Saturday, February 28, 2015

Losing yourself in the underworld

There is a creepy underworld in The Princess of the Midnight Ball. There is also a creepy underworld in the The Girl Who Could Fly. In a book club for tween girls, two girls had just made the connection.

L, a friend of mine who leads the club, was excited. "That's a great point of comparison between the two books: their creepy underworlds," she began, anticipating a discussion about archetypes.

But did the girls know the word "archetype"? L hadn't kept close tabs on what today's kids have been learning in English and Language Arts class, but she knew things were different.

"Do you know what that's called?" she continued.

"A text-to-text reference!" chimed a chorus of tweenaged voices.

"A what?"

I couldn't help laughing when L told me the story, so starkly did it highlight how many of today's K12 horrors she's missed out on. What L was asking about vs. what the girls thought she was asking for was the difference between the beauty of literary themes and the ugliness of education jargon. It was the difference between losing yourself in a world of literature and losing that world in order to find yourself--in all your meta-cognitively reflecting glory.

And it was, finally, the difference between the potential joys of reading and the creepy underworld of K12 expert-driven "best practices."

Thursday, February 26, 2015

Math problems of the week: Common Core-inspired high school math test problems

The eight questions on the sample 12th grade math test from Smarter Balanced Assessments, which is developing Common Core tests for 31 states:

Extra Credit:

Compare these problems to the sample math problems on the high school math exam given in Finland, and connect this to the ongoing buzz about why Finnish students are outperforming ours.

Tuesday, February 24, 2015

Why Education Experts are Obsessed with Top-Down Accountability–But You Don’t Have to Be

Another recent addition to the New York Times’ extensive literature on 21st century innovation needs is Dana Goldstein’s review of Anya Kamenetz's The Test: Why Our Schools are Obsessed with Standardized Testing–But You Don’t Have to Be.

Goldstein begins by laying out Kamenetz's arguments against standardized testing:

...Kamenetz probes psychometry, or the science of testing, demonstrating its roots in the deeply held racism of the early-20th-century I.Q. movement. She shows why today’s achievement tests, designed to evaluate ability on a specific day, typically at the end of the school year, are poor tools for helping either teachers or students improve their practices in real time. “They conceptualize proficiency as a fixed quantity in a world where what’s important is your capacity to learn and grow,” she writes. “They are a 20th-­century technology in a 21st-century world.”
In this brave new world, we learn, current skills and knowledge are no longer important; instead what's important are the future skills that people are capable of eventually acquiring. So, for example, when I’m hiring a programmer, or choosing a doctor or lawyer or accountant or music teacher, I shouldn’t consider their “fixed” proficiencies in programming, medicine, law, accountancy, or music pedagogy, but only how much they seem capable of learning and growing down the line.

Given these compelling conclusions:
…the book’s most urgent contribution is its exploration of how we might hold our schools, teachers and students accountable if we were to scrap high-stakes standardized testing entirely. As in her previous book, “DIY U,” Kamenetz is open to seemingly radical, technology-driven solutions. She reports on artificial-­intelligence experts who would harness the addictive qualities of gaming to instruct and assess kids online; computer programmers who seek to perfect the flawed software currently used to grade essays and track student performance over time; and school administrators experimenting with new measures of social-emotional growth, like student surveys meant to evaluate a child’s happiness and ability to persevere in the face of adversity.
Ultimately, Kamenetz advocates the kind of approach she observes in action at Bate Middle School in Danville, Ky., and the Urban Academy Laboratory High School in New York City. These schools assess students using long-term projects heavy with writing and public speaking. Their practices hark back to the “exhibitions” of early Republic schools, in which parents and the community observed children as they demonstrated newfound knowledge. Kamenetz shows how fundamentally American it would be to turn toward a more holistic system of evaluating educational outcomes.
It doesn’t seem to occur to Goldstein, or to Kamenetz, that "addictive" gaming software might detract from "learning and growing." Or that “student surveys meant to evaluate a child’s happiness and ability to persevere in the face of adversity” and “long-term projects heavy with writing and public speaking” might be just as stressful, just as time-wasting, and just as unreliable as “tools for helping teachers or students improve their practices in real time,” as standardized tests are.

Regardless of which particular century we happen to be living in, there is a much better way to hold schools accountable. Imagine if all parents had real school choice. Imagine if all the programs currently beset with impossibly long waiting lists--Montesseri, KIPP, and language-immersion, for example--could expand to meet parental demand. Imagine, further, if parents could request specific teachers--with popular teachers getting larger classrooms and extra support staff.

Of course, because it empowers the amateurs, who supposedly have much less sense than the experts do of whether their kids are learning anything useful, this sort of accountability will never be advocated by the experts. Especially by those who suspect, deep down, that most parents don't want what they are offering.

Sunday, February 22, 2015

Why is the answer always "innovation"?

Even this past week's Education Week admits that things are pretty bad for America’s high school and college graduates as compared with their peers in most other development countries.

Of course, what Ed Week doesn't acknowledge is that much of the blame falls on K12 schools and all the problems with today's trends in K12 education (Reform Math; Constructivism, Balanced Literacy, student-centered learning, etc., etc.). But were I to identify the top things to fix at the college level, I'd say they are:

1. the extra costs, passed on to students on their families, of the steep rise in the proportions of salaried administrators; and of growing numbers of non-academic perks like rec centers, weaving studios, and luxury dorms.

2. the decline in the humanities in instruction of basic knowledge, analytical skills, and writing skills (via the drop in survey courses and the dominance of “critical theory” and postmodern claptrap over facts and communicative clarity).

3. the shrinking time college students spend studying, which, over the last fifty years, has dropped from 24 hours a week to about 15.

In a recent Op-Ed in the New York Times, however, Jon Cohen and Jim Kessler, respectively the president and senior vice-president for policy at the Third Way, assert that the top problem is something completely different: namely, the general quality of college-level teaching:

At the K-12 level, the No Child Left Behind law required training, evaluation and assessment of teachers. But at the college level, professors are mostly on their own. They typically come through the ranks of Ph.D. programs, receive little training on how to teach, and are — at research universities — granted tenure primarily for scholarship, not effective instruction.
Currently, the federal government gives just 24 cents in postsecondary education improvement grants for every $100 in grants for research; that number should be at least doubled. By 2020, every college that gets federal aid should be required to have a plan to train professors, improve the quality of instruction and measure student learning. This need not be a top-down mandate; the universities should be allowed to compete for federal funds to design the best assessments of whether and how students learn.
While it’s probably true that many college professors could teach better, the likely result of any pressure to "have a plan to train professors and improve the quality of instruction" will give carte blanche to education schools to tell other departments how to teach. This, in turn, will result in a decline in the quality of instruction, as professors are pressured to get in line with all those enduring education-school fads: to step down from their lecterns, to further de-emphasize discrete bodies of basic factual knowledge and the mastery of discrete skills, and to guide from the side while students work in groups doing hands-on, interdisciplinary activities with the latest so-called "educational" technology—all of those key elements of what some people call "innovative teaching."

Indeed, "innovative teaching methods" are exactly what the authors want, so certain are they that it’s a lack of innovation, rather than a trend away from traditional teaching practices, that explains why things have deteriorated:
A research study commissioned by the Bill and Melinda Gates Foundation recently found that just 20 percent of faculty members used innovative teaching methods, like team-teaching across subjects, soliciting real-time student feedback in class and using social media to spur discussion outside the lecture hall.
No wonder, then, that 45 percent of a sample study of more than 2,300 students demonstrated no significant gains in critical thinking, complex reasoning or writing after two years of college, as the education scholars Richard Arum and Josipa Roksa concluded in a landmark 2011 book, “Academically Adrift.”
Perhaps my own college experience failed to bestow "gains in critical thinking" upon me—after all, none of my professors used innovative teaching methods—but I simply can’t fathom why, when things get worse, the answer is to innovate rather than to go back those practices (of professors, of students, and of colleges as a whole) that coincided with the heights from which our society has fallen.

Friday, February 20, 2015

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

From's "Common Core Test Prep" page:


Extra Credit

American educational priorities often confuse labels with concepts. Identify those problems, above, where the primary challenge is knowing the meaning of a particular mathematical label, as opposed to understanding a mathematical concept.

Wednesday, February 18, 2015

Conversations on the Rifle Range 26: Moving On and the Sedimentation of Students

Barry Garelick, who wrote various letters published here under the name Huck Finn, is at work writing what will become "Conversations on the Rifle Range". This will be a documentation of his experiences teaching math as a long-term substitute. OILF proudly presents the final episode (26) to this series.

I am currently working at a middle school in a neighboring school district. I do not have my own classes; I assist the math teachers there by identifying and working with students who are struggling. Like most schools these days, it has fallen under the spell of Common Core, with a disturbing amount of instruction spent on writing about how they solved a problem, explaining their reasoning and why they think the answer is reasonable. I work there four days a week; I started in August and will continue until school lets out. While I miss having my own classes, I like it for the most part. One key advantage is that it allows me to focus on teaching students the basic skills they are missing rather than on having them explain their reasoning for problems they cannot solve because of procedures they cannot perform.

The district I’m in has recently contracted with SVMI (the Silicon Valley Math Initiative), just like the school district where I was working last year. These are the folks who developed the Problems of the Month to stimulate "algebraic thinking" outside of algebra courses and who also constructed the test that was now being given as an extra barrier to taking algebra 1 in seventh or eighth grade in my old district. There is no word yet on raising the barriers for qualifying for the traditional algebra 1 course in 8th grade. But one never knows.

I have not kept in touch with anyone from my previous school (Lawrence Middle School), though occasionally I look at the website for pictures of the students. I see pictures of some of my seventh graders, now eighth graders. All appear to be doing well. I don’t know how any of my former eighth graders are doing now in high school.

In case you’re curious, my algebra classes managed to do better on the chapter test on quadratics than they had on the quiz. We moved on to algebraic fractions and various word problems had one last test, and that was that.

My prealgebra classes also wrapped things up nicely. I recall with particular fondness my Period 2 class. They were my favorite of all my seventh grade classes; they were generally very sweet, though over the months since I took over they were much more talkative and rambunctious as they proceeded on their relentless path to becoming eighth graders. On the day before the last test, we were reviewing multiplication of binomials and a boy asked “the question”: “Am I ever going to be using polynomials in my life?”

The question of “When will I ever use this stuff” gets a lot of play these days. I don’t recall it being asked that much when I was in school, but maybe I wasn’t aware of it. Fifty years ago, when I was in junior high, the space race had begun in earnest and there seemed to be no doubt in my mind, or in the minds of many of my classmates, of why algebra or math in general would be of any use. Given today’s technological age, one would think the same reasoning prevails, but students keep hearing that with the Internet you can just Google the answer to many questions. Furthermore, I think the press and others plant the idea in peoples' minds that math must be relevant and kids seem to delight in asking "How am I ever going to use this in life?" I get the feeling that they've picked it up from various sitcoms and other venues that use this as a stock phrase and laugh-getter. Kids only ask this question because they are –essentially—told to ask it.

Mario, the boy who asked the question, had ambitions of being a wrestler. “Well, if you go into wrestling, I doubt you will use polynomials much. And those of you who go into law or journalism, or any field that doesn’t typically use a lot of math—well you probably won’t use polynomials all that much.”

The class listened quietly—they were the only pre-algebra class that would do that.

"But,” I continued, “If you go into math, the sciences or engineering, you will use polynomials almost on a daily basis. They are a mainstay of mathematics and used in just about every math course you will take from now on. Formulas in physics that plot the trajectories of rockets are polynomials. But aside from polynomials and what you will use in life, I don't have a crystal ball. I don't know what any of you will do. My job—and the job of all teachers—is to prepare you as best I can to give you as many opportunities as possible. Maybe you aren't interested in science now, but suppose you change your mind. The algebra you take will then prepare you to take science classes and other math classes. It would be totally unfair of me to single someone out and say 'Oh that person will never be in science, so let's not waste time teaching him math' because we just don't know what that person will do. If you had told me when I was in seventh grade that I would end up majoring in math, I would have thought you were crazy. I didn't do well in it then. But here I am. Anyway, that's my sermon for the day."

I expected to then move on, and was suddenly surprised when the whole class applauded. "That's the first time I ever got applause for that little speech,” I said. There are other reasons to study algebra that I didn't get into with my students, one of them being the "sheer beauty and importance of the structure of mathematics". But I had the applause so I went with that.

I’ve given variations on that speech where I am now, and on some occasions I have again received applause. It’s mid-February as I write this, and a little past the one-year anniversary of when I started my assignment at Lawrence Middle School. It has taken me a while to let go of the students there and stop missing them. When I started at my present school, I resisted getting to know the new students well, as if it would spare me the pain of saying goodbye later.

But my new students have grown on me. They won’t ever replace my former students; they’ll just add to the collection. The white boards in my classroom on the last day of school come to mind here. Each class wrote their names and greetings on the white board, some erasing what was there before, some writing over it, like sedimentary layers of rock. That’s what my memories of students will be like over time, I think.

I’ve left some pictures of those white boards so you could see. I’d much rather leave you photos of the students themselves but privacy laws prevent me from doing so.

I wish you could meet them all. I know you’d love them.

Monday, February 16, 2015

President's Day Special: Entangling Alliances, the Education Industrial Complex, and WriteToLearn vs. Learning to Write

In order to participate with success in the general curriculum, students with disabilities, as appropriate, may be provided additional supports and services, such as...Assistive technology devices and services to ensure access to the general education curriculum and the Common Core State Standards.
From the single page in the entire Common Core Standards website devoted to students with special needs. And so, the floodgates open to Education Industrial Complex behemoths like Pearson. From Pearson’s website:
Beginning this school year, the Common Core State Standards will require students to develop more rigorous writing skills with a stronger emphasis on the ability to synthesize and summarize informational text, formulate an argument and respond appropriately to source documents. To help students prepare for the rigor of the Common Core, Pearson today unveiled updates to its award-winning online literacy tool, WriteToLearn.
“In today’s information-driven world, strong writing skills are crucial to success in college and career, regardless of what path an individual chooses,” said Alistair Van Moere, president, of the Knowledge Technologies business of Pearson. “These updates to WriteToLearn are focused on ensuring that students have the tools for developing the skills that the Common Core State Standards have set forth as requisite for achieving that success.”
… WriteToLearn’s grammar checking has been updated to detect more common types of errors with improvements of 20 percent in areas such as subject verb agreement and using the correct verb form…
To further support struggling readers and writers, WriteToLearn now features Texthelp’s word prediction technology. This tool allows students to select correct word choices with fewer keystrokes and, ultimately, produce writing products with greater skill. The Partnership for Assessment of Readiness for College and Careers (PARCC) has proposed word prediction as an allowable accommodation for students with disabilities on its Common Core writing exam.
WriteToLearn qualifies for for [sic] a wide variety of federal funding sources such as Title I, IDEA and Race to the Top. For more information, visit
Yup. And so, yet again (see here and here), public money pours into Pearson.

Meanwhile, as I asked earlier, how will these “access”-providing assistive technologies actually cause language-impaired students to improve their writing skills-- or, in Pearson’s eloquent (WriteToLearn-assisted?) words, “produce writing products with greater skill”?

Saturday, February 14, 2015

Do all students need to read fiction?

The idea that all students should read fiction is one of the unquestioned assumptions of the education establishment in general, and of the Common Core State Standards (CCSS) in particular.

Some in the education establishment have criticized the CCSS for de-emphasizing fiction. But on their Myths vs. Facts page Core authors reassure us that the emphasis on fiction in English and Language Arts classes will persist:

Myth: The standards do not have enough emphasis on fiction/literature.
Fact: The Common Core requires certain critical content for all students, including classic myths and stories from around the world, America’s founding documents, foundational American literature, and Shakespeare. Appropriately, the remaining crucial decisions about what content should be taught are made at the state and local levels. The standards require that a portion of what is read in high school should be informational text, yet the bulk of this portion will be accounted for in non-ELA disciplines that do not frequently use fictional texts. This means that stories, drama, poetry, and other literature account for the majority of reading that students will do in their ELA classes. In addition to content coverage, the standards require that students systematically acquire knowledge in literature and other disciplines through reading, writing, speaking, and listening.
Factor in the CCSS's one-size-fits-all approach (see also here and here) to preparing students for college and career, and you have "stories, drama, poetry, and other literature" for all.

But how well does this requirement serve kids on the autistic spectrum? I first raised this question here several years ago; I raise it repeatedly with my students. Many of them, even though they themselves are teachers of students on the autistic spectrum, share the general assumption that all kids need to learn to read fiction, AS students included. They share this assumption despite the fact that, as they themselves have seen, and as I noted a couple of days ago, reading fiction is one of the most challenging academic tasks that many AS students face.

The many AS students who struggle with fiction are unlikely to be English majors in college. They are unlikely to have jobs that require reading fiction. True, fiction might serve as a medium for them to work on their social reasoning and empathy skills: why was Hamlet so mean to Ophelia?; why did Lady Macbeth assail Macbeth's manhood? But more targeted, simplified, social skills training conducted by trained professionals and specifically tailored to AS kids and focused on real-life interactions is probably more effective.

In other words, it's highly questionable whether the CCCSS requirement that "that students systematically acquire knowledge in literature" helps AS students attain the CCSS's ultimate goal for all students: "preparation for college and career."

So why should autistic students be required to read fiction? I'm still waiting for an answer.

Thursday, February 12, 2015

Math problems of the week: Common Core-inspired sequence problems vs. sequence problems from the 1920s

From, where "All of IXL's dynamic math and language arts skills are aligned to your standards, including: The Common Core State Standards All 50 states and D.C."

Accessed from ixl's high school math page, here are three problems from the "Find terms of a sequence (Precalculus - U.1)" page:

The arithmetic series problem set in Wentworth's New School Algebra:

ixl bases its pre-calculus sequence problems on this standard from the Core Standards for High School:
High School: Functions » Interpreting Functions » Understand the concept of a function and use function notation. » 3
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

Extra Credit:

Arguably, ixl's problems meet the above standard: arguably, doing ixl's problems encourages students to have the various recognitions that the standard specifies. Recognizing "that sequences are functions," etc.,  doesn't necessarily involve finding particular functions for particular sequences, or, for that matter, actually doing anything with sequences. Recognizing, after all, is not the same as doing.

So, in choosing words like "recognize" and "understand," have the Common Core authors chosen their words wisely?

Tuesday, February 10, 2015

Conversations on the Rifle Range 25: Undoing a Conspiracy, and Heading to the End of the School Year

Barry Garelick, who wrote various letters published here under the name Huck Finn, is at work writing what will become "Conversations on the Rifle Range". This will be a documentation of his experiences teaching math as a long-term substitute. OILF proudly presents episode number 25 which will be the penultimate episode.

I was in a mild state of panic after seeing the results of the quiz on quadratic equations. The mean of the classes was 74—it’s usually in the high 70’s or low 80’s. (I did allow students scoring below 70% to turn in corrections, to raise the score to a maximum of 70, which was Mrs. Halloran’s policy.) I was pleased to see that eight students successfully derived the quadratic formula for extra credit. But I could see that for problems like x2 – 5x = 0 some students forgot that it can be solved by simple factoring. And though some knew how to complete the square, there were not as many as I would have liked. They knew the quadratic formula by heart and how to apply it. But some were missing some key concepts.

During my first period prep on the day I was to return the quizzes to my algebra classes, I went through the giant binder for algebra that Mrs. Halloran had left me. The binder was filled with the tests, quizzes and other materials for both pre-algebra and algebra. While she often planned for practice quizzes for the pre-algebra classes—a dress rehearsal of the real quiz—she didn’t do that for the algebra class. Or so I thought. I found that for the chapter on quadratic equations, she had planned for a practice test for the entire chapter. The quiz had covered the first half of the chapter. This might come in handy, I thought.

As I expected, students were not pleased with the results of the quiz. Pamela, one of the students who I suspected of complaining about my teaching to the counselor, had received a score in the 70’s. She took the lead in the discussion of the quiz results, and ended with a definitive bottom line. “Don’t you think that with so many students failing the quiz that you should reteach and give a re-test?”

There were twelve A’s on the test, then mostly B’s and C’s, a few D’s, and three F’s for both classes, but exaggeration is a key tool in winning arguments. So effective, in fact, that Bryan (who I suspected was the other student lodging a complaint about my teaching) turned around and raised his arm in a victory salute to Pamela and mouthed “Right on!”

Given that Bryan had received a 90 percent on the quiz, I could see he was goading Pamela. So I said what no teacher is supposed to say to a student. “As I recall, you got a pretty high grade on the quiz, so shut up Bryan.” The class became quiet. There are other terms to use that are acceptable like “zip it” or “cool it” or “knock it off”. But I was too busy thinking to apologize.

I suddenly remembered the practice test I had seen earlier and said “How about this? I’ll give a practice test before the chapter test. Whattya think?”

This was met with an enthusiastic response, including “We love you, Mr. G!” so I knew I was on the right track. Over the next week, as we went into the last part of the chapter on quadratics, I noticed that Bryan—despite my breach of teacher conduct, or maybe because of it—was much less disruptive, more respectful, and even asked me for help, which he had been unwilling to do previously. I also worked more with Pamela—also more respectful—to make sure she could do the problems. I can’t say for sure what had been going on between Bryan and Pamela. Some things forever remain mysteries.

Around that time, I saw that my school had advertised for two math teaching positions. I knew the principal had his sights set on a teacher in another school. Also a sub filling in for a teacher who had taken off in May for health reasons also appeared to have the inside track. Nevertheless, I applied.

The application contained the following question: “Describe your knowledge of the shifts occurring in Common Core State Standards.” The “shifts” referred to are also known as “instructional shifts,” which seems at odds with statements made from up on high that Common Core does not dictate pedagogy. Most likely, the term embodies the apocryphal claim that prior to Common Core, math was taught as a series of disconnected rote procedures without context or “understanding”. Thus, the reasoning goes, Common Core requires shifts in instruction.

I knew the question required some adroitness. The crux of my answer was: “The biggest shift is towards conceptual understanding and problem solving. Math classes will be increasingly problem- and project-based, student centered, and inquiry-based. Math problems will be engaging and rich, motivating students to learn the procedures needed to solve such problems.” I could have put in more buzzwords but I felt that any more would have destroyed credibility.

The end of the school year was becoming a distinct reality now, and many of my seventh grade students were asking me if I would be back in the fall. I didn’t realize it but I had become somewhat of a hero. This became clear on open house night the second week in May. My room was packed with parents thanking me for stepping in mid-year and telling me how much their son or daughter enjoyed my class. A seventh grade boy named Jamie who was in one of the algebra classes introduced me to his parents and asked if I would be back in the fall. “Don’t know,” I said “but I did apply for a math teaching position.”

“ALL RIGHT!” he yelled. “I get to have you for geometry!”

“Yeah, well, let’s wait to see if I get an interview,” I said. “Then we’ll make plans.” We both laughed.

After a certain point, my room became suddenly empty and I was the only one there. The principal came in to my classroom exuding a warmth I had come to know and distrust. “If you’re wondering where everyone went, they’re at the presentation in the gym,” he said.

I listened politely as the principal, standing in my empty classroom talked about how great the open house night had turned out, and then left as quickly as he had come in. I wished he had dropped by when the room was packed. But I doubt that anything would change in the long run. An e-mail reply from the school district would reach me in July saying: “Thank you for submitting an application for the math position at Lawrence Middle School. Unfortunately, this is to let you know that you were not selected for an interview.”

While I loved teaching my students, I had sometimes wondered if I would really want a job at a school heading in the direction of student-centered, group-work-oriented, and textbook-free teaching. I would be lying if I said I wasn't willing to risk it."

Sunday, February 8, 2015

Another preview: more on the Lexile Framework

Adapted from another passage I recently wrote for this book (...when really I should have been blogging):

One factor that educators consider in deciding which texts to assign to which students at which grade levels are the texts' Lexile ratings. These ratings are determined by a text-processing tool known as the Lexile Analyzer. The Lexile Analyzer measures two things: how challenging the individual words are (based on their frequency) and, as a proxy for syntactic complexity, how long the sentences are. The problem, however, is that sentence length correlates only weakly with the aspects of complexity that make sentence processing challenging. A relatively long sentence may be quite easy to process if it consists of a series of simple short sentences conjoined with a coordinating conjunction like “and”: 
 “I love you and you love me and we’re a happy family" 
while a relatively short “garden path” sentence like  
“The horse raced past the barn fell” 
can be quite difficult to process. Identifying the kinds of syntactic complexity that make reading challenging—particularly for children with Specific Language Impairment and autism—requires more sophisticated linguistic processing than that performed by the Lexile Analyzer.

One indicator of how complex a sentence is how embedded its subordinate clauses are. But where exactly these subordinate clauses are embedded also makes a difference. Generally, so-called "right-branching" sentences like: 
 “This is the cat that chased the rat that ate the cheese that lay in the house that Jack built”
no matter how much embedding they contain, are easier to process than corresponding "left-branching" sentences like:
"The cat’s prey’s cheese’s location’s builder was Jack."
Most challenging of all is what’s called “center embedding,” seen in sentences like:
 “The cheese that the rat that the cat chased ate lay in Jack’s house.”
Or sentences in which what looks like the most obvious structure turns out to be wrong, as in: “The horse raced past the barn fell.”

There are also factors beyond vocabulary level and syntactic complexity that figure in text difficulty. These include the challenges of deducing the antecedents for the various pronouns and other anaphoric devices, including underspecified noun phrases like “that idea” and “this strategy.” An automated text-rating system might search for pronouns and deictics like “this” and “that” and compare the ratio of such terms to the number of noun phrases. A high ratio would indicate a highly interconnected, internally-referential text that requires lots of inferences to determine antecedents and flesh out the content.

The amount of inferencing that readers must do, in fact, is a large part of how hard a text is. Beyond the inferences that determine antecedents for anaphors, there are a host of others, including the pragmatic inferences that make sense of dialogs, the social inferences that make sense of character interactions, and the perspective-taking inferences that make sense of actions in general. Such inferencing tasks are particularly challenging for children with autism. And, yet, they pervade most reading assignments, especially fiction. They are the reason why reading fiction is one of the most demanding school-based tasks that autistic children face. But nonfiction is also challenging. Many texts, fiction and nonfiction, require yet another sort of inference: inferences that draw on general background knowledge. General background knowledge is the type of knowledge that most children pick up incidentally from social interactions and overheard conversations. Autistic children, less attuned to these sources of information, commonly have knowledge deficits, and, therefore, further deficits in reading comprehension.

An automatic text analyzer might give rough estimates of social and emotional-based inferencing demands in the same way that the Lexile Analyzer gives rough estimates of syntactic complexity.  For example, it might search for social and emotional vocabulary terms and compute their density within the text. However imperfect a measure of this is of the social and emotional-based challenges for reading comprehension, it still would be a highly useful one, given that these challenges are a huge determiner of text difficulty for autistic readers, and given that they don’t figure at all in current text rating systems.

Friday, February 6, 2015

Math problems of the week: Common Core Inspired 7th grade word problems

From, where "All of IXL's dynamic math and language arts skills are aligned to your standards, including: The Common Core State Standards All 50 states and D.C."

Accessed from ixl's seventh grade math page, here are three problems from the "Add and subtract integers: word problems" sample problems:


Extra Credit :

The most relevant 7th grade Common Core Standard is:
CCSS.Math.Content.7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Have the Common Core authors done a good job writing this standard?

Wednesday, February 4, 2015

Conversations on the Rifle Range 24: The Quadratic Formula Redux and an Unintended Act of Defiance

Barry Garelick, who wrote various letters published here under the name Huck Finn, is at work writing what will become "Conversations on the Rifle Range". This will be a documentation of his experiences teaching math as a long-term substitute. OILF proudly presents episode number 24:

On a late-start Monday in early May, the math department had a meeting. Sally, the person from the District, had called it for the purpose of discussing what to do about “below grade” students next year (those getting a D or failing). In particular, she wanted to explore how Common Core deals with such students. It must have been an important meeting because even the principal was there.

Despite its importance, I have trouble recalling what was said. I remember Sally admitting that the standards for Algebra 1 under Common Core do not cover everything that the current Algebra 1 course does. “Common Core takes a deeper dive into math than the mile-wide inch-deep approach we used to use,” Sally said. Common Core was going to be so much better than the "procedural" approach we use now. "Procedures don't stick with kids; they forget them. They need to learn critical thinking and problem solving."

Jim, one of the math teachers to whom I turned for advice now and then—a very nice man who had been teaching there a while—mentioned that some of the “below grade” students were missing key knowledge from day one. “Some of them don’t know the basic math facts, or how to do basic operations.”

“That’s because they haven’t been taught how to think,” Sally pronounced.

“No, that’s not it at all, Sally” Jim said.

I had recently learned that Sally had been a math teacher at the school. From what I heard, she was pretty good at it. Her husband had passed away a few years ago, and she took a leave of absence for a year. When she returned, she took her present position at the District.

She did not reply to Jim, though it was evident she knew what he was saying. To me, a newcomer, it appeared that their past shared experiences created a loyalty between them that allowed Jim to accept what her circumstances and the swing in the educational pendulum had turned her into. This loyalty extended to a lot of teachers who may also have been affected by the pendulum’s swing. In fact, there was a lot of love for her among the teachers.

The principal—also a newcomer to the school—added his two cents about Common Core at the end. “Common Core is requiring us to rethink how we teach,” he began.

It doesn’t really, but that’s the prevailing narrative in education that blends in with a host of others.

“What’s really important is collaboration,” he said. “If you look at workplaces nowadays, it’s all about collaboration. You have to know how to work as a team. Now I’m not saying that we abandon individual learning. But we also have to foster how to work together.”

I disagreed but said nothing. In the adult world, people bring their individual expertise and knowledge to the team, based on my experience. In the student world, they are novices. It’s either the blind leading the blind, or the one smart kid who gets stuck with all the work.

The meeting ended shortly after that and I took that opportunity to scour the metal supply cabinets in the room for pencils and whiteboard markers that weren’t dried out. The principal, oblivious to me, was talking with Mrs. Perrin, the math department chair, about a "great math teacher" he saw at another school. “She’ll fit right in here,” he said. I could imagine that his view of what was “great” likely included student-centered, group activities, inquiry-based math and facilitating rather than teaching. The fact that he sought to have this conversation out in the open with me in full sight was an indicator that I wasn’t exactly being groomed for any kind of position there.

I tried to put all that out of my mind, given I had a full day of teaching ahead, plus a meeting at the end of the day on a student’s “504 plan”. A "504" is an accommodation plan, usually given in lieu of students receiving special ed services. It lists accommodations for the student that teachers can make, like having a peer give the student notes, or having the student take tests in a quiet room.

The student, Calvin, was in my algebra class—currently averaging a D. He had been homeschooled for the first part of eighth grade, and was re-enrolled in the school and placed in algebra. At the meeting, his teachers were there, his counselor (a young woman named Theresa), his mother, and a tutor from the learning center in which he was enrolled. He had been diagnosed with ADHD and the mother explained that Calvin has test anxiety and doesn’t perform well on tests but that he was very capable. Most teachers told a different story and all agreed that though he was very cooperative and good natured, he had a difficult time focusing and absorbing what was being taught. When the discussion turned to math, they asked for my input. I said the same—his difficulty was not confined to just tests. He had been struggling all semester.

Theresa explained that next year all schools will be teaching math via Common Core. “So no more ‘here's the assignment from the book, and there'll be a test on the material next week’. It will be more about understanding". She added cheerily that this could be helpful because Calvin wouldn’t be burdened with memorization of procedures. He will be required to explain how he got an answer, and could get credit for explanations even if the computations are wrong.

At this point, Calvin, perhaps wanting to prove to Theresa that memorization was not a burden to him (and not picking up on the Common Core party line she was spouting) interrupted. “I actually memorized the quadratic formula,” he said and then recited it perfectly.

“Excellent! Well done, Calvin!”, I said. I turned to the others. “We’re having a quiz this Friday on quadratic equations.” Theresa didn’t appear impressed.

“Of course, under Common Core, he might not be required to memorize the quadratic formula, but would have to explain how and why it works,” she said.

How a student could be deemed to understand the quadratic formula without knowing it was puzzling. I suppose they could memorize “The quadratic formula is obtained by solving the general quadratic equation by completing the square”. Such rote understanding might pass for explaining how and why it works in the world of Common Core. But I’ll take as demonstration students who can complete the square or who can reproduce the derivation of the quadratic formula for the extra credit points on the upcoming quiz. Or Calvin’s memorization of the quadratic formula.

I knew my approach would likely not pass muster with Theresa or Sally or the principal. I also knew that I was proud of Calvin.

Monday, February 2, 2015

A preview of coming attractions...

I've finally met a deadline for this book I'm co-authoring, having gotten way behind in blogging in the process. So today, partly inspired by Susan Pinker's piece in this past weekend's New York Times on the problems of technology in classrooms, I'll share an excerpt of some stuff that I just finished writing:

Whether or not we’re looking at linguistic technologies in particular, or at accommodation strategies in general, it’s important to beware of the potential pitfalls of either over or under-accommodating. Ideally, we want tasks to fall within a child’s Zone of Proximal Development—the zone just between her current level of mastery and what she can do only with help from others. It’s hard to get this right; but crucial to try.

Under-accommodation may result from a faulty first step: a faulty assessment of task demands. Especially for children with autism, tasks may present subtle challenges that fly under the radar of neurotypical people, teachers included. Perhaps most commonly overlooked in language-based tasks (for example, reading assignments) are subtasks that require the socio-emotional inferences or use of general background knowledge that come naturally to non-autistic individuals. It’s important to remember that rating scales, including automatic rating scales like the Lexile Analyzer, do not take these challenges into account. A book that looks quite easy to others, and that rates low on the Lexile scale, may still be quite challenging to students with autism.

Then there’s the possibility of over-accommodating and not sufficiently challenging the child. Text completion software in particular raises this possibility, potentially putting words in the child’s mouth that she is capable formulating independently.

As far as text completion and other assistive communication technologies go, the inherent uncertainty on the part of outside observers about much students are doing on their own vs. how much the software is doing for them is yet another concern. To what extent are users intentionally communicating rather than simply selecting—perhaps somewhat arbitrarily--among suggested words or icons? Might we be overestimating their communicative skills? Might there be more to remediate than we realize?

And how does this affect everyone’s incentives—particularly the incentives of students and teachers? In general, the more efficacious the assistive technology appears to be, the more it potentially reduces the urgency of teaching and practicing the skills that are being assisted. Text-to-speech devices potentially reduce the incentive to teach decoding skills for reading; they may also reduce the incentive for students to work on their reading skills by actually reading. Speech-to-text devices, similarly, may reduce the incentive to teach and practice spelling skills; assistive communication devices and text completion software, the incentive to teach and practice independent communication skills. It is essential that assistive technology be treated only as such—namely, as assistive—and not as grounds for reducing remediative instruction and practice.

A final concern pertains to autistic children in particular: the extent to which technology takes these children, already diminished in their social interactions, away from the face-to-face exchanges on which they may be especially dependent for their social and socio-pragmatic development. Screens, as we’ve observed, are no substitute for the pragmatics of open-ended, real-world interactions. But too often, whether or not the students are autistic, one finds classrooms and other settings in which students are mostly looking at and interacting with screens rather than with one another.

Heightening these concerns are two things. One is the proliferation of technology in the classroom, with purchasing decisions made by individuals or committees who are often insufficiently informed about educational value and efficacy, especially where special needs students are concerned. The other is the unprecedented pressure that today’s schools and teachers are experiencing. In the U.S., most language-impaired students are included in regular classes with same-aged peers, and these classrooms are under increasing pressure to teach to the new Common Core State Standards and tests. In English and Language Arts, these standards set high expectations for reading and writing and take a one-size-fits all approach to students at a given, typically age-based, grade level. In light of this, fewer and fewer teachers, even special education teachers, feel that they have time to remediate basic skills—especially when the growing prevalence of assistive devices makes remediation seem ever less urgent. Indeed, some of assistive technology websites, e.g., Classroom Suite, explicitly mention the Common Core standards as motivating their use in the classroom.

In fact, remediation and accommodation should go hand in hand. The ultimate goal, after all, is to optimize the learning environment such that students reach their potential, and, ultimately, are liberated from assistive technology to the largest extent possible.