Lowering Standards

I'm not one of those mythical teachers who likes to put trick questions on a test or quiz so everybody flunks.  My assumption is that I could probably write an assessment that the vast majority of my students would fail--but what's the point in that?  I teach the material, and then assess to see if the students learned what they were supposed to have learned.

What's a "reasonable" grade distribution in a class?  (Not that I'll get into it here, but I'm in sort of a "debate" with a parent about just that topic in one of the courses I teach.)  I both teach to and assess to a standard; thus, it's possible that every student could get an A, and also possible that every student could get an F.  In that latter case I'd have to reflect and determine if poor teaching on my part was to blame for the poor result, but what about the former case?  If everyone got an A, would that mean my standards were too low?

Not necessarily.  I teach two types of courses, spanning the academic abilities of my school's students.  In two of the three courses I teach, most of the students are college-bound and thus are expected to do well.  In two of the three courses I teach, the vast majority of the students are seniors and often take "senioritis" to new heights.  In one of the courses I teach, the academic level is about that of upper elementary school or at most 7th grade.  I doubt anyone would expect the grade distribution in that class to be the same as the grade distribution of a class of college-bound students.  Remember, the content of that last class is already low, I don't need to make a mockery of it by not expecting students to meet even those low standards.

So in one of my heavily senior, college-bound classes yesterday, I gave a quiz.  Of the 22 students in that class, 5 received an A+, 5 received an A-, and 8 received F's.  As I've discussed with teacher friends in other departments, this "upside-down normal curve" distribution is a common one.

Almost half the students in the class got an A, and almost as many scored an F.  Does that sound like an issue of poor teaching?  It's clear that the material was put out.  Does it sound like an issue of a poor quiz?  Again, it doesn't appear that the material was at all out of reach of the students--unless you think that most students should get an A, and that I taught primarily to only the A students.

Some people say that if almost half my students got an A, that the quiz was too easy.  I don't agree with that.  The material wasn't very difficult, but it is important foundational material for the rest of the semester--that's why I quizzed it, to make sure students understood it, and the quiz involved nothing more and nothing less than what we'd gone over in class.  To be blunt (and I was told this by more than one applicable student), those who failed did so mostly because they didn't study at all, and thus couldn't remember all the steps that went into the topic material.

That's what other teachers are seeing, too, and not just math teachers--this "upside-down normal curve", where there are a lot of A's and a lot of F's and not much in between.  In many cases it is a case of lowered standards--unless you think A's should be the most common grade in a class--and those who fail often do so because they put in no effort at all.

Some teachers have a real problem with giving a lot of low grades. They'll lower standards in order to "get the grades up", but all that does is lower standards for everyone.  Those who fail due to lack of effort will fail due to lack of effort no matter if the standard is high or low.  Those at the top with high standards will also be at the top with low standards.  And a student who will do just enough to get by will do that with high standards or with low standards.  Those students who try, though, get higher grades when you lower standards.  Thus, the B's and C's get pushed up to A's, but the bottom grades stay where they are.

I resist lowering standards.  Today's academic standards are not as high as they were 20 years ago, despite what the Common Core zealots will tell you, so what I teach isn't as rigorous as it was 20 years ago.  Does anyone deny that lower standards, and the grade inflation they help bring about, are an issue in education?  And yet, still so many failing grades.

I have no doubt that the results of this chapter's test will be better than the results of this one quiz.  Still, though, the "upside-down normal curve" issue isn't going away any time soon.

Standardized Testing

If you want to know if students are truly learning, you have to have an objective test, given and graded by objective people.  That just seems obvious to me:

Now, consider what has transpired over the past twenty years in the USA. We were headed in the direction of other countries’ testing system structures at the turn of the millennium, with state-led consequential achievement tests for students administered only every few grade levels.[1] Plus, we benefitted from two competing college admission tests, whose scores could be submitted for consideration simultaneously to thousands of universities worldwide. [2]

Then came three disruptions, each of which, I would argue, served to undermine the utility of US educational testing.

First came passage of the No Child Left Behind (NCLB) Act (2001–2002), which imposed a federal mandate on all public schools (including charters). The NCLB insistence on annual administrations of tests across seven grade levels virtually guaranteed lax security: teachers administer tests in their own classrooms to their own students and principals manage the distribution and collection of test materials in their own schools. Then, we judge schools and teachers based on those NCLB test scores they themselves proctor.

Now, consider what has transpired over the past twenty years in the USA. We were headed in the direction of other countries’ testing system structures at the turn of the millennium, with state-led consequential achievement tests for students administered only every few grade levels.[1] Plus, we benefitted from two competing college admission tests, whose scores could be submitted for consideration simultaneously to thousands of universities worldwide. [2]

Then came three disruptions, each of which, I would argue, served to undermine the utility of US educational testing.

First came passage of the No Child Left Behind (NCLB) Act (2001–2002), which imposed a federal mandate on all public schools (including charters). The NCLB insistence on annual administrations of tests across seven grade levels virtually guaranteed lax security: teachers administer tests in their own classrooms to their own students and principals manage the distribution and collection of test materials in their own schools. Then, we judge schools and teachers based on those NCLB test scores they themselves proctor.

Read the whole thing.

A Better Method Than the Quadratic Formula?

Uh, no.

Two days ago I wrote about an article describing a faster way to multiply than the standard multiplication algorithm.  I closed that post with "The article originally appeared in Popular Mechanics.  They should probably stick to what they know best, because they're way out of their league here."  I could close this post in exactly the same way, as PM has stepped in it again.

First, the article.  Go ahead and read it, it's brief.  Supposedly, a Dr. Loh at Carnegie Mellon has developed a way to solve quadratics equations that is easier than the quadratic formula or completing the square.  In the video posted on his own web site, Dr. Loh states that while pieces of this new method have been known for hundreds of years or more, "How can it be that I've never seen this before, and never seen this in any textbook?"  Well, I'll tell you, Dr. Loh.  But first, let me bring up two points:

1)  He didn't "develop" this, it's well-known to those of us adept at algebra, and

2)  How practical is this method when the answers don't come up integers?

Here's the video mentioned above, in which Dr. Loh explains his new and exotic procedure. Take 3 minutes and 48 seconds to watch it.

After you've watched it, ask yourself this:  How did he get the sum and the product needed to solve the problem?  

It took me a moment to figure it out, but then it came to me.  Follow my reasoning here.

Take any quadratic equation.  Manipulate it so that there is 0 on the right side of the equal sign.  Complete the square.  In a couple more steps you've derived the Quadratic Formula, which will allow you to solve any quadratic equation.  Bottom line:  you know the quadratic formula works because you can follow each step of the "completing the square" process (assuming you know that, which is something any Algebra 1 student should understand).  

Given a quadratic equation of the form

you can use the Quadratic Formula to solve for the two solutions, which will always be

.

Add those two solutions together and you get -b/a, multiply them and you get c/a.  That's the information that Dr. Loh used in his method, which you would not understand unless you knew these answers from the Quadratic Formula.  In the video, -b/a=8 and c/a=12.

Also, we know that a quadratic of the form above has a vertical axis of symmetry which, being vertical, always crosses the x-axis and goes through the vertex of the graphed parabola.  Thus, if there are any real solutions to this problem, the x-intercepts, they must be equidistant from this line.  This distance is what Dr. Loh calls "u".  So, if you need a sum to be 8, (4+u) and (4-u) work as the two roots because they sum to 8 and are equidistant from the line of symmetry, and then you multiply them together and set the product equal to 12.

So far, so good.  Well, not good, but not horrible--Dr. Loh's method is great for those of us who already understand algebra, but it's what we call "mathemagic" for people who are learning algebra.  One of the Algebra 1 standards in California's 1997 Math Standards was that students would be familiar with the derivation of the Quadratic Formula by completing the square.  They would know where the formula came from, and that it wasn't conjured from thin air by some mystic.  No such luck doing that with Dr. Loh's method, where you have to just accept his this-will-work pronouncements.  His method is like that of the ancient Babylonian "algebraists"--just follow these step-by-step instructions, don't worry about where they came from, and your answer will be correct.  It's very utilitarian, it leads to being able to get an answer but it doesn't lead to any understanding.  In this way, Dr. Loh's method is the very antithesis of what is supposed to be one of the big selling points of Common Core:  understanding.

In the Popular Mechanics article and in Dr. Loh's own video, the quadratic equation to be solved had a=1 (students love those because they're much easier) and the answers came out to be integers.  What happens if those two conditions aren't the case?  Dr. Loh never explicitly mentioned "-b/a" or "c/a", I had to infer the former from his work and the determine the latter from of my own knowledge.  Here's how to solve such a problem using the Quadratic Formula as well as Dr. Loh's method:

click to enlarge

Is it obvious to you that Dr. Loh's method is better than the Quadratic formula?  It's certainly not to me, especially in this problem where the solutions aren't integers.  Dr. Loh's method is one of those cool applications that those of us already adept at algebra delight in, but as a tool for teaching the foundations of quadratic equations, I find it lacking in many ways.

The bottom line is that we should not be getting math information from Popular Mechanics--not if we want anything meaningful, that is.

Common Core in the Age of Coronavirus

These folks have rewritten the Common Core standards for education during the coronavirus home isolation.  One of my favorites:

Domain 2: Screen Time

...

Grades 6-8

2-A. Students will learn that their parents do not want to know what a “TikTok” is, nor do they want to see your “TikTok,” but it had better be appropriate.

Does anybody besides another teenager really want to see your "TikTok"?

Two others:

Domain 4: Content

...

Grades 9-12

3-A. Students will learn that Romeo and Juliet had it easy, because they only had to contend with an inter-family feud, and not the cancellation of prom, or the indefinite postponement of “going to the next level,” which their significant other definitely gave affirmative consent for, via text, last week...

3-C. Students will learn exactly how irritating, boring, aggravating, and absurd it can be to live through history. They will also learn that attendance in History IRL is mandatory.

Where Might Ed Reform Turn Now?

Forbes has an interesting piece on ed reform, where we've been and where we might be going:

Have the past ten years been a “lost decade” for education reform? Or is the focus finally shifting to something that might actually work?

Ten years ago, reformers were confident they were on the brink of fixing the U.S. education system—especially for the most disadvantaged students. As a neophyte in the movement, I often heard some version of “We know what works.” The agenda included:

· Replacing bad teachers with “rock stars;”

· Creating schools—outside the traditional system, if need be—where there was order instead of chaos;

· Focusing relentlessly on reading and math skills;

· Relying on data from frequently administered tests in those subjects to guide instruction; and

· Using end-of-the-year test scores to determine which schools were providing a high-quality education.

All this plus the Common Core standards, released in 2010, was to usher in an era where all teachers and students would be held to high expectations, backed up by rigorous tests. A child’s zip code, as the saying went, would no longer determine her destiny.

None of this worked...

Now that the decade is coming to a close, there’s a small flurry of retrospection. One conservative commentator, calling the 2010s “ed reform’s lost decade,” advises those aiming to reduce poverty to focus instead on initiatives like “incentivizing work.” A progressive responds that he sees “a lot of good things happening” in ed reform, but they’re modest compared to the hopes of a decade ago (for example: U.S. test scores at least remained stagnant while some other countries’ declined). They and others argue we need more school choice. Still others, including Democrats competing for the presidential nomination, blame too much choice for our lack of progress—along with low teacher salaries, poverty, and racism.

At the same time, there’s a development in the education world that has gotten relatively little attention and seems to belong to another universe. It’s not about school choice or teacher quality or any of the other things that have dominated the public conversation. Instead, it’s about what gets taught in classrooms and how—a subject in which reformers have shown surprisingly little interest.

The huge and largely unreported story is that American educators are trained to believe in ideas and methods that have little or no evidence behind them—and often conflict with what scientists have discovered about the learning process. Classroom materials rest on similarly flawed assumptions. The disjunction between evidence and practice makes it unnecessarily difficult for teachers to do their jobs and for all but the ablest and most advantaged students to learn. The glimmer of hope is that a growing number of teachers—along with some administrators, policymakers, philanthropists, and parents—are beginning to push for change.

The leading edge of this movement has focused on reading, and primarily on the aspect of reading commonly known as phonics. That’s understandable. The debate over phonics has been around for a long time, and it may be easier for people to wrap their minds around it—although it’s also easy for them to dismiss it. Many teachers believe they’re already teaching phonics when in fact, because of deficiencies in their training, they’re not...

Teacher-training programs promote the idea that education is ideally a natural process in which students discover or “construct” knowledge for themselves. “Teacher talk,” therefore, should be kept to a minimum, and group work or inquiry-based learning should be maximized. Under this theory, if teachers provide comprehension “skills,” they don’t need to build knowledge; kids can eventually use their “skills” to do that through their own reading. But cognitive scientists have found that when learners don’t know much about a topic, it’s far more effective for an expert to explain it and guide discussion than for them to try to figure it out on their own. Similarly, if you know nothing about chemistry or biology, you’re going to have a hard time acquiring knowledge from reading an article on DNA, no matter how many times you’ve practiced “finding the main idea.”

The sad truth is that in their well-intentioned zeal for “data,” reformers have only made this problem worse.

Go read the whole thing. Seriously.  And then think, what is the problem in math?

College Entrance Exams

In general I support objective tests, but the devil is in the details.  I don't really like AP, for example, because I believe AP content is too narrow in the classes about which I know.  If this article is right about the ACT and SAT, I'll support their use even less, too:

Since college preparedness exams became standard, education has become woefully uninspired. Students graduate with the basics of reading and writing under their belt but have engaged little with some of the most crucial aspects of education. Students read too little of the conversations and works that have informed some of the most impactful intellectual and social developments in history.

That’s because most states now abide by Common Core, a set of K-12 educational standards in math and English incentivized by federal grants. It’s a boxed-in method of teaching that requires teachers, by 8th grade, to prioritize functional texts in exposition over works of literature. By the twelfth grade, 70 percent of texts read in English classes must be informational in nature. So, then, the literary works that require deep reading and the development of abstract thought fall to the wayside in favor of the simplistic and mundane. This is just one example of Common Core’s overall emphasis of skills training over meaningful content—a system that discourages creativity and hampers student desire to be a life-long learner.

The SAT and Common Core standards have the same pedigree: David Coleman, president of the College Board, re-vamped the SAT in an effort to align the test with Common Core, telling the Institute for Learning that “teachers will teach towards the test. There is no force strong enough on this earth to prevent that.” Of course, these tests, like the curriculum they reflect, facilitate neither genuine academic growth nor the understanding of human virtue. The organization behind the ACT also publicly supported Common Core standards when the initiative began. But this testing/standards relationship really only stunts student learning.

Read the whole thing. What do you think?

If We Judged Govt Programs By Their Actual Outcomes Rather Than Their Wish-For Outcomes....

Why does no one seem to care?  Is it because Common Core was pushed by Saint Barack's administration?  Had any Republican been so instrumental in this, people would (justifiably) be marching with pitchforks:

At the topline, we have seen a story of decline ever since 2013. My fear is that this is not a coincidence. From 2013 onward, the Common Core took firm root in most states and we saw a sea change in school discipline and an apparent explosion of tablets and laptops in the classroom. I’ve grown increasingly concerned that the education reform movement has hurt the students it is trying to help, especially students of color.

Of course, NAEP can’t confirm this hypothesis. It can tell us what is happening but not why.

But I wanted to know more about what was happening, focusing on African American achievement in districts and states from 2013–2019, and what I found, as displayed in table 1, seems well worth ringing an alarm about...

At the state level, the larger sample sizes allowed me to look into African American achievement by gender. I found that, at the national level and in many states, African American males saw greater losses than African American females. Given this alarming pattern—and that, as Fordham’s Erika Sanzi has lamented, boys are often left out of public policy conversations—I decided to display the data in table 2 for African American males from 2013 to 2019...

Folks who claimed that the Common Core, discipline reform, and more tablets and laptops would lead to significant gains for African American students have, at this point, seen their hypotheses fairly well falsified...  (boldface mine--Darren)

The ghastly data on African American achievement should have raised major alarm bells. But in a movement ostensibly dedicated to racial equity, it seems to have gone mostly unnoticed.

I Never Did Like Common Core

Years ago I anticipated this would be the problem, at least in math:

With irresistible prodding by Gates and then-President Obama, the Common Core national standards were adopted by the vast majority of states, which have also adopted tests and curricula aligned with those standards.

But a new large-scale study by the federally funded Center for Standards, Alignment, Instruction, and Learning (C-SAIL) has found that since the adoption of Common Core there has been a decline in key test scores.

C-SAIL researchers analyzed changes in student performance on the National Assessment of Educational Progress, or NAEP, from 2010 to 2017.

They had assumed that Common Core would raise student performance on the NAEP exam, but they were in for a surprise.

“Contrary to our expectation,” they reported, the data revealed that the Common Core standards produced “significant negative effects on 4th graders’ reading achievement during the 7 years after the adoption of the new standards.”

When analyzing the results of a selected group of states, fourth-grade reading achievement would have improved more “had the states continued with their old standards, thus reflecting negative effects of the new [Common Core] standards.”

In other words, if those states had ignored the entreaties by Gates, Obama, et al., they would have been better off.

In addition to the decline in reading performance among fourth graders, the C-SAIL study also found that Common Core “had a significant negative effect on 8th graders’ math achievement.”

What’s more, the performance of students declined significantly in specific reading and math categories, such as literacy experience and numbers properties, the longer Common Core was in effect.

Study co-author Mengli Song said: “It’s rather unexpected. The magnitude of the negative effects [of Common Core] tend to increase over time…”

…Some blame the failure of Common Core on process issues, such as lack of adequate teacher training, but the key culprits are the standards themselves and the type of teaching promoted by Common Core.

When Common Core was first being adopted by states, James Milgram, a Stanford math professor who served on a key Common Core committee, warned that by the end of the fifth grade the material covered by Common Core’s math standards “was more than a year behind the early grade expectations of high-achieving countries,” and that “by the end of the seventh grade, [Common] Core standards are roughly two years behind.”

By high school, “Common Core — in its fullness — does not prepare students even for a full pre-calculus class,” notes Ze’ev Wurman, a former senior education policy advisor under President George W. Bush.

It wasn't hard to look at the standards and see the difference.

How Are Kids Doing Under Common Core

Are all our students Stanford-bound now?

It’s been about nine years since the Obama administration lured states into adopting Common Core sight unseen, with promises it would improve student achievement. Like President Obama’s other big promises — “If you like your doctor, you can keep your doctor” — this one’s been proven a scam.

“If you set and enforce rigorous and challenging standards and assessments; if you put outstanding teachers at the front of the classroom; if you turn around failing schools — your state can win a Race to the Top grant that will not only help students outcompete workers around the world, but let them fulfill their God-given potential,” President Obama said in July 2009.

He went on to state his faith that Common Core — at that point unwritten — would “not only make America’s entire education system the envy of the world, but we will launch a Race to the Top that will prepare every child, everywhere in America, for the challenges of the 21st century.” Race to the Top was a $4 billion money pot inside the 2009 stimulus that helped bribe states into Common Core.

So here we are, nine years later. Common Core has been officially rolled out into U.S. public and even many private schools for at least three to five years now. Are American children increasingly prepared for the “the challenges of the 21st century”? We’re actually seeing the opposite. They’re increasingly less prepared. And there’s mounting evidence that Common Core deserves some of the blame.

I'm glad the author said "some of the blame", as I've previously chronicled too many examples of forces outside of schools having a negative impact on learning.

Still, we teachers own a large part of this blame.  Saint Barack wanted Common Core, so large swaths of teachers and their unions jumped on that bandwagon.  Like so many other mistakes, we continue to try to find ways to make it work rather than admitting failure and trying something more rational.

I won't speak to the English standards, but the California math standards that were replaced by Common Core were more clear, more understandable, and more rigorous than the Common Core math standards, and California students did better under those old standards.  And just so you know, they were imposed by a Democratic governor.

Common Core Disaster

I'm not qualified to comment on the Common Core English standards, but I'm qualified enough to comment on the CC math standards.  I stand by what I've said since those math standards were first published--they're not as rigorous as California's 1997 standards.  Nor are they as clear.

Essentially, they're crap compared to what we had.

But if students are learning more, they're not crap, right?  The proof is in the pudding, right?  Why yes, yes it is, and California's kids aren't doing better in math:

The Common Core curriculum-content standards are a national listing of topics that students are expected to learn in the subjects of English and mathematics. An independent initiative of three Washington, D.C.-based organizations created the national standards, but they were endorsed and promoted by the Obama-era U.S. Department of Education. The standards were released in June 2010. Their summer launch meant that teachers and parents did not have much of an opportunity to discuss their merits and drawbacks. Abiding by the standards was necessary for states to be eligible for massive federal grants. California adopted the national standards and fully implemented them in 2014-2015.

This was a mistake. Looking at how the state’s students performed in math before and after the standards were implemented, it’s clear that the old system served students much better. Before Common Core, California had its own mathematics curriculum-content standards. They had been written largely by the faculty of the Mathematics Department at Stanford University and were adopted by the state in December 1997...

After the 2010 vote, we wrote an opinion piece where we explained why adopting Common Core was the wrong decision for California, and we predicted that only “an elite few students will be able to succeed” in eighth grade algebra under Common Core. Eight years later, that, indeed, seems to be the case...

Because California set up its 1997 standards to prepare all students for Algebra I in eighth grade and because it attempted to place all those who were ready into such classes, the biggest beneficiaries of this effort were ethnic-minority and low-income students. While the whole cohort success increased by a factor of three, the rates of success jumped by factors of five for African Americans and six for Latinos and low-SES students—double the rate of the whole cohort...


From the outset, California’s education officials recognized that improving student achievement so substantially would take time. The state overhauled its entire math curriculum. New instructional plans introduced pre-algebra concepts as early as third grade. School districts augmented on-the-job math training for teachers, approved math textbooks that matched the curriculum, and revised the state accountability system to include teacher supports and rewards for teaching Algebra I by eighth grade.

But with the Common Core standards, this progress began to stall. Common Core expects Algebra I in the ninth grade. That threw a monkey wrench in California’s longstanding effort introducing the math class to students earlier. As seen in the chart below, in the four years under Common Core, the number of eighth graders taking Algebra I in California dropped precipitously to 19 percent in 2017, taking California back to where it was around 1999, when early algebra taking was the privilege of the elite. And while all demographic groups lost ground, the loss for Latino and African American students was much deeper than for white and Asian Americans.

Common Core proponents repeatedly praise it for its “rigor,” how it will prepare children for the twenty-first century, enable more American students to pursue STEM, and increase America’s competitiveness in the world. Yet when it comes to the clearest benchmark of rigor and expectations on par with international high-achievers—Algebra I in eighth grade—the Common Core not only punted, but it retarded and reversed the progress California had made during the pre-Common Core period, and the Common Core regress disproportionally hit disadvantaged minorities. The reduced rigor in K-8 education has resulted in less enrollment in advanced mathematics courses in high school, particularly of low-income and minority students. This reduces their chances of pursuing challenging and rewarding careers...

California’s adoption of Common Core caused an earthquake in mathematics education in the state. In K-12 education, the gains of the previous 10-15 years—as reflected in large increases in students successfully taking Algebra I early, and in students taking more advanced math courses in high school—have been reversed. As worrisome is the fact that disadvantaged minorities (who made faster gains than the rest of the cohort before Common Core) are losing ground after Common Core at faster rates...

Adopting the Common Core math curriculum standards has proven to be a setback for California. When California had its own mathematics standards before Common Core, its students performed significantly better in math than they have after the Common Core was put into effect. The hardest hit by this change were the most vulnerable students. The state of California Education under Common Core is not good.

I posted the first comment at the link above:

8th grade Algebra 1 is one valuable marker, and you rightly point out that California's students have slipped on that metric since California adopted Common Core.  But wouldn't a better standard be "how well are students learning?"  How were California students performing on benchmark tests before CCSS, and how does their performance now compare?

They Will Keep Asking The Question Until We Give The Answer They Want Us To Give

A few years ago, after California adopted the Common Core standards, our district suits pondered whether we should keep our traditional algebra-geometry-algebra pathway or change to an integrated math pathway.  Actually, they didn't ponder at all, the decision was made as soon as someone came up with the idea, but I'll come back to that.  Anyway, a meeting was held at the district office, and dozens of math teachers from our middle and high schools came.  Only three teachers voted to change to the integrated pathway--two from our lowest performing school, saying, "Our kids are so low we're willing to try anything", and one who liked the old CPM program and wanted to return to it.  The rest of us were adamant:  NO.

The rationale given for the "potential" change was this:  "If we switch to Common Core but keep the traditional pathway, our teachers won't change the way they teach.  If we make this major switch, they might be more willing to change how they teach."

Right there, that's two slaps in the face for the math teachers in our district.  Everything's the teachers' fault.

Last year there was a "listening circle" in which students in Integrated Math 1 were brought in to discuss what might be done to improve the program.  The students were clear, they wanted a real textbook, as opposed to the paperback fill-in-the-blank monstrosities we issue them.  That comment, the most common comment from students, was conveniently left out of the listening circle's summary report.

Another slap in the face.

This week all the math teachers in my district got an email from a district suit.  We were told that our district is contracting with an organization that will help determine what is wrong with the math program in our district, and we need to click on a link and take a survey from this vendor.  Did they ask the math teachers what would help improve things?  When I was a manufacturing manager, if we had quality problems on a particular line, I'd ask the operator what the problem was.  They could usually tell me, and as often as not would provide a solution. But my district didn't ask the math teachers what can be done, they went straight to a consultant.

That's a fourth slap in the face.

The survey itself was a treat.  The questions included gems like, "What professional development do you need in order to do a better job?" and "Do you feel competent to teach ?"

At the end was the perfunctory "Please put in any additional comments here" box, and boy, did I.  The problem is that no one will read it, and no one will care.  My comments are not wanted or needed, because whatever they're going to do, the decision has already been made.  My district has made me cynical enough to believe that whatever it is they're doing, it's only window dressing so they can say they're "doing something".

Our integrated math program is a shambles, but I don't think it's because our district's math teachers are bad teachers.  Partly it's because integrated math makes about as much sense as integrated science or integrated foreign language, part of is because our textbook adoption process is an abomination, partly it's because the rules imposed on us (e.g., all Integrated 1, 2, and 3 books must come from the same publisher) force us to buy lousy books, and partly it's because the math isn't as "integrated" as it is "hodge-podge".

They've told me to dig a hole, but only gave me a screwdriver with which to do it.  Now they're asking what professional development I need in order to do a better job at digging holes with screwdrivers.

Yes, Please Focus On This Instead

Small schools and Common Core?  Thank Bill Gates.

Quit screwing with other people's kids, Bill.

I'm probably doomed to get Alzheimer's.  Both my grandmothers had it, and...  So, I'm doomed.

I don't know if Bill's money would direct research into dead ends or if it would open up new roads, but I know that I'm probably going to get Alzheimer's either way.

So, after screwing up education, would Bill and his money be a benefit in Alzheimer's research, or a hindrance?  I'm willing to give him a shot.  After all, those with a predilection for Alzheimer's are already screwed, unlike the children on whom Common Core was thrust.  They were only screwed after Common Core.

A Reasonably Pleasant Day--With Yahtzee!

I didn't have a prep period today--three 2-hr classes!

Usually such days are murder.  No one, not even a math teacher, likes being in a math class for 2 solid hours.  But today I was able to take a little of the edge off.

I taught some new material.  We took a brief recess.  And then I taught my students to play Yahtzee.

Huh?  Wha?  You want to know where Yahtzee is in the Common Core math standards?  I'll admit that it's not explicitly called out, but there are plenty of standards relating to probability.  And that's how I used Yahtzee.

It used to be fairly common on probability tests to ask questions related to the probability of drawing such-and-such a card from a deck, or the probability of getting this card followed by that card if you don't replace the first card, etc.  The problem is that so many of today's young people don't know what constitutes a deck of cards!  What used to be common knowledge isn't so common anymore.  So rather than continue to ask questions about a deck of cards, I taught my students how to play Yahtzee and in the process of doing so, asked probability questions. 

For example, I might have rolled 2 3's, 2 4's, and a 5 on my first roll.  What's the probability of getting a full house?  If I roll a 2-2-3-4-5 on the first roll, what's the probability of getting a large straight?  (BTW, both of those answers are the same.)  If I get a 1-2-3-4-6 on the first roll, what's the probability of getting a large straight?

I admit that a large reason for playing this was for fun, and make no mistake, there was lots of hooting and hollering and flexing when great things happened!  Still, though, I was able to make the lesson almost as much about math as it was about having fun. 

It was much more enjoyable, and much easier, to teach Yahtzee than to teach any number of card games (along with their associated probabilities).  And when I ask questions about probabilities in Yahtzee on the test, I won't have to explain what I mean by "large straight" or "full house", etc.

Several of my students said they were going to download Yahtzee onto their phones :-)

A Refresher On What's Wrong With Common Core

I was searching my old posts for one I'd written about the Gates Foundation's failure in the small schools movement, and thus I was looking through posts that contain the word "Gates".  I came across this "Some Of What's Wrong With Common Core" post from 3 1/2 years ago, and link to it here so you can read it again.  The criticisms are still as fresh today as they were then.

Update:  the 100-year-old lady in this video is right.

Trillions Of Dollars Later, The Hubris Is Illuminated

I don't think it comes as a big surprise that I've not been a big fan of the Common Core standards.  The standards in math are not clearly written, and they're not as good as the 1997 California math standards they replaced.  I won't speak to the English standards, but the math standards are definitely a stop down.  California's 1997 math standards were benchmarked against Singapore's, as well as those of other countries whose students routinely outperform US students.  The Common Core standards were piloted and benchmarked against...someone's idea.  And the cost has been astronomically high, both in dollars and in failed education:

Since 2009, the Gates Foundation’s primary U.S. activity has focused on establishing and implementing Common Core, a set of centrally mandated curriculum rules and tests for what children are to learn in each K-12 grade, with the results linked to school and teacher ratings and punitive measures for low performers. The Gates Foundation has spent more than $400 million itself and influenced $4 trillion in U.S. taxpayer funds towards this goal. Eight years later, however, Bill Gates is admitting failure on that project, and a “pivot” to another that is not likely to go any better.

“Based on everything we have learned in the past 17 years, we are evolving our education strategy,” Gates wrote on his blog as a preface to a speech he gave last week in Cleveland. He followed this by detailing how U.S. education has essentially made little improvement in the years since he and his foundation — working so closely with the Obama administration that federal officials regularly consulted foundation employees and waived ethics laws to hire several — began redirecting trillions of public dollars towards programs he now admits haven’t accomplished much.

“If there is one thing I have learned,” Gates says in concluding his speech, “it is that no matter how enthusiastic we might be about one approach or another, the decision to go from pilot to wide-scale usage is ultimately and always something that has to be decided by you and others the field.” If this statement encompasses his Common Core debacle, Gates could have at least the humility to recall that Common Core had no pilot before he took it national. There wasn’t even a draft available to the public before the Obama administration hooked states into contracts, many of which were ghostwritten with Gates funds, pledging they’d buy that pig in a poke.

But it looks like this is as close to an apology or admission of failure as we’re going to get, folks. Sorry about that $4 trillion and mangled years of education for American K-12 kids and teachers. Failing with your kids and money for eight years is slowly getting billionaire visionaries to “evolve” and pledge to respect the hoi polloi a little more, though, so be grateful.

Gates and his foundation were also ardent supporters of the "small school movement", which failed so bad that any mention of it was at one time completely erased from the foundation's web site.  At least no students were harmed by the failures of DOS 4.0 and Windows 8.

The Impetus Behind Common Core--One Man's View

Jim Milgram, the Stanford professor who was the primary author of California's 1997 math standards, sent the following email to a list of which I am a member, and gave me permission to quote it here with attribution:

I wish you were right, but here in California, Ze'ev Wurman's work shows that the 12 years of reasonable standards and state enforcement actually did reduce the achievement gap and in the right way. Scores for "minority" groups went up significantly, while scores for others were roughly unchanged.

As you know, I was on the Common Core Validation Committee, so I had a first row seat to what was happening. You should have seen the sudden increase among the math educators involved -- when Ze'ev's results first appeared -- in their desire to get rid of the CA standards.

I had a long argument with the most well known among them. I focused on explaining our results in eighth grade algebra which had shown a very high percentage of those minority kids passing the course and scoring pretty well on the state exam.

The more they understood what was going on, the more determined they became. I recall that when I mentioned that fully 2/3 of the CA students were taking eighth grade algebra, one of them said that's horrible, and the others agreed. That's when I realized I wasn't speaking the same language they were, I had to get out, and I finally felt I had to report to Governor Schwarzenegger's office that CA should not get involved with Common Core. Unfortunately, the Race to the Top money had already been announced, and CA was desperate for funds. So it was too late. He tried to keep eighth grade algebra, but it only took Jerry Brown and Mike Kirst one or two years to get rid of it.

Jim

He has had more direct experience in this than I have, and I have no reason to doubt his sincerity.

I Figured Out Why One Of My Classes Has Me Down

My district switched to so-called integrated math a few years ago, and at my school we've added a new course each year.  We started with Integrated Math 1 two years ago, added Integrated Math 2 and 2+ last year (2+ is a fast track to calculus), and this year we added Integrated Math 3 and 3+ (students in 3+ will take calculus next year, by passing pre-calculus). 

Would I rather have stuck with Algebra 1, Geometry, and Algebra 2?  Heck yes!  And so would the vast majority of my district's math teachers.  That wasn't the input the district suits wanted, though....

Anyway, my department co-chair and I are teaching the two 3+ classes.  We've already planned out which lessons are to be covered each day for the entire school year so that we can cover the material needed to prepare students for calculus.  Not only is there no time for reteaching, there's not enough time for teaching in the first place.

I've been somewhat stressed lately, feeling like I'm not a very good teacher in that course.  These are exceptionally capable students, and I'm just shoveling information at them as fast as they can take it.  If they can take it, what's the matter, right?  Aren't I usually the person who says we should let students accelerate as fast as they can handle?  Yet here I am, in a super-accelerated class, and I feel like I'm not really teaching. Since I pride myself on my teaching, this class has me down.

Something's not right, and I couldn't quite put my finger on it--until yesterday.

As I said, I'm shoveling those students the information as fast as I can. The problem is that I'm not teaching.  I'm showing students how to solve problems, teaching them what they need to know how to do, but I'm not teaching them why what I'm teaching them works.  I'm not giving them the background information that explains an algorithm or amplifies a concept.  Here's the task, learn it, move on.

All that deep understanding, all the Common Core stuff?  That's what I'm not doing.  Believe me when I tell you that there isn't time to do so.  I've stated that I have these kids drinking from a fire hose, and that analogy isn't so extreme.  There isn't time in a 60 minute class to teach more.

That's what's been bothering me.

College and Career Readiness

If "equality" means everyone is equally dumb and unprepared, to heck with that kind of equality:

While ersatz “credit recovery” and grade inflation devalue the high school diploma by boosting graduation rates even as NAEP, PISA, PARCC, SAT, and sundry other measures show that no true gains are being made in student achievement, forces are at work to do essentially the same thing to the college diploma.

Observe the new move by CalState to do away with “remediation” upon entry to its institutions and instead to confer degree credit for what used to be the kinds of high-school-level content and skills that one had to master before gaining access to “credit-bearing” college courses.

The new term for these bridge classes for entering college students is “corequisite” and California isn’t the only place that’s using them. One study at CUNY—dealing with community colleges, not four-year institutions—says greater success was achieved when ill-prepared students were placed in “regular” college classes but given “extra support” than when they were shunted into “remediation.” Perhaps so. Perhaps placement tests aren’t the best way to determine who is actually prepared to succeed in “college level” work. But that’s not the same as saying—as CalState seems to be saying—that anyone emerging from high school, regardless of what they did or didn’t learn there, deserves entry into “regular” college classes.

That essentially erases the boundary between high school and college, and not in the good way being undertaken by sundry “early college” and “Advanced Placement” courses, the purpose of which is to bring college-level work into high schools. Now we’re seeing high-school-level work being brought into college, there to count for credit toward bachelor’s degrees.

But, equality!

I despise the term "college and career readiness", as if the two parts are synonymous.  One need not have completed Algebra 2, or a lab science, or a visual/performing art to be career ready, depending on the career.  Take a look at any list of what constitutes "college and career readiness", and you'll see it slants heavily to the college side.  Not everyone can or should go to college, and we (college graduates who work in education) do students a terrible disservice by, in effect, telling them that if they don't go to college, they're failures straight out of the gate.

Maybe, just maybe, many of the students in the article above shouldn't even be in universities in the first place (community colleges are the places for such students).  And Common Core standards, with their myriad misguided emphases, will only exacerbate the problem:

Vince Bertram, president and CEO of an organization called Project Lead the Way, argues that Secretary of Education Betsy DeVos must focus less on controversial issues such as school choice and Common Core, and more on the goal of education — which he identifies as straight workforce-development. “DeVos’ most important task,” Bertram writes, “will be to cast a vision for what education can be for our next generation to meet the demands of a global economy.” He uses a litany of progressive-education buzzwords — “critical thinkers, collaborators, and problem solvers” — to describe the types of human products our schools must turn out for industry. If there is any other purpose to education, Mr. Bertram doesn’t acknowledge it.

But is developing a workforce for corporations what schools should be about? Such a constricted view of the purpose of education is in fact a central tenet of the utilitarian Common Core (to which standards Bertram’s organization aligns the curricula it creates), but it ignores the deeper purpose that underlies traditional, classical education. That purpose is to offer students the best in human thought so that they may assume their place as knowledgeable citizens, able to cultivate their own gifts and participate wisely in governing their society. It is to educate children so that they can appreciate life, understand others, and fully exercise their liberties.

Common Core’s “workforce development” view is less about education and more about training. The idea is to teach students skills that transfer directly to the modern world of work. By implication, anything that doesn’t contribute to that goal is less important and should be minimized if not discarded. It is the latest iteration of progressive education philosophy. But make no mistake about it, this is not the type of education to which elitist propagators of Common Core — people like Bill Gates or Barack Obama — subject their children. As Woodrow Wilson argued:

We want one class of persons to have a liberal education, and we want another class of persons, a very much larger class… to forgo the privilege of a liberal education and fit themselves to perform specific difficult manual tasks.

Bertram and Project Lead The Way apparently focus exclusively on STEM (science, technology, engineering, and math) disciplines. It’s thus ironic that they would support Common Core — which, as renowned mathematician Dr. James Milgram has repeatedly warned, is so deficient that it cannot prepare students for future STEM studies.

Common Core, coming as it did with a push from the Obama Administration, is fixed in concrete here in California. And of course, we teachers will be asked to jump through even more hoops to try to unscrew what the state government has screwed by adopting these standards, universities will twist into ever more elaborate contortions to keep paying but grossly under-prepared students in their seats.

Essentially, education in California is screwed.  Before too long I wonder if we'll be preparing kids for college or careers.

Gauss-Jordan Elimination

After Sputnik went up in '57, plenty of Americans worried that our education system was substandard.  How could it not be, they presumed, given that the Russkies beat us into space?  Part of the solution became known as New Math.

By the time young Darren got into elementary school in the 70s, the New Math was firmly rooted.  I recall learning about set theory and numbers in different bases--presumably, the "smart" people decided that if students learned and understood those two topics, our deficiencies in math would be over.

I didn't pay much attention to education in the 80s, I was too busy protecting America from the commie hordes.  But the 90s turned us to "fuzzy math", and the counter-swing to that in the 2000s was a "back to basics" approach.

So here we are in 2010s, Common Core-ing away, and it looks to me like the "smart" people have decided that if students learned and understood matrices, our deficiencies in math would be over.  In the past I've taught how to add and multiply matrices, and even how to use Cramer's Rule (an application of matrices) to solve systems of equations.  But today--ah, today I taught Gauss-Jordan elimination.

It doesn't matter if you know what that is or not.  What matters is that I've never taught it before, so I did plenty of prep work to ensure it went smoothly.  I even created a step-by-step worksheet that my students and I worked on together.

It went so smoothly.  Before they knew what was happening, they'd solved a 4x4 system of equations and hadn't even broken a sweat!  Such a feat would have been extremely difficult and time-consuming using algebraic elimination or Cramer's Rule, but the Gauss-Jordan algorithm made light work of it. 

It was great fun teaching something new :-)

Evaluating Schools

We ditched our high-quality state standards (at least in math, I cannot comment on English standards) and content-specific tests for vague (and modified) Common Core standards and a nationwide test (Smarter Balanced) that's not entirely aligned to our standards.  If that isn't bad enough, we have to use such testing to evaluate schools:

In an unexpected move, the State Board of Education postponed approving the method for determining a key element of its new school accountability system on Wednesday, potentially delaying by weeks or longer the release of the first district and school “report card” that it had promised for early 2017.

Board members said they’d prefer a better methodology instead of producing a report using flawed criteria and revising it next year. They want to take another look in January, at their next meeting.

At issue is how to measure student performance on the Smarter Balanced tests in math and English language arts, one of a half-dozen statewide metrics that will make up the new report card. The state board objects to the approach that for years the state has used – and the federal government has required – but staff at the state Department of Education haven’t yet presented an alternative.

It's not cynical to believe California is doomed, the evidence is right in front of our eyes.