kitchen table math, the sequel

Saturday, April 19, 2014

I updated "Failure of future learning"

Update here.

Retrieval practice, the bad news

I was thinking the incredible results people find with retrieval practice sounded too good to be true, and now I'm worried they are:

Failure of further learning: the limits of repeated study and retrieval practice

Wish to heck I could pull the study. All I've got for the moment is the abstract:
Abstract

Previous research has shown that little benefit is achieved through spaced study and recall of text passages after the first recall attempt, an effect that we term the failure‐of‐further‐learning. We hypothesized that the effect occurs because a situation model of the text's gist is formed when the text is first comprehended and is consolidated when recalled; it dominates later recall after verbatim memories of more recent study episodes have been lost. Experiments 1 and 2 attempted to circumvent the effect by varying the activities of participants and requiring interactive exploration. In both experiments, recall after four, weekly sessions showed little benefit beyond performance on the first recall. Experiment 3 interfered with the formation of an immediate situation model by introducing passages that were hard to comprehend without a title. Performance improved substantially across four sessions when titles were not supplied, but the standard effect was replicated when titles were given. Experiment 4 made verbatim memories available by incorporating all re‐presentations and tests into one session; as predicted, recall improved over successive tests.

Failure of further learning: Activities, structure, and meaning
Catherine O. Fritz,
Peter E. Morris,
Barbara Reid,
Roya Aghdassi,
Claire E. Naven
Unfortunately, I don't understand the final sentence in the abstract.

I see that "interactive exploration" didn't help students remember anything beyond what they recalled during their first retrieval practice. (Another nail in the coffin of hands-on, guide-on-the-side activities as the cure for limited remembering and understanding.)

I see that difficult reading passages without titles (!) helped. That finding is especially striking in light of the SQ3R approach to reading comprehension, which involves paying attention to titles. (SQ3R isn't necessarily incompatible with this finding, but still...)

It sounds like the last sentence refers to a complete, or near-complete, re-creation of the original learning-and-quizzing episode.

Did students re-read and quiz themselves, both in the same "session"?

I should go read the summary at Jung's Biology Blog.

I'm probably going to enjoy it:
In other experiments, Fritz et al. show that FOFL occurs even when ideas are presented as itemized lists on Powerpoint slides (why am I not surprised).
Update: OK, I should have read first, posted later.

The last sentence has to do with word-for-word memorization, which does improve with repeated retrieval practice.

As for the rest of it, in fact, recall does improve over time, but not by nearly as much as one would hope.

"Elaborative" study techniques -- underlining, annotating, diagramming (Make It Stick highly recommends elaboration) -- had no effect at all.

Difficult texts without titles offer no advantage I can see from the summary: students recalled less during their first retrieval practice and then, over time, continued to recall more until they reached the level of students who had read a clearly-written text with a title. Lots more pain, no gain.

At this point, I don't think this study tells me too much. The authors' theory - which I do find quite interesting - is that a student's mental model blocks further learning. Specifically, the student's mental model blocks learning of content that didn't make it into the model.

That strikes me as highly likely; I've experience a "gist" effect myself, and I think "gist effects" are a major problem in any kind of reform effort.

However, fields of study are different from a book you are trying to remember, which is what the students in this study were trying to do.

When you study a field, one of the things you are learning is the field's organization and categories.

New content gets slotted into pre-existing categories. That's why the more you know about a subject, the easier it is to learn new aspects of that subject. You have a mental 'gist' of the subject that is 'hungry' for new content, or at least wide-open to it.









Make It Stick - is 3 the magic number?

I'm reading Brown, Roediger, and McDaniel's Make It Stick in a mixed state of trepidation and fascination.

Trepidation because the wording is so incautious and, often, so imprecise that I think it's entirely possible we'll see Make It Stick touted as justification for bad teaching of every stripe.

e.g.: the preface spends a great deal of time denigrating "drill and kill," which the writers take to mean massed practice. Also, "easy" lessons are slammed on grounds that learning should be hard. (So drill and kill is too easy?) And at one point the text baldy avers, sans footnote, that "people do have multiple intelligences" while in the same breath asserting that there's no evidence learning styles have anything to do with anything. So instead of worrying about our learning styles we should all use all of our multiple intelligences all the time because you learn better when you "go wide," drawing on all of your aptitudes and resourcefulness, than when you limit instruction or experience to the style you find most amenable.

What can any of this possibly mean?

Hard is good but hard drill-and-kill is bad .... learning styles are meaningless but we should deploy all of our "intelligences" all of the time (dancing in math? math-ing in dance?) ...

And does the exhortation to "go wide" mean multisensory programs are always to be preferred? I'm completely open to that possibility myself, but there's no listing for "multisensory" in the index, so who knows?

But that's the preface.

The first chapter, on retrieval practice, is riveting.

Retrieval practice, or the testing effect, refers to the finding that taking a test -- any kind of test, in-class or a quiz you give yourself -- increases your memory of the material you are trying to learn. In other words, taking a test or a quiz is a form of practice in which you practice remembering.

What's more, simple retrieval practice is probably superior to the kind of "active," "higher-order" learning students are purported to do via concept mapping. It also appears likely that retrieval practice produces knowledge that is readily transferred to new contexts and to problem solving.

In short, memorization makes you smart. (That's not how Brown, Roediger, & McDaniel put it.)

What is shocking to me is the tiny amount of retrieval practice the middle-school students in Roediger's studies needed in order to recall the material they had covered in class: just 3 "low-stakes" (ungraded) clicker quizzes in all. One quiz at the beginning of the class (on material they were supposed to have read the night before), one quiz at the end of the class (after the teacher's lecture on the same material) and one before the unit test a few weeks later. Students scored a full letter-grade higher on quizzed than on un-quizzed material.

When Roediger expanded the study to 8th-grade science, students scored an average of 92% on quizzed material, 79% on un-quizzed material. They still remembered the quizzed material eight  months later, for the final.

After 3 ungraded quizzes no one had to study for.

Is 3 the magic number?

Here are Rawson & Dunlosky on "How Much Is Enough?"
The literature on testing effects is vast but supports surprisingly few prescriptive conclusions for how to schedule practice to achieve both durable and efficient learning. Key limitations are that few studies have examined the effects of initial learning criterion or the effects of relearning, and no prior research has examined the combined effects of these 2 factors. Across 3 experiments, 533 students learned conceptual material via retrieval practice with restudy. Items were practiced until they were correctly recalled from 1 to 4 times during an initial learning session and were then practiced again to 1 correct recall in 1–5 subsequent relearning sessions (across experiments, more than 100,000 short-answer recall responses were collected and hand-scored). Durability was measured by cued recall and rate of relearning 1–4 months after practice, and efficiency was measured by total practice trials across sessions. A consistent qualitative pattern emerged: The effects of initial learning criterion and relearning were subadditive, such that the effects of initial learning criterion were strong prior to relearning but then diminished as relearning increased. Relearning had pronounced effects on long-term retention with a relatively minimal cost in terms of additional practice trials. On the basis of the overall patterns of durability and efficiency, our prescriptive conclusion for students is to practice recalling concepts to an initial criterion of 3 correct recalls and then to relearn them 3 times at widely spaced intervals.
The chapter also says that short answer and essay tests are probably superior to flash cards and multiple choice, but flash cards and multiple choice produce superior retention, too.

Clicker quizzes work.

I need a clicker.

Just imagine

Utopia can't wait



(As the parent of two autistic kids I've spent years of my life listening to Barney sing "Just Imagine...")

College Board takes leave of its senses

In a new type of advanced government class at Seattle’s Garfield High, the students rarely sit quietly taking notes while their teacher stands and lectures.

Instead, they debate each other. They write legislation. They run for president in mock elections and pretend they’re lawyers arguing cases before the U.S. Supreme Court.

They sometimes even stand up and holler, as Sanai Anang did recently, playing a member of a Virginia-based group that lobbies for strict immigration controls.

In a simulated public hearing, Anang, who loves to ham it up, jumped to his feet without being recognized and declared, in a mangled Southern accent, “Ee-lee-gals come over and take our jobs. They don’t bee-long here.”

His classmates and teacher Jerry Neufeld-Kaiser cracked up.

They are all part of a teaching experiment that began six years ago in the Bellevue School District when a handful of frustrated government teachers teamed up with University of Washington researchers and turned the usual Advanced Placement curriculum inside out.

[snip]

The [College Board] is watching the teaching experiment carefully, interested in its promising results. In 2012 the board invited project leaders to its A.P. conference to present their ideas to A.P. teachers from across the nation.

It’s important that students gain an in-depth understanding of a subject, said Auditi Chakravarty, an A.P. program vice president. “And that requires more than the passive sit-and-get kind of learning.”
Sit and get.

That's a new one on me.

And when did high-school kids making fun of southern accents (and southern people) become a hands-on learning activity?

We are a long way from debate club.

Cliff Mass has a good comment in the comments thread.


153 words, 3 days

I just spent 3 days writing 169 words.

Good thing I'm not a poet.

Princeton Concludes that America is basically an oligarchy.

Princeton Concludes What Kind of Government America Really Has, and It's Not a Democracy   
April 16, 2014

A new scientific study from Princeton researchers Martin Gilens and Benjamin I. Page has finally put some science behind the recently popular argument that the United States isn't a democracy any more. And they've found that in fact, America is basically an oligarchy.

This is a familiar topic to those of us who oppose the Common Core Standards Initiative.  I've been scratching my head, literally for years, trying to understand how Common Core took hold, quietly and quickly, in America's representative republic.  In my state of Missouri, it became clear to me that the "initiative" capitalized fully on the top-down governance structure in our education policies and their implementation.  I believe that Missouri state statutes were violated in the adoption process, but unfortunately, there was no oversight mechanism in place to stop Common Core from the onset.

After researching the opposition to the Common Core Standards Initiative throughout the country for a number of years, there is no doubt in my mind that our American oligarchs were well aware that state legislatures were not equipped to investigate and address adoption of Common Core Standards in 2009-2010. 

(posted by concerned)

Sunday, March 30, 2014

Numbers to 20 and the prevalence of making tens

Someone else commented that their impression was that the making tens stuff comes and goes relatively quickly in Singapore math as students learn their addition facts.

I have a couple of comments: first, to take off on what CassyT says, we are handicapped by our length of living. It may seem to the adult whose child has grown that this making tens stuff goes relatively quickly as their mathematical competence comes in. But that isn't true in the time frame of grade 1.

By the end of grade 1, PM has kids doing mental math to 100, so yes,big picture, the specific strategy of making tens doesn't last long. But to the first grader, it's what they do for nearly all year, constantly, repeatedly, and for weeks on end. Successful mastery of it will make the learning of addition and subtraction facts much easier, and students who have committed the answers to memory don't rely on them anymore. That process takes thousands of examples for many children.

Second comment: most people here used Singapore math primarily as a home or after-schooler. Often, the parent was mathematically talented and often, so was the student. Few of these people saw or read in detail about the pedagogy used in PM. Almost none *did* the main portion of that pedagogy: the concrete portion, skipping often to the textbook almost immediately. I will speak more about this in another post.

Here's the outline of the unit showing the prevalence of Making Tens:




Making tens for subtraction, PM standards ed.

As per post below, here are some small examples of how frequent and explicit the making ten strategies are in addition and subtraction in Primary Math, standards ed. This not not meant to be enough to explain these methods, just to show what an actual Teacher's Guide says.

This is a subtraction lesson, the hardest, where you can't just decrement the ones by the subtrahend.






Saturday, March 29, 2014

No, it doesn't work this way

Peter Elbow on the composing process

I remember posting this before (or at least discussing it in Comments -- I think I recall gasstationwithoutpumps saying something about wives copy-editing their husbands' work) but I was just cleaning up some old drafts sitting in the queue and found this one, so here it is.

Again.

Still funny after all these years!

Boys are stupid, throw rocks at them


Fundraising flier from Wellesley.

Which pretty much rules out contributions from Wellesley grads who are: a) married to men and/or b) the mothers of boys.



Congratulations Steve H!

Steve had some fabulous news on Thursday!!!

(Has he posted?? In the comments somewhere??)

If he hasn't, I'm not telling!

Thursday, March 27, 2014

No more fat versus small envelope surprises

T-minus seven hours and counting. It's like the owls in Harry Potter when the electronic acceptances (or rejections) come in. However, he already has an acceptance, a rejection, and a waitlist (polite rejection), and the acceptance comes with no aid. Thank you out-of-state universities! The scholarships they do give won't come until summer after you have committed. Had I known... So as of now, he isn't going to college next fall. Sooooo many students seem to be rejected or waitlisted so far this year. Students are having trouble getting into "likely" schools (unless they pay full price). Likely and reach school admittances seem to have little to do with academics at all levels, and some schools might reject you because they think they are a safety. If a school can reject you for whatever holistic reason they want, then students can't reliably know what "reach" means. What is the probability of being rejected at all of your schools? My son applied to 10, and I'm thinking that it wasn't enough.

Wednesday, March 26, 2014

Debbie at Ed Week!

I edited! (So I'm bemoaning a couple of too-long-for-onscreen-reading sentences...

Seeking the Top Score (Part I)
By Helen Yoshida on March 25, 2014 5:34 PM

Tuesday, March 25, 2014

From 1992 - David Klein and Jerry Rosen on fuzzy math and why we have it

The 1992 Mathematics Framework for California Public Schools governs, to a considerable extent, the mathematics curriculum in California's public schools. It is a model of mediocrity. The Framework recommends that calculators be issued to kindergartners and used in all K-12 grades; it strongly discourages placing students by ability or achievement; it advocates that teachers do more "facilitating" and less "teaching;" it discourages testing, and promotes portfolios, "authentic assessment," and "holistic scoring rubrics;" it de-emphasizes basic skills and promotes "cooperative work" over individual responsibility. In short, it is the bible of "fuzzy math."

[snip]

Why is this kind of mediocrity promoted by so many education professors and education experts? We suggest that it is simply good intentions gone awry, resulting in institutionalized "liberal racism." Liberal education experts fear that minority students can't learn real math because of "cultural differences." They recognize that it would be preposterous to lower standards only for those students while maintaining high standards for other groups. Thus, the education experts lower standards for everyone, with "authentic assessment" replacing hard-core, standardized tests, and so-called "higher order thinking" supplanting basic skills.

The clearest refutation of the racism disguised by the Framework comes from the work of Jaime Escalante, the teacher who was immortalized in the movie, "Stand and Deliver." Mr. Escalante proved beyond any doubt that minority students from poor neighborhoods can do as well in mathematics as any other group. His methods were traditional and "non fuzzy."

HOW EXPERTS DUMB DOWN MATH EDUCATION
Los Angeles Daily News
May 31, 1996
HOW EXPERTS DUMB DOWN MATH EDUCATION
by David Klein and Jerry Rosen
Ten years ago, I would have rejected this explanation out of hand.

But today, as a classroom instructor teaching "basic" composition, I wonder.

I've mentioned this before, but it bears repeating: college freshmen whose skills are far below where they need to be can be perfectly intelligent and 'smart' when you stick to spoken language.

They can be and they are.

In fact, it's not necessarily possible to tell which students have better skills and which poorer by listening to classroom discussion.

The Cambridge Pre-U courses are a case in point. I gather Cambridge Pre-U is being sold to districts (and to parents) as a rigorous replacement for AP courses that does not require grouping. All kids, at all levels of skill and ability, can take the same course and it's still advanced.

The reason that claim can be made is that the courses -- at least the one I witnessed -- primarily involve Googling (there is no assigned reading), creating group Powerpoints for presentation to the class, and class discussion. (The class I saw required one paper, written at the end of a year and a half of 'study.')

On the day I visited a Cambridge Pre-U class, one of the students strongly challenged a presentation four other students were giving. Every point the challenger made was dead-on.

Afterwards, the principal told us how wonderful the class is because you can't tell the AP kids apart from the non-AP kids.

Then he said proudly that the student who had done all the challenging was a kid who would never have been allowed to take a regular AP course in his school.

Naturally, that got my dander up. A talented student who hadn't been prepared by his school to take an AP course didn't seem like something a principal should be talking about with anything other than embarrassment and regret.

Today I feel a bit differently.

I certainly believe that the student I saw in action should have been prepared by his school to take one Advanced Placement course by graduation. He was headed for college, and that being the case, preparing him for AP was the school's job.

On the other hand, I now know that being smart and capable in speech does not mean being smart and capable in writing. Not even close.

I also know that writing really is thinking in any number of ways. Which means if you can't write....you're not the smartest person in the room.

So, back to Klein and Rosen. It now seems entirely plausible to me that, like me, a large contingent of education reformers has registered the fact that that underprivileged students fare better talking than writing (or doing math).

Education reformers don't have to have decided consciously to tackle the achievement gap by making math into a discussion subject in order to have done just that.

Allison on big data

12 months ago, you could raise funding for your startup overnight if you were doing "big data" for education (even though the data was quite paltry in size). The future hope of a Diamond-Age like mechanism to have kids worked in flipped classrooms at their ZPD ["zone of proximal development"] all without teachers needing to do anything to differentiate instruction was the holy grail.

6 months ago, the perfect storm of Anti-Common Core backlash, NSA domestic spying, and IRS abuse of 501c4 citizen groups meant Bog Data for Ed was in serious jeopardy.
I first realized this at a talk I was giving at a school that had chosen in May of 2013 to improve their math program: a goal of Singapore Primary Math in K-6, Shoseki in 7, Dolciani in 8, complete with real math training for all teachers and a FT BS math degreed teacher for 6-8. Oh, and state standrads-based standardized tests for the first time ever to measure student progress relative to their peers and state requirements.

The parents were on board in May. I gave the same talk in September, and the climate had changed.

Parents were so anti-data that they wanted no standardized test. Never mind that there was no way to measure student progress without a benchmark.

In order to make some basic determination about where these students were mathematically that first May, MSMI had devised a test based on state sample item. In September, I actually had a parent say to me "I know you took data on my child."

Another parent who stood by as I spoke to a family asking for how I could help their child get a bit of higher content in their math class said "I heard you ask that family for their child's name and grade."

The paranoia was rampant. The push to "opt out" was so great that we were in serious jeopardy of having any way of measuring if we'd done any good, let alone if kids had learn a year's math in a year's time.

Parents no longer trust their schools. This is perhaps the biggest legacy of the politicization of civic institutions. It is earned in many cases, but probably is worse in result than even lousy curricula. It will take a long long time to fix.
On the one hand, people habituate: the bad gets normal, as Temple always said. So this may blow over.

On the other, sans habituation almost at the level of mass amnesia, I don't see how this gets fixed.

I remember, very clearly, the moment a few years back when our district was suddenly required to weigh students, record their weights, and report the data to Albany.

I was furious. Chris had always struggled with his weight and was very sensitive about it (he lost 50 pounds last summer and has kept it off since!): it's not as if overweight children don't know they're overweight.

And it's not as if the grown-ups passing these regulations are universally thin themselves.

Needless to say, I protested, as I always do, and, needless to say, the administration and board blew me off, as the administration and board always do. High-school students would be weighed "with sensitivity," they said. And that was that. Everyone seemed to agree that weighing students and reporting the data to Albany was a bad idea, but admin & board follow regulations, good or bad. Except when they don't, of course.

The obstacle to habituation this time, as I see it: Americans believe that American schools are locally run.

Schools haven't been locally run in a very long time; superintendents speak in tongues, and bamboozled boards rubber stamp. The people vote, but the people don't get the schools they vote for.

Until now, though, parents busy with kids and jobs and volunteer work for the PTSA could lead their lives without knowing the schools aren't run by them, or that our overlords in Albany (or, even worse, Washington) don't give two figs for what we think, want, or hope.

With the constant, visible presence of Bill Gates and David Coleman and Arne Duncan and "Albany" and Washington D.C. in our lives, not-knowing has become a great deal more challenging.

Monday, March 24, 2014

Death by data, Part I've-lost-count

A compelling vision of the data-driven future of K-12 schooling? Or a chilling description of a brave new educational world in which even students' smallest actions are converted to digital data and used to build permanent "learner profiles"?

A new report from London- and New York City-based educational publishing powerhouse Pearson is likely to generate both reactions, depending on whom you ask.

Released this week, "Impacts of the Digital Ocean on Education" is intended as "an aspirational vision of what success might look like" in the rapidly changing world of "big" educational data and personalized learning.

Report authors Kristen DiCerbo and John Behrens of Pearson's Center for Digital Data, Analytics, and Adaptive Learning sketch out a vision in which end-of-year, summative tests of narrowly defined skills and content knowledge are replaced by a constant stream of digital data generated by "in vivo naturalistic tasks" that thoroughly blur the line between assessment and instruction.

Such data—generated from a variety of sources and activities, and focusing on students' social connections and interactions, rather than just their isolated individual experiences—would be constantly tracked and used to update profiles that follow each student across classrooms, grades, and schools, helping facilitate more customized learning experiences for each.

"The devices and digital environments with which we interact are designed to record and store experiences, thereby creating a slowly rising ocean of digital data," DiCerbo and Behrens write in the report. "We believe the ability to capture data from everyday formal and informal learning activity should fundamentally change how we think about education."

Just as big data and analytics have transformed finance, insurance, retail, and professional sports, the report says, they will change education. Until recently, the authors write, data collection and storage was expensive, limited, and isolated, and students' educational records were not portable, easy to share, or able to be quickly analyzed.

But the digital revolution has changed that reality, DiCerbo and Behrens contend. They argue that the abundance of increasingly fine-grained data available to educators "can help pinpoint the moments when learning occurs or a learner's approach to a problem changes" and then be used to help tailor suggestions or recommendations to help each student's learning continue.

'Ocean' of Digital Data to Reshape Education, Pearson Report Predicts
By Benjamin Herold on March 19, 2014 11:24 AM
A tidal wave of data could personalize learning

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."

Sunday, March 23, 2014

If you don't live in New York

Our airwaves are saturated with unbelievably effective pro-charter ads (from Charters Work).

This one in particular is riveting; I watch it all the way through every time it comes on. It's like a little mini-narrative -- not so much on first viewing, but on repeats. You get to know the kids; you know the sequence you're going to see them in; and pretty soon you start to feel a build-up of dread each time you watch, knowing what's coming next, which is that the beautiful children will disappear one-by-one, and the little boy looking at you over the top of his spectacles will be the first to go.

It's like a terrifying work of dystopian sci fi, for pete's sake.

Or one of those horrifying news clips like the Challenger explosion that you watch every time it's shown, hoping the ending will be different this time.

Watch this ad ten times in ten days and you'll see what I mean.



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.

What century is it again?

"You just don't in the 21st century behave in 19th century fashion by invading another country on completely trumped up pre-text," Kerry told the CBS program "Face the Nation."
Kerry condemns Russia's 'incredible act of aggression' in Ukraine
BY WILL DUNHAM
WASHINGTON Sun Mar 2, 2014 10:40am EST
I read this out loud to Ed over breakfast the other day and we both burst out laughing.

We've spent a lot of time stewing over our district's obsession with 21st century skills. Ed's line: "The schools are teaching 21st century skills, so we have to teach the 19th-century ones."

Here's our new fantastically well-compensated superintendent telling the board how warmed-over, pre-crash Tony Wagner is "being used district-wide":



The super is a Common Core enthusiast, too.

Pop quiz: how many times do the words "21st-century skills" appear in Common Core?

Tuesday, March 18, 2014

Off-topic: the plane

This pilot, as I say, was a hero struggling with an impossible situation trying to get that plane to Langkawi. No doubt in my mind. That's the reason for the turn and direct route. A hijack would not have made that deliberate left turn with a direct heading for Langkawi. It would probably have weaved around a bit until the hijackers decided on where they were taking it.

Surprisingly none of the reporters, officials, other pilots interviewed have looked at this from the pilot's viewpoint. If something went wrong where would he go? Thanks to Google earth I spotted Langkawi in about 30 seconds, zoomed in and saw how long the runway was and I just instinctively knew this pilot knew this airport. He had probably flown there many times. I guess we will eventually find out when you help me spread this theory on the net and some reporters finally take a look on Google earth and put 2 and 2 together. Also a look at the age and number of cycles on those nose tires might give us a good clue too.

Fire in an aircraft demands one thing - you get the machine on the ground as soon as possible. There are two well remembered experiences in my memory. The AirCanada DC9 which landed I believe in Columbus Ohio in the eighties. That pilot delayed descent and bypassed several airports. He didn't instinctively know the closest airports. He got it on the ground eventually but lost 30 odd souls. In the 1998 crash of Swissair DC-10 off Nova Scotia was another example of heroic pilots. They were 15 minutes out of Halifax but the fire simply overcame them and they had to ditch in the ocean. Just ran out of time. That fire incidentally started when the aircraft was about an hour out of Kennedy. Guess what the transponders and communications were shut off as they pulled the busses.

Get on Google Earth and type in Pulau Langkawi and then look at it in relation to the radar track heading. 2+2=4 That for me is the simple explanation why it turned and headed in that direction.

Smart pilot. Just didn't have the time.

MH370 A different point of view. Pulau Langkawi 13,000 runway.

Monday, March 17, 2014

Getting creaky

This blogger interface is getting seriously creaky. It's ancient; no one's updated the code in a gazillion years, and glitches I can't fix crop up.

The latest: I no longer see the "Sign in" menu at the top right-hand side of the screen.

Does anyone have any opinions on the possibility of moving to Wordpress?

I've been using Wordpress for quite a while now, and I love it.

Among other things, on Wordpress I can attach pdfs files.

Crimson Wife and Anonymous on teachers instilling grit

Crimson Mom and Anonymous.

Think how much grit kids will develop once you flip all the classrooms.

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.





Sunday, March 16, 2014

The joke's on you

So I've finally delved into the Common Core ELA standards, and....yikes. Always worse than you think.

Reading the standards in the wake of attending 3 district Common Core presentations (a fourth awaits on YouTube) is like a good news/bad news joke without the good news.

The bad news is Common Core.

The other bad news is my district has no idea what Common Core actually says, and they're doing it all wrong.

e.g.: nowhere in the Common Core will you find the words "21st century skills."

It's like that old Woody Allen joke, The food is terrible and the portions are too small.


MIA

Sorry to be MIA...I've been thinking this winter, which continues apace, has actually affected me metabolically.

I need SUN.

And more DEGREES.

LOTS MORE.

Birth of a meme

The new character education, coming soon to a district near you: grit.

Students need grit, and it's the school's job to foster grit.

Because grit is more important than knowledge.

Also: grit is best fostered by means of teachers telling students to do something they don't know how to do, then refusing to answer questions. In any other context, that would be rude, but never mind.

Our new superintendent, the one who was to bring accountability and every-child-every-dayness to our district, is a big fan of grit. Hosted a book club for parents on How Children Succeed the week after winter break.

He's a fan of Tony Wagner, too, while we're on the subject of expensive new superintendents with bad instincts. Vintage, pre-crash Tony Wagner, even better. (With increasing abundance, people want unique products and services!!!! So it's time to redefine rigor!!!)

Wrong again.

Here's Hirsch. And here's Peter Meyer.

At Education Week:

Unlearning Learned Helplessness



"I need help," several students said in their geometry class at Esperanza Academy in Philadelphia.

"I don't think so," teacher John Roman replied.

Roman had just given students a handout with several unmarked triangles on it, and asked them to determine which of the triangles were congruent. He also gave them patty paper (tracing paper), and said that it might help them complete the task. He did not, however, show or tell students what to do with it.

[snip]

[K]nee-jerk calls for help are indicative of a common reason students don't learn to their potential: learned helplessness. They encounter an unfamiliar task (or word, formula, etc.), and immediately shut down or seek help.

The good news is that because it's learned helplessness, it can also be unlearned. And because students have learned it from enabling educators like me (until I stopped spoon-feeding them), we're in the best position to help them unlearn it....Turns out, for example, that John Roman's students had sufficient prior knowledge of congruent triangles. They were also more than capable of figuring out how to use patty paper to perform the assigned task. What they lacked was a problem-solving mindset. They lacked qualities such as determination and resourcefulness.

Yet students will only acquire those qualities if we put them in situations that require those qualities. ...After commiserating for a couple of minutes, a few students picked up the patty paper and began tracing triangles. Soon all students did this, with no help from Roman besides subtle reminders to a few students that the patty paper might be helpful.

The value for students of experiences like this has more to do with confidence than content. The more they learn with little or no help from us, the more they believe in themselves and their abilities. Sure it's important for students to learn math and science and social studies. But the real lesson for kids when teachers do what John Roman did is that confusion is where learning begins, not where it ends.

And the lesson for us as educators is that students will only unlearn helplessness when we unlearn helpfulness.
Bad character comes from sages on stages.

Good character comes from guides on sides.

A likely story.



For the record, actual learned helplessness has nothing to do with the scenario described above.

The term comes from Martin Seligman's experiments with dogs in the 1960s, which entailed giving the dogs electric shocks and inducing a state of "learned" helplessness, learned in the sense that after being repeatedly shocked with no means of escape, the animals learned not to even try to save themselves, not even when the avenue of escape was directly in front of them. Instead, when the shocks came on again, they trembled and cried, and displayed all the signs of human depression. The experiments were cruel, though I don't think the experimenters knew they were cruel, going in.

I was taught the learned-helplessness experiments in college, and the image that formed in my mind of the cowering, crying dogs too distraught to exit the shock zone -- or even try to exit -- has stayed with me.

(On the other hand, having since experienced a very similar scenario on two separate occasions, I now see things a bit differently. But that is a story for another day.)

For a teacher to appropriate the term "learned helplessness" as a description of his own students is wrong in so many ways.

UPDATE 3/17/2014: See Crimson Mom's comment. (And don't miss the never-to-be-missed Anonymous.)

Friday, March 7, 2014

Any Comments on the New SAT?

For 2016, the SAT is reverting back to a 1600 based test, with the composition section optional.

The composition will be about 50 minutes rather than 25, and will focus on evidence rather than opinion.

I expect that most colleges will require this section.

"Changes in the annual test that millions of students take will also do away with some vocabulary words such as "prevaricator" and "sagacious" in favor of words more commonly used in school and on the job."

"Currently, students lose a quarter of a point for wrong answers, but no points for omitted responses. Moving forward, they will simply receive credit for correct answers."

Just this one change will squeeze the bell curve higher and reduce differentiation.

The new math test will have a portion where calculators are prohibited.

"It [math] will also focus on narrower topics — described in a College Board press release as "problem solving and data analysis; the heart of algebra; and passport to advanced math" — that Coleman suggested will most contribute to a student's college and career readiness."

"advanced math"? Remember that college and career readiness means passing a course in college algebra.

""No longer will the SAT only have disconnected problems or tricky situations students won't likely see again," he said"

How else will they create a bell curve at the top end using a limited range of material?

What do colleges think of these changes? Did the College Board ask them?

"It is time to admit that the SAT and ACT have become disconnected from the work of our high schools," he said.

This is interesting. They don't want to be seen as just following the ACT and they are trashing their competitor at the same time.

"Mr. Coleman believes changing the focus of the exam also will change instruction, from rote learning of SAT vocabulary from flashcards to deeper learning. He said the new SAT "will measure the best of what students are working on in class -- the work that most prepares them for college and career success.""

Which is it? Will the new SAT reflect what's going on in class, or will it be used to drive what should be going on in class?

"...that such standardized tests can create "unproductive anxiety" for students and lead to expensive private test prep and coaching that "reinforces privilege rather than merit."

Coleman can't have it both ways. The point of the test is to show how students compare on a nationally normed test. The score will be used by colleges to separate them. That's the whole point of their product. There will ALWAYS be test prep that favors students with involved parents or those willing to spend the money. The only way to eliminate the benefit of test prep is to truncate the bell curve at the top end. Many more students will then get perfect scores. How many colleges will want the scores from a test that shows how many students can tie their shoes?

I like it that they want to eliminate those questions used only for creating the bell curve at the top end, but wonder what they are going to replace it with. Will there be more content, say from their SAT II tests? Will they add AP-level questions? Or, will the new SAT drive the trend towards less academic differentiation and more fuzzy holistic college admissions? Even the SAT II tests and the AP tests can't differentiate students at the upper end of the curve.

Friday, February 28, 2014

Debbie at RJ Julia tomorrow morning

From Debbie:

I'll be speaking/q & a'ing tomorrow (March 1 at 11 a.m.) at RJ Julia in Madison, CT. Come say hello if you are in the area.


Donna Jackson's new(ish) book

The Last Best Cure: My Quest to Awaken the Healing Parts of My Brain and Get Back My Body, My Joy, and My Life

Donna and I have been out of touch way too long!



Blast from the past

The Tri-State Consortium tries and fails to Trailblazerize my district

Really existing Common Core

Part 1: Help Desk, Common Core edition

Our high school principal explains the centrality of modeling to high school math:
55:23 This is a very important slide and one that you’ll hear me talk about a number of times.

Because modeling, we really look at modeling as the way to really permeate through all of the different levels of mathematics at the high school level. And we really look at it from a standpoint of pedagogy. When we talk about modeling, what we’re really talking about is the conceptual side of mathematics. Recently, and there’s been a shift to a very computational format for teaching mathematics, especially at the high school level. And that’s where we would start to break things down and scaffold them into very fine points. But what we have found is mathematics teachers over the last 10, 15, 20 years, when this pattern was happening, was that students were starting to learn their broader understandings of mathematics. 56:19 There was a big need to pull back and get back to the point of teaching to deeper understanding and to the conceptualization of math, not just about being able to compute the correct answer. So modeling we really look at as the link to be able to do that. It’s the opportunity to create real-life problem-solving situations where students need to understand the conceptualization of what’s going on in the math as well as how it relates to the real world.

Geometry, obviously, is when we start talking about shapes and sizes and the relative position of objects, and statistics and probability gives us the opportunity to start looking at mathematics and creating analysis and really looking into the chances of opportunity and things occurring.

57:07 So again, as I mentioned, modeling becomes a real important focal point for us. And the phrase that we’ve been talking about is it becomes this umbrella for us. It’s the umbrella that brings the whole mathematics curriculum at the high school level together, and a way for us to keep progressing through and thinking about how it matches up. So when we think about constantly naming and reinforcing the work that the students are doing we want to constantly bring them back as well to these broader-scale concepts. 57:39 So this slide and the next slide starts to talk about that even within those conceptual designs that I mentioned before, even within algebra, there’s an aspect of modeling that’s critical and important for them to understand in the algebra as well as the other mathematical concepts within.

Similarly you have functions here, and again, there are pieces of it that we pull out and we understand how do we create real-life conceptualization and contextualization for our students so that when they’re working through this, they understand again not just the specific calculation of an equation or formula but what it really relates to.

Similarly we do the same things in geometry and we do the same things in statistics and probability. Again, for me, this is about teaching to big ideas and perspective. We’ve been talking at the school about deep understanding and I said that would be one of those shifts that we keep coming back to, and I think that that’s really one of the most important messages that we can deliver about the mathematics instruction and how the Common Core starts to create a shift for us.

Irvington UFSD School Board Meeting - February 11th, 2014
This strikes me as fundamentally wrong, but if you guys tell me it's sound, I'll have to revise my view.

My understanding of math, of what math is, is that …. mathematics is not essentially, or even first and foremost, a system for representing empirical reality. The fact that math so powerfully -- and so eternally -- does capture many aspects of empirical reality is, in my view, either a) beside the point, or b) creepy.

Math, as I think of math, has a mathiness that cannot be reduced to modeling; math is a thing unto itself and should be taught as a thing unto itself -- or, at least, students should be made aware of the fact that to a mathematician math is not just a code-writing tool.

(Again, setting aside the possibility that math is just a code-writing tool.)

"Constructionism"

Constructionism is a philosophy of education in which children learn by doing and making in a public, guided, collaborative process including feedback from peers, not just from teachers. They explore and discover instead of being force fed information, or subjected to a regime of social control as in the Prussian system adopted in the US and elsewhere, sometimes called Instructionism. Constructionist guidance has to be informed by a knowledge of what there is to explore and discover, including our ignorance, and of a variety of approaches that can be used for children at different developmental levels with various degrees of preparation.

More on this topic can be found by exploring Google using keywords such as "constructionism", "education", "philosophy". See for instance openworldlearning, Seymour Papert's website, http://www.papert.org , and the wikipedia article on constructionist learning. Constructionism is implemented on the OLPC XO in the form of collaborative discovery.

"I hear and I forget. I see and I remember. I do and I understand." - Attributed to Confucius.

Constructionism is built on the foundation of Constructivism, the theory of childhood learning created by Jean Piaget, Lev Vygotsky, and many others.

One Laptop Per Child
No fun.

Thursday, February 27, 2014

Help Desk, Common Core edition

Two weeks ago, when our high school administrators gave a presentation devoted exclusively to Common Core "shifts" ("shifts," not "curriculum areas") the principal told us that henceforth math will be taught as modeling first and foremost. All math, it seems, in all math courses.

That strikes me as a terrible idea. Dreary, too.

Math for math's sake, math as a liberal art, math as a thing of beauty...math in my district is apparently a vocational art, not a liberal one. Kids are going to be explaining their answers a lot, too. (The explanation we saw opened with the words "We used the rules we have learned about discriminants.")

If you have thoughts, let me know.