pull on his schooner of Lagunitas IPA and sets it down.

“A new study came out,” I said, “and apparently, many high school algebra and geometry courses have titles that don’t actually match the course delivered.”

Dale, who clearly thought I was going in a different direction, did a double take. “Wait. What?”

“The word used was ‘rigor’. Like, some Algebra I courses don’t actually cover algebra I. Same with geometry.”

He looks at me. Takes another pull. “Like, not all algebra teachers actually cover the work formula?”

“Like, not all algebra teachers cover integer operations and fractions for two months. Like not all algebra teachers spend two weeks explaining that 2-5 is not the same as 5-2.”

“Uh huh. Um. They did a study on this?”

“They did.”

“They could have just asked me.”

“They can’t do that. They think math teachers are morons. But there’s more.”

“Of course there is.”

“Apparently, the more blacks and Hispanics and/or low income students are in a class, the less likely the course’s rigor will match the course description.”

He sighs. “I need more beer. Ulysses!” (that’s actually the bartender’s name.) “I’m assuming that nowhere in this study did they even mention the possibility that the students didn’t know the material, that the course content depended on incoming student ability?”

“Well, not in that study. But you know what happens when we point that out.”

“Oh, yeah. ‘It’s all that crap they teach in elementary schools!’ Like that teacher in that meeting you all had the year before I got here. ‘Integer operations and fractions! Damn. Why didn’t I think of that?‘”

“Yes. Actually, the researchers blamed the textbooks, which was a pleasant change from the platitude–and-money-rich reformers who argue our standards are too low.”

“Did anyone ever tell them if it were that simple, whether textbook or teacher, then we could cover the missing material in a few weeks and it’d all be over? Wait, don’t tell me. Of course they told them. That’s the whole premise behind….”

Algebra Support!” we chorused.

“But then there’s that hapless AP calculus teacher stuck teaching algebra support. He spent, what, a month on subtraction?”

“And the happy news was that at the end of the semester, the freshmen went from getting 40% right on a sixth grade math test to 55%.”

“The bad news being at the end of the year, they forgot it all. Net improvement, what–2 points?”

“Hell, I spend the entire Algebra II course teaching mostly Algebra I, and while they learn a lot, at the end of the course they’re still shaky on graphing lines and binomial multiplication. And I don’t even bother trying to teach negative numbers, although I do try to show them why the inequality sign flips in inequalities.”

“But it’s our fault, right?”

“Of course. But that’s not the best part.”

“There’s a best part?”

“If you like black comedy.”

“The Bill Cosby sort, or the Richard Pryor catching himself on fire sort?”

“Someone doesn’t know his literary genres.”

“Hey, we can’t all be English majors. What’s the best part?”

“The best part is that Common Core is supposed to fix all this.”

“Common Core? How?”

“By telling us teachers what we’re supposed to teach.”

I’d forgotten to warn Dale, who was mid-gulp. “WHAT???”

I handed him a napkin. “You’ve got beer coming out your nose. Yes. Checker Finn and Mike Petrilli always use this example of the shifty, devious schools that, when faced with a 3-year math requirement, just spread two years of instruction over three!”

“Wow. That’s painful.”

“Well, they don’t much care for unions, either, so I guess they think that when faced with a mandate that’s essentially a jobs program for math teachers, we teachers use it as an opportunity to kick back. But that’s when they are feeling uncharitable. Sometimes, when they’re trying to puff teachers up, they worry that teachers will need professional development in order to know the new material.”

“How to teach it?”

“No. The new material.”

“They think we don’t know the new material?

“Remember, they think math teachers are morons. On the plus side, they think we’re the smartest of teachers. (Which we are, but that’s another subject.) There’s still other folks who complain because ed schools don’t teach teachers the material they’re supposed to be teaching.”

“But we know that material. That’s what credential tests are for. You can’t even get into a program without passing the credential test.”

“Do not get me started.”

“So when the test scores tank, they’ll say it’s because teachers don’t know the material?”

“Well, they’ve got the backup teachers don’t have the proper material to teach the standards, in case someone points out the logical flaws in the ‘teacher don’t know the material’ argument.”

“Sure. If it ain’t in the textbook, we don’t know it’s supposed to be taught!”

“Don’t depress me. Yes, either we don’t know what’s supposed to be taught or we don’t know how to teach it without textbooks telling us to.”

Dale starts to laugh in serious. “I’m sorry, Governor. I would have taught vectors in geometry, but since it wasn’t on the standards, I taught another week of the midpoint formula.”

“I’m sorry, parents, I would have dropped linear equations entirely from my algebra two class, but I didn’t know they were supposed to learn it in algebra one!”

“Damn. A whole three weeks spent teaching fraction operations in algebra when it’s fifth grade math. I could have spent that time showing them how to find a quadratic equation from points!”

“I didn’t know proofs were a geometry standard. Why didn’t someone tell me? Here I had so much free time I taught my kids multi-step equations because my only other option was showing an Adam Sandler movie!”

“Stop, you’re killing me.”

“No, there’s too many more. Who the hell went and added conics to the standards and why wasn’t I informed? Here I spent all this time teaching my algebra II kids that a system of equations is solved by finding the points of intersection? Apparently, my kids didn’t bother to tell me that they’d mastered that material in algebra I.”

“I can’t believe it! Four weeks killed teaching kids the difference between a positive and a negative slope! Little bastards could have told me they knew it but no, they just let me explain it again. No wonder they acted out–they were bored!”

My turn to snarf my beer.

“Jesus, Ed, I’ve wondered why we’re pulling this Common Core crap, but not in my deepest, most cynical moments did I think it because they thought we teachers just might not know what to teach the kids.”

“That’s not the most depressing, cynical thought. Really cynical is that everyone knows it won’t work but the feds need to push the can—the acknowledgement that achievement gaps are largely cognitive—down the road a few more years, and everyone else sees this as a way to scam government dollars.”

“New texbooks! New PD. A pretense that technology can help!”

“Exactly. I’d think maybe it was another effort to blame unions, but no.”

“Yeah, Republicans mostly oppose the standards.”

“Well, except the ‘far-seeing Republicans’ who just want what’s best for the country. Who also are in favor of ‘immigration reform’.”

“Jeb Bush.”

“Bingo. You’ll be happy to know that libertarians hate Common Core.”

“Rock on, my people!”

“Yeah, but they want also want open borders and privatized education.”

“Eh, nobody’s perfect.”

“But all that depressing cynicism is no fun, so let me just say that I would have taught sigma notation except I thought that letter was epsilon!”

“Hey, wait. You do get sigma and epsilon confused!”

“No, I don’t, or I wouldn’t call the pointy E stuff sigma notation, dammit. I just see either E shape out of context and think epsilon. Why the hell did Greeks have two Es, and why couldn’t they give them names that start with E? Besides, the only two greek letters I have to deal with are pi and theta, and really, in right triangle trig there’s no difference between theta and x.”

“Well, you’re going to have to stop making that mistake because thanks to Common Core, you’ll know that you’re supposed to teach sequences and series.”

“Damn. So I won’t be able to teach them binomial multiplication and factoring and let them kick back and mock me with their knowledge, which they have because they learned it all in algebra I.”

“Here’s to Common Core and math research. Without them, America wouldn’t be able to kid itself.”

We clinked glasses just as Maya, Dale’s girlfriend walked in, a woman who actually uses centroids, orthocenters, and piece-wise equations in her daily employment. The rest of the evening was spent discussing my search for more real-life models of quadratics that don’t involve knowing the quadratic formula first. She offered road construction and fruit ripening, which are very promising, but I still need something organic (haha), if possible, to derive the base equation. So far area and perimeter problems are my best bet, which gives me a good chance to review formulas, because until Common Core comes out I won’t know that they learned this in geometry. I wondered if velocity problems could be used to derive it. Dale warned me that it involved derivations. Maya was confused by my describing velocity problems as “-16 problems”, since gravity is either gravity is either 32 ft/sec/sec or 9.8 m/s/s. Dale interpreted. I’m like Jeez, there are people who know what gravity is off the top of their heads? This is why I don’t teach science. (edit: I KNEW I should have checked the numbers. I don’t do physics or real math, dammit. Fixed. )

But all that’s for another, happier, post.