Saturday, August 31, 2013

One Test to rule them all, One Test to find them, One Test to bring them all and to the Standards bind them

No matter how bad things get in education, there have always struck me as three escape hatches for bright but languishing kids:

1. Standardized, independent tests like the SATs and the ACTs, which, as normed aptitude tests, help colleges see through the often distorted images of student abilities given by grades and teacher recommendations.

2. The competition between the SATs and the ACTs, which, should current education fads start to affect one testing company, theoretically motivates the other one to resist these fads in order to tap into the resulting market of fad-bucking students.

3. Home schooling.

But as Paula Bolyard writes in a recent post on Pajamas Media, all three are being threatened by the insidious influence of the Common Core standards:

Many homeschooling families believe that they can remain insulated from the effects of the unpopular Common Core curriculum by maintaining control of their curriculum in their home...
Unfortunately, Common Core, if it continues to be adopted by states across the country, can and will trickle down into private schools and homeschools. Those of us who have had the experience of sending our kids to college know the importance of standardized tests like the ACT and SAT, especially for homeschoolers who sometimes lack other academic credentials that colleges require...
As it turns out, these tests are not only working closely with those designing and advocating the Common Core, but they are now redesigning their tests to align with it.
Yes, the Common Core Standards are "voluntary." But it's states, not parents, that decide whether to adopt them. And yes, the Common Core Standards are "merely guidelines" that "don't dictate curricula or pedagogy." But as I've argued earlier, this very vagueness has had the effect of further enabling current fads.

And the more these fads penetrate what once were independent aptitude tests, the more they diminish the educational options of bright, eccentric, fad-bucking students.

Thursday, August 29, 2013

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

4th grade multiplication and division estimation problems:

I. From the "How Many Packets? How Many Groups" unit of the 4th grade Investigations Student Activity Book [click to enlarge]:

II. From the "The Four Operations of Whole Numbers" unit of the 4th grade Singapore Math Primary Mathematics 4A Workbook [click to enlarge]:

Sunday, August 25, 2013

The latest "normal child inside"

Just yesterday, a couple of days after I wrote my post on the "Normal Child Inside Fallacy," I find myself reading about yet another nonverbal, autistic child who, despite all we know about the deep brain differences in autism and its fundamental nature as a disorder of social communication, somehow emerges as communicatively normal.

The child in question is Naoki Higashida, a Japanese 13-year-old whose book, "The Reason I Jump," has just been translated into English and is reviewed in this week's NY Times Book Review. According to reviewer Sally Tisdale, Higashida wrote by "spelling out words on a Japanese alphabet letter board."

The book focuses on Higashida's difficulties with sensory processing, organizing itself around questions like “Why do you speak in that peculiar way?”, “Why do you like spinning?”, and, of course, "Why do you like to Jump". On this last topic, Higashida's book says:

The motion makes me want to change into a bird and fly off to some faraway place. But constrained by ourselves and by the people around us, all we can do is tweet-tweet, flap our wings and hop around in a cage.
Apparently, Higashida can type on a computer and read aloud what he has written. Given this, one would hope for a chapter called "Why are you considered nonverbal when you can write and read out loud?"

In Tisdale's words, Higadisha also "can’t remember rules, sit still or make sense of time." Nonetheless, he is "bright and thoughtful" and "maintains a blog and has written other books." His American publisher calls him a “motivational speaker.”

What do we make of yet another individual who supposedly meets the criteria for autism and can't speak extemporaneously but who somehow writes with a level of introspection and a non-literal literary style far beyond anything ever been written by the best-known, most studied autistic writer whose high functioning autism is totally without question???

In making sense of Higashida in particular, Tisdale reports, there's an additional layer of uncertainty:
The book comes to English readers through the passionate efforts of David Mitchell, the author of “Cloud Atlas” and the father of an autistic child. Mitchell and his wife, KA Yoshida, provided the translation.
The book, Tisdale notes, contains such English colloquialisms as "It really gets me down.” Did the original Japanese sound as neurotypical?

And how much is David Mitchell's translation colored by his personal agenda and wishful thinking?
Mitchell believes the book is proof that the standard definition of autism is wrong, that autism’s obvious restrictions of socialization and communication “are not symptoms of autism but consequences.” Higashida, he has also said, is “more of a writer than I am.”
As Tisdale writes:
... Unfortunately, it’s impossible to sort out what is Higashida here and what is Mitchell. The two have never met in person, and Higashida had almost no involvement in the English edition. Mitchell has said that Yoshida “did the heavy lifting” from the Japanese, and that he “provided the stylistic icing on the cake.”
But how much does the icing flavor the cake? Tisdale, herself the parent of an autistic child, concludes her review with this powerful point:
Mitchell writes that reading “The Reason I Jump,” he “felt as if, for the first time, our own son was talking to us about what was happening inside his head.” No parent of an autistic person — and I include myself here — can help longing for such a chance, and looking for it wherever we can. We have to be careful about turning what we find into what we want.
Whatever is really going on here, Higashida no more represents the norm for autism than the similarly nonverbal and yet "introspective" and "poetic" Carly and Tito do. And yet the author(s) and translator(s) of Higashida's book--who constantly use the 1st person plural to speak for "us kids with autism"--present their depictions of Higashida as containing deep revelations about autism in general.

Friday, August 23, 2013

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

Problems for the chapters on volume in 4th grade Singapore Math vs. Everyday Math.

I. From the end of the 4th grade Singapore Math Primary Mathematics 4B Workbook "Measures and Volume" chapter [click to enlarge]:

II. Supplemental material for the 4th grade Everyday Math Student Math Journal "3-D Shapes, Weight, Volume, and Capacity" chapter [click to enlarge]:

Wednesday, August 21, 2013

Autism and the "normal child inside" fallacy

Much has been learned about autism since the days of the "normal child locked inside" paradigm, in which mute children were taken away from their "refrigerator" mothers and psychoanalyzed into normalcy by the likes of Bruno Bettelheim.

Now we know that autism involves deep brain differences, both in overall neural connectivity and in specific structures like the amygdala. We know that, even among the highest functioning autistic and Asperger's children, significant delays persist in the social-emotional sphere, particularly in facial expression reading and in perspective taking skills. Neuropsychiatric research suggests that, along pretty much every cognitive dimension except for visual processing, autism correlates with weaknesses in complex information processing.

Simply put, there is no normal child inside--anywhere you look.

But that hasn't stopped the popular media, popular culture, and the wishful thinking of hopeful parents. A decade ago we had Tito and his introspective poetry:

I have fancied a little dream and the world is left unseen… with the light of your eyes through the darkness of the night… I have held that little dream beyond my world, beyond all scenes./ and in that dream I saw perhaps...the bleeding drops of my heart... through all smiles through all tears...Coming from far but never near...I have held it close since then...close within my darkest pain.
Today we have Carly and her letters to her father:
Dear Dad, I love when you read to me. And I love that you believe in me. I know I am not the easiest kid in the world however you are always there for me holding my hand and picking me up. I love you.
And her novel:
I want you to close your eyes and imagine a girl all alone in the middle of the jungle. All she can hear are the sound of the animals. But what she does not know is that the sounds aren't just random sounds. In fact the animals are talking to each other. People think that a lion's roar is its way to scare you. But let me tell you from experience that a roar is not just a ROAR. Actually a roar can mean many things depending on the tone. I think that humankind is just oblivious to many things that have been around for years. I think that humans are so silly.
It would seem that, even where they are now, both Tito and Carly meet the official diagnostic criteria for autism. Neither of them speaks; their eye contact appears minimal; they don't appear to do much "sharing of attention" with others--something that involves monitoring what other people are attending to and moderating one's behavior accordingly.

But is either of them really a normal child locked up inside an autistic one?

One thing that raises this question is the level of introspective, communicative, and perspective-taking skills seen in the above writing samples. These go far beyond what we see in the most high functioning autistic individuals who are able to speak, for which Temple Grandin is the best known example.

Perhaps neither Tito nor Carly is actually autistic, but only appears so, superficially, because of a severe apraxia that makes it difficult to track eye gaze and impossible to speak.

Then there's the second video of Carly in which we actually see her type.

Sentences take minutes of strenuous work to complete (along with a steady of flow of chips and dip); every word can be chosen from a drop-down menu; the sophisticated language and perspective taking of the first video (where we don't see her type) are nowhere to be seen; and answers seem driven by simple associations of key words (e.g., Cape Cod to Boston).

Whatever is really going on here, it's safe to say that neither Carly nor Tito represents the norm for autism.

...And yet the media is happy to serve up the opposite impression--along with a lot of false hopes.

Monday, August 19, 2013

The decline of remediation, II

Rivaling the decline in advanced programming for advanced students is that of remediation for those below grade level. The biggest force behind this is the Common Core, whose standards are keyed to grade level, which in turn (in this age of "social promotion") is keyed to calendar age.  Everyone is expected to be capable of achieving, through one "entry point" or another, the learning goals decreed for their grade level, and, as far as I can tell, the word "remediation" doesn't appear anywhere in the Common Core standards. Remediation, in short, is something to be avoided.

We see this in special ed, where remediation has been upstaged by "accommodation." We see this in programs for disadvantaged students, where "boring drills" have been upstaged by college prep pipe dreams. And we see this, most recently, in summer school programs, as discussed in a recent article in Edweek:

Summer school, once thought of as a place for failing students, is being overhauled.  
Districts and communities are shifting from offering duplicative Algebra 2 and U.S. history classes to using the summertime as an opportunity to experiment with innovative teaching and learning methods.  
This summer, students are learning the science involved in crime-scene investigations in Florida, the math involved in constructing infrastructure for a community center in Michigan, and how the themes of one novel can apply to various academic disciplines in California.
The article cites 25 districts "that are shifting from traditional remedial offerings to a new type of summer school" that includes "blended academics and enrichment," and "enhanced features" like field trips and projects. Specific examples?
In Sacramento, Calif ...middle and high school students are improving their academics through hands-on service-learning projects they select and design.

Working with several partners, the 48,000-student district has students create community projects rooted in a social-justice, youth-development framework, and then has teachers integrate academic lessons into them.

Past summer projects have included designing a disaster-preparedness robot, creating AIDS- and homeless-awareness campaigns, building a community garden, and writing books for elementary students on bullying, said Zenae Scott, the district's youth-development coordinator.
What about students who aren't reading fluently and can't change fractions to decimals? Apparently, they are better off than they were before:
Many traditional summer school programs have been shown to have minimal impact on student performance.  
...Research indicates that today's new models are showing early positive results for students' academic and developmental needs.
I'm looking forward to the follow-up article that discusses the long term positive results--in particular growing rates of basic literacy and arithmetic skills--as Project Based Learning takes over summer remediation.

Saturday, August 17, 2013

Where everyone is way, way, way above average

Related to the growing practice of restricting challenging K12 academics to just a tiny percentage of students is the growing practice of restricting top grades to just a tiny percentage of those who’ve gone beyond the standard.

Ironically, those who perpetrate this practice come (most recently) from institutions in which the opposite practice prevails. I’m speaking, of course, of our graduate schools of education, and their rampant and ever rising grade inflation.

I hadn’t realized how bad it had gotten until an administrator from our local ed school told me that she routinely fields complaints from students about B plusses and A minuses. A minuses? It would seem that A’s are the most common grades. Which, of course, explains why my students’ GPA’s are typically in the high 3.90’s.

Since I don’t want to penalize students for taking my class—by lowering those much-cherished GPA’s—I’ve taken my standards yet another notch down. And yet, I simply can’t countenance giving A’s to more than half of my class—unless, of course, it should turn out that all of them are brilliant.

Most of my non-A recipients don’t complain, but every once in a while, one of them pulls out all the stops.

1. I have A’s in all my other classes [read: It’s you, professor, not me!]
2. I need a 4.0 in order to have a stab at a really competitive scholarship that I need in order to afford my degree.
3. I promised myself I’d maintain a 4.0 throughout my graduate career and this is the very last class on my transcript.
4. I will let down my entire extended family if I don’t maintain the 4.0 I promised them.

The psychological pressure can be tremendous, and you wish there were private discussion boards for professors to discuss the requests they’ve received from particular students. Yes, perhaps Student A received As in all his/her other classes, but perhaps all these As were groveled for.

And, increasingly important though these “skills” are in life “success,” do we really want 4.0’s to reflect such manipulative self-promotion?

Here’s my dirty little secret. In order to give my most high-achieving students their due, I’ve started quietly doing something I've never done before: giving out a small handful of A+s.

Thursday, August 15, 2013

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

Problems for the chapters on decimals in 4th grade Singapore Math vs. Everyday Math.

I. From the end of the 4th grade Singapore Math Primary Mathematics 4B Workbook"The Four Operations of Decimals" chapter [click to enlarge]:

II. Supplemental material for the 4th grade Everyday Math Student Math Journal "Fractions, Decimals and Percents" chapter [click to enlarge]:

Tuesday, August 13, 2013

Autism Diaries: By the way, this is D, Katharine's husband

During his summer down time, J’s been keeping busy with his iPhone. Besides playing chess, editing Wikipedia, and surfing the web, he’s recommenced his impersonations. Generally he impersonates either me or D, his father, and what motivates him aren’t just the thrills of deception, but also things like weaseling out of spending time on his summer homework with his tutor, or getting various people tell him about their ceiling fans or deceased loved ones.

Three mornings in a row I’ve received messages from friends forwarding me suspicious text messages. For example, to E, his tutor:

Hi, this is Katharine. My phone battery is dead so I’m using J’s phone. I just want to take J to Valley Green today so I’ll see you tomorrow. 
Or to P, whose father just died:
I’m very sorry to hear about your father. Is his body buried? By the way, this is D, Katharine’s husband.  
I also received this message from S, and old friend from college:
Hi K + D, I’ve been getting some cryptic phone messages and texts lately, and a couple of days ago, I had an h-ha moment. J! Lo and behold, is was. No harm done. Some of the follow-up texts have purported to be from D, but I have a feeling they also may have been from J.
Perhaps all this can be challenged into a remunerative career in hacking. Or, better yet—I’m thinking of back when J changed his email alias to “Mailer Daemon,”--in spamming.

Indeed, another of J’s natural talents is the equivalent of spam-filter foiling. When we told him to stop texting the s-word, his response was:

Sunday, August 11, 2013

Everyday arithmetic: where calculators don't help

What with the proliferating meme that calculators can substitute for most real-world human calculations, and with restaurant bills that increasingly calculate the various tip possibilities for you (15%, 20%, 25%), it's harder and harder to find examples of cases in which, say, there's no good substitute for knowing your multiplication tables.

But on a recent airplane flight, one such case suddenly jumped out at me. Before the flight took off, the flight attendants were asked to verify that all the passengers were on board. There were six seats per row on what seemed to be a maxed-out flight, and one of the older flight attendants knew exactly what to do. Walking down the aisle, she rapidly counted by 6's: 6, 12, 18, 24, etc...

Think about it... There's no faster way to count rows of airplane passengers than to apply your memorized multiplication tables.

How much longer would it have taken for the flight to take off, I couldn't help wondering, if one of the younger flight attendants had taken charge?

Friday, August 9, 2013

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

Problems for the chapters on fractions in 4th grade Singapore Math vs. Everyday Math.

I. From the end of the 4th grade Singapore Math Primary Mathematics 4B Workbook "Fractions" chapter [click to enlarge]:

II. Supplemental material for the 4th grade Everyday Math Student Math Journal "Fractions and Their Uses; Chance and Probability" chapter [click to enlarge]:

Wednesday, August 7, 2013

Why one school chose Investigations

...and why I'm glad my son has already graduated!

Excerpts from an article entitled "Investigating Math," published in the school's "Studies in Education," recently sent out to all parents and alumnae (bold face added).

The big decision:

After two years of working with particular math programs, coupled with deep examination of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics, the lower school decided to use Investigations in Number, Data, and Spaces [sic], a math program that not only provides the most appropriate mathematics sequence for elementary-age students, but also is aligned closely with our school's academic culture. Having a mathematics program that promotes high levels of critical inquiry is important.
Back then, when I was considering sending my daughter to this school, I asked whether they had also considered Singapore Math. The then-head of the lower school told me that they had considered considering it. "I can't remember why we decided not to," she told me.

Indoctrinating the teachers:
The lengthy implementation process provided a vehicle for the faculty to engage in a cycle of collegial, intentional, and continuous professional development. There were three types of professional development offered. One was a workshop developed by the authors of the curriculum. It familiarized teachers with the content of the curriculum and focused on the teachers' [sic] being mathematical learners themselves, as well as being facilitators of collaborative learning.
...Understanding the implications of talking as a vehicle for learning, the leaders of the workshop focused on how to orchestrate conversations that have students discussing math content, debating strategies, deepening their individual knowledge, while also extending the knowledge of the class as a whole.
Overall, the various approaches to professional development have had a significant impact on our teaching practices.

All..of these professional development opportunities and approaches exemplify [sic] the lower-school faculty's commitment to be a reflective [sic] learning community and to provide the best possible cohesive and comprehensive math education for our students.
Not all teachers are happy, and some sneak in supplemental material. A few, though, are true believers. When a friend of mine who happens to be a math expert questioned one of them, she become defensive and nasty.

Managing the parents
Once the new math curriculum was implemented in all the grades, we thought it time to formally share the excitement with all the lower-school parents. The first Math Night for Parents was organized to help parents learn more about our lower-school approach to teaching mathematics and to suggest ways that they could help their children at home.
Parents had the chance to actually experience the math curriculum by doing math themselves in order to see how it is taught in their children's classrooms and to experience how different (or not) it is from the way most of them learned math (often quite different from how the parents were taught!)

They then went off to classrooms to play some of the games that are a key component of our math curriculum. A group of teachers and teaching assistants was stationed in each classroom to teach the games, and after the parents played the games, to facilitate parents' discussion of the math content in the games and of the ways that they can support their children's math learning. ...

On Math Night parents played a variety of games, but they all played "Close to 1,000" [see here]. Afterwards the parents gathered together to process the experiences of playing that game...

"I was surprised that I enjoyed Math Night," said one parent. "When I found out that the parents would be doing the math games, I was a little nervous--math has never been my strength--but I had a blast playing with the other parents! The games are challenging, but not frustrating, and the process is social and fun. It was amazing to see that the school has found a way to teach math that actually makes it fun for the kids. I wish I had been taught math in this way."
Such sentiments aren't shared by the parents I happen to be acquainted with, but perhaps they are more mathematically capable (and/or appreciative of actual math) than this particular parent--who was the only parent whose reaction was cited.

Faculty reactions to Math Night
"The Math Night was great; it was fun to see the adults play with numbers and be surprised by the complexity of the underlying concepts. This has been a thoughtful, cooperative venture that has united the faculty and benefited our students."
[The only faculty reaction cited]

Faculty impressions of students:
"For me, the biggest change has been that children now speak about their math understandings in the same way that they might express their thoughts about a character in a story or the ideas uncovered in a poem. They describe their various paths to solution with enthusiasm, smiling as they say, 'This is the way the numbers make sense to me...' [They have developed an] ability to problem solve in a way that is not rote, but is based in number sense and their own exploration. It's a pleasure to support and guide them in their journey."

[From a veteran 2nd grade teacher.]
Fourth grade students seem ever so slightly less enthusiastic:
"The students are comfortable with their own thinking and ideas. They understand that a problem may have a specific answer, but they know that there are multiple ways to reach it. The children are able to dissect their thought processes using more specific math vocabulary. Although they groan at times when asked to write down their thinking, they are becoming much more fluent at expressing the ins and outs of their work. Most importantly, they realize that we (the teachers) value their methods and ideas. On so many occasions I have been amazed at the creative thinking of my students." 
The 5th grader who, as her mother tells me, keeps crying "I hate Investigations!" gets no mention.

This is one of the top private schools in the Philadelphia area, and it's striking how even it hasn't been immune to the math-dumbing effects of NCTM Standards--or from the mind-numbing double-speak they engender. We'll see how the private math tutoring industry fares when these students reach high school and parents start panicking. My math-expert friend, in fact, has already reworked her whole career around after-school remediation for Investigations victims. Business is booming and she's opening up satellite branches as Investigations proliferates around the greater Philly area.

"I love Investigations," she privately admits.

Monday, August 5, 2013

"Evidence-based" assessments for standardized essay tests

Today's standards for K12 essays are ever more evidence-based--not necessarily in their underlying rationale, but in their notion of what students should be doing. Over Internet-based homework assignments and writing rubrics, citations of "Cite three pieces of evidence" (and the like) are ever more numerous. They infuse state k12 proficiency tests, as well as the new Common Core Standards.

Particularly committed to such "evidence-based" measures is former CCS co-author and current College Board president David Coleman. As this week's Education Times reports:

Over and over, Mr. Coleman returns to the need to prod students into marshaling their evidence. “The heart of the revised SAT will be analyzing evidence,” he said.
But in the cut and paste world in which too many students and teachers operate, a failure to marshal "evidence" is not the heart of the problem. Key word Internet searches will turn up all sorts of "evidence" for all sorts of conclusions, however implausible. The Internet, as well all know, offers "evidence" for pretty much anything under the sun, from pseudoscience to conspiracy theories to joke claims to the -isms of every imaginable prejudice.

Given the state of the Internet, and of contemporary Edworld culture, the problem today's students have with writing and argumentation isn't primarily a failure to cite "evidence." Rather, it's a failure find the best evidence, to analyze that evidence in depth, to track down and take on the most compelling counter-evidence, and to make clear and convincing cases against reasonable (actual or possible) counter-arguments.

These requisites lie at the heart of good essay writing; they're also the most challenging things to execute. And they're the among most challenging things to teach and to grade. For all Mr. Coleman's aspirations for "improved" assessments, the grading challenge is particularly prohibitive when what's being graded are millions of essays for state tests or the College Board--whether the graders are exhausted human beings or automated text-processing software programs that know even less than students do about real-world evidence and argumentation.

Saturday, August 3, 2013

The beauty of armchair science

Education experts have long assumed that the best way to engage students is to make learning as hands-on as possible. The subject that most legitimately lends itself to this is science. Hands-on science--i.e., science experiments--would seem the perfect way to get students thinking scientifically and seeing the excitement of real-life hypothesis testing. Not to mention the excitement of Bunsen burners and explosive reactions.

The main argument that skeptics have leveled against hands-on science concerns elementary school students: they aren't "little scientists" but novices who need a strong foundation in content before their lab experiences can be meaningful and memorable.

In terms of the broader discipline, of course, experiments and knowledge go hand in hand: labs are essential for the advancement of science. But are they essential for learning what's already been empirically established? And is lab-based learning necessarily more fun and engaging than learning from teachers and textbooks?

Labs, after all, can be a real headache. Measurements can be slow and tedious; many things can go wrong; results often don't make sense; some procedures involving long periods of standing, bending over, and careful monitoring. Different people have different levels of tolerance, and many students end up hating the lab component of courses they otherwise find interesting.

A friend of mine recently described to me her favorite college science course--in fact, one of her favorite courses of all. It was a class focused entirely on the psycho-neurology of the flatworm, run entirely as a seminar. First the professor would present some general topic in psychology or neurology; then he'd extend it to the flatworm and pose a few questions, soliciting various hypotheses from students.

He'd then ask them: "How would you set up an experiment to test that?"

The students would flesh out the experimental design.

Did they then go out and perform the experiment? Nope. Instead the professor would say: "That exact experiment just happens to have been done, and here's what they found."

"It was great," my friend told me. "We went through all the interesting steps in thinking through the experiment without actually having to do it!"

Thursday, August 1, 2013

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

The final problems in the chapters on volume in 4th grade Singapore Math vs. Everyday Math.

II. From the end of the 4th grade Singapore Math Primary Mathematics 4B Workbook "Measures and Volume" chapter
[click to enlarge]:

I. From the end of the 4th grade Everyday Math Student Math Journal "Shapes, Weight, Volume and Capacity" chapter [click to enlarge]: