Thursday, July 30, 2015

Math problems of the week: Common Core-inspired 4th grade test questions

From the Smarter Balanced Assessments, a Common Core-inspired, standardized test consortium now consisting of about 12 states: the next three problems on the sample 4th grade practice test.

Extra Credit

Discuss the various ways in which the emphasis on conceptual understanding and interpreting the thought processes of other "mathematical thinkers" undermines more challenging applications of procedures.

Tuesday, July 28, 2015

A test is only as good as its graders

A recent article in the New York Times raises yet another concern about the new Common Core tests: who exactly is grading them? This concern stems from the fact that these tests "put less stock in rote learning and memorization" and therefore require fewer multiple choice questions

and far more writing on topics like this one posed to elementary school students: Read a passage from a novel written in the first person, and a poem written in the third person, and describe how the poem might change if it were written in the first person.
The two big Common Core testing companies are Pearson and PARCC. For Pearson, according to the Times:
About three-quarters of the scorers work from home. Pearson recruited them through its own website, personal referrals, job fairs, Internet job search engines, local newspaper classified ads and even Craigslist and Facebook. About half of those who go through training do not ultimately get the job.
As for PARCC:
Parcc said that more than three-quarters of the scorers have at least one year of teaching experience, but that it does not have data on how many are currently working as classroom teachers. Some are retired teachers with extensive classroom experience, but one scorer in San Antonio, for example, had one year of teaching experience, 45 years ago.  
Compare this to the AP requirements:
For exams like the Advanced Placement tests given by the College Board, scorers must be current college professors or high school teachers who have at least three years of experience teaching the subject they are scoring.
Of course, much smaller numbers of students take the AP tests, thus fewer graders are needed, thus higher standards are possible.

But if the Common Core test questions really live up to claims about the high-level thought processes they measure, then surely we need measurably high-level thinkers grading them:
The new tests are much more complicated and nuanced than previous exams and require more from the scorers, said James W. Pellegrino, a professor of psychology at the University of Illinois at Chicago who serves on advisory boards for Parcc and Smarter Balanced. “You’re asking people still, even with the best of rubrics and evidence and training, to make judgments about complex forms of cognition,” Mr. Pellegrino said. “The more we go towards the kinds of interesting thinking and problems and situations that tend to be more about open-ended answers, the harder it is to get objective agreement in scoring.”
I've written earlier about the virtues of well-constructed multiple choice tests. This article highlights one of them.

Sunday, July 26, 2015

Why not teach Harry Potter?

It's not great literature, but it's better written, and surely more interesting, than the tedious realistic fiction that passes for literature in today's elementary schools.

On this, my latest round of education students have given me new insight.

First of all, it's taken as given that one key way to develop reading skills is by making personal connections. And, naturally, it's harder for students to make personal connections if the book takes place a long time ago, or far away, or in an imaginary or futuristic world.

More profoundly, it's taken as given that students aren't interested in books that they can't relate to their personal lives. Many of my students seem to deeply, deeply believe this.

They are willing to grant that realistic fiction is comparatively difficult for kids on the autistic spectrum: we discuss how such children often lack the necessary background knowledge to make sense of these stories, and how fantasy and science fiction level the playing field. But for all other "learners," they're certain, realistic fiction is not only best for learning, but what students prefer.

So what about Harry Potter, I ask. How can that be so popular?

Silence. Confusion. My students appeared never to have considered this question before.

Then one student finally said something about how they can't teach Harry Potter anyway because of concerns about schools endorsing witchcraft.

I looked that up and, as far as I can tell, only a few school districts have banned Harry Potter for that reason. Everywhere else, I'm guessing, it's all about real-life relevance. And the depressing notion that children are only interested in reading about slight variations on their own lives.

Another strike against fantasy and sci fi comes from the world of literary criticism, which prefers obscure, nonlinear, writerly prose to imagination and character-driven plots.

How many people, as a result are missing out on gems like this one--just published by my friend and colleague Stella Whiteman?

Friday, July 24, 2015

Math problems of the week: more Common Core-inspired 4th grade test questions

From the Smarter Balanced Assessments, a Common Core-inspired, standardized test consortium now consisting of about 12 states: the next three problems on the sample 4th grade practice test.

Extra Credit:

Discuss the 21st century challenges posed by these problems in terms of verbosity (problem 7), clarity (problem 8: the meaning of "gives each student 1 card"), and understanding the user interface as opposed to understanding addition with regrouping (problem 9).

Wednesday, July 22, 2015

Social-emotional studies

From the U.S. history book American Vision, the text used in Philadelphia's public high schools:

Monday, July 20, 2015

A.P. update: what does it take to show your work?

We learned last week that J managed to get a 5 on his AP BC Calculus exam, defying expectations about whether he'd be able to step out of his shoes enough to show his work. None of his practice tests earned 5s, and so it's very satisfying to see this one, especially as it bodes well for his potential to show his work in college-level math classes this coming year.

On the other hand, he only got a 3 on the AP Computer Science exam, which presumably means there's more work to do in making sure his programs (which he dashes off quickly, and which get the job done, but are often quite lacking in clarity) conform to specifications. Apparently, this is even harder for him than showing his work in math.

Except that there's another possible explanation for J's superior performance on the BC Calculus exam--and for his uncharacteristic eagerness to find out his score. It turns out that his math teacher had promised the class to organize a lunch at Dave & Buster's if they all did well.

And Dave & Buster's--you guessed it--has lots and lots of ceiling fans.

Saturday, July 18, 2015

Do American secondary school contribute to radicalization?

I've written frequently here and elsewhere about how America's K12 schools are particularly challenging for unsocial children. The uniquely American quantity of extra-curricular school-based activities--sports, clubs, student government, athletic events, dances--have transformed American junior high and high schools into institutions that are much more social in nature than their counterparts in other countries. American high schools are major centers of social gravity, with social hierarchies based more on athletic skills, extracurricular activities, and leadership than on academic interactions. Factor in the rise of mandatory group work inside and outside of American classrooms, and the social pressures are inescapable. From this, the quirky, unsocial introvert, in comparison with his counterparts in other countries, will find little refuge.

On top of this, there seems to be something particularly trying about American teenagers in particular. One Asperger dad I know sends his son to a Canadian summer camp because, as the son has observed, Canadian teenagers are nicer.

All this makes me wonder about the role played by American junior high and high schools in marginalizing, and thereby radicalizing, certain psychologically unstable and susceptible kids: the school shooters, the skin heads, and the ISIS recruits. Of course, there are plenty of other factors at play here, from the availability of guns here in America, to homegrown homophobic, White Supremacist ideologies, to the lure of the Caliphate in the Middle East. But it's worth appreciating what nasty settings those institutions that concentrate together large numbers of teenagers can potentially be--especially when child-centered ideologies empower kids to create and run the social hierarchies in settings where the adults should really be in charge.

Thursday, July 16, 2015

Math problems of the week: more Common Core-inspired 4th grade test questions

From the Smarter Balanced Assessments, a Common Core-inspired, standardized test consortium now consisting of about 12 states: the next three problems on the sample 4th grade practice test.

Extra Credit

Discuss the relative roles played by language skills (knowledge of labels, careful reading) vs. math skills in these problems.

Tuesday, July 14, 2015

Going "deep" with Common Core algebra

It's time for another exegesis of an article in Edweek, this one on what the Common Core is doing for algebra students:

Under the Common Core State Standards, Algebra 1 is a much tougher course than what was taught previously in most states, teachers and standards experts say, in part because many of the concepts that historically were covered in that high school class have been bumped down into middle school math.
Actual Common Core-inspired algebra problems tell a different story.
Some say those changes could complicate efforts around the country to put 8th graders in Algebra 1—a still-debated trend that's grown over the past two decades.
And thus the Common Core, besides all the other fashionable K12 practices it endorses, has become yet another excuse not to accelerate students, but rather to impose a one-size-fits-all on everyone based on their calendar age.
And while that kind of move can disappoint some parents, educators point out it doesn't mean 8th graders aren't learning algebra.
Well, that depends on what you mean by "algebra."
"There's big confusion between the Algebra 1 course with a capital A and algebra, the mathematical subject," said William G. McCallum, a mathematics education professor at the University of Arizona, in Tucson, and one of the lead writers of the common standards. "If you follow common core, there's now tons of algebra content in the 8th grade."
Well, that depends on what you mean by "algebra."
"Traditionally in Algebra 1, a lot of time was spent looking at linear functions," said Diane J. Briars, the president of the Reston, Va.-based National Council of Teachers of Mathematics. "But a lot of that work now has been moved into 8th grade common core."
Right. Kids in 8th grade (and younger) are filling in input and outputs on function charts, guessing and checking and plotting points on grids, and solving for x in simple equations involving minimal mental (or algebraic) manipulation. Then there's ratio and proportion.
"The common core… built much higher expectations for conceptual understanding regarding ratio and proportional relationships [in 8th grade] to prepare students to understand the ideas of slope and rate of change."
It sounds pretty impressive:
Simultaneous linear equations and functions and their graphs—concepts also typically taught in Algebra 1—are now also taught in 8th grade under the common core.
The catch is that those simultaneous equations never have more than two variables in them, even in today's Algebra 2, and that they require little in the way of symbolic manipulation.
The idea is that by the time students get to Algebra 1, they will have developed deep understanding of some basic algebraic concepts, and can dive into more complicated coursework.
The "complicated coursework," though, is about applying these concepts to "real-world" situations, not to situations of mathematical complexity:
Students are focused on applying the algebra they're learning, rather than seeing it as a series of procedures and algorithms.
For instance, rather than doing a set of problems from the textbook, Mr. Ryan said, students in Algebra 1 might collect data on the weight of students' backpacks, plot them on a graph, and model them with an algebraic function.
What's challenging about math, however, often isn't the concepts themselves. How hard, after all, is the concept of a function, or a slope, or an algebraic "model" of a simple, real-world situation like the weight of students' backpacks?

What's challenging about math, rather, is the mathematical complexity and abstraction that emerges from applying functions, slope, and algebraic models, not to real-world situations, but to mathematically complex situations, with layer upon layer of abstractions, abstract patterns, and symbolic manipulations. What students need practice mastering is this emergent property of complex, abstract math, and not the building-block concepts themselves--or their real-world applications. Yes, students need to engage with the concepts in action, but most especially in an abstract, mathematical way that few are seeing today.

Here are some examples of what they are missing, and will miss--throughout their years of Common Core-inspired high school math:

--simultaneous equations involving more than two variables.
--simultaneous quadratic equations.
--equations involving abstract quadratic patterns.
--real-world situations that take some real mathematical thinking to model mathematically.

Sunday, July 12, 2015

Autism diaries: the question of authorship

"I just assumed you were coming back to the kitchen," says J. "In fact, I did not even think of trying to leave the fan on all night."

In fact; assume--to my ears, coming out of J's mouth, these words sound almost miraculous. Not only are they the sort of subtle, conversational terms that are supposed to elude even higher functioning Aspies and auties, they're also words J's picked up on his own, simply by overhearing people use them. Nearly all the words in his vocabulary, until recently, had to be deliberately pointed out or defined for him, sometimes repeatedly. Now, through the incidental learning that typifies most neurotypical language learners but eludes most individuals with autism, these words have become fully J's own.

I've written frequently about the question of authorship in autism. While this question arises most especially vis-a-vis the "facilitated communication" of nonverbal individuals, where it's for from clear who (or what) is actually doing the communicating (see here, here, and here), it also arises with verbal kids who communicate independently. Kids on the spectrum often have copious memories and can regurgitate verbatim large tracks of memorized discourse and large bodies of memorized facts. Some of them go through intensive behavioral therapy that drills them in prepackaged conversational phrases and formulas. Autism autobiographies may undergo extensive re-writing by editors--even if those editors manage to maintain, more or less, the original authorial voice. Those rewrites, in turn, may be memorized and regurgitated by the original authors in book talks and other post-publication speeches.

The flat facial affect, flat tone of voice, and overall lack of expressivity of autistic speakers only heightens the question of who is really communicating. Is it the individual with autism, drawing spontaneously on internally processed knowledge, and putting words together independently and extemporaneously? Or is what we're hearing ultimately the product of a facilitator, a behavioral script, a book editor, a word-button or word-prediction program, or an author of a text that has been read and reread out of obsessive autistic interest?

It's often hard to say--and the line between the two extremes is often fuzzy. It's probably somewhat fuzzy even for neurotypicals: all of us do some cutting and pasting of other people's words.

In J's case, however, the same things that have limited him over the years have minimized questions about authorship. He doesn't sit for drills; his verbal memory is poor; he reads very little by choice; his only obsession is ceiling fans, and even this tremendously high-interest topic doesn't inspire much reading; nor does he publish memoirs and give book talks.

What this means is that what comes out of J's mouth or his various keyboards really is J--through and through. There's absolutely no illusion whatsoever...

Except that there is--at a whole new level.

Yes, what comes out of J's various keyboards really is J, through and through. But, as we've seen repeatedly, he often tries to pass off his words as belonging to someone else. He's regularly, and often successfully, impersonated each of his parents, along with a few others--for example, those lucky individuals whose email accounts he's hacked.

At his "best," in other words, J not only isn't echoing others, but is surpassing even himself.

Friday, July 10, 2015

Math problems of the week: Common Core-inspired 4th grade test questions

From the Smarter Balanced Assessments, a Common Core-inspired, standardized test consortium now consisting of about 12 states.

Extra Credit:

Discuss how these problems exemplify the phenomenon (discussed earlier) that often the "deep concepts" are relatively easy, while more complex calculations involving those concepts (conspicuously absent in these problems) are where the real challenge emerges.

Wednesday, July 8, 2015

The Common Core applies to college

It used to be that K12 schools were supposed to prepare students for college. But increasingly it's colleges who are supposed to prepare for students.

Colleges are supposed to prepare, in particular, for the radically different students now graduating high school under the banner of the Common Core Standards. At least, that's the position taken by Harold G. Levine, the dean of the school of education at the University of California, Davis, and Michael W. Kirst, the president of the California state board of education and a professor emeritus of education at Stanford University.

In an April article in Edweek (I'm way behind), Levine and Kirst argue that colleges shouldn't be so focused on the degree to which the Common Core reduces the need to provide remedial level courses--after all, given how high the Standards are, and how deeply they've improved student learning, it goes without saying that such remediation needs will vanish. Rather:

As common-core implementation continues to expand and evolve in the K-12 system, how are the thousands of higher education faculty members who teach freshman and sophomore courses in English and mathematics (and the sciences, of course) preparing for their newly admitted students (roughly 3.3 million first-time freshmen projected for 2016), who will almost certainly have different expectations of what and how they learn and are taught? It is worrisome that we do not yet see the broad-based discussions, let alone planning initiatives, among either higher education leaders (including deans and department chairs) or, especially, their faculties and academic senates, to alter the curriculum or the pedagogy for all those introductory courses to take advantage of the new style of learning and teaching engendered by the common core.
Of course, the Common Core Standards are supposed to be pedagogically neutral. We know this because, whenever someone like me worries out loud that the Standards favor Constructivist principles like collaborative, inquiry-based, interdisciplinary, hands-on learning, or math that de-emphasizes algorithms in favor of "concepts" and "real-world application," a Common Core defender is quick to remind us all that the standards are pedagogically neutral. Nonetheless, according to Levine and Kirst:
What will be characteristic of common-core students entering college are learning experiences featuring more inquiry-based learning and collaborative problem-solving, sequenced skills by grade level and learning across the curriculum, and more hands-on work. In addition to the essential skills in math, students will focus on "conceptual" math, that is, understanding the reasoning behind the correct problem solution rather than the algorithm. They will also have experienced applying mathematical concepts to real-world problems, and will have been focused on fewer subject areas.
However pedagogically neutral these K12 "learning experiences" are, colleges, worry Levine and Kirst, are far from embracing them:
These are not likely to be the skill sets or course-taking experiences called for in the majority of today's college-level freshman and sophomore courses. Rather, these tend to be large-enrollment, minimally interactive, and textbook-based. For the sciences, there is likely to be a lab section, but as an adjunct to the lectures and where the experiments have known outcomes. Memorization of materials in the arts and sciences at the college level is critical to performing well on tests, as is performing procedures.
But the Common Core Standards offer hope:
We believe that with the support at the classroom level by university faculty and departments, and more concerted efforts toward the alignment of K-12 standards with higher education admission and "knowledge and skill" requirements, the common core that is implemented in our public K-12 schools will lead to a far more meaningful college learning experience for generations to come. It's now time to ensure that when the common core creates more "college ready" students, the colleges they enter are ready for them—and what they know and don't know, and how they have been taught to learn.
I've said it before, but I'll say it again now. For generations, parents and students the world over have clamored for admission into American colleges and universities. But how many are clamoring to get their kids into our elementary schools, junior highs, and high schools? People come to America for plenty of other reasons, but few, I'm guessing, come here for what's uniquely American about our K12 classrooms--whether it's first-generation Constructivism... or Common Core-inspired Constructivism 2.0.

Monday, July 6, 2015

Modern Day Calvinisim, II: predicting grit

In the modern Edworld, the "Elected" are graced not with godliness, but with grit. It is they, the Grit-Graced, who will thrive in the world to come, the Brave New World of 21st Century Skills.

But who are these modern-day Elected?

As it turns out, it's just a matter of time before the Higher Powers of the Edworld will be able to tell us. As a recent article in Edweek reports:

The nation's premiere federal testing program is poised to provide a critical window into how students' motivation, mindset, and grit can affect their learning.  
Evidence has been building for years that these so-called noncognitive factors play a role in whether children succeed both academically and socially. Now, the National Assessment of Educational Progress, often dubbed the "nation's report card," is working to include measures of these factors in the background information collected with the tests beginning in 2017.
So important are these "non-cognitive factors" that, according to Chris Gabrieli, described in Edweek as "an adjunct lecturer with the Transforming Education project at Harvard Graduate School of Education and a co-founder of the National Center on Time and Learning in Boston,"
Teachers self-report spending 10 percent of their teaching time on noncognitive skills. That's more time than students spend on any subject other than English and math—more than they spend on arts...
No matter that even Angela Duckworth, grit's coiner-in-chief, has said publicly that no one knows how to teach grit:
Every day, parents and teachers ask me, "How do I build grit in kids? What do I do to teach kids a solid work ethic? How do I keep them motivated for the long run?" The honest answer is, I don't know.
So let's keep being honest.

And let's see this gambit for what it really is: yet another instance of the Edworld (like the Autism World) taking the easiest course, and assessing what it doesn't know how to teach instead of teaching what it does (or should), yes, know how to teach.

Saturday, July 4, 2015

You can never have enough maps, II

And even when you do have maps, opportunities are missed.

Here's another example from my son's U.S. History text, which we are continuing to read even after his graduation from high school (still a few more decades of the 21st century left).

Notice how the "Geography Skills" textbox completely obscures the Suez Canal:



Thursday, July 2, 2015

Math problems of the week: Common Core-inspired 3rd grade test question

From the SMARTER Balanced Assessment, 3rd Grade Mathematics Sample Items:

Extra Credit:

Compare the simple vocabulary and sentence structure of the Sample Top-Score Response with other aspects of its communicative demands, and relate this to the communication skills of 3rd graders.