kitchen table math, the sequel

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Peter Meyer just sent me the link:

Re “Are You Smarter Than an 8th Grader?,” by Nicholas Kristof (column, April 26):

American kids aren’t inherently less intelligent than kids in Singapore, or so one hopes. That’s the good news. The explanation for the Americans’ continued dismal performance in math therefore lies elsewhere.

Having watched my kids navigate the local public schools for the past 11 years, I know that one of the problems is that educators still seem to be trying to figure out how to teach math. My daughters have been through the Singapore approach, with its traditional emphasis on mastery of number facts and arithmetic procedures; the reform approach, with its confusing inquiry-based philosophy; and now the “can’t we all just agree” Common Core standards approach. Why are we still trying to figure this out?

Math has been taught to children at least since ancient Greece, Rome and Egypt, and those kids grew up to use their mathematical skills to build the Parthenon, aqueducts and pyramids, which are still standing. The math taught in K-12 hasn’t really changed much since Gottfried Leibniz and Isaac Newton invented calculus in the 1600s, so one would think that educators have had enough time to figure out how to teach it.

How about if educators stop experimenting with our kids, adopt whatever approach the Finnish or Singapore schools use, and get on with it?

ELIOT BRENOWITZ

Seattle

The writer is a professor of psychology and biology at the University of Washington.

Our Students' Below-Average Math Abilities | New York Times | May 4, 2015

A say: go with Singapore.

Not Finland.

From Nicholas Kristoff's column in the Times today:

What is the sum of the three consecutive whole numbers with 2n as the middle number?

A. 6n+3

B. 6n

C. 6n-1

D. 6n-3

More than three-quarters of South Korean kids answered correctly (it is B). Only 37 percent of American kids were correct, lagging their peers from Iran, Indonesia and Ghana.

~~~~~~~~~~

A piece of wood was 40 centimeters long. It was cut into 3 pieces. The lengths in centimeters are 2x -5, x +7 and x +6. What is the length of the longest piece?

Only 7 percent of American eighth graders got that one right (the answer is 15 centimeters). In contrast, 53 percent of Singaporean eighth graders answered correctly.

~~~~~~~~~~

How many degrees does a minute hand of a clock turn through from 6:20 a.m. to 8 a.m. on the same day?

A. 680 degrees

B. 600 degrees

C. 540 degrees

D. 420 degrees

Only 22 percent of American eighth-graders correctly answered B, below Palestinians, Turks and Armenians.

~~~~~~~~~~

Correlation isn't causation, but the absence of correlation is meaningful.

Fifteen years of constructivist mathematics programs adopted in virtually every public school in the country, fifteen years of teacher-training in authentic problem solving and guide-on-the-sidery, and here we are.

At a minimum, we can say that constructivist math has not been a blinding success.

~~~~~~~~~~

Back to Kristoff, I love this brain teaser for some reason:

You’re in a dungeon with two doors. One leads to escape, the other to execution. There are only two other people in the room, one of whom always tells the truth, while the other always lies. You don’t know which is which, but they know that the other always lies or tells the truth. You can ask one of them one question, but, of course, you don’t know whether you’ll be speaking to the truth-teller or the liar. So what single question can you ask one of them that will enable you to figure out which door is which and make your escape?
Are You Smarter Than an 8th Grader?

Julie writes:

My 7th grader, who was in an accelerated math class this year (in GA) experienced these same math stations. He said it was like being in elementary school all over again.

This same teacher "flipped" her classroom by making videos of her reading the textbook and examples aloud. He was expected to watch the videos each night before doing homework problems...but he couldn't stand it. He wanted to just read the book to himself and get the homework done.

Same teacher wanted parents and students to follow her on Twitter to keep up with daily assignments...my son has no interest in using Twitter.

Part of what is going on in my district, and I imagine in Julie's district, is that administrators here are focused first and foremost on "infusing technology into the curriculum." This is the prime directive.

Just how to infuse technology into the curriculum remains a mystery, however, so the district has elected to buy a bunch of stuff and have teachers "innovate."

Which reminds me of a funny conversation. (Not funny ha-ha, I'm afraid.)

A fellow dissident here in the district invited me to a meeting she had scheduled with the high school principal re: flipped classrooms. As we sat down, the principal, who is new to the district, told us he "believes in" flipped classrooms.

"I encourage teachers to take risks," he said.

Having spent years of my life chewing over this and related issues, I had a response at the ready: "You're taking risks with other people's children," I said.

"Teachers have tenure and a union, they're not the ones taking the risk. The kids are taking the risk, and they haven't been asked whether they want to take the risk you're forcing them to take."

(I actually said these sentences, out loud. I didn't just think of saying them later on and wish I had. Very satisfying!)

The principal, who seems like a very nice guy, looked horrified. Clearly, it had never crossed his mind that "teachers taking risks" could be construed as anything other than an unalloyed good--let alone a borderline abuse of his authority as head of school, which is pretty much what I was suggesting.

Since then the administration has gotten a bit of an earful on the subject of experimenting with other peoples' children.

But the experiments continue apace.

"Station math" is, I gather, another effort to infuse technology into the curriculum, I guess because one of the stations has movies, and movies are technology.

So....time flies. I'm old enough to remember when SMART Boards were technology.

My district has beaucoup SMART Boards. We had to buy one for every classroom because we had a SMART Board equity gap.

I learned this week that our 6th-grade math teachers have adopted a new way of teaching math.

Steve Leinwand, principal researcher at the American Institutes for Research’s education program, also argues that America’s math teachers should embrace the shift away from right answers. “Common Core has the audacity to use the word ‘understand’ 218 times,” said Leinwand.

Why so many parents are freaking out about Common Core math

Using the word "understand" 218 times while using the words "right answer" 0 times seems a tad out of whack to me.

Speaking of right answers, I was going through a stack of Education Weeks yesterday & found this:

Ask a child to name a favorite class, and odds are you’ll hear two letters: P.E. Ask an adult which subject has been most valuable in life, and the most popular answer turns out to be math.

That’s according to new survey results by the Gallup organization. About one-third of adults (34 percent) picked math. The next in line was English, at 21 percent, followed by science at 12 percent.

"Gallup Poll Social Series: Work and Education" September 18, 2013

Dollars to donuts, every one of those respondents thinks getting the right answer is a major reason why math is valuable.

Constructivists seem to want authentic, "real-world" problems without authentic, real-world right answers.

I will never get that.

Steve Leinwand, btw, has been singing the same song for decades.

Here he is in 1994:

It's time to recognize that, for many students, real mathematical power, on the one hand, and facility with multidigit, pencil-and-paper computational algorithms, on the other, are mutually exclusive. In fact, it's time to acknowledge that continuing to teach these skills to our students is not only unnecessary, but counterproductive and downright dangerous.

[snip]

Shouldn't we be as eager to end our obsessive love affair with pencil-and-paper computation as we were to move on from outhouses and sundials?

It's Time To Abandon Computational Algorithms By Steven Leinwand | February 9, 1994

Outhouses, sundials, paper and pencil.

Now there's an analogy that hasn't panned out.

As it turns out, it was the analogy between outhouses and paper and pencil that was not only wrong, but counterproductive and downright dangerous.

Letters from John Dewey/Letters from Huck Finn: A Look at Math Education from the Inside by Barry Garelick

Go order it right this minute!

Parents are in an uproar here.

We've hired a curriculum director who is a smart, fantastically hard-working true believer in the wisdom of mini-lessons and students designing their own "literacy" curriculum by choosing their own books to read for class and discussing them in pairs or pods.

A smart, fantastically hard-working true believer gets a lot more done than a dull and lazy true believer.

(Ed and I and numerous others fought to keep that position from being filled, by the way. Fought.)

So, where Common Core is concerned--Common Core as understood by a public school curriculum director--we are ahead of the curve.

Which means that after 10 years of strife over Math Trailblazers we have unceremoniously dumped Trailblazers and adopted the engage^ny math modules, which are being written and posted as we speak. No teacher has ever taught engage^ny math, no student has ever learned engage^ny math, engage^ny math does not yet exist in toto, and the vast set of engage^ny material has to be downloaded from the internet.

And this is what we're using.

Because, you know, COMMON CORE.

Those are the magic words, COMMON CORE. Once an administrator invokes the name of COMMON CORE, s/he is absolved of all responsibility for children actually learning math.

So here we are:

1. The children have no math textbooks
2. Because Trailblazers was so slow, children in later grades don't have the skills to begin grade-level engage^ny units, but they have all been forced to begin grade-level engage^ny units anyway, regardless of preparation
3. Because we've never had a scope and sequence for any subject in the district (this state of affairs finally came to light at the last board meeting, after I requested a copy of our scope and sequence) no one has any idea what skills the kids are supposed to possess
4. Because the district has never held itself responsible for children actually learning the content being covered in class (and retaught at home by parents & tutors) there is no mechanism in place to figure out what skills kids are missing
5. Because no one apart from high school math teachers has any expertise in math, neither teachers, building principals, nor the curriculum director has any idea what the proper sequence of skills actually is & thus no idea how to assess the kids' "gaps" (lots of gaps talk amongst parents and teachers; calls to mind the early days of ktm)
6. Although engageny promises a year-long "scope and sequence" for its curriculum "modules," the promised scope and sequence for math either: a) does not yet exist or b) does exist but is unusable by people absent a deep and hands-on knowledge of K-5 math and math curricula.

I attended Thursday night's Common Core meeting, and the atmosphere in the room was pretty much one of controlled pandemonium.

No one knows anything, and, very clearly, no one is going to know anything any time soon.

I've seen a lot of bad math teaching in my day (a whole lot), and a lot of bad math curricula, but I've never seen anything like this.

The problem is the name has changed, but the song remains the same.

Common Core is the new "new Math", unfortunately the umbrella name for everything happening in math ed these days as the standards get put in place, including things that really have nothing to do with standards.

The Common Core State Standards were, and are, a set of standards. Standards are lists of requirements. It's true that CCSSI were more proscriptive than typical standards, but they were still just standards. Standards are not curriculum. For more on this, see my post.

The CC standards in k-8 are better than NY's previous standards. That is about the end of the good I can say in NY's implementation of the new standards.

For whatever reasons, probably largely related federal funding, states adopted CCSS. Except they did so before any textbooks had been written. And before the assessments against the standards had been written.

So NY schools and teachers were supposed to magically teach from the new standards about which they had been told nothing, or use hastily repackaged curricula that wasn't really changed, or who knows what.

But help was on the way! Engage NY was created! It would be an entire curriculum online, free to everyone, digital! No need for textbooks! Isn't that great? And famous mathematicians and math teachers who are pro Singapore math had signed up to lead the writing of the curriculum on EngageNY.

At some point last spring, I saw several job reqs from EngageNY. They needed curriculum writers. I considered taking the position. Then I looked at what was already on EngageNY.

I saw a fraction lesson that was fundamentally wrong from beginning to end. I saw other lessons with equally egregious errors. I told someone who told someone high up at EngageNY. The response was, yes, it's wrong, and the writer was informed, but the writer could not understand what was wrong with it and refused to rewrite it, saying they knew it was better for kids this way.

EngageNY is still beholden to the same NYS ed people. The math people who were supposedly leads don't control the curriculum; the bureaucrats do, and are actually telling the math people what the scope and sequence must be.

This is now all called "Common Core."

Given the difficulty of the Common Core tests, I wonder if we'll see so many parents up in arms that .... that school boards will finally have to wake up.

Till now, the math warriors in any community were always a minority, but now everyone's child is failing math.

That said, here in Irvington sentiment in the one and only survey ever taken on the subject, was around 80% anti-Trailblazers, and the board still voted to reject Singapore Math & keep Trailblazers.

Of course, the Interim Curriculum Director announced at the time that the survey was favorable to Trailblazers. She also announced, again, that the Parents Forum (me) had misled the public.

I always enjoyed that, sitting in the audience at school board meetings, being slandered via innuendo.

Or is that libeled?

I never remember which is which.

I learned the legal meaning of the word innuendo through direct personal experience of innuendo about me, purveyed by sitting members of the school board and by central administrators.

I'm going to go read the link Allison left to Wu's piece now.

I'm thick in the middle of things, but in my travels today I came across this passage (two seconds ago, actually) and I had to post.

Dan Meyer, 31, is in the process of becoming a celebrity math teacher (hey, it’s a small group). Much of his rapid trajectory upward can be explained by his message, which involves a digital curriculum that will (he says) instantly engage and perplex kids and thus resolve all classroom management issues (more on this later), a message tailor-made to appeal to both techies, since it implicitly attacks all teachers, and progressive educators, since it is inherently constructivist.

Dan Meyer and the Gatekeepers
educationrealist

He had me at "instantly engage and perplex kids and thus resolve all classroom management issues."

background: Educational malpractice for the sake of reform math

FERPA protects the identities of individual students, not schools.

If FERPA protected the identities of schools, No Child Left Behind would be illegal. Clearly it is not.

Ms. Boaler should release her data.

District-wide
Monday, 12/10 - Workshop for Parents on the Common Core Learning Standards - 7:00-8:00 pm; Alexander Hamilton HS Auditorium, 98 S. Goodwin Avenue, Elmsford, NY. You have heard much about the many changes to the landscape of NY public education. Many of them are rooted in the newly adopted Common Core Learning Standards which will change what and how teachers deliver particular instruction. If you are interested in learning more about this shift in curricula, you may be interested in attending this workshop entitled Introduction to the Common Core Learning Standards for Parents which is sponsored by Southern Westchester BOCES. Click here for more information.

As far as I'm concerned, the Common Core standards have been well and truly hijacked.

Barry writes:

A few weeks ago, I wrote an article for TheAtlantic.com describing some of the problems with how math is currently being taught. Specifically, some math programs strive to teach students to think like "little mathematicians" before giving them the analytic tools they need to actually solve problems.

Some of us had hoped the situation would improve this school year, as 45 states and the District Columbia adopted the new Common Core Standards. But here are two discouraging emails I received recently. The first was from a parent:

They implemented Common Core this year in our school system in Tennessee. I have a third grader who loved math and got A's in math until this year, where he struggles to get a C. He struggles with "explaining" how he got his answer after using "mental math." In fact, I had no idea how to explain it! It's math 2+2=4. I can't explain it, it just is.

The second email came from a teacher in another state:

I am teaching the traditional algorithm this year to my third graders, but was told next year with Common Core I will not be allowed to. They should use mental math, and other strategies, to add. Crazy! I am so outraged that I have decided my child is NOT going to public schools until Common Core falls flat.

This may sound wildly off topic, but the struggle a third grader has "explaining" why two plus two equals four strikes me as being of a piece with the struggle basic writers have trouble writing a conclusion, especially a conclusion in a 5-paragraph essay, a highly compressed form that leaves you no room to "ask a rhetorical question" or "suggest future lines of inquiry" or "close with a quotation that captures your view" and the like.

With the 5-paragraph essay, when you get to paragraph 5 you've said everything you were going to say (if you're lucky), but the teacher wants you to say something more.

But what?

One thing I always liked about William J. Kerrigan's X-1-2-3 approach is the fact that he didn't bother with introductions and conclusions. The introduction was 1 sentence - Sentence X - and the conclusion was 1 sentence, too. Kerrigan called the final sentence the "rounding off" sentence, as I recall. Really, that's all anyone should do in a very short paper; otherwise your introduction & conclusion - 2 paragraphs out of 5 - take up 40% of the essay.

I've had to abandon Kerrigan's one-sentence policy, though, since I'm pretty sure other instructors don't look kindly upon one-sentence introductions and conclusions, not that I've asked.

So my students, like the 3rd grader trying to explain 2+2, solve the problem they've been set and then struggle to say something else about the something they've just said.

A ktm reader sends this question from her daughter's 2nd grade math book.

Brad De Long:

MOST BERKELEY STUDENTS DO NOT KNOW THAT 2^5=32 AND 2^10≈1000
How can they expect to survive in the modern world without knowing these things?
And why haven't they learned them?

To which I can only say: Brad DeLong has not been paying attention!

I've just started reading the comments. Calculators in grade school aren't faring well thus far.

From the first Comment:

The best students are great, but the quantitative reasoning skills of even the average student at a good university are worse than those of a typical waiter/waitress 40 years ago.
invhand

re: Fill-in-the-blank has a really bad idea

I'm of two minds whenever I hear of particularly dumb ideas being floated in the school systems.

On the one hand, I'm thinking, "Cool, this gives my kids a leg up over the competition."

Then on the other hand, I realize that the overwhelming vast majority of the next generation of citizens are being educated with these cockamamie ideas and I think: "We are so hosed."

I'm on both sides of that fence with just one (typical) kid!

C. is now an official Math Victim of U.S. schools (including his Catholic high school, sad to say). And, at the same time, he's way out in front in the verbal realm compared to most h.s. seniors in America (also thanks to his Catholic high school, as well as to family background).

Speaking of 'official,' C. has just now reached the point of maturity at which he realizes, without being told by his mother: Holy ****, I don't know any math.

He has two weeks left in high school. He came home the other day, said he'd had a talk with his math teacher (statistics!), who had convinced him he needed to take math in college. So he was wanting to know whether NYU has remedial math courses.

K-12 kids don't know, while they're K-12 kids, that they're going to be sorry they didn't learn math or writing or science or whatever else they didn't learn. I remember Glen, I think it was, once saying that we have to advocate for our children's future selves: for the selves they're going to be, eventually.

That's exactly right.

In summary, our data show a clear decline in the level of Michigan State University mathematics courses taken by Core-Plus graduates. The existence of that decline is statistically significant at any reasonable level. The decline in course level is accompanied by a decline in average grades for all but the very top students, as well as a decline in the percentages of those who eventually passed a technical calculus course. These trends occur in data that include students from a variety of communities. The data from individual high schools show that the timing of these declines corresponds precisely to the implementation of the Core-Plus program.
A Study of Core-Plus Students Attending Michigan State UniversityRichard O. Hill and Thomas H. Parker Thomas Parker

"We provide classroom teachers with lessons that allow them to teach standards-based math using topics students care about...Instead of teaching fractions and percent, teachers get to teach "Is The Wheel of Fortune Rigged?"
Mathalicious

I left a comment at eduwonk.

and see: stop the multiverse, I want to get off

A popular textbook on special education (Rosenberg, et. al, 2008), notes that up to 50% of students with learning disabilities have been shown to overcome their learning difficulties when given explicit instruction.
Mathematics Education: Outwitted by Stupidity Barry Garelick

So the sequence is:

a. Collaborative group inquiry with spiraling
b. Huge increase in children diagnosed w/learning disabilities
c. Provision of explicit instruction (w/o spiraling?) to children diagnosed w/learning disabilities
d. Followed by 50% of learning disabilities resolving

Back on my home planet, we didn't bother with Steps A, B, and D.

In a well-publicized paper that addressed why some students were not learning to read, Reid Lyon (2001) concluded that children from disadvantaged backgrounds where early childhood education was not available failed to read because they did not receive effective instruction in the early grades. Many of these children then required special education services to make up for this early failure in reading instruction, which were by and large instruction in phonics as the means of decoding. Some of these students had no specific learning disability other than lack of access to effective instruction. These findings are significant because a similar dynamic is at play in math education: the effective treatment for many students who would otherwise be labeled learning disabled is also the effective preventative measure.
Mathematics Education: Being Outwitted by Stupidity by Barry Garelick

The effective treatment for many students who would otherwise be labeled learning disabled is also the effective preventative measure.

and see Galen Alessi's classic: Diagnosis Diagnosed

In Waterloo, Iowa, Investigations in Number, Data and Space, is being used and getting rave reviews, according to this article.


Here's a quote taken right from the article. Stop me if you've heard it before:

"Administrators describe the curriculum, published by Pearson Education, as providing rich, problem-based, student-centered lessons that foster inquiry and develop critical thinking skills. They believe the result of developing those skills will be increasing student achievement."