Monday, March 30, 2015

Stimming on stemming STEM

It’s hard to know where to begin reacting to Fareed Zakaria’ recent Washington Post article, Why America’s obsession with STEM education is dangerous. So I’ll begin at the beginning.

If Americans are united in any conviction these days, it is that we urgently need to shift the country’s education toward the teaching of specific, technical skills.
Nope. To the extent that there’s a trend, it’s away from teaching specific, technical skills. Cf. interdisciplinary “21st century skills,” the whole, well-rounded child, and most of the Common Core Standards.
Every month, it seems, we hear about our children’s bad test scores in math and science — and about new initiatives from companies, universities or foundations to expand STEM courses (science, technology, engineering and math) and deemphasize the humanities.
We also hear about the push by arts-oriented educators and foundations to change STEM to STEAM (science, technology, engineering, art, and math).
From President Obama on down, public officials have cautioned against pursuing degrees like art history, which are seen as expensive luxuries in today’s world. Republicans want to go several steps further and defund these kinds of majors. “Is it a vital interest of the state to have more anthropologists?” asked Florida’s Gov. Rick Scott. “I don’t think so.”
The relatively few public officials that have much such remarks have gotten a lot of flak.
… The United States has led the world in economic dynamism, innovation and entrepreneurship thanks to exactly the kind of teaching we are now told to defenestrate.
How do we know we have teaching to thank? Why single out schools in particular, when so many factors affect economic dynamism? Maybe it’s the entrepreneurial spirit of past and recent immigrants, plus the country’s political and economic freedoms and fluidity (which keep attracting these immigrants), plus our ongoing role as a global currency reserve (which keeps us wealthy, full of investment capital, and… attractive to immigrants).
In truth, though, the United States has never done well on international tests, and they are not good predictors of our national success. Since 1964, when the first such exam was administered to 13-year-olds in 12 countries, America has lagged behind its peers, rarely rising above the middle of the pack and doing particularly poorly in science and math. And yet over these past five decades, that same laggard country has dominated the world of science, technology, research and innovation.
This is large part in thanks to the large numbers of top scientists who live here now but were foreign born and educated—immigrating here, not for our K12 schools, but for our colleges, universities, and job markets.

I’m only halfway through the article, but for now I’ll stop here.

Saturday, March 28, 2015

Plus ça change, plus c'est la même chose--or worse

If I were running a school, there are a number of things I would do to save money at no academic cost. (And, naturally, I would spend some of these savings on what counts the most: teachers, who, regardless of any official credentials, demonstrate great teaching and classroom management skills and extensive knowledge in their instructional fields—though I would attract them not just with reasonable salaries, but with much greater respect and autonomy than they get elsewhere).

Here’s how I would save money at no extra academic cost. I would eschew so-called “educational” technology. I would run the school locally, free from distant, salaried administrators. And, finally, I would avoid buying new books (where new generally means higher cost and lower academic quality), instead using as many ancient books that are now in the public domain (and essentially free) as possible.

In other words, my spending priorities would be the opposite of what so many large school districts do—for example the Philadelphia School District. Take old books, for example. As a recent article in the Philadelphia Inquirer reports (In cash-strapped School District, a hidden treasure trove of books), the districts has “thousands and thousands” of books

from two dozen city schools shuttered two years ago. Perfectly usable. All sitting boxed up and unused in the basement of the Philadelphia School District's headquarters.

A city block of books. Some of them shrink-wrapped. Some of them dumped in boxes. Some stacked on the floor. Few labeled. Nothing organized. Kindergarten readers next to high school books. Expensive Storytown reading series, gathering dust. Science, algebra, literature textbooks. Literary kits and phonics sets. Books for English-language learners.
These books include “classics like Jack London and Mark Twain.” It gets worse:
There are thousands more unused books - and other things city kids badly need, including pianos and other instruments - piled up in the hallways and classrooms of the shuttered Bok High School in South Philadelphia.

In a district where almost 60 percent of the kids cannot read at grade level, the library is heartbreaking. Many shelves are still stocked. There are hundreds of dictionaries.
And the marching band equipment, pushed into a corner of the library: Five pianos. Bass drums. Kick drums. Trombones. The green-and-white band uniforms lie on the floor like the empty cloak of the Wicked Witch of the West.
The article’s author, Mike Newall, asks:
In a broke district, there's no music program that could use that stuff?
District spokesman Fernando Gallard “offered bureaucratic explanations that indicated this is not a new problem.”
Much of the material in the district basement, he said, were from outdated curricula taught during the administrations of Superintendents Paul Vallas and Arlene Ackerman.

If that's the case, how many thousands of dollars in waste is lying around there? 
Math doesn't change. Chemistry doesn't change. Literature is timeless.
Indeed, in terms of the introductory material that should be the focus of K12 schools, most subjects don’t change.

Newall asks:
And in a district in financial crisis, aren't old textbooks better than no textbooks?
I’d go further: most old textbooks are better than new textbooks.

Many people around here in Philadelphia blame the plight of the Philadelphia School district on state government stinginess. The big picture is a bit more nuanced.

Thursday, March 26, 2015

Math problems of the week: Common Core-inspired Math problems

From, the first problem on a "math Common Core Sampler Test."

Extra Credit:

1. Given the instructions, should acceptable answers include the rewrite provided below?

5j - (j - 2k) + 5k + 36

2. Supposing that the immediate goal is to have students combine like terms, and that the long time goal is to have students apply math to real-life situations, rewrite this problem as a real-world application that implicitly requires students to combine like terms.

Tuesday, March 24, 2015

When it matters whether 1 is prime

As I write this post, my home schooled daughter is over at a neighbor’s house spending one school day on what her public school peers have had to devote a week or more of their school year to. That is, she is taking a standardized test. To satisfy Pennsylvania’s home school law, she had to do this once in 4th grade, and once (now) in 8th grade. And since we can pick whichever standardized test we want, we pick the best one: the tried and true Iowa Test of Basic Skills (ITBS). And since anyone can apply to be a certified ITBS administrator, we walk a few blocks to the nearest neighbor who has, a fellow homeschooling mom.

As a tried and true standardized test (I took it several times several decades ago), and one with straight forward, well-written questions, the ITBS will give us results that are actually useful. In other words, it isn't anything like the new Common Core-based tests. 

Nonetheless, in some ways I would rather my daughter could forgo testing altogether. Useful as a good standardized test is for diagnosing her weaknesses, not to mention for preparing her for other standardized tests, there are probably better things we could do with our time--both right now, and during the couple of hours we spent preparing for this test. Even the best of multiple choice tests risk occasionally testing knowledge of labels rather than knowledge of concepts, and therefore, so that she wouldn’t feel stumped for stupid reasons, I found myself drilling her on things I really couldn’t care less about. Things like:

Is 1 a prime number?

Is 0 a natural number?

What is the “median” vs. the “mode”?

What does the expression |X| mean?

What is scientific notation?

But, as far as the Labels as Concepts Fallacy goes, the ITBS is much better than its Common Core counterparts.  So I didn’t find it necessary to drill her on the meanings of “kite” and “number sentence” and “rate of change” and “Cavelieri’s Principle”, not to mention “dilation,” “reflection,” and “translation.”   It could have been a lot worse—and for so many kids and their parents, it is.

Friday, March 20, 2015

Math problems of the week: Common Core-inspired test questions

Another from the sample 3rd grade math test from Smarter Balanced Assessments, which is developing Common Core tests for 31 states:

Extra Credit:

Compare the problem's mathematical challenge to the challenge of figuring out what exactly it's asking about.

(Maybe it's just me, but I had to reread it a couple times, and I've had a bit more experience interpreting math problems than your average 3rd grader).

Wednesday, March 18, 2015

“Universal access” to The Answer

Many teachers, as I discussed earlier, are obligated by their superiors to assign literary works that are many grade levels ahead of that of their students. But how, short of massive grade inflation, do you keep your students from failing the class? The answer is to relegate the actual works to window dressing, replacing them with simplified texts like No Fear Shakespeare, or movie versions, or graphical representations of the story and its characters.

While these moves may be purely pragmatic in some cases, I’ve heard some education professionals discuss them as reasonable ways to provide special needs students with “equal access” to the great works of literature. Withholding Shakespeare from students with language delays, after all, would be an ableist bigotry of low expectations.

The problem is that what makes Shakespeare et al great literature isn’t translatable into simplified texts and visual representations. Great literature is a function of great writing: evocative word choices, turns of phrase, rhythms of prose. Simplifying that writing not only reduces its quality, but also much of its more intricate content. Replacing poetry or prose with visuals or cinematography removes all that isn’t visually or cinematographically depictable: the characters’ introspections or interior monologues, the narrator’s nonvisual descriptions (e.g., of personalities), and other nonvisual reflections, commentaries, and foreshadowings. This kind of access isn’t real access.

Instead, it creates a mockery of real literature, reducing it to basic plot, simplified characters, and a simplified notion of authorial intent.

Somehow this reminds me of Reform Math. In endorsing multiple ways to get the answer, or "multiple pathways" to “demonstrate understanding,” Reform Math ignores the importance of specific mathematical strategies. No matter if you counted on your fingers or guessed and checked in lieu of following general rules to find patterns and manipulate expressions and equations: as long as you write some sort of verbose explanation for how you solved the problem, that’s all that matters. Similarly, Universal Design-inspired literature classes ignore the importance of the specific means the author has used to convey the literary “answer” (the work’s content and theme). As long as you “demonstrate understanding” of what the "answer" is, it doesn’t matter how you got there. In this version of education--of “access” to “learning”-- it’s the final destination, not the journey, that matters.

Monday, March 16, 2015

The Full Inclusion illusion

Even as J winds down his final year in the Philadelphia public school system, I’m still learning new things about how the district operates. For example, I recently learned that the one-size-fits-all approach to high school English predates the Common Core. For at least the last dozen years, all Philadelphia high school English teachers have had to choose from a specific list of literary works/authors, which include Steinbeck, Edgar Allen Poe, the Canterbury Tales, and Shakespeare plays. It doesn’t matter that, according to a 2013 report, only 53.4% of the school district’s 11th graders scored proficient or advanced on the Literature section of the state’s new Keystone test, and that only 10.1% and 10.6%, respectively, of English Language Learners and special ed students with IEPs scored proficient or advanced in Literature.

For all but the most intellectually impaired of these students, it’s full inclusion in regular classrooms. In other words, Steinbeck, Edgar Allen Poe, the Canterbury Tales, and Shakespeare, for nearly everyone who scores Basic or Below Basic in Literature.

Many of my own students, special ed teachers who teach children with autism, have long been concerned about how all this affects their students. They report, however, that higher powers keep them from making modifications and from telling parents how bad things are. On a recent discussion board, one student wrote:

I was stuck between the school district and the parent who wanted their child placed in an outside placement because the child was struggling behaviorally and academically. It was difficult because I did not feel that this student needed placed outside. The problem actually was that the regular education was not properly modifying his classroom and work for the student needs. Of course, I could not tell this to the parent. I worked my hardest to get the teacher to understand how inclusion works with no luck.
When I asked her why she felt she couldn’t tell the parent what was going on she wrote:
I was told not to tell the parents because they are famous for making complaints with the state (which I don't blame them because I would have too). … Everyone here is too worried about getting in trouble for not following the rules, simply because they know they aren't. They fear that telling a parent could result in the filing of a due process complaint.
Another student has the same feeling about: administration not wanting the special education teachers to tell the "whole" truth about how they feel things are going. I feel that some schools want to make it look and sound like everything that needs to be done is being done when it may not be. Many teachers try to get students different curriculum that will best meet their needs and they are shut down. When teachers suggest pulling out for more intense instruction at the students level, it was frowned upon and said we are "full inclusion." With some persistence some teachers now pull out which has been very beneficial to those students. Some schools want to "look" so much like what the public thinks is full inclusion and not what it should really be... Many teachers work behind the scenes to try and fix the problem, which causes a lot of stress on them.
Another student writes:
I have definitely seen students not necessarily getting what they need in a specific area, especially if they are included in the mainstream when they probably shouldn't be.
And another student writes:
I am a regular classroom teacher with GIEPs and IEPs. I have to widen my instruction and materials for levels from 1st grade to 5th grade in reading and math. I have no support teacher or aide and this is honestly a big challenge. My school believes that one person, me, should be able to handle this with no problem and challenge/meet the needs of 22 students. This is where I believe that schools are in the wrong with full inclusion and students not getting what they need.
But is anyone listening?

Saturday, March 14, 2015

More maps; fewer portraits

I've always felt that, when it comes to history texts, you can never have enough maps. Especially cartographically-challenged are America's K12 history books--something I was reminded of recently when checking out this page of J's American history book:

In place of the "Picturing History" portrait of Pike, why not a map showing--all at once--the Louisiana purchase and the paths of the Lewis and Clark and the Pike Expeditions, complete with rivers and mountains. Something like:

This would seem a more relevant way to picture history than what exactly Pike may have looked like in his officer's uniform with his soldiers in the background.

Of course, students can always "look it up on the Internet," as I did (expending all of about two seconds). But, in the age of mapless navigation and shrinking cartographic literacy, how many will be inspired enough, and motivated enough, to bother?

Thursday, March 12, 2015

Math problems of the week: Common Core-inspired test questions

From the sample 3rd grade math test from Smarter Balanced Assessments, which is developing Common Core tests for 31 states:

Extra Credit:

Discuss these problems in terms of:

1. 21st century skills
2. the Common Core Standards' goal of preparing students "for college and career," and
3. the difference between labels (where the primary challenge is knowing the meaning of a particular mathematical label) vs. concepts (where you have to understand a non-trivial mathematical concept).

Tuesday, March 10, 2015

Introducing the SentenceWeaver(TM)

We're almost ready to beta test an iPad version of my GrammarTrainer, and so I thought I'd "scoop" it here, now.

(And, in the process, I thought I'd mention its name with its trade mark a few times so as to claim it before someone else does).

Here goes:

The SentenceWeaverTM

A unique, interactive tool for language learning in autism

The SentenceWeaverTM is an interactive tool for children with language delays, particularly autism. It helps these children put words together into phrases, basic sentences, and, eventually, long complex sentences. It also helps children learn proper pronoun use and perspective-taking skills.

The SentenceWeaverTM is unlike any other linguistic software tool currently available. It is unique both in terms of methodology, and in terms of breadth and depth of topics.


*Unlike other programs, the SentenceWeaverTM doesn’t tell just users that their answers are right or wrong, but highlights what’s wrong with their answers.

*Unlike other programs, the SentenceWeaverTM doesn’t just give away the correct answers, but interactively helps the user to construct correct answers through step-by-step self-corrections.

Breadth and depth of topics:

*Unlike other programs, the SentenceWeaverTM extends far beyond basic phrases and sentences to include all the fundamental sentence structures of English.

*Unlike other programs, the SentenceWeaverTM teaches all pronoun forms, all verb forms, and abstract prepositions.

*Unlike other programs, the SentenceWeaverTM teaches all types of subordinate clauses, including those that enhance Theory of Mind reasoning skills.

Beyond mere comprehension to productive language:

*Unlike other programs, the SentenceWeaverTM teaches users how to actively produce phrases and sentences, not just how to passively comprehend them.

Beta testing:

We are currently beta-testing two completed modules of the SentenceWeaverTM: PhraseTrainer and Pronouns.

PhraseTrainer, a basic phrase training module, has users constructing simple phrases and sentences in order to answer questions about shapes and colors.

 Pronouns, a higher-level module, has users determining proper pronoun use by watching the gestures and eye gaze of animated characters with speech bubbles.

Related to this, here's a brief commentary on things to watch out for in programs that purport to teach grammar, excerpted from this book:
With programs that claim to teach grammar, there are several things to watch out for. Is the main focus really on grammar and its general rules and structures, or is it on vocabulary and specific phrases? If the program does focus on general rules, are these the kinds of grammar rules that language-impaired students need help with and that have been our focus throughout this book—word order and word endings—or are they the kinds of rules aimed at all students—part of speech labels, rules specific to the standard dialect, and the conventions of written language (punctuation, the spelling of homophones, and rules of style). Here, it’s important to distinguish between “school grammar,” also called “prescriptive grammar,” which many students need help with, and the more basic grammar discussed throughout this book, which only language-impaired students need help with.
Once you’ve insured that the latter sort of grammar is addressed by the program, there are additional questions to ask. Does the program teach this grammar explicitly, or merely provide incidental exposure? Incidental exposure may still be effective, but, as discussed in Chapter 3, it’s impossible to ensure that the user is paying attention. Does the program teach productive grammar, or only receptive grammar? Receptive grammar is worth instructing in its own right, but, as discussed in Chapter 3, mastery of particular receptive grammar skills doesn’t guarantee mastery of corresponding productive grammar skills. Finally, if the program teaches productive grammar, how wide a range of structures does it teach, and how much of the grammatical work is done for the student instead of by him?

Sunday, March 8, 2015

Bad things

Actor and science popularizer Alan Alda feels that America’s scientists should learn “how to present their research to the public.” He also feels that the best way to do this is through improvisational acting exercises. Here’s one example, described in an article in this past week’s New York Times Science Section:

Martha Furie [a professor of pathology at Stony Brook University] stormed into the room and huffily sat down in a chair.  
“Well, you know, I’ve been working really hard, studying Lyme disease,” she said, her voice tinged with disdain, to the woman sitting in the next chair. “It’s been a long process. It’s hard to talk about it.”  
The other woman, Bernadette Holdener [a professor of biochemistry and cell biology at Stony Brook University], was somewhat befuddled. ”How does it make you feel?” she asked.  
“Lyme disease?” Dr. Furie sneered. “It can have all sorts of bad things.”
As the Times’ Kenneth Chang explains
The exercise, called “Who am I?,” challenges one of the participants — Dr. Furie, in this case — to convey an unstated relationship with another, and everyone else must try to deduce the relationship. “She sounded very angry,” Dr. Holdener said.
Why was she angry?
People guessed variously that Dr. Furie was a Lyme researcher who had contracted the disease, that she just been denied tenure and was venting to the head of her department, that she was expressing passive-aggressive anger toward her spouse.
Facilitating the exercise was none other than Alan Alda:
“You’re so close,” Mr. Alda said.  
Dr. Furie explained that Dr. Holdener “was my long-lost sister who stole my husband away.” The other participants laughed at the convoluted, unlikely setup.
Though no one guessed this set up, Alan Alda was pleased with how things went:
Mr. Alda said that Dr. Furie, focusing on her role as a wronged sister, intently observed her audience — Dr. Holdener — and the effect of her words. “What I find interesting about this is you’re suddenly talking about your work in a way you’ve never talked about it before,” Mr. Alda said.
How pretending to be aggrieved, long-lost sisters helps scientists present their research to the public is unclear to me. But Alda, who has no difficulty whatsoever presenting his ideas to the public, was able to convince Stony Brook to set up a Center for Communication Science in 2009, renamed the Alan Alda Center for Communicating Science in 2013. Despite initial skepticism that “improv would be a distraction”
two graduate programs now require students to take the center’s classes. All medical school students receive 10 hours of training.  
… In addition, four organizations — Dartmouth College, the University of Vermont, the Robert Wood Johnson Medical School in New Jersey and the American Chemical Society — have become affiliates of the center. Other universities, inspired by Stony Brook, are considering setting up similar programs.
Given all the teaching and grant writing that scientists do, and how easy it is for experts to forget the perspectives of outsiders, I’m sure that many can and should improve their communication skills. But I’m wondering whether, just maybe, a verbal coach might be more effective than an acting coach. Were I advising Martha Furie on how best to communicate the effects of Lyme disease, for example, I would focus, not on her ability to play an aggrieve, long-lost sister talking about Lyme disease, but on her actual words. “It can have all sorts of bad things”: perhaps my verbal expectations are unreasonably high, but I say it’s those words, first and foremost, that need work.

“Despite the paucity of evidence, even medical experts can fall into marketing traps.” This sentence isn’t from the Alda Article, but from an adjacent article discussing skepticism about vitamin supplements. Yet, paucity of evidence and marketing traps are equally afoot chez Alda.

How can scientists, whose stock-in-trade is (or ought to be) skepticism, particularly about correlation vs. causation, and basic logic, fall for pseudo-syllogisms like these?
Alan Alda is good at improvisational acting exercises.
Alan Alda is good at communicating science
Therefore requiring scientists to do improvisational acting exercises will make them good at communicating science.
Or, perhaps, like Lyme disease, it can have all sorts of bad things.

Friday, March 6, 2015

Math problems of the week: Common Core inspired test question

From the sample 8th grade math test from Smarter Balanced Assessments, which is developing Common Core tests for 31 states:

Extra Credit:

The aim of the Common Core Standards is to prepare students for "college and career." How does assessing a student's ability to perform reflections and translations of the sort of shape seen above contribute towards this goal?

Wednesday, March 4, 2015

Bases for conceptual understanding

Pam asks, "How can we as teachers encourage the flexibility and generalized use of strategies discussed above so that students can reason abstractly and quantitatively?"  
Perhaps the best way to encourage flexibility and abstraction in mathematical thinking is to move beyond the tyranny of the Base 10 number system, which, after all, is simply an anthropocentric artifact of our having 10 fingers. I propose Base 2 for starters; then Hexadecimal. These, after all, are the number systems of our 20th and 21st century computers, and, therefore, of 21st century math skills.  
Of course, once students have done these problems in Base 2 and Hexadecimal, they can relate their solutions to the anthropocentric counterparts in Base 10. As Eric points out, "it's just wise to take a problem and look at many different ways to approach it and then compare and consider those approaches."
This is the comment I left two days ago on a blog post over at (Hat tip to Barry Garelick). Given some of the some of the other comments in the thread, I was perfectly happy to look like a total lunatic to those who didn’t detect irony.

But then the more I thought about it, the more that irony started escaping me.

Maybe bases are the best way to encourage the flexibility and abstraction in mathematical thinking that so many math education experts say they want. What better way, in particular, to teach the concepts underlying the place value system? What better way to illustrate the abstract structure underlying 1, 10s, and 100s places than to compare this to the structure underlying the 1s, 2s, 4s, 8s, 16s, 32s and 64s places? Or to compare the decimal system—the tenths and hundredths places, etc.—to the halves, quarters, eighths, sixteenths, thirty-seconds, and sixty-fourths places? Not to mention myriad other possibilities, like long division in base 8, repeating decimals in base 3, and fraction-to-decimal conversions in base 7.

I loved learning bases back in 6th grade in France. I still remember the revelations they gave me about the “anthropocentric” arbitrariness of the Base 10 number system and of the gorgeous abstractness of number systems in general. And I’ve tried to share that passion with my kids—most successfully with J.

Why does no one teach bases anymore? Historically, they’re associated with the garbage of Sputnik-inspired New Math; mathematically, they require training that most teachers don’t get; pedagogically, they’re challenging to teach—and (for all the child-centered explorations they might inspire once taught) require the kind of direct instruction that’s been going out of fashion for decades

On that note, here’s some preliminary direct instruction in Base 8 from the Master:

Note the aside about today’s school kids (“the important thing is to understand what you're doing, rather than to get the right answer”). A reminder that the troubling trajectory of American math education is over a half a century old now.

Monday, March 2, 2015

Why is innovation always the answer?, II

An article in the Philadelphia Inquirer has just announced that

Three Philadelphia School District leaders... will be meeting with Education Secretary Arne Duncan and other top principals from around the country in Washington.
The occasion? A program called "Principals at ED," which
"brings groups of highly innovative and successful principals from across the country to the Education Department to learn more about federal programs and to share experiences from their jobs as school leaders."
Guess which three principals have been chosen?

The principal of the school that has consistently scored first place citywide in the Pennsylvania School Performance Profile, based on test scores, attendance, AP and SAT scores, and teacher impact.

The principal of the school that currently scores first place, and has long scored second place, in the Pennsylvania School Performance Profile.

The principal of the school which, after years of obscurity, currently scores second place in the Pennsylvania School Performance Profile.


The principal of a school whose students score poorly on AP tests but which is a project-based, technology-empowered school that has "received national attention and prizes for [its] innovation."

The principal of school that has only been operating for two years but is a satellite of the project-based, technology-empowered, national attention and prize-winning school.

The principal of another school that has only been operating for two years but is a project-based, real-life-application school that has "received national attention and prizes for [its] innovation."

Hint: the article quotes one of the chosen principals as saying that "school should really be about problem solving, communicating, persistence, self-awareness, and project management."