Thursday, August 30, 2012

Math problems of the week: 4th grade Investigations vs. Singapore Math

I. The second-to-last coin problem in the 4th grade Investigations Student Activity Book, Unit 9, "Penny Jars and Plant Growth", p. 66 [click to enlarge]:



II. The final coin problem in the Singapore Math Primary Mathematics 4B Workbook. Review II, p. 163 [click to enlarge]:

Tuesday, August 28, 2012

Why Johnny can't do math, II: the principal responds

Her response is mostly an enthusiastic reflection on an article on Constructivism that Johnny’s mother sent her; a few parts of her letter, however, pertain to Johnny:

Community is one of the benefits that we have to offer gifted students such as Johnny.
We aren’t looking for students to come to a group consensus of how to determine the area of a triangle, but we are looking for students to realize, through participation in a group, that there may be more than one way to describe the understanding of that area. In Johnny’s case, for example, I think he will always grasp geometry more quickly in both theory and visual representation than many of his classmates. What we have to offer him is active listening to how other kids might see that same information. It doesn’t change what a triangle is, but it can help Johnny to eventually be more persuasive to his audience when he is presenting at conferences as a graduate student and an adult.
Participating in the collective intellectual endeavor has value for Johnny, though. It reminds me of his comments about a tiger’s motivation, where he never challenged the essential premise that tigers cannot speak. We love that combination in Johnny of heightened understanding and childlike fantasy, and we really appreciate that you have nurtured that at home. His performance as the tiger definitely took advantage of a collective endeavor to convey a tale.
In other words, beyond stating that the “active listening” offered by Johnny’s classroom can improve his presentations at conferences when he's a graduate student and an adult, the principal did not address any of Johnny's mother's questions regarding what Johnny will learn in math class this year.

Sunday, August 26, 2012

Autism diaries XXXVII: stepping outside yourself

J knows that he's different: he's deaf and autistic. To him, deafess means hearing through a cochlear implant, never having motion sickness (because none of the chambers of his inner ear communicate with his brain), and (incidentally) knowing sign language. Autism, meanwhile, means being obsessed with Ceiling Fans and the Number Two to the point of partial or total obliviousness to the other things around him.

He knows he's not the only deaf, autistic person in the world, and I've shown him some of the books on my shelves that were written by people with autism. Pretending to be Normal by Liane Holliday Willey stands out in particular, partly because, as I've told him, in order to get a job you need to pretend to be normal.

Every once in a while, he echoes this back. "Is that right? To get hired, I need to pretend to be normal." Or, "To pass my driver's test, I need to pretend to be normal." Recently while saying this his face flashed in the delight of a new insight. "Is that right?" he rephrased at higher volume, "To pass my driver's test I need to hide myself." Yes, indeed, pretending to be normal means hiding yourself. And if anyone else but him had voiced this conclusion, it would have sounded profoundly sad. But, for J, the thrill of the epiphany overrode any inkling of dismay.

Indeed, there probably never was any dismay to begin with.

Nor is there any about deafness. The cochlear implant lets him hear what he needs to, and what interests him, including sounds of passengers throwing up in the bathroom of the ferry boat we took several years ago during the tail end of Hurricane Bill. Nearly everyone on board was sick except for him, and J knew he had his nonfunctioning inner ears to thank for this.

J also knows that the cochlear implant gives him the auditory equivalent of a lower-than-normal resolution image; a couple of nights ago he wondered for the first time about qualitative differences in sound perception. "Maybe things sound different to me than to you," he proposed.

"But," he added, "high notes still sound smooth and low notes rough. And high notes still are light and low notes dark." Somehow the bizarre universality of this sound-sight synesthesia was apparent even to deaf, autistic J.

Friday, August 24, 2012

Math problems of the week: 4th grade Investigations vs. Singapore Math

I. The rectangle area problem set in the 4th grade TERC/Investigations Student Activity Book, Unit 4, pp. 67-68 [click to enlarge]:


II. The rectangle area problem set in the 4th grade Singapore Math Primary Mathematics 4A workbook, pp. 169-170 [click to enlarge]: :




III. Extra Credit
Comment on Investigations' sense of interior decorating.
(As for my sense of layout, I'm having troubles with blogger and am getting too bored to continue trying to fix them!)

Wednesday, August 22, 2012

Why Johnny can’t do math

A reader of this blog and of Left Brain Child recently shared with me this exchange she had with her school principal about her son Johnny (names changed to protect identity), who is going into 5th grade and already knows most of the 5th grade math curriculum:

Principal to mother:

We want Johnny to learn more about how to function in a group of students working in mathematics, where he has a profound understanding to share. He still has more to learn about how to effectively work in a group. Having a small repertoire of active listening strategies is going to get in his way in high school and in the rest of his education, since this case-study approach is likely to prevail for a while. I figure if he can learn how to share his understanding and how to listen to other perspectives, it’s going to make the rest of his education so much easier. Right now, he prefers going off on his own and working independently. Or he makes off-putting remarks at the beginning of a group exercise in order to get away from the group process. He is truly a smart kid, and his life will be easier if that intelligence is flexible enough to recognize the social impact as well as the intellectual impact. He doesn’t yet see the value of bringing others around to his point of view.
Mother to principal:
School starts in a couple of weeks and I know that the teachers are back, so I think it is time to address the things you brought up in your email. Specifically, I think we need some direction about how you see Johnny achieving the goals you have set for him below and how he will be judged in respect to these goals. Here are some questions.

How will the teacher teach Johnny more about how to function in a group of students working in mathematics? How will she teach him to share his profound understanding of math? What methodologies will he be taught to carry out this sharing? What supervision will be provided while he is practicing these methodologies? What, specifically, will the teacher do to broaden his repertoire of active listening strategies? How many active listening strategies are there? What are they? How do you decide which active listening strategy is appropriate for Johnny to use in a given classroom situation and how will this be taught to Johnny?

How many different perspectives is it reasonable to accommodate in math class? For instance, if a student insists that there is no such number as pi, is that reasonable? If the group construct is that the only definition of pi is as a dessert to be eaten with ice cream, does that become the group reality that everyone must except, or is it reasonable at that point to work independently? Is accepting such a construct in order to fit in with a group and prioritize for social impact necessary to demonstrate that one's intellect is flexible? When involved in a group with such a construct, how will Johnny be expected to bring others around to his point of view? Is he allowed to use direct instruction? Will Johnny be judged based on his ability to accept the group construct and prioritize for social impact, or for his ability bring others around to his point of view? How will this be assessed? Who will do the assessing? How will the teacher teach Johnny the skills necessary to share his original insights with his peers in math class? Where does learning some math fit in to this?

In short, what is it that you actually expect Johnny to do in math class?
Emailing me separately, Johnny’s mother writes:
By the way, the thing with pi actually happened last year in math class. The kids were drawing circles when Johnny told his group about the number pi and how you could use it to calculate the circumference of a circle. One of the girls in the group laughed at him and asked if there was also a number called "cake" and a number called "cookie" and all the kids in his group had a good chortle at his expense. He was quite upset. Of course there was no teacher around. The teacher introduced the math concept about two months later. No one said anything about it to Johnny. Constructivism brings playground group-think and bullying into the classroom.
Well said. I talk about this phenomenon a bit in chapter one of my book, and also in my critiques here on this blog of people who think that classroom groups can help reduce bullying.

Equally important is when will Johnny be allowed to do math. If the mother receives an answer from the principal, I'm hoping she will share it with us.

Monday, August 20, 2012

Madeline Levine on "hyperparenting"

If you're a high-profile therapist writing an advice book, the first thing you should do is ask yourself what your selection bias is. Do your clients perhaps disproportionately represent certain demographic groups (i.e., those who can afford to pay you) with certain types of real or perceived psychological problems (i.e., problems that drive them to pay you)?

The next thing you should ask is whether, when you venture out of your field into complex new areas like education, you actually know what you're talking about.

Madeline Levine's Teach Your Children Well is the latest in a series of advice books (c.f., The Over Scheduled Child, Einstein Never Used Flashcards, or Levine's earlier The Price of Privilege) that assume that a certain (to them) highly conspicuous, highly competitive subsector of American parents represents all of us. It's also the latest in a series of books and articles in which the author makes assumptions about the American education system without taking a close look at current trends.

Levine, who was just interviewed today on WHYY's Radio Times in Philadelphia, thinks we're pushing our kids too hard academically. Evoking scenarios of parents trying to pressure their four year olds to read books and their adult children to become surgeons rather than mechanics, she argues that our kids would do better, even academically, if we stopped pushing them so hard. Like so many people who think our schools are overly academic, she blames the relentless testing of No Child Left Behind, and evokes the later starting age (age 7) of schools in Finland as responsible for the much greater academic achievements of Finnish students.

It doesn't occur to Levine that, for the majority of us whose kids attend public schools, the low bar set by No Child Left Behind tests have watered down the academic standards, such that ever fewer kids are being pushed academically at school. It doesn't occur to her that, when parents decide to push their kids extracurricularly, it's often to make up for the growing academic deficiencies in their classrooms.

Everyone who wants to cite Finland as a reason to stop pushing kids academically should read these paragraphs from a 2008 Wall Street Journal article:

Visitors and teacher trainees can peek at how it's done from a viewing balcony perched over a classroom at the Norssi School in Jyväskylä, a city in central Finland. What they see is a relaxed, back-to-basics approach. The school, which is a model campus, has no sports teams, marching bands or prom. 
... 
Finnish high-school senior Elina Lamponen... spent a year at Colon High School in Colon, Mich., where strict rules didn't translate into tougher lessons or dedicated students, Ms. Lamponen says. She would ask students whether they did their homework. They would reply: " 'Nah. So what'd you do last night?'" she recalls. History tests were often multiple choice. The rare essay question, she says, allowed very little space in which to write. In-class projects were largely "glue this to the poster for an hour," she says. Her Finnish high school forced Ms. Lamponen, a spiky-haired 19-year-old, to repeat the year when she returned.
Forced to repeat the year? This doesn't sound like Teaching Your Children Well. Perhaps Levine should think twice about whether we should be emulating Finland.

Saturday, August 18, 2012

Engineering Act II

I'm in the process of dropping my oldest child off at college. He's attending his first choice, a university (not a liberal arts college; not a tech school) with an engineering department, located in a very decent-sized city (interesting restaurants and urban exploring opportunities are particularly desireable), somewhere south of the 42nd parallel (not requiring heavy winter clothing). This choice was entirely his, as is his declared major, chemical engineering.

But he has been refreshingly open to advice about how to fill his distribution requirements. I've long warned him that much of the humanities have been ravaged by Post Modernism, and Critical Theory, and I happily warned him away from such courses as "Computers and Society" and "Music, the Arts, and Ideas." Avoiding scheduling conflicts was quite the challenge. After an hour or two of searching he found a course that both fit in with the rest and sounded good (even great!) to Mom: "The History of Archeology."

This is my shy child, who's no longer shy; my math boy, who's no longer so interested in math. He prefers to work in groups and do hands-on activities--but in the best sense of group work and hands-on. Working as part of a team of caterers and busboys has earned him his freshman year spending money; interning among engineers is how he pictures spending future summers. Or perhaps that history of archeology class will open up another pathway to meaningful, hands-on teamwork.

Thursday, August 16, 2012

Math problems of the week: 4th grade Investigations vs. Singapore Math

I. The first place value assignment in the 4th grade TERC/Investigations Student Activity Book, Unit 5: 'Landmarks and Large Numbers":



II. The first analogous assignment in the 4th grade Singapore Math workbook, Primary Mathematics 4A, Unit 1: "Whole Numbers":


Tuesday, August 14, 2012

The true parent trigger option

The growing stranglehold of Constructivism on our K12 schools (including many private and charter schools) means that, for growing numbers of parents, there may be only one true "parent trigger option" left. For those of us with flexible work schedules, at least, there'll always be home schooling.

Just days ago a local friend told me she's decided to homeschool two of her kids. She came over yesterday afternoon to look at my materials. Like me and my daughter, she and her kids are tired of all the busywork, all the developmentally inappropriate expectations, and all the judgmental assessment-for-the-sake-of-assessment (as opposed to assessment for the sake of instruction).

She's anticipating what I've found to be the case: that it's not much more time consuming, and a lot less stressful for all concerned, to home school your kids than to help them survive regular school. (Where by survive school I mean get through it without suffering long-term psychological damage, academic delays, and an increasing distaste for learning).

In brief, she says, she's homeschooling in order to reduce stress.

Wouldn't it be nice if flexible work options continue to grow so that more and more parents have this educational option? I'm assuming, of course, that no other state will try what California has tried and failed to do, and that, no matter how bad it all gets, we will always have home schooling.

Sunday, August 12, 2012

Completing the circle: from the Common Core to the College Board

We live in an age of growing centralized control over K12 curricula and instruction, wielded by a combination of national and state departments of education, the education division of the NSF, powerful textbook companies like Pearson Publishing (the current publisher of Investigations math) and McGraw Hill (the publisher of Everyday Math), and deep-pocketed funders like the Gates Foundation, along with the prominent ed-school affiliated "education experts" who advise them, and the Constructivist philosophy that binds them all together.

One of their top priorities are national K12 curriculum guidelines ("Common Core"), to be aligned with with state-devised, state-wide tests--guidelines whose "written-by-committee" vagueness, as I've argued, further entrenches current Constructivist practices. Another priority: national pedagogical standards, to be enforced by Pearson Publishing, on who gets certified to teach. If the Powers that Be get what they want, it'll be all Constructivism all the time.  And a generation of poor readers and poor writers, uninformed in history and science and unprepared for college-prep math.

At least, I've always thought to myself, we've got the College Board. At least there still exists an independent entity measuring the aptitude and achievement of a significant portion of K12 students. At least, in the SATs and the Advanced Placement tests, we have an independent measure of how the current generation is faring compared to its predecessors. If test scores really plummet, surely pressure will emerge to release the Constructivist stranglehold.

Of course there'll be confounding factors: in particular, wealthy parents who wise up and hire tutors, and "experts" who claim that SATs and the APs don't measure what's important. But surely the drop-off in College Board scores that will occur once a nationwide cohort of students educated exclusively via Reform Math, Balanced Literacy, etc., starts taking these tests (and competing for college admission with students educated in non-Constructivist classrooms abroad) will be steep enough that most of us can't simply ignore it.

The College Board tests, however, have changed over time. They've been "recentered"; essays have replaced analogies; testers can now use calculators. What's to stop them from continuing to "adjust" to current circumstances? And what if the dominant Constructivist paradigm grows irresistible? Alas, that may already be happening. In May of this year the College Board appointed a new president, David Coleman, who happens to be one of the architects of the Common Core. His mission? To reshape the SATs so that they reflect the Common Core standards. As reported in Education Week:

Mr. Coleman’s hope of reworking the SAT could play a role in moving the standards from a set of guidelines used in college course placement to one considered in college admissions. That, to Mr. Coleman, goes to the heart of the standards’ intention.
Mr. Coleman doesn't take office until October, and he notes that the changes he wants will have to be gradual. His true agenda is also unclear. But it'll also take time before we have a whole generation of students that have experienced only Constructivist classrooms. By the time they're taking the SATs and the Advanced Placements, the tests as we currently know them may no longer exist.

And all of us will be none the wiser.

Friday, August 10, 2012

Math problems of the week: 4th grade Investigations vs. Singapore Math

I. The final problem set in the 4th grade Investigations Student Activities Book "Moving Between Solids and Silhouettes" unit (Unit 7, p. 52):

II. The final problem set in the 4th grade Singapore Math Primary Mathematics 4B Workbook "Measures and Volume" unit (Unit 11, p. 154):



Wednesday, August 8, 2012

Online learning and equal opportunity for autistic students

As I've noted in an earlier blog post, there are serious problems with online learning programs like the Khan Academy and Carnegie Mellon's Cognitive Tutor. From a software development perspective, as I know from personal experience, it's extremely difficult to automate the subtler aspects of instruction, assessment, feedback: to ensure that the student is paying sufficient attention and focusing on the intended concepts; to determine what he or she needs to work on; and to give him or her appropriate feedback and assistance.

Empirical data questioning the efficacy of online learning environments have had no apparent effect on the exponential growth in online courses, which now include more and more college-level courses and whole institutions (most notably, Stanford and MIT). More and more professors are making their lectures available on line; outfits like Coursera are offering growing numbers of online college courses for which colleges (e.g., the University of Washington) are starting to offer credit.

And, for my part, I'm starting to see this as an unequivocal boon--not for your typical student, but for your student with high functioning autism.

Take my son, J, for example. His greatest weakness is attending to what he's supposed to during class time. He spends much of his school day unfocused, or focused on the wrong things. Even in classes that match his abilities and interests, he finds it difficult to sustain attention for 45-minute intervals. He benefits little from the presence of peers, or from other face-to-face aspects of his classes. Many of his teachers, lacking deep familiarity with autism, simply don't know how to relate to him.

In short, J gets little or nothing out of the in-person, brick and mortar aspects of education. Indeed, many of the features of traditional school actually impede his learning: the 45 minute-long periods; the extended desk time; the often anti-social interactions he has with classmates; the one-size-fits-all instruction. In an online learning environment, none of this would be missed.

For all their downsides, online environments offer special perks to the autistic student. Various studies show autistic students more comfortable, and more successful, learning from computers than from humans. Part of what's conducive are the reduced social demands and the predictability of the format and feedback. Also, ideal for language-impaired, attention-impaired kids like J, lectures can be watched in short installments over and over again, and unknown words looked up--online. Furthermore, the sorts of courses that best lend themselves to online instruction--math, science, engineering, and, first and foremost, computer programming--are those that are most suited to autistic strengths and interests.

Some advocats for autistic students see online learning as a cop out. Colleges and universities, they insist, should be focusing their efforts on making the brick and mortar campus experience as accessible to autistic students as possible rather than relegating such students to "second class" online status. But for those who are as language imparired, attention impaired,  and socially aloof as J is, this isn't really feasible.

Indeed, without the possibility of online learning, my son, for all his analytical and computational skills, would never be able to get a college degree. Now it's starting to look like a real possibility, and I am tremendously thankful for the one educational trend that I actual see as beneficial--at least to particular sorts of left-brained students.

Monday, August 6, 2012

More power for Pearson: screening out would-be teachers

I've long thought teacher certification programs over-emphasize theory at the expense of actual teaching. So how could it not be a good thing that, as the New York Times reported last week:

New York and up to 25 other states are moving toward changing the way they grant licenses to teachers, de-emphasizing tests and written essays in favor of a more demanding approach that requires aspiring teachers to prove themselves through lesson plans, homework assignments and videotaped instruction sessions.
...
The new assessment system replaces two of the three written exams, made up of multiple-choice questions and essays, and introduces the classroom assessment elements.
The most obvious concern is what might be lost if writing skills no longer factor into teacher certification. A much bigger concern is that current fads will dictate how those lesson plans, homework assignments, and videotaped instruction sessions are graded:
Under the system, a teacher’s daily lesson plans, handouts and assignments will be reviewed, in addition to their logs about what works, what does not and why. Videos of student teachers will be scrutinized for moments when critical topics — ratios and proportions in math, for instance — are discussed. Teachers will also be judged on their ability to deepen reasoning and problem-solving skills, to gauge how students are learning and to coax their class to cooperate in tackling learning challenges.
Here we see a few red flags of Constructivism: "deep reasoning and problem-solving," cooperative learning, and that tell-tale emphasis on assessment. And why wouldn't there be a Constructivist bias when this is the philolosophy promoted by all the powers-that-be in education, including Linda Darling-Hammond and her colleagues at the Stanford ed school, who developed this Teacher Performance Assessment, and by Pearson Publishing, who is training those who will evaluate the teaching videos:
The new system will require teachers to electronically submit their work, including the videos, for grading by trained evaluators who have been recruited by the education company Pearson.
As the Times notes:
Because the new assessment programs are not yet in place, data about what kind of teachers they produce is a long way from being available.
So one can only wonder what sorts of ratings will be earned by a teacher whose video shows him or her standing in front of the class directly instructing his or her students in ratios and proportions, rather than walking around "gauging how students are learning" while the students discover things about ratios and proportions while cooperating in mixed-ability groups. The Times has already published articles about certified teachers losing points for this. Now new applicants who employ non-Constructivist teaching methods may not even get certified. Principals, however non-Constructivist their philosophies, will never even have the option to hire them.

Demonstration lessons are a great idea--as part of the hiring process at specific schools. To instead make them part of the pre-hiring screening process, imposing uniform standards informed by dubious educational ideology and overseen by a private entity like Pearson that already has way too much influence on public education is totally different prospect:
“Our decisions are being outsourced,” said one faculty member at a state university in New York who supervises student teachers and asked not to be identified because she feared retribution from her employer. She said other educators in the audience that day also expressed concern that the new evaluation system would undermine their role in supervising aspiring teachers.
Some of that sentiment has been exhibited in Massachusetts, which is testing the new licensing procedure. At the University of Massachusetts, 67 of the 68 students in a program for future middle and high school teachers refused to submit two 10-minute videos of themselves teaching, as well as a 40-page take-home test. The students said that evaluators chosen by Pearson were not qualified to judge their abilities, and should not be allowed to do so over their own professors.
Ironically, if you turn to the next page in the paper edition of this edition of the Times, you'll find an article on what looks to me to be the most penetrating form of oppression by Beijing on Hong Kong to date: the introduction into Hong Kong's public schools of the Chinese national education curriculum:
The new curriculum is similar to the so-called patriotic education taught in mainland China. The materials, including a handbook titled “The China Model,” describe the Communist Party as “progressive, selfless and united” and criticize multiparty systems, even though Hong Kong has multiple political parties. Critics liken the curriculum to brainwashing and say that it glosses over major events like the Cultural Revolution and the Tiananmen Square crackdown. It will be introduced in some elementary schools in September and be mandatory for all public schools by 2016.
The U.S. is apparently not the only country experiencing the penetration into its once public, once autonomous schools of a data-resistant ideology perpetrated by unelected, unaccountable, centralized Powers that Be.

Saturday, August 4, 2012

More on left-brainers and creativity

Does creativity favor the "right-brain" mindset or the "left-brain" mindset?

Our stereotypes would say the latter. So do some recent findings by neuroscientist and creativity researcher John Kounios:

1. Feelings of sudden insight coincide with bursts of electrical activity in the right hemisphere.
2. Compared to others, creative types appear to be less narrowly focused (in Kounios' words, "Their attention seems to be more diffused, spread out") and more easily distracted--consistent with the notion that creativity involves improbable connections between normally non-associated stimuli or concepts.

But Kounios' studies of the split seconds leading up to creative insight show something else:

1. Momentary reduction in the brain's flow of visual information
2. ...allowing the brain to turn inwards and notice its (initially weak) associations that may then pop into consciousness as sudden bursts of insight.

"Chance favors the prepared mind," Kounios quotes Louis Pasteur as saying. In the case of creativity, the prepared mind appears to be an introspecting one that momentarily cuts itself off from incoming visual distractions.

In other words, creativity seems to require both dispersed and focused attention, and both a susceptibility to outside distractions and a capacity for tuning things out and turning inwards.

With the shower--rather than the cup of coffee--providing the most conducive environment.

Thursday, August 2, 2012

Math problems of the week: 4th grade Investigations vs. Singapore Math

I. The second problem set involving translation between numbers and words in the 4th grade Investigations Student Activity Book, (Unit 5, "Landmarks and Large Numbers," p. 6):


II. The first problem set involving translation between numbers and words in the 4th grade Singapore Math Primary Mathematics 4A Workbook, (Unit 1, "Whole Numbers," pp. 8-9):