Subitize this

Matthew Tabor has just posted a video called "Common Core Explained" on The 74.

I watched half of it, and am now having so much trouble finding words to express my astonishment, that I'll just leave it to Matthew:

I love The 74 -- they (generally) do an outstanding job, with news and opinion worth reading. I read all of it every day and point people to their perspective whenever I can.

However, the appropriate academic term for this Math 2.0 video series is "absolute horseshit."

You can say that again.

In the first minutes of "Math 2.0," we learn that "Common Core math" teaches children to subitize.

"Subitizing" means you see 3 pennies and immediately know you have 3 pennies. You don't have to count.

Subitizing, as it happens, is an innate ability. Chimpanzees can subitize, too; in fact, chimps do it better than humans. They can subitize up to the number 6. We stop at 5.

I'm pretty sure I remember that all creatures can do it, but I'm not going to spend 15 minutes Googling "Can goldfish subitize" to find out.

Another thing: I'm having a hard time believing that formal instruction in subitizing is part of the Common Core, but I'm not going to Google that, either.

Cheers.

Help desk - math HW

What's the story with this little boy's homework? (And how old do you think he is? I'm guessing 2nd grade - ?)

If you click on the link, you'll see a photo of a little guy crying, presumably about his math homework. The worksheet is titled "Using Mental Math to Add" or "Doing Mental Math to Add."

This photo was posted. Watch what happened next.

Assuming he's crying over the worksheet (I have no reason to think he's not) -- what's the problem?

By this point, would he know his addition facts?

Or is he having to do these problems without knowing his facts by heart?

Is there something else going on?

One thing I've become concerned by of late: children spending their days engaged in mini lessons and peer discussion, then doing the 'hard stuff' at home, when they're tired.

I was talking to the mother of a second grade child here who has some sensory issues. The little girl is getting completely overwhelmed at night, trying to do her homework. She melts down and sobs unless her other is in the room with her. Even with her mother by her side, she struggles to get through the work.

I asked how much homework she's doing, and it sounded like a lot. Too much. In math alone, she has a full worksheet to do and several minutes of computer practice.

Listening to the mom, I suddenly realized: it's entirely possible students here are doing no worksheets during class time at all.

The kids have to do worksheets because Common Core, but worksheets aren't constructivist and we are now a Tony Wagner district so .... maybe all the worksheets have to happen at home. Out of sight, out of mind.

But that means kids go through a full day of school and a full raft of after school activities before they start the real work.

Jason Zimba teaching his children math

For passersby, Jason Zimba is one of 3 writers of the Common Core math standards.

Every Saturday morning at 10 a.m., Jason Zimba begins a math tutoring session for his two young daughters with the same ritual. Claire, 4, draws on a worksheet while Abigail, 7, pulls addition problems written on strips of paper out of an old Kleenex box decorated like a piggy bank.

If she gets the answer "lickety-split," as her dad says, she can check it off. If she doesn't, the problem goes back in the box, to try the following week.

"I would be sleeping in if I weren't frustrated," Zimba says of his Saturday-morning lessons, which he teaches in his pajamas. He feels the math instruction at Abigail's public elementary school in Manhattan is subpar — even after the school switched to the Common Core State Standards.

But Zimba, a mathematician by training, is not just any disgruntled parent. He's one of the guys who wrote the Common Core.

And four years after signing off on the final draft of the standards, he spends his weekends trying to make up for what he considers the lackluster curriculum at his daughter's school, and his weekdays battling the lackluster curriculum and teaching at schools around the country that are struggling to shift to the Common Core.

[snip]

Zimba gave up an academic career in which he had the freedom to wonder about abstract physics problems in the peace and quiet of his Vermont barn. But, he says, "I'm now participating in a much more urgent problem."

That problem is how to elevate the academic achievement of American students, especially the most disadvantaged, so the country can maintain its competitive advantage in the global economy. These days, Zimba and his colleagues acknowledge better standards aren't enough.

"I used to think if you got the assessments right, it would virtually be enough," he says. "In the No Child Left Behind world, everything follows from the test."

Now, he says, "I think it's curriculum."

The Man Behind the Curtain

The theory behind CC was that common tests were the ticket.

Common standards would produce common tests would produce common curricula.

No more race to the bottom.

More unfortunate headlines

(Unfortunate headline number 1)

Also on page 1 of the 12/3 Education Week:

Parents Get Schooled on New Math Standards

Schools around the country are holding math nights, sending letters home, and posting videos on their websites to teach parents about the Common Core State Standards for mathematics, which require students to use calculation methods that many parents never learned.

Math nights?

Like this one?

Reminds me of that great piece of advice from the Math Trailblazers people re: how to deal with parents:

Be pro-active with parents. Don’t wait until complaints hit. People have done a lot of things to involve parents, from math nights to big math carnivals, where the kids teach the activities to the parents. There are letters in the program that go home to parents.

Math nights are never a good sign.

How to Get Parent Buy-In

Rote understanding

Late to the party ---- I've just read Barry's "Undoing the ‘Rote Understanding’ Approach to Common Core Math Standards"!

I love that phrase: rote understanding.

Exactly.

I was interested to see that Barry was taught "making ten" when he was in grade school:

The “making ten” method is included in the math program used in Singapore—a nation whose fourth and eighth graders have consistently obtained the highest scores in international math tests. Specifically, in Singapore’s Primary Math textbook for first grade, the procedure for adding by “making tens” is explained. Of particular importance, however, is that the procedure is not the only one used, nor are first graders forced to use it. This may be because many first graders likely come to learn that 8 + 6 equals 14 through memorization, without having to repeatedly compose and decompose numbers in order to achieve the “deep understanding” of addition and subtraction that standards-writers—and the interpreters of same—feel is necessary for six-year-olds.

“Making tens” is not limited to Singapore’s math textbooks, nor is it by any means a new strategy. It has been used for years, as it was in my third-grade arithmetic textbook, written in 1955...

I have a question about the teacher's explanation of the number 6:

“So if we can partner 9 to a number and anchor 10, we can help our students see what 9 plus 6 is. So we’re going to decompose our 6, and we know 6 is made up of parts. One of its parts is a 1 and the other part is a 5. 

How do mathematicians think about whole numbers?

Do they see them as "made up of parts"?

Or as decomposable into parts?

(Or both --- ?)

To me, "made up of" and "decomposable into" seem like two different things.

Another question: if 6 is "made up of parts," is 6 one of the parts?

Is 0?

I bet right this minute there are kids all over America who are royally confused by the ramifications of making ten.

Elizabeth Green is funded by Bill Gates

Needless to say, I was horrified by Elizabeth Green's Why Do Americans Stink at Math?, which is the single most breathless endorsement of constructivism I've ever seen in the Times. Actually, it may be the only breathless endorsement of constructivism I've seen in the Times.

I read it this morning, just before a meeting with Ed and his editors at Oxford, and as we were rushing to get ready I joked that Green was probably funded by Bill Gates.

Then tonight it occurred to me that I should check.

Chalkbeat: About Us

The Times has no business publishing an advocacy piece, albeit an advocacy book excerpt, without disclosing the Gates connection.

UPDATE 7/29/2014: Bill Gates is very likely the major funder of Elizabeth Green

"How Bill Gates pulled off the swift Common Core revolution" (& the free for all)

The man behind the curtain

Diane Ravitch: Time for Congress to investigate Bill Gates' role in Common Core

And here is William McCallum, lead writer of CC math standards, winning friends and influencing people.

Ed and I were talking about McCallum's post last night. People who know him say he's a nice guy, and I'm sure that's true. But his post is a lollapalooza of name-calling and nitpicking, both of which continue apace in the comments thread.

Which took me aback, because it's not the tone I'm used to hearing college professors take in public. (It's not the tone I'm used to hearing college professors take in private.)

I'm used to college professors sounding....you know, professorial.

I never hear college professors sounding furiously wronged and internet-y.

For me, this situation is something of a first. I'm accustomed to academic content coming from publishing houses, which have corporate leaders and marketing departments, and which, as a consequence, do not have textbook authors venting in public.

But with Common Core, there's no corporate parent and no marketing department. There's just Bill Gates and the many NGO's, state departments of education, and think tanks he bankrolls, plus the federal Department of Education (whose head was previously bankrolled by Gates), so there's no party discipline. Gates appears to see himself as CEO and absolute ruler of his foundation in the same way he was CEO and absolute ruler of Microsoft, but when push comes to shove, where Common Core is concerned, he can't actually fire anyone.

He can't order Common Core defenders to vet their posts with marketing.

The federal government can't step in, either, mostly because the federal government isn't supposed to be writing national standards in the first place (not mandatory ones), and because Arne Duncan's one foray into enlightening suburban parents as to the non-brilliant state of their schools & their children was a debacle of epic proportion. For months now, we've have silence from the top.

So...the defense of Common Core is turning into a free-for-all, and the story-line is getting lost in a bombardment of "process" stories and op-eds about the tea party (bad) and the Democratic Party's standardized-test-hating base (also bad).^*

Op eds about the tea party and the Democratic base are bad for Common Core. I'm pretty sure.

They're bad because nobody likes being told they're an idiot for not agreeing with David Brooks -- especially not being told they're an idiot for not agreeing with David Brooks by David Brooks. Being told that only tea partiers and members of the Democratic Party's standardized-test-hating base don't like Common Core makes me not like Common Core. Also, it makes me want to join the tea party and the Democratic base.

Point is: if the defense of Common Core is to be left to volunteers, then Common Core is going to die an unusually painful death.

Bill Gates "Letter to Our Partners" (the aforementioned NGO's, state departments of education, and think tanks plus the federal Department of Education) is just the start.

I think.


^* David Brooks, has yet another bad idea.

Jen on testing the "scaffolding"

The distinction being made here between the content standard and a strategy for showing that standard IS the crux of the problem for CC.

The tests could be made to test only for the concept, but are much more likely to be made in such a way that you have to know the specific strategy meant to "scaffold" you to the concept, rather than be secure in the concept itself.

It reminds me of a district level math supervisor when my oldest kids were in elementary. The district was using EDM (I know, I know, it was actually great for my kids and did what it was supposed to do, but I did realize as the years went on that it really didn't work for 50+% of their classmates).

The supervisor was explaining how they were trying to make sure that every teacher was really using the curriculum in exactly the way prescribed. It had clearly come to their attention that some teachers found the program lacking and were modifying it.

Their solution? They were making up district-wide unit tests for the lower grades that would ask the students specific questions about the games and activities that were to be included. That is, besides some questions that actually tested the concepts the kids were to be learning, they'd also have questions that tested whether they knew how the games were played, or what the rules were for playing them.

So, now the students were being tested on...nothing...so that the district could ding the teachers/school for it. And that, in a nutshell, is also the big problem for CC. Instead of asking questions that determine if they know and are fluent with their facts to 20, they are instead going to design questions that try to tease out HOW they were taught them and ding those who didn't use the specified "strategies."

Ze'ev Wurman on Bill Gates on Common Core

Bill Gates: OK. So what is the Common Core? It’s a very simple thing. It’s a written explanation of what knowledge kids should achieve at very various milestones in their educational career. So it’s writing down in sixth grade which math things should you know, in ninth grade which math things should you know, in twelfth grade which math things should you know.

Ze’ev Wurman: That, indeed, is what content standards are supposed to be.

BG: And you might be surprised to learn how poor those I’ll call those standards, but to be clear, it’s not curriculum. It’s not a textbook. It’s not a way of teaching. It’s just writing down should you know this part of algebra? Should you know trigonometric functions? Should you know be able to recognize a graph of this type?

ZW: Wrong. I wish Mr. Gates would actually read the standards rather than rely on what others tell him. Common Core standards are more than just content standards, they also dictate pedagogy and hence curriculum. Here are a couple of obvious examples.

“Grade 1 standard 1.OA.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).”

This standard does not require only knowing addition and subtraction within 20, as a content standard should. It insists on knowing four specific ways to add and subtract. In other words, it dictates pedagogy and curriculum.

Bill Gates Needs an Education on Common Core

I haven't read the math standards start to finish, and I probably won't. (I'm working on the ELA standards, Appendix A in particular.)

Nevertheless, I think it's fair to observe that a "standard" instructing teachers to "use strategies such as counting on..." is more than just a content standard. Quite a bit more.

Unfortunately, in the context of American public schools, the word "strategies" means something quite different from what it does outside of public education.

Within public education strategies is a formal term for guide-on-the-sidery.

I remember being semi-gobsmacked, a decade ago, sitting in on a CSE meeting and hearing the word "strategies" repeatedly used to describe the district's approach to educating children with behavioral and/or learning difficulties. The student in question that day, a 5th grader with emotional and behavioral problems, was going to be given "strategies" he could use to stop acting the way he was acting and start acting the way the other kids were acting.

In another meeting, the same psychologist said a child with dyslexia would be given "strategies" she could use to read.

She wouldn't be taught to read; at least, that wasn't the focus.

Instead, she would be given strategies she could deploy, as needed (the child was to be the judge of that), to help herself read better than she was reading now.

Even then, before I'd delved into all these things, I knew it was all rubbish.

A 10-year old with emotional and behavior problems isn't going to use "strategies" to stop having outbursts, and a 10-year old with dyslexia isn't going to use "strategies" to read at grade level.

Jean on Common Core in California and the history of us

I have a Common Core math question. My 8th grader daughter (a homeschooler) is taking algebra I this year. She was talking with her friend, who is in 7th grade and wanted to take algebra this year but was not allowed--for the first time they were only letting 8th graders take it. (This kid btw is older than her classmates, owing to a late birthday and having started school in another state with an earlier cutoff date.) So she wants to take it next year, but now they won't let her do that. From now on, algebra I will only be taught at the high school. This is said to be a CC thing.

We are in CA, and for years they've been pushing algebra in 8th grade. I am, of course, against kids taking it if they're unprepared, but I can't see why they won't let prepared students do it. Does anyone understand this?

At dinner tonight, we were joking that my husband should start an underground algebra class...

I wonder whether the history of 8th-grade algebra in my district is scattered across the two ktm blogs? It might be.

I first got into the afterschooling business when I discovered, at the end of the school year, that Chris had flunked a test on fractions in 4th grade. I found a crumpled test in his backpack. (I was working under an insane deadline -- actually, an insane missed-the-deadline-by-a-mile-and-now-everyone-wants-to-kill-me deadline, which is worse -- so I found out after the fact.

As it turned out, he hadn't just flunked a test. He had flunked a unit. And it wasn't just one unit, it was two, both involving fractions, as I recall. (I discovered the crumpled test from the other unit at least a year later, maybe longer -- short attention span theater.)

The school had told us nothing about any of this, and intended to do nothing about it, a fact I simply took for granted at the time. Why would our fantastically well-funded suburban school district concern itself with whether children actually learned the math teachers were teaching?

Not only had the school told us nothing, but on the one occasion I did acquire evidence, in real time, that Chris was collapsing in math his teacher told me, "Don't worry about his grade. He understands." That sounded wrong to me, but, on the other hand, what did I know? His teacher said he understood, so fair enough.

But now it was summer, and I was in possession of a test on fractions with a grade of -- was it 39?

38?

Pretty sure the exact numerical grade is findable via the About Kitchen Table Math link.

So I decided to teach my child fractions, not knowing that 4th-grade fractions are the math cliff; that's where all the kids plummet off the ledge to the rocky math shoals below. Ignorance being bliss, I sallied forth .... and I discovered right away that teaching fractions is not easy, especially when you had a mediocre education in math yourself. (I still remember feeling enthralled when I read H. Wu saying a fraction was a number! And I vividly recall Carolyn writing a post or comment quoting a boy who said a fraction was a division problem he didn't have to do.)

That was the genesis of kitchen table math: I needed help teaching Chris fractions. (Carolyn Johnston -- who co-founded the blog with me -- was in the same boat, except she happened to be a mathematician, so she did the rowing.)

Within a few days of discovering that I was not an elementary school math teacher, I had in my hands a copy of Wayne Wickelgren's Math Coach, and it was from Wickelgren that I learned that teaching algebra 1 in the 9th grade is not one of the 10 Commandments. After that my goal was to get Chris into the 8th-grade algebra class, which I did, but given how horrifically bad the teaching was in 7th and 8th grades, and how horrifically over-accelerated the curriculum was, that was probably the wrong way to go, in hindsight.

(On the old blog we used to call that class the Death March to Algebra, which should give you young 'uns some idea.)

Then again, the other kids who dropped out of the accelerated class fared poorly in the non-accelerated class, too. I was then in close contact with a mom who had been fighting the math wars for years; by the time her daughter was in 6th grade, she already had an appointment with the superintendent to discuss the situation.

Ed and I didn't make it to the superintendent's office till 8th grade.

(Have I mentioned our new superintendent isn't panning out, either?)

The other mom finally gave up the ghost. The daughter was desperate to get out of the accelerated class and her mom finally consented, and then promptly discovered that the kids who had moved down were struggling in the new class, too.

So the real hindsight question is: better to learn next to nothing in the accelerated class or the non-accelerated class?

I probably can't answer that, and having Chris take algebra in the 8th grade meant that he had me re-teaching nearly every concept, doing all of his homework sets every night myself (the publisher wouldn't sell me the Teacher Edition), and going over all of his homework and having him re-do problems he'd missed. I don't think I would have done that with Chris in 9th grade, especially not since he had by then enrolled in Hogwarts.

So, given the realities of an unreal situation, our decision to keep him in the accelerated track was either the right decision or 6 of one, half dozen of another. Plus, think of the grit!

(Which reminds me: I don't think I've told you Chris's story about unit multipliers. Unit multipliers were another revelation for me, writing the first kitchen table math. Will get to that later.)

So there I was, sitting at the kitchen table picnic table outside the kitchen, trying to teach fractions --  and then, 5 seconds later, trying to accelerate my 4th-grade son by a full year so he could take algebra in the 8th grade.

Without knowing a lot of math myself, and without hiring tutors.

The 5th-grade teachers were warm and on-board for the quest, and one of them told Ed and me that the middle school would not move Chris no matter how well-prepared he was. (She was right about that.) If we wanted him moved, she needed to move him up then.

So she did.

He wasn't ready. We needed the summer to work on math so he could move up come fall, a plan that made sense and had the potential, at least, to work beautifully. But, again, my extremely well-funded, nominally high-performing suburban school district does not concern itself with the fates of individual children. There will always be 10-year olds, and they will always score better on the state tests than underprivileged black and Hispanic children living in the city. So good enough.

Sometime during the move-up period I discovered how my district was handling acceleration.

My district was handling acceleration by having the 4th grade kids skip the entire 5th-grade textbook and, when they started 5th grade, go straight to the 6th-grade book, without telling the parents. All the parents knew was that suddenly their mathematically talented kids were struggling in math--for no obvious reason they could see--so they hired tutors. (I learned about the tutors from a math-teacher dad in town who told me the 5th-grade accelerated class was a disaster.)

Even without knowing a lot about math, I knew that skipping an entire year's worth of material was a terrible idea, so I went to talk to the interim principal about it.

He told me I was wrong. The 5th grade kids hadn't skipped an entire book, he said. Yes they did, I said. No they didn't, he said.

A couple of days later he called me in to his office and said, "You're right. They skipped an entire book."

Then he told me the class was a disaster, too. He didn't actually use the word "disaster." He used the nonverbals. His wife was a high-school math teacher, and he was obviously aghast.

Which brings me to the present.

I would like to know how my district is handling acceleration now that we have engageny math.

I would like to know, but I don't know. Finding out is going to take a lot of badgering of yon superintendent.

Fortunately, I'm good at that.

Funny how you never hear "badgering the superintendent for a straight answer" mentioned as a 21st century skill.

An Interesting Common Core Exchange

Common Core and Curriculum Controversies

Something really struck me as strange during Fordham's panel discussion last week. At 54min 50sec in the video, there's a very basic, yet revealing, question posed by this young lady.

 Question: Garrett Fryer American Youth Policy Forum Was there ever a discussion, when you all were designing it, to implement it on a kindergarten level and letting it grow with the students as they aged on through each grade, as oppossed to implementing it with the entire school system nation wide? 

Answer: Jason Zimba This is something that states have each approached differently. Some states have done something more like that, some states have done something less like that. I seem to remember at one point I saw a MA plan where the grade level wasn’t the key parameter, but they had a Venn diagram, you know, what we do now the Common Core doesn’t do, what the Common Core does that we don’t, and then what sort of overlap, where we want to do it better. And they decided to take those three... in year one, we’re gonna focus on the overlap and do it better. In year two, we’ll drop things… and then in year three, we’ll add… I got the details of that wrong, but… my only point is that different states all approached it differently, and we may find out that some states were much wiser than others in this way. Singapore has a long standing, high functioning system in which they not only revise their syllabus ever so often, but they do it actually on the basis of how kids do, so think about that, a performance-based loop, a feedback loop. Which is something we are taking halting steps toward, but can only imagine. And so roughly every six years or so, they’ll put out tweaks to the thing. This year I noticed that they’ve rolled out a new thing in kindergarten. 

Lisa wonders... How in the world can one "image" OR take "halting steps toward" creating a "high functioning system" based on a "performance-based feedback loop" when we are STARTING with a top-down DESIGN by the name of Common Core?

The chairs

From the "High School" section of Illustrativemathematics.org:

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary.

This video shows an excerpt of a conversation between two students comparing approaches to solving a problem and trying to understand why they got different answers and where one of them made an error.

PROBLEM:

Three halls contained 9,876 chairs altogether. One-fifth of the chairs were transferred from the first hall to the second hall. Then, one-third of the chairs were transferred from the second hall to the third hall and the number of chairs in the third hall doubled. In the end, the number of chairs in the three halls became the same. How many chairs were in the second hall at first.

I haven't watched the video, but I hope one of the approaches the two students consider involves asking the teacher what the problem means by "the chairs."

By happenstance, my students and I read the first half of G.K. Chesterton's essay on fairy tales in class today. When I say "read," I mean that my students and I read each sentence individually and out loud and then stopped so I could explain what the sentence meant and why after first asking the person who had just read to take a crack at it.

Chesterton's opening lines:

Some solemn and superficial people (for nearly all very superficial people are solemn) have declared that the fairy-tales are immoral; they base this upon some accidental circumstances or regrettable incidents in the war between giants and boys, some cases in which the latter indulged in unsympathetic deceptions or even in practical jokes. The objection, however, is not only false, but very much the reverse of the facts.

I asked my students what the words "the objection" meant. When nobody knew, I pointed out that the words "the objection" function as an anaphora: the definite determinative (the) tells you that you already know which (or what) objection because you've seen it before, in the text. It's the objection, not "an objection."

So, if you've already seen "the objection," and you've only read one other sentence, what is the objection? It's got to be inside that one other sentence.

At that point, my student who was educated outside the United States in his early elementary years (and who speaks very lightly accented English) figured it out.

..................

My answer to the Illustrated Math problem, which I arrived at on my own and without a lot of conjecturing and solution-pathway-planning and special-case mongering and the like is: 4,938.

..................

The Common Core era is going to be an unhappy one for mathematically gifted children.

I predict.